Advances in Child Development and Behavior Volume 7

ADVANCES I N CHILD DEVELOPMENT

AND BEHAVIOR

VOLUME 7

Contributors to This Volume Jean L. Bresnahan Rochel Gelman Klaus F. Riegel Arnold J. Sameroff Martin M. Shapiro Michael D. Zeiler

ADVANCES IN CHILD DEVELOPMENT AND BEHAVIOR edited by Hayne W. Reese Department of Psychology West Virginia University Morgantown, West Virginia

VOLUME 7

@)

1972

ACADEMIC PRESS

New York

London

COPYRIGHT 0 1972, BY ACADEMIC PRESS, INC. ALL RIGHTS RESERVED. N O PART O F THIS PUBLICATION MAY BE REPRODUCED OR TRANSMITTED IN ANY FORM OR BY ANY MEANS, ELECTRONIC OR MECHANICAL, INCLUDING PHOTOCOPY, RECORDING, OR ANY INFORMATION STORAGE AND RETRIEVAL SYSTEM, WITHOUT PERMISSION IN WRITING FROM THE PUBLISHER.

ACADEMIC PRESS, INC. 1 1 1 Fifth Avenue, N e w

York. N e w York 10003

Uniled Kingdom Edition published by ACADEMIC PRESS, INC. (LONDON) LTD. 24/28 Oval Road, London N W l

LIBRARY OF

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PRINTED IN TH E UNITED STATES

NUMBER: 6 3 - 2 3 2 3 1

OF AMERICA

Contents LIST OF CONTRIBUTORS ..............................................

vii

PREFACE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

ix

CONTENTSOF PREVIOUS VOLUMES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

xi

Superstitious Behavior in Children: An Experimental Analysis MICHAEL D. ZEILER I. Superstition and the Reinforcement Process . . . . . . . . . . . . . . . . . . . . . . . 11. Deliberate and Adventitious Reinforcement . . . . . . . . . . . . . . . . . . . . . . . .

111. Control of Multiple Responses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IV. Other Effects of Response-Independent Reinforcement . . . . . . . . . . . . . . V. Concluding Comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2 6 19 23 27 28

Learning Strategies in Children from Different Socioeconomic Levels JEAN L. BRESNAHAN AND MARTIN M. SHAPIRO

I. Introduction

............

.........................

11. Concept Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111. Reward Preferences . . . . . . . . . . . . . . . . . . . . . ...........

32 34 57

IV. Instructions and Training . . . .................... V. Summary and Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . References .......................

Time and Change in the Development of the Individual and Society KLAUS F. RIEGEL

I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11. The Concept of Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111. Developmental Changes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

82 83 96 111 V

vi

Contents

The Nature and Development of Early Number Concepts ROCHEL GELMAN I. 11. 111. IV. V.

...................................... 116 Introduction . . . . . . . Estimators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 Estimator Confidence . . . . . ............................ 143 Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 Summary and Discussion ..................... . 162 References ..................................... 165

Learning and Adaptation in Infancy: A Comparison of Models ARNOLD J. SAMEROFF Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Infant Conditioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Parameters of Conditionability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Models of Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

170 171 191 202 211

AUTHOR INDEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

215

SUBJECTINDEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

219

I. 11. 111. IV.

List of Contributors Numbers in parentheses indicate the pages on which the authors’ contributions begin.

JEAN L. BRESNAHAN Emory University, Atlanta, Georgia (31)

ROCHEL GELMAN Psychology Department, University of Pennsylvania, Philadelphia, Pennsylvania (115)

KLAUS F. RIEGEL Department of Psychology, University of Michigan, Ann Arbor, Michigan (81)

ARNOLD J. SAMEROFF University of Rochester, Rochester, New York (169)

MARTIN M. SHAPIRO Emory University, Atlanta, Georgia (31)

MICHAEL D. ZEILER Emory University, Atlanta, Georgia (1)

1 Present address: Department of Psychology, Lehman College, City University of New York, New York, New York.

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The amount of research and theoretical discussion in the field of child development and behavior is so vast that researchers, instructors, and students are confronted with a formidable task in keeping abreast of new developments within their areas of specialization through the use of primary sources, as well as being knowledgeable in areas peripheral to their primary focus of interest. Moreover, there is often simply not enough journal space to permit publication of more speculative kinds of analyses which might spark expanded interest in a problem area or stimulate new modes of attack on the problem. The serial publication Advances in Child Development and Behavior is intended to ease the burden by providing scholarly technical articles serving as reference material and by providing a place for publication of scholarly speculation. In these documented, critical reviews, recent advances in the field are summarized and integrated, complexities are exposed, and fresh viewpoints are offered. They should be useful not only to the expert in the area but also to the general reader. No attempt is made to organize each volume around a particular theme or topic, nor is the series intended to reflect the development of new fads. Manuscripts are solicited from investigators conducting programmatic work on problems of current and significant interest. The editor often encourages the preparation of critical syntheses dealing intensively with topics of relatively narrow scope but of considerable potential interest to the scientific community. Contributors are encouraged to criticize, integrate, and stimulate, but always within a framework of high scholarship. Although appearance in the volumes is ordinarily by invitation, unsolicited manuscripts will be accepted for review if submitted first in outline form to the editor. All papers-whether invited or submitted-receive careful editorial scrutiny. Invited papers are automatically accepted for publication in principle, but may require revision before final acceptance. Submitted papers receive the same treatment except that they are not automatically accepted for publication even in principle, and may be rejected. I wish to acknowledge with gratitude the aid of my home institution, West Virginia University, which generously provided time and facilities for the preparation of this volume. HAYNEW. REESE ix

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Contents of Previous Volumes Volume 1 Responses of Infants and Children to Complex and Novel Stimulation Gordon N . Cantor Word Associations and Children’s Verbal Behavior David S . Palermo Change in the Stature and Body Weight of North American Boys during the Last 80 Years Howard V . Meredith Discrimination Learning Set in Children Hayne W . Reese Learning in the First Year of Life Lewis P. Lipsitt Some Methodological Contributions from a Functional Analysis of Child Development Sidney W . Bijou and Donald M . Baer The Hypothesis of Stimulus Interaction and an Explanation of Stimulus Compounding Charles C . Spiker The Development of “Overconstancy ” in Space Perception Joachim F. Wohlwill Miniature Experiments in the Discrimination Learning of Retardates Betty J . House and David Zeaman AUTHOR INDEX-SUB

JECT INDEX

Volume 2 The Paired-Associates Method in the Study of Conflict A l f red Castaneda Transfer of Stimulus Pretraining in Motor Paired-Associate and Discrimination Learning Tasks Joan H. Cantor xi

xii

Contents of Previous Volitmes

The Role of the Distance Receptors in the Development of Social Responsiveness Richard H . Walters and Ross D. Parke Social Reinforcement of Children’s Behavior Harold W . Stevenson Delayed Reinforcement Effects Glenn Terrell A Developmental Approach to Learning and Cognition Eugene S. Gollin Evidence for a Hierarchical Arrangement of Learning Processes Sheldon H . White Selected Anatomic Variables Analyzed fdr Interage Relationships of the Size-Size, Size-Gain, and Gain-Gain Varieties Howard V . Meredith AUTHOR INDEX-SUB

JECT INDEX

Volume 3 Infant Sucking Behavior and Its Modification Herbert Kaye The Study of Brain Electrical Activity in Infants Robert J . Ellingson Selective Auditory Attention in Children Eleanor E. Maccoby Stimulus Definition and Choice Michael D . Zeiler Experimental Analysis of Inferential Behavior in Children Tracy S . Kendler and Howard H. Kendler Perceptual Integration in Children Herbert L. Pick, Jr., Anne D . Pick, and Robert E . Klein Component Process Latencies in Reaction Times of Children and Adults Raymond H . Hohle AUTHOR INDEX-SUBJECT

INDEX

Volume 4 Developmental Studies of Figurative Perception David Elkind

Corrterits of Previous Volumes

xiii

The Relations of Short-Term Memory to Development and Intelligence John M . Belmont and Earl C . Butterfield Learning, Developmental Research, and Individual Differences Frances Degen Horowitz Psychophysiological Studies in Newborn Infants S . J . Hutt, H . G . Lenard, and H . F. R. Prechtl Development of the Sensory Analyzers during Infancy Yvonne Brackbill and Hiram E . Fitzgprald The Problem of Imitation Justin Aronfreed AUTHOR INDEX-SUBJECT

INDEX

Volume 5 The Development of Human Fetal Activity and Its Relation to Postnatal Behavior Tryphena Humphrey Arousal Systems and Infant Heart Rate Responses Frances K . Graham and Jan C. Jackson Specific and Diversive Exploration Corinne Hutt Developmental Studies of Mediated Memory John H. Flavell Development and Choice Behavior in Probabilistic and Problem-Solving Tasks L . R . Goulet and Kathryn S . Goodwin AUTHOR INDEX-SUBJECT

INDEX

Volume 6 Incentives and Learning in Children Sam L. Witryol Habituation in the Human Infant Wendell E. Jeffrey and Leslie B. Cohen Application of Hull-Spence Theory to the Discrimination Learning of Children Charles C. Spiker Growth in Body Size: A Compendium of Findings on Contemporary

xiv

Contents of Previous Volumes

Children Living in Different Parts of the World Howard V . Meredith Imitation and Language Development James A . Sherman Conditional Responding as a Paradigm for Observational, Imitative Learning and Vicarious-Reinforcement Jacob L. Gewirtz AUTHOR INDEX-SUB

JECT INDEX

SUPERSTITIOUS BEHAVIOR IN CHILDREN: AN EXPERIMENTAL ANALYSIS Michael D. Zeiler EMORY UNIVERSITY

I. SUPERSTITION AND THE REINFORCEMENT PROCESS . . . . . . A. THE IMPLICATIONS O F SUPERSTITIOUS BEHAVIOR . . . . B. REINFORCEMENT DEPENDENCIES AND CONTINGENCIES

2 2 4

11. DELIBERATE AND ADVENTITIOUS REINFORCEMENT . . . . . . A. PROBABILITY O F RESPONSE . . . . . . . . . . . . . . . . . . . . . . . . . . . B. TEMPORAL PATTERNS OF RESPONDING . . . . . . . . . . . . . . . C. STIMULUS CONTROL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D. REINFORCEMENT AND TEMPORAL CONTIGUITY . . . . . .

6 6 10 13 18

CONTROL O F MULTIPLE RESPONSES . . . . . . . . . . . . . . . . . . . . . . A. CONCURRENT RESPONSE-INDEPENDENT AND RESPONSE-DEPENDENT REINFORCEMENT . . . . . . . . . . . . . . . . B. SOME COMMENTS ON MEDIATION AND INDIVIDUAL DIFFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. A NOTE ON REINFORCING NOT RESPONDING . . . . . . . . .

21 22

IV. OTHER EFFECTS O F RESPONSE-INDEPENDENT REINFORCEMENT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. ELICITATION O F PREVIOUSLY PROBABLE RESPONSES . . B. ELICITATION O F A NEW RESPONSE: AUTO-SHAPING . .

23 23 25

CONCLUDING COMMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

27

111.

V.

REFERENCES

.............................................

19

19

28

1 Preparation of this paper was facilitated by Research Grants HD-04652 and GB-25959 from the National Institute of Child Health and Human Development and the National Science Foundation respectively. The three previously unpublished experiments described in Sections IIB, IIC, and IVD were conducted at the Institute of Child Behavior and Development of the University of Iowa with support by Research Grant HD-02845 from the National Institute of Child Health and Human Development.

1

2

Michael D.Zeiler

I. Superstition and the Reinforcement Process A. THE IMPLICATIONS

OF SUPERSTITIOUS

BEHAVIOR

In 1948, Skinner brought the study of superstition into the realm of science. In so doing, Skinner’s work initiated fruitful analyses into how behavior is controlled by its consequences and generated concepts which may explain much complex behavior. Skinner’s experiment was simple: He presented food to pigeons every 15 seconds independently of their behavior. After a number of these food presentations, Skinner observed the behavior and found that each bird displayed consistent responses. One turned in a counterclockwise direction several times between each food delivery, another repeatedly tossed its head, a third hopped from one foot to the other, and others showed still different behavior. Since these responses were not prevalent prior to the first food presentation and stopped when it was discontinued, the delivery of food was the responsible agent. Yet the responses did not influence food presentations. The parallel to the kinds of behaviors classified as superstitious outside the laboratory led Skinner to describe his experiment as involving superstition in the pigeon. In either the natural or the experimental setting, the term “superstition” refers to behaviors which are emitted as if they have environmental consequences, but in fact do not. Herrnstein ( 1966) has pursued the relation between experimental analogues of superstition and folklore critically and in detail, and points out some provocative similarities and differences. The present discussion concentrates on laboratory situations and the relevance of experiments on superstition to an understanding of how reinforcing stimuli control behavior. Skinner’s experiment has important theoretical implications. Apparently a particular behavior predominated because it happened to occur in close temporal contiguity with the presentation of food. Food was a reinforcing stimulus even though the correlation with behavior was adventitious. Once the frequency of some behavior increased, it became even more likely that the same behavior would be contiguous with the next food presentation so that its frequency would increase still further. This circular relation eventually made the behavior so probable that it became apparent during the intervals separating food presentations. Is there a difference between this phenomenon and the typical operant conditioning situation in which a response increases in frequency when it produces a reinforcing stimulus? Perhaps not, except that in the superstitious situation the response that will be contiguous with the stimulus is unspecified by the experimenter, whereas in the typical operant conditioning

Superstitious Behavior in Children

3

situation this response is preselected by the experimenter. In either case, the behavior immediately prior to the delivery of the reinforcing stimulus increases in frequency of occurrence, is thereby even more likely to precede the stimulus in the future, and eventually becomes predominant over all other behaviors. Superstitious behavior serves as the clearest example that the temporal relation between responses and reinforcing stimuli is the critical one. Setting aside philosophical considerations about the nature of causality, superstition indicates that the cause and effect relationship maintained when reinforcing stimuli depend on a response is not essential. Although it is plausible to assume that reinforcing stimuli affect the frequency of responses via the temporal relations, a position maintained by most if not all reinforcement theorists, it is an unproven hypothesis that the essential relation is in fact temporal. The reason for the hypothetical status is that experiments involving a causal relationship between a response and a reinforcing stimulus have revealed other effects besides that of increasing the probability of the response. Until these other effects can also be observed in the absence of a causal relationship, the inference that the essential relationship is temporal rather than causal remains plausible but hypothetical. Therefore, in order to maintain that the temporal correlation is the necessary and sufficient one, it is essential to demonstrate more than that a stimulus delivered without reference to behavior increases the frequency of the temporally contiguous response. For example, response-dependent presentations of reinforcing stimuli influence the way in which responses are distributed in time depending on the schedule according to which the reinforcing stimulus is presented. That is, the pattern of responses varies depending upon whether reinforcing stimuli follow the first response occurring at regular time intervals (fixed-interval schedules), or the first response occurring at irregular time intervals (variable-interval schedules), or whether they depend on the execution of a constant or varied number of responses (fixed-ratio and variable-ratio schedules). Also, the responsedependent presentation brings behavior under the control of exteroceptive stimuli if the availability of the reinforcing stimulus is correlated with the presence or the absence of certain discriminative stimuli. To the extent that the temporal relation of behavior to reinforcing stimulus presentation is the only essential condition, superstitious behavior should mimic all of the effects observed when reinforcing stimuli occur dependent on a response. As seen in Section 11, superstitious behavior in children does reveal effects on probability of response, patterns of responding, and stimulus control when temporal rather than inevitable causal relations are scheduled by the experimenter.

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Michael D.Zeiler

B. REINFORCEMENT DEPENDENCIES AND CONTINGENCIES Several critical words, phrases, and procedures must be defined at the outset, because historically they have had multiple meanings and consequently are subject to confusion. A prime candidate is reinforcement and its derivatives. Catania (1969, p. 845) pointed out that “the vocabulary of reinforcement includes at least three nouns: reinforcer as a stimulus, reinforcement as an operation, and reinforcement as a process or as a relationship between an operation and a process.’’ The definitions used in the present paper follow from his discussion and thereby correspond with those used in the major discussions of operant behavior and reinforcement schedules (Ferster & Skinner, 1957; Morse, 1966; Skinner, 1938). By process o f reinforcement is meant an observed increase in responding, and a reinforcing stimulus or reinforcer is a stimulus which increases the frequency of the response that it follows. Reinforcement is confined to its operational sense; it refers to the presentation of a reinforcing stimulus. A schedule of reinforcement refers to the arrangement according to which reinforcing stimuli are presented. None of the definitions involves inferred events or states of the organism; all have reference to stimulus presentations and changes in response frequency. Contingency is another word that has had multiple meanings in psychology. In addition to explaining present usage, a discussion of the meaning of contingency helps to clarify the significant relationships treated in this paper. Webster’s New World Dictionary ( 1968) defines contingent as: “1. that may or may not happen; possible. 2. happening by chance; accidental; fortuitous. 3. dependent (on or upon something uncertain) ; conditional. 4. [Archaic], touching, tangential. 5. in logic, true only with certain conditions or contexts; not always or necessarily true. n. 1. an accidental or chance happening.” Other noun uses are given, but these refer to another class of meanings. Contingencies, then, properly refer to events which are not specified as necessities but which may occur. In the study of behavior, contingencies often refer to the relation between responses and reinforcement. In one use, contingency describes an independent variable, the conditions of reinforcement: The reinforcer will be presented if certain conditions are met and will not be presented otherwise. Thus, reinforcement is not a certainty but is contingent upon the occurrence of other events. In this usage, contingency is synonymous with schedule, that is, it states the conditions under which reinforcement will occur. There are two general types of condition. On the one hand, there are those requiring a specified response; these include ratio schedules which prescribe the number of responses required for reinforcement, interval schedules which specify the time that must elapse since the last reinforcement before the

Superstitious Behavior in Children

5

next response is reinforced, and schedules in which reinforcement depends on the time that has elapsed between successive responses. On the other hand, the second condition involves no response requirement; these are time schedules in which reinforcement occurs after a specified period of time elapses. Schedules involving response requirements can be referred to as involving contingent reinforcement without doing violence to the dictionary definition of contingent, since the reinforcement may or may not occur depending on whether the criterion response does or does not occur. However, although noncontingent reinforcement has been used to describe time schedules, this does not accord with the dictionary definition and, in fact, is confusing or even contradictory if taken literally. Since reinforcement is scheduled in relation to time, it is contingent on something (time), although it may be noncontingent with respect to responses. It is important to distinguish between schedules requiring responses and those that do not, but contingent and noncontingent are not the best way of doing so. The distinction is unambiguous if the classes of schedules are referred to as response dependent and response independent. A different usage of contingency refers to a dependent variable by expressing the relation between responses and reinforcement with the emphasis on the response. In this vocabulary, contingent is not synonymous with schedule but refers to the behavior that happens to occur prior to reinforcement. Although every response-dependent schedule at least requires that the specified response occur and may make it likely that other responses occur as well, none prescribes all of the behavior that may precede reinforcement. Response-independent schedules leave all of the behavior free to vary. Contingencies refer to the complex behavior that happens to occur prior to reinforcement whether the behavior is required or not. Reinforcement cannot be noncontingent because some form of behavior must occur and thus has a contingent relationship to reinforcement. Contingency in this sense is shorthand for scheduled and adventitious effects of reinforcement on behavior. The distinction between dependency and contingency derives from the efforts of Catania (1968) and Reynolds (1968) who use dependency to refer to events which must occur if reinforcement is to occur and contingency to refer to events which do not have a perfect probability of occurring prior to reinforcement. Their definitions (which a survey of recent volumes of the Journal of the Experimental Analysis of Behavior shows as being adopted with increased frequency) coincide with the present suggestion that dependencies relate to schedules and contingencies to the responses which may precede reinforcement. In summary, schedule and dependency describe how the experimenter arranges his apparatus to dispense reinforcement in relation to (or independent of) responses, and con-

6

Michael D . Zeiler

tingencies describe the behavior that is affected by reinforcement. A schedule may or may not involve a response dependency, but all involve contingencies. Students of superstitious behavior deal with contingencies in that they study behavior that need not occur. Sometimes the contingencies refer to responses, sometimes they refer to antecedent discriminative stimuli which may or may not precede reinforcement as well. Contingencies also arise in response-dependent reinforcement because behavior other than that required may also occur in relation to reinforcement. Basically, the concern is with experiments using response-independent, response-dependent, stimulusindependent, and stimulus-dependent reinforcement schedules to explore contingencies.

11. Deliberate and Adventitious Reinforcement A. PROBABILITY OF RESPONSE Although Skinner’s (1948) paradigm is the most straightforward one for revealing how response-independent reinforcement affects the probability of responses, it places severe demands on the experimenter. The experimenter has no way of knowing what response to observe, instead he must wait to see if some behavior emerges and then find some way to measure and record it objectively. A solution has been to circumvent the problem by first generating the response via response-dependent schedules and then to observe how the behavior is maintained when the response is no longer required. It must be noted though that this solution places the emphasis on the maintenance rather than on the acquisition of behavior, and thus is not the strongest test of the hypothesis that response-independent and response-dependent reinforcement are equivalent with respect to response probability. It seems fortunate, therefore, that there have been several instances in which experimenters have observed that a response-independent schedule did establish a new response as well as maintain an old one. Both initial establishment and maintenance of a response have been observed with children. Zeiler (1970) first exposed four- and five-year-old children to a fixedratio schedule. The child received candy whenever a total of 30 responses had occurred to two response keys; these responses could be distributed in any proportion to the two keys. One key was blue and the other red. Stable behavior consisted of equal responding to each key. The children either executed an entire ratio on one key and then switched to the other, or alternated keys with successive responses. Following the development of

Superstitious Behavior in Children

I

stable behavior, the schedule was changed so that responses to the red key had no effect (extinction), while not responding to the blue key for periods which were increased up to 60 seconds produced candy ( D R O 60-second schedule). This combined schedule was a concurrent extinction DRO 60second schedule. The change from the fixed-ratio to the concurrent schedule had rapid and striking effects. Responses to the blue key slowed and then stopped in accordance with the dependency between candy presentations and the absence of responses. Simultaneously, though, most of the children maintained a high rate of responding to the red key even though these responses actually were irrelevant to candy deliveries. That the responses to the red key depended on the candy deliveries was apparent in that these responses stopped when the DRO schedule was changed to extinction so that candy deliveries ceased. The behavior on the red key was similar to that observed when children received reinforcing stimuli for some response according to a fixed-interval schedule (e.g., Long, Hammack, May, & Campbell, 1958). Even though the candy was independent of responses to the red key, it maintained or increased the probability of responding. It was not necessary that the particular form of behavior emitted prior to reinforcement be pressing the red key; whatever behavior happened to occur at that time could increase in frequency. The behavior of two other children in fact did reveal different forms. Their behavior was reminiscent of Skinner’s ( 1948) pigeons. Neither of these children maintained presses of the red key during the concurrent schedule phase. One of the children instead sat quietly and watched the tray. picking up a piece of candy when it appeared. This subject had alternated successive responses between the keys during the fixed-ratio schedule phase, and early in the concurrent schedule phase had received all of the candy during rest periods following periods of sustained responding. The other child explored the room and floor between candy presentations during the concurrent schedule rather than press the keys. Early in the concurrent schedule phase, he received several pieces of candy via the DRO schedule while searching on the floor for a dropped piece. Subsequently, hc spent the time crawling around the floor, reaching up to get each piece of candy when it was discharged into the tray. These characteristic behaviors of each child also stopped when the DRO schedule was changed to extinction. It appears, therefore, that the particular forms of behavior that a child emitted prior to reinforcement became predominant whether that behavior was key-pressing or something else. Some of these data, then, indicated that a response was established that had no scheduled relation to reinforcement, and the rest indicated that the rate of a previously established response could be maintained or increased.

8

Michael D . Zeiler

Another experiment also showed the ability of response-independent reinforcement to maintain responding in children. In two experiments, Weisberg and Kennedy (1969) first trained two- to five-year-old children to press a lever by delivering snacks according to either a variable-interval or a variable-ratio schedule (Phase 1) . They then changed to a schedule which delivered the snacks independent of responses at either variable or fixed time periods (Phase 2). The remaining children were shifted from the response-dependent schedules (Phase 1 ) to extinction (Phase 2 ) . The behavior of the groups in Phase 2 provided between-group comparisons of the ability of response-independent and extinction schedules to maintain responding. Additional manipulations provided a within-subject comparison. The children who had been given the response-dependent schedule in Phase 1 and the response-independent schedule in Phase 2 were returned to the response-dependent schedule (Phase 3 ) and then were changed to extinction (Phase 4). Those who had the response-dependent schedule of Phase 1 followed by extinction in Phase 2 were returned to the responsedependent schedule (Phase 3 ) and were then changed to a responseindependent schedule (Phase 4). A comparison of Phases 2 and 4 revealed the effects of response-independent reinforcement and extinction on the behavior of each child. Weisberg and Kennedy therefore provided both within- and between-subject comparisons of the ability of response-independent and extinction schedules to maintain a previously established high probability response. The results were unequivocal. Under extinction conditions the rate of lever pressing quickly dropped to a low level. With response-independent food presentations, however, responding persisted for a much longer time before dropping to a low level. In fact, three of the four children who were shifted from the response-dependent variable-ratio schedule of Phase 1 to the response-independent fixed-time schedule of Phase 2 pressed the lever throughout the ten experimental sessions. One child showed no decrease, a second dropped to a low stable level, and the third responded at a higher rate in the response-independent schedule phase. All three subjects subsequently stopped responding after being shifted from the Phase 3 variableratio schedule to extinction. The data suggested that the durability of responding during the responseindependent phase might depend on the rate of the response when that phase began. Subjects differed in their response rates in the variable-timc schedule were ordered just as they were under variable-interval: The higher the rates during variable-interval, the higher the rates and the more persistent the behavior under variable-time. The variable-ratio schedule established still higher response rates than did the variable-interval, and responding seemed even better maintained with the shift from the ratio than

Superstitious Behavior in Children

9

from the interval to the response-independent schedules. Prevailing higher response rates imply the greater probability of a given response occurring in close temporal contiguity to reinforcement under a response-independent schedule, so that it is consistent that behavior should be better maintained if it is occurring at a high rate. These data show that stimuli which reinforce behavior when presented according to response-dependent schedules also reinforce behavior when presented independently of responses. Thus, the data support the hypothesis tkat response-independent and response-dependent presentations have similar effects with respect to developing and maintaining behavior. The only difference seems to be that the response-dependent case guarantees that a specified response will be contiguous with reinforcement, while the response-independent case leaves the particular response free to vary. Why did the rate of responding decline in the response-independent schedule phase with many of the children in the Weisberg and Kennedy (1969) study? Similar rate decreases also occur when nonhuman subjects are shifted from response-dependent to response-independent reinforcement (Appel & Hiss, 1962; Herrnstein, 1966; Zeiler, 1968). The explanation is straightforward. Skinner ( 1948) noted that when reinforcements occur independently of responses, it is likely that although a certain form of behavior is most probable that precise behavior will not always immediately precede reinforcement. Although a reinforcing stimulus does strengthen behavior that is not exactly contiguous with it, the strongest effects are on the immediately preceding events (Dews, 1960). If a behavior incompatible with the response being measured should have the closest contiguity with reinforcement (e.g., withdrawing the hand from the key after pressing is incompatible with pressing in that both cannot occur simultaneously), the measured response eventually should be replaced by the other. Thc new behavior could be of any form based on exactly what did occur at the moment of reinforcement. Skinner observed that the nature of superstitious rituals emitted by pigeons changed over time. This drift in behavior probably is due to the sort of events just described, and illustrates an important difference between response-independent and response-dependent schedules. In the response-dependent case the response requirement precludes drifting by maintaining the close temporal relation between reinforcement and the prescribed response. The recognition of drift raises the question: Why should a certain form of behavior ever persist indefinitely with response-independent reinforcement? Weisberg and Kennedy's results showed that for some children the response did persist, and Herrnstein and Morse (Herrnstein, 1966) reported similar results. Informal observations by several experimenters have suggested that a previously required behavior can continue indefinitely

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Michael D.Zeiler

under a response-independent reinforcement schedule. Why this should occur is a puzzling and unsolved question. All that can be said at this time is that apparently behavior which has been established strongly can be maintained, perhaps permanently, under certain as yet unspecified conditions.

B. TEMPORAL PATTERNS OF RESPONDING

In nonhuman subjects, response-dependent reinforcement schedules have effects on behavior other than affecting its overall probability. According to the particular schedule in force, the distribution of responses in time (the pattern of responding) varies. Thus, with fixed-ratio schedules of moderate or large size, a pigeon pauses after reinforcement and then quickly changes to responding at a high rate which continues until the next reinforcement. Fixed-interval schedules also produce a postreinforcement pause, but then responding gradually accelerates to a high rate. Variable-interval and variable-ratio schedules generate stable rates without long pauses throughout the periods between successive reinforcements. To the extent that response-dependent and response-independent reinforcement are the same, response-independent schedules should also produce characteristic patterns. Schedules involving temporal specifications are of necessity the meeting point of response-dependent and response-independent schedules. Fixedand variable-ratio schedules specify only response number as the requirement for reinforcement; by definition, there can be no response-independent analogues of ratio schedules. Fixed- and variable-interval schedules, in contrast, involve both time and response requirements: either reinforcements follow the first response occurring after fixed periods or after variable time periods. Response-independent schedules can mimic the temporal aspect of interval schedules. I n this respect, fixed-time schedules correspond to fixed-intervals and variable-time schedules correspond to variableintervals. Research with nonhuman subjects indicates that fixed- and variable-time schedules do indeed generate distinctive patterns, and, in fact, produce patterns like those occurring with fixed- and variable-interval scHedules (Appel & Hiss, 1962; Herrnstein & Morse, 1957; Zeiler, 1968). There is no published work with children on this problem; however, one might anticipate difficulty in obtaining differences between fixed- and variable-time schedules because children respond similarly on fixed- and variable-interval schedules. Both produce fairly steady response rates with occasional pauses in responding (e.g., Long et al., 1958). In a previously unpublished study, Zeiler and Orr investigated the pat-

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terns of responding established in four- and five-year-old children by candy presented according to either fixed- or variable-time schedules. For some children the initial schedule was a fixed interval in which the first response occurring after 30 seconds produced candy; for others, it was a variable interval having a mean interreinforcement interval of 30 seconds. The purpose of these schedules was to generate substantial rates of pressing the response key. After there were at least three sessions and responding had stabilized, the schedules were changed to provide candy independent of responses. The children who had been on the fixed-interval schedule now received candy on a variable-time schedule : Candy appeared at irregular intervals averaging 30 seconds. The children who had been on the variableinterval schedule now obtained candy on a fixed-time schedule providing candy every 30 seconds without reference to behavior. For one child the change from variable interval to fixed time occurred in the middle of a session, but for the others changes were made at the beginning of a session. Although there were substantial differences among the five children in the average response rate in the first phase, these differences were unrelated to whether the schedule was fixed or variable interval. Cumulative records revealed similar patterns of responding with the two schedules: All of the children responded at a fairly steady rate although pauses did occur during some interreinforcement periods. Pauses did not often occur immediately after candy deliveries but were distributed throughout the intervals. This sort of behavior is typical of children under fixed- and variable-interval schedules. The record shown in segment A of Fig. 1 is for a child given a variabletime schedule. The behavior continued much as it had been under fixed interval, with responses emitted at a fairly stable and high rate. The change from the fixed-interval to the variable-time schedule had little effect on behavior. The change t o the fixed-time schedule had rapid effects. Segment B of Fig. 1 shows the behavior on the first day of the fixed-time schedule for one of the children. The behavior up to the first two candy presentations was like that observed previously under the variable-interval schedule. Subsequently, responding became more erratic, and then was marked by periods of pauses followed either by a n abrupt shift to responding at a high rate or by positive acceleration. Pauses after candy presentations were evident. Still later in the session responding was often first positively, and then negatively, accelerated in each period so that the records were S-shaped. The next session showed similar behavior. Segment C of Fig. 1 shows the behavior of the child changed from the variable-interval to the fixed-time schedule midway through a session. Although the prevailing rate was low under both schedules, the patterns of

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Michael D . Zeiler

I

8 Minutes

-I

Fig. 1. Cumulative records obtained by Zeiler and Orr. ( A ) A full session o f the variable-time schedule, ( B ) a frill session of the fixed-time schediile, and ( C ) a sessioii in uBhich the schedule n'as changed from variable interval to fixed time. The record is broken at the point of transition. Deflections of the response pen indicate candy preserr tafiorrs.

responding were like those of the other children. The variable-interval schedule generated a rather erratic pattern : In some intervals responding was steady and in others it was positively accelerated. With the switch to the fixed-time schedule, responding was positively accelerated in nearly every interval. Two other children were first trained with a variable-interval schedule and were then shifted to fixed interval to determine whether the change in temporal patterning of reinforcement from variable to fixed was responsible for the change in the pattern of responding observed for children switched from the variable-interval to the fixed-time schedule. However, the change from variable- to fixed-interval produced no noticeable changes in behavior. These data revealed that the response-independent schedules did control distinctive patterns of response. In fact, the difference in the behavior under fixed-time and variable-time schedules was much greater than that between fixed-interval and variable-interval schedules. It remains unclear as to why the two types of interval schedule usually have generated similar behavior in children but not in nonhuman subjects. What is particularly puzzling is why both forms of variable schedule as well as the fixed-time schedule generate behavior in children like that observed with other species, while fixed-interval schedules differ. One possibility is that there is no research

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with children involving fixed intervals with substantial temporal requirements: Positive acceleration in pigeons does not always occur with short intervals (Ferster & Skinner, 1957). Perhaps fixed-time schedules will show positively accelerated responding at temporal parameter values too low to reveal such behavior under fixed intervals in human subjects. Weisberg and Kennedy ( 1969) studied transitions from variable-interval and variable-ratio schedules to variable-time and fixed-time schedules. The only data provided on patterning was on fixed-time following variable-ratio training. These data confirmed Zeiler and Orr's finding that fixedtime schedules engender positively accelerated rates of responding. Two of the children displayed positively accelerated patterns during the variableratio schedules but the pattern was enhanced by the fixed-time schedule. The third subject had a fairly stable rate under variable-ratio reinforcement and then displayed positive acceleration with the fixed-time schedule. These limited data on patterns of responding under response-independent schedules indicate that variations in the response-independent conditions do produce different patterns of response. The data confirm those of nonhuman subjects given fixed- and variable-time schedules. It may be, however, that children differ from nonhumans in that fixed response-independent and response-dependent schedules (fixed-time and fixed-interval) produce different effects. Since the data are scanty, all that can be said now is that the results are equivocal with respect to the similarity of the two forms of fixed schedule; obviously, final conclusions await further research.

C. STIMULUS CONTROL One important property of response-dependent reinforcement is that when the availability of reinforcement is differentially related to environmental stimuli, organisms usually come to respond differentially with respect to the stimuli. Stimulus control, therefore, is observed under experimental paradigms in which a response ( R ) is followed by a reinforcing stimulus (SR) in the presence of a certain antecedent stimulus (S). In one familiar instance of the S-R-S" paradigm, responding is reinforced in the presence of one stimulus and not reinforced in the presence of another; other common cases involve reinforcement in the presence of two or more stimuli with a distinctive schedule correlated with each. In any event, stimulus control is evidenced when subjects' responses differ in some respect (e.g., rate or pattern) depending on the prevailing stimulus. These typical situations involve a two-way dependency : Reinforcement requires the presence both of a certain stimulus and of a certain response. Discriminative behavior should also occur with response-independent reinforcement if the response-dependent and independent cases involve the

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Micliuel D . Zeiler

same essential processes. However, the general problems encountered in studying response-independent reinforcement in nondiscriminative situations also arise, and, in fact, seem evcn more burdensome in the discrimination situation. What response should be observed? Will the experimenter notice it if and when it occurs? In addition, how can the experimenter rigorously evaluate whether the observed superstitious behavior is differentially related to the prevailing stimuli? One possible solution is the one already described, namely, generate a high probability response by prior training and then shift to a response-independent schedule while manipulating stimuli. Although such a procedure would be of interest and might well prove effective, it apparently has not been used. Instead, a different procedure, one first reported by Morse and Skinner (1957), has proven valuable and provides related information. It consists of a maintained response-dependent schedule with changes in stimuli that have no scheduled relation to the availability of reinforcement. The procedure consists of having reinforcement be stimulus-independent while continuing to be response-dependent. Differential responding under these conditions indicates that the three-term S-R-SR dependency is not necessary for obtaining stimulus control, but is perhaps effective only because it guarantees certain temporal relationships between discriminative stimuli, responses, and reinforcement. Thus, the procedure provides a way of breaking up part of the three-term dependency to determine if in fact it is essential for stimulus control to occur. Morse and Skinner found that pigeons pecking a key which produced food according to a variable-interval schedule had a different response rate in the presence of each of two colors, although the colors were only adventitiously related to the reinforcement schedule. Thus, in pigeons, different scheduled consequences for responding to two stimuli are not necessary to establish discriminations; pigeons responded differently to two stimuli when each provided the same outcome. Tt is appropriate to refer to this phenomenon as a “superstitious discrimination” since differential responding occurred in the absence of differential requirements. The experiment reported here investigated further the occurrence of discriminations in the absence of experimenter-scheduled differential reinforcement. The research had two main purposes: ( 1 ) to investigate the generality of the Morse and Skinner effect with children and ( 2 ) to determine whether discriminations would develop with a reinforcement schedule other than variable interval. The first purpose, assessment of generality, stemmed from the absence of any data bearing on this problem with children. The second arose because previous research used only variable-interval schedules. Both variable-interval and fixed-ratio schedules were used to determine

Supersiiiioiis Behavior in Children

15

if the superstitious discriminations occur only with irregular temporally determined reinforcement presentations. The subjects were 12 children ranging in age from four to five years. During the 10 experimental sessions, they received candy for pressing a key according to either a variable-interval schedule having a mean interval of 30 seconds or a fixed-ratio schedule maintained at 15 responses per candy presentation. Six children were exposed to each schedule. The significant aspect of the experiment was that key pressing produced candy according to the schedule in force independent of the color of the key. The color alternated between red and blue, staying red for 30 seconds and changing to blue for 6 seconds. The occasional interruptions of one color by another was the same general procedure used by Morse and Skinner, although their intervals involved the presentation of the second stimulus for 4 minutes once per hour and a baseline schedule of variable interval averaging 30 minutes between reinforcements. In the first session most of the children responded at nearly equal rates in the presence of the two stimuli. Differences in rate began to develop by the end of the session. With additional sessions, 9 of the 12 children had a substantially higher rate in the presence of one stimulus than the other, and several had more than a 10-fold rate difference. Figure 2 shows the largest differences obtained in any session for children exhibiting a higher rate in red, for those having a higher rate in blue, and for those with n o clear rate difference. Figure 3 presents cumulative records showing a higher response rate when the key was red under both the variable-interval and the fixedratio schedules. The rates during each stimulus can be analyzed by com-

A

B

C

D

E

F G SUBJECT

H

I

J

K

L

Fig. 2. The largest rate differences nttained to the two Jtinirtli b y each child. The figure is segmented io show higher rates in red, higher rates irz hlite, and equal rates to boih stimuli. Thc solid bars show the rate during the blue stitnrrlus, and the striped bars show the rate during the red stimulus.

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Michael D. Zeiler

I

I

1 0 Minutes

Fig. 3. Citmrtlafive records indicating a higher response rate in red than in blue. T h e key was red f o r 30 seconds and changed fo blue during the 6-second periods ihai the response pen W ~ deflected. S Cirrve A shows an FR 15 schedule; curve B shows a VI 30-second schedule. T h e o c c ~ t r r e ~ ~ofc ecandv deliveries is riot shown.

paring the slopes in the records when the pen was in its normal position (during red) and when it was deflected (during blue). The children responded at a substantial rate (as fast as 2.00 responses per second) when the key was red, but virtually stopped pressing during the 6-second periods when it was blue. Counters and observations by the experimenter indicated that all candy was obtained either during the red periods or immediately after the color changed to blue. The overall rate of responding did not differ consistently with the two types of schedule, except that there was some pausing after candy deliveries with the fixed ratio. Figure 4 presents records showing a higher response rate in blue than in red. Again there were no marked schedule effects. With the fixed-ratio schedule children began responding during the 6-second blue periods and continued to respond until the delivery of candy. Then they paused until the next blue period. Candy

k

10 Minutes

I

Fig. 4. Cirmirlative records indicating a highrr response ratr in bliir than in red. Recording was described for Fig. 3. Cirrve A shows an F R 15 schedrrle; cirrvr B shows a V l 30-second schedule.

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presentations usually occurred in red following a burst of responses initiated by the change from red to blue. With the variable-interval schedule, they either did not respond at all in red or responded at a low rate. Almost all candy presentations occurred in blue. Different children exhibited various time courses of the discrimination. F o r some, the stimuli maintained different rates of responding over the 10 experimental sessions. Others showed a discrimination in the first four o r five sessions, but then came to respond equally during both stimuli. For others, stimulus control developed after several days of training. This sort of variability and changes in differential responding typically occurs in experiments on discriminations appearing in the absence of scheduled differential reinforcement in subjects other than children (Lander, 1968; Morse & Skinner, 1957). Also, the failure of a superstitious discrimination to occur for some subjects is not unusual in experiments of this type. Morse and Skinner pointed out that, although the stimulus which is present at the time of reinforcement is accidental, the reinforcement may increase the future rate of responding during that stimulus. If reinforcement now should happen not to occur when the second stimulus is present for any of a number of possible reasons, responding to that stimulus is likely to decrease. Now, given a greater likelihood of responding in the presence of one of the stimuli, the subject is more likely to meet the schedule requirements and to obtain additional reinforcements during the first stimulus. This sort of circularity would eventually result in a substantial degree of differential responding with respect to the two stimuli. The only difference between the superstitious discrimination and discriminations occurring when differential reinforcement is scheduled explicitly is that the superstitious case allows the stimulus which is correlated with reinforcement to vary. Because of that, either stimulus could control the higher response rate, and, because reinforcements may occur during the stimulus correlated with the higher rate (unless the subject completely stops responding), the discrimination either could disappear or even reverse its direction over a number of sessions. (Reversals in the stimulus which controlled the higher rate were not observed in the children.) These hypotheses would seem to be reasonable accounts of the nature of superstitious discriminations; as such, they demonstrate the similarity in process for the events responsible both for superstitious and experimenter-determined discriminations. Apparently, the prevailing reinforcement schedule is not critical since similar behavior occurred with both fixed-ratio and variable-interval schedules, perhaps because both schedules produced similar rates and patterns of responding in children. It seems likely, however, that supmtitious discriminations probably require at least a moderate degree of intermittency in

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the response-reinforcement relation. Continuous reinforcement or schedules having little intermittency probably would establish such a high probability of reinforcement in the presence of both stimuli that rate differences and the ensuing circular relationship between ongoing behavior, reinforcement, and consequent behavior would not develop. One new observation was that children did not require a strict correlation between reinforcements and stimuli to establish the superstitious discriminations. Some subjects had a higher rate during the blue stimulus even though the candy presentations occurred during red. Since the run of responses always did begin in blue, it seems as if the stimulus present when responding began was more important than the one present at the moment of reinforcement. This may be a difference between children and nonhuman subjects; however there are insufficient data to evaluate this possibility.

D. REINFORCEMENT AND TEMPORAL CONTIGUITY The preceding review demonstrated the close similarity between adventitious reinforcement, be it response-independent or stimulus-independent, and the effects of reinforcements scheduled to occur only under specified and experimenter-controlled stimulus and response conditions. Although there are differences which limit final conclusions, they may be more apparent than real because of the absence of sufficient data concerning the behavior of children. At the present time, the similarity in the effects of adventitious and deliberate reinforcement appears compelling. A reinforcing stimulus seems to strengthen ongoing responding even though the reinforcing stimulus and the responses and the prevailing discriminative stimuli are only temporally related. Furthermore, the behavior is essentially the same as when reinforcements require the presence of certain responses and discriminative stimuli. The temporal relation describes both the necessary and the sufficient conditions for modulating behavior. The critical events, therefore, are the same in both the adventitious case and the case in which reinforcement is delivered dependent upon the occurrence of a response and/or the presence of a specified discriminative stimulus. The only difference between superstitious behavior and the ordinary operant behavior observed with response- and stimulus-dependent reinforcement is that the dependent cases specify the behavior contiguous with reinforcement while the adventitious cases leave the behavior free to vary. Thus, behavioral control is identical for reinforcements given for specific responses and reinforcements having an accidental relation to responses and discriminative stimuli; reinforcement has the same temporal relation to behavior and stimuli in either case.

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111. Control of Multiple Responses A. CONCURRENT RESPONSE-INDEPENDENT A N D RESPONSE-DEPENDENT REINFORCEMENT A number of experiments (e.g., Antonitis, 195 I ; Skinner, 1938) have shown that reinforcement affects several forms of behavior simultaneously. For example, when a rat obtains food dependent on a bar press, the probability of bar pressing increases. In addition, other aspects of behavior, e.g., the duration o r the topography of the bar press, become stereotyped even though the reinforcement occurs independently of these aspects of behavior. (Except, of course, that the duration must exceed the minimum value specified as a n acceptable response by the programming equipment, and that the lever must be pressed in some fashion.) These data suggest that the response-dependent presentation of a reinforcing stimulus not only influences the behavior scheduled to precede it but concurrently operates on the behavior which accidentally precedes it. Some data with children also support this conclusion. Bruner and Revusky (196 I ) studied the behavior of adolescent boys when a response to one telegraph key earned five cents whenever at least 8.2 seconds but less than 10.25 seconds elapsed since the preceding response to that key. This is a differential-reinforccment-of-low-rateschedule ( D R L 8.2-seconds) with a limited hold of 2.05 seconds. In addition to the telegraph key correlated with this schedule, there were three other keys. Responses to these other keys had no consequence with respect to the delivery of nickels. The complete schedule, involving all of the keys, was a concurrent [ ( D R L 8.2 seconds limited hold 2.05 seconds) extinction extinction extinction] schedule. Subjects were instructed to press one key at a time and were permitted to use only one hand. T h e four boys all had a higher rate of pressing the irrelevant keys than the one correlated with the delivery of nickels: Three of the four confined the high rate responses to one of the extinction keys, while the fourth boy responded about equally to two of the three keys. Responses to the DRL key were spaced sufficiently in time so that nearly every such response was followed by the presentation of a nickel. When the schedule on the D R L key was then changed to extinction so that nickels were no longer available, responding became more erratic. Apparently, the responses to various keys in the D R L phase were being maintained by the nickels even though presses of all but the one key were irrelevant with respect to the reinforcing event. Bruner and Revusky interpreted their data as indicating a chain of behavior which served to bridge

Michael D.Zeiler

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the time gap between successive presses of the DRL key. What is more important is that the response-dependent delivery of reinforcement according to one schedule also generated stable behavior which had a responseindependent relation to deliveries of the reinforcing stimulus. Such effects are not peculiar to DRL schedules. In Zeiler’s (1970) study referred to in Section IIA, four- and five-year-old children began with candy presented according to a fixed-ratio schedule. There were two keys, one red and one blue, and the ratio requirement could be met by a total of 30 responses distributed in any proportion between the two keys. Every child established a systematic pattern of responding. Some alternated keys with every response, and others alternated keys after each candy presentation, Thus, the fixed-ratio schedule: ( a ) increased the probability of keypressing, the behavior on which candy presentation depended, and ( b ) fixed the way in which the responses were emitted even though such stereotypy was superstitious in that it was irrelevant to reinforcement deliveries. Tritschler’ has found similar stereotyped and often even more complex patterns of response in college students required to execute a fixed ratio on any of five telegraph keys. In the next phase of Zeiler’s (1970) study, responding to one of the two keys had no scheduled consequence and not responding to the other key for a specified period of time resulted in candy (concurrent DRO Extinction schedule). Two forms of behavior resulted. The children stopped pressing the DRO key. In addition, the DRO schedule maintained behavior which did not influence the delivery of candy. Either the children pressed the extinction key at a high rate or they consistently performed other behavior such as crawling on the floor or sitting and staring at the candy tray. Again, a reinforcing stimulus influenced both required behavior and behavior which had only an adventitious relation to the stimulus presentations. Catania and Cutts (1963), studying college students, demonstrated that the close temporal contiguity of the superstitious behavior to reinforcement maintains the behavior. Their subjects had two push buttons with responses to one reinforced on a variable-interval schedule and responses to the other having no scheduled consequences (concurrent variable-interval extinction schedule). The subjects maintained a high rate of responding to both buttons, and one subject actually responded at a much higher rate to the extinction button than to the variable-interval button. Catania and Cutts then added a new requirement: A press on the variable-interval button could not be reinforced if it followed a press on the extinction button within a certain time. The imposition of this change-over delay greatly reduced the superstitious responses to the extinction button; without the change-over 2

J. Tritschler, personal communication, 1970.

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delay, superstitious responses were maintained because they could occur in close temporal contiguity to the response deliberately reinforced on the variable-interval schedule. I t seems reasonable to hypothesize that the superstitious behavior in Bruner and Revusky’s and Zeiler’s experiments was maintained in the same way. The obvious conclusion is that reinforcing stimuli influence several forms of behavior simultaneously even when they have a response-dependent relation to one and a response-independent relation to the other.

B. SOMECOMMENTS O N MEDIATION AND INDIVIDUAL DIFFERENCES When superstitious behavior occurs during DRL or DRO schedules which require periods of not performing the criterion response if reinforcement is to occur, it may be tempting to attribute a mediating function to the superstition. The implication would be that the behavior serves to facilitate the acquisition of reinforcement by filling the time interval. The possible advantages of such behavior, though, should not obscure the fact that the particular behavior that occurs could only be strengthened because it accidentally preceded reinforcement delivery and is maintained because it continues to have this temporal relation. To pose an extreme position, perhaps mediation refers to nothing more than collateral adventitiously reinforced behavior. Although superstitious behavior would seem to have no beneficial function with schedules such as fixed ratio or variable interval where the subject can respond continuously, similar collateral behavior does occur with those schedules. Hence, the collateral behavior need not be useful for it to occur and be maintained; it occurs and is maintained because it continues to bz reinforced. Tt is possible that the same kind of independence characterizes human verbal and motor behavior. namely, that these are separate response systems which may be simultaneously affected by reinforcement. This is a different notion than the common one that verbal mediation is instrumental in producing certain kinds of motor behavior (e.g., choices in discrimination learning) ; perhaps the motor and correlated verbal responses d o not always serve a functional role with respect to each other and are related only in the sense that both can be established by the same reinforcing event. T h e concurrent establishment and maintenance of deliberately and adventitiously reinforced responses may provide some insight into the basis of individual differences. Herrnstein ( 1966) pointed out that when reinforcements depend on a certain response the specification usually involves only some of the dimensions of the response. For example, the experimenter specifies the location and minimum force of an acceptable response but does not also specify its precise topography, rate. maximum force, or dura-

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tion. Yet if these aspects of behavior are conditionable, whatever values they assume will be correlated with reinforcement and will thereby become more probable. Since the values are unspecified, they are likely to differ among individual subjects. That the laboratory situation may be analogous to the natural environment in this respect does not seem farfetched. In the natural environment children generally receive reinforcements for similar behaviors, for learning to care for themselves, for doing well in school, for obeying adults, etc. Despite this general homogeneity, many other aspects of behavior can vary. A child may answer a question in a low or a loud voice, and the reinforcement given for answering correctly may also increase the probability of speaking softly or loudly in the future. Could similar accidents play a role in creating different behavioral styles? Although speculative, it is an alternative to usual explanations of individual differences.

c. A NOTEON REINFORCING NOTRESPONDING In a DRO schedule, a reinforcement occurs whenever a specified response has not occurred for a specified period of time because reinforcements depend on the subject’s not emitting a certain response. These schedules have proven useful in rapidly eliminating behavior and as controls in a number of contexts. The delivery of a reinforcing stimulus following not responding, though, has led to some curious interpretive problems. These apparently stem from reluctance to treat the nonemission of a specified response as a functional response. Instead, starting with Reynolds ( 1961 ), DRO schedules have been defined as “differential-reinforcementof-other-responses,’’ the implication being that the reinforced behavior is not the absence of a response but rather is the occurrence of some other, although unobserved, behavior. Unfortunately, this definition of the schedule involves a theoretical account of its method of action instead of an objective description of the dependency. It may also obscure the possible fact that not emitting a particular response may actually have functional response properties. In any case in which a given behavior is occurring with some frequency, if its probability decreases following consequences for its nonoccurrence, the absence of the response meets the requirements of a functional response. To attribute the behavior to the strengthening of some other behavior is an unsupported inference even if other behavior should be observed to occur, and certainly should not be involved in the name of the schedule. It is interesting that Lane (1961 ) also used the initials DRO to describe the schedule almost simultaneously with Reynolds but translated the initials as “differential-reinforcement-of-no-responding.” Thus, the two earliest uses of

Siiperstitious Behavior in Children

23

the initials defined them differently. [At almost the same time, Kelleher ( 1961 ) used the schedule and called it DRP: “differential-reinforcementof-pausing.’’ Kelleher’s provides an objective description, but his terminology was not adopted subsequently.] It does turn out that DRO schedules can strengthen some behavior other than that prescribed as prerequisite for reinforcement (not emitting a certain response). However, the strengthening of behavior in addition to that required is true of every other reinforcement schedule as well; there is nothing unique about DRO in this respect because adventitious strengthening of responses appears to be a general property of reinforcement. Therefore, it would be appropriate to describe any schedule as involving reinforcement of “other” behavior. The concurrent reinforcement of several aspects of behavior has played an important part in theoretical explanations of how reinforcement schedules establish their distinctive effects on behavior. Thus, first Skinner (1938) then Ferster and Skinner (1957), and then Morse (1966) hypothesized that the combination of response-reinforcement dependencies and response-reinforcement contingencies operate on different schedules of reinforcement. Although we do not yet have an adequate theory of reinforcement schedules, it seems likely that a comprehensive theory will be unable to ignore the relation of reinforcement to required and unrequired behavior in all schedules.

IV.

Other Effects of Response-Independent Reinforcement

Reinforcing stimuli are defined by their ability to affect the probability of responses that precede them; however, such stimuli also have other effects on behavior. These effects do not involve a dependency between the behavior and the reinforcer and thereby qualify as response-independent effects. Staddon and Simmelhag (1971) consider such behavior to be of such fundamental importance thJt it justifies (in fact requires) revised thinking about the nature of reinforcement. Commentary on their provocative arguments go beyond the scope of the present paper, however, a number of the effects they consider important have been observed in children. A. ELICITATION OF PREVIOUSLY PROBABLE RESPONSES

One property of a reinforcing stimulus presented independently of behavior is that it may elicit a response which previously had a high probability but presently is not occurring. Reid (1957) reported such an effect. He found that when pigeons, rats, or humans had been trained to make a

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Michael D . Zeiler

response by following it with the presentation of a reinforcing stimulus, subsequent discontinuation of reinforcement deliveries eliminated the behavior. After several days of the extinction procedure, Reid delivered the previous reinforcing stimulus once without reference to behavior. The subjects immediately resumed their previously trained response. Instead of the response-independent stimulus delivery having its major effect on the behavior which immediately preceded it, the effect was on the behavior which had occurred the last time the reinforcement had appeared. Skinner ( 1938) had described somewhat similar results. Reid suggested that the stimuli provided by reinforcement delivery or by consummatory responses may have been the first part of a behavioral chain and that the free food delivery may have reinstated responding by providing the early components of the chain which had never been affected by the extinction procedure. Although this hypothesis has not received further study, the basic finding has been replicated and extended. Spradlin, Girardeau, and Horn (1966) delivered tokens to retarded adolescents after every fiftieth pull of a plunger. All of the subjects attained a high rate of responding under this fixed-ratio schedule and emitted more than 1500 responses in the last four 20-minute sessions. The schedule was then changed to a variable DRO averaging 2 minutes: A token was delivered when the subjects did not pull the plunger for periods ranging from one to four minutes. An additional degree of intermittency was added by requiring that the no-response criterion be met twice for each token delivery. This complex schedule is a second-order schedule in which the behavior under the DRO schedule is treated as a unitary response and is reinforced according to a fixed-ratio schedule: In second-order schedule notation, the schedule is F R 2 (variable DRO 2-minutes). This schedule insured that the subjects were not operating the plunger in close temporal contiguity with token deliveries. All of the subjects pulled the plunger in the period following prescntation of a token. Five of the six subjects did decrease these responses with maintained exposure to the complex DRO schedule. Even after 25 scssions, however, the remaining subject continued to pause after receiving a token, then operated the plunger at a high rate, and then paused until receipt of the next token. These data indicated that the plunger pulls were elicited by the tokens evcn though they could never precede token delivery by less than one minute. This last subject was changcd to a schedule providing tokens every 30 seconds independently of behavior (fixed-time 30-second schedule ’) . The behavior became distinctly fixed-ratio-like in that most interreinforcemcnt periods showed a pause after token presentation followed by a high response rate which usually continued until the next token appeared. This last behavior is most parsimoniously considered as maintained by adventitious

Siiperstitiorrs Behavior in Cliildren

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correlations with token deliveries rather than as elicited by a reinforcing stimulus. Other data (e.g., Zeiler, 1970) suggest that responding maintained for long periods with D R O schedules is unusual. Typically, as with the majority of the children in the Spradlin et a[. experiment, responding stops. This suggests that the ability of a reinforcing stimulus to elicit a response which once preceded it may disappear. There is no obvious explanation for the extremely persistent responding of the one child in the Spradlin et al. study. The only obvious difference between her and the other subjects was that she was the only subject with a history of response-dependent reinforcement under a differential-reinforcement-of-low-rate ( D R L ) schedule, although it is unclear as to why or whether this history should be important. O F A N E W RESPONSE:AUTO-SHAPING B. ELICITATION

In 1968 Brown and Jenkins reported the novel finding that responseindependent but stimulus-dependent presentations of food resulted in key pecking in pigeons that had not previously been shaped to peck the key. Just presenting stimuli in certain ways elicited the key-peck, a response which previous investigators developed with the explicit differential reinforcement involved in response shaping. Their procedure was as follows. A trial consisted of an 8-second period with a white key and terminated with the response-independent delivery of food. In the intertrial interval, which varied from 30 to 9 0 seconds, the key was dark. Within 160 trials all of the pigeons pecked the key during the white period. Control procedures revealed that what was essential was that the key have some distinctive stimulus during each trial and that food presentation occur after the trial stimulus came on. Brown and Jenkins ( 1 9 6 8 ) called this phenomenon “auto-shaping.” Rachlin ( 1969) observed auto-shaping when the trial stimulus was followed by the termination of electric shock; it seems, therefore, that the emergence of pecking directed at the key is the outcome of the correlation between antecedent stimuli and the occurrence of reinforcement. N o response rcquirement is involved. Some previously unpublished data show that auto-shaping also occurs with children. Four- and five-year-old experimentally naive children were given no instructions other than to stay in a small room and d o whatever they pleascd. Experimental events were programmed and recorded automatically; however, the experimcnter also observed the children through a onc-way vision window. The front wall of the booth contained a response key and a tray into which pieces of candy could be dispensed. The key was transilluminated with either red or green light; the lights alternated from

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Michael D . Zeiler

red to green, staying red for 30 seconds and changing to green for 6 seconds. The green light terminated simultaneously with the delivery of a piece of candy into the tray. Pressing the key at any time resulted in the immediate presentation of a piece of candy. Each child pressed the key during either the first or the second session of training, with the first press occurring somewhere in the middle of the session. One girl never pressed the key with sufficient force for the apparatus to record a response but instead touched the key on each trial. The key-manipulating behavior emerged much as it did in Brown and Jenkins’ study. In the early trials the children did not appear to be looking at the key. With additional trials they seemed to orient more toward the key and began to approach it when it became green. Finally, they touched or pressed it during the green periods. All of the pressing and touching began during green, but later occurred during the red periods as well. The essential finding, though, was that the pressing emerged from the responseindependent but stimulus-dependent presentation of candy. Of course, once the child began to press the key the dependency between pressing and candy deliveries undoubtedly was responsible for the increase in response rate. Research with infants has shown a similar finding, namely, that responses initially established to a stimuli via stimulus pairings become even more probable if they are followed by reinforcement. PapouSek (Reese & Lipsitt. 1970) rang a bell and then elicited head-turning either by tactile stimulation of the cheek or by manually turning the infant’s head. Each head turn was followed by reinforcement (milk). This combination of stimulus pairings which elicited the response and reinforcement following the response produced a substantial frequency of head turns. Williams and Williams ( 1969) demonstrated the noninstrumental nature of the auto-shaped key-peck by finding that auto-shaping occurred in pigeons even when key-pecking was negatively correlated with the presentation of food. They used the Brown and Jenkins paradigm with the added consideration that a peck during the stimulus that was correlated with food presentation cancelled the food delivery and reinstated the intertrial interval ( a DRO schedule). Here, where pecks eliminated reinforcement, the pecks occurred anyway. The peck was elicited and maintained by the stimulus dependencies when the consequences of the peck precluded food presentation. These results imply that auto-shaping may not involve operant behavior but rather an eliciting property of certain stimulus arrangements correlated with the response-independent presentations of food. The auto-shaping procedure involves the straightforward use of the Pavlovian conditioning paradigm : Two stimuli are paired without reference to behavior. The second stimulus (food) depends on the presence of a

Supersfirioics Behavior in Children

27

certain antecedent stimulus ( a red key) but is independent of any response. Auto-shaping does, however, differ from what is commonly considered as Pavlovian conditioning (and PapouSek’s procedure) in that the response which comes to occur during the first stimulus has no necessary counterpart in an unconditioned response to the reinforcing stimulus (cf. Rachlin’s experiment) and in that the response is directed toward the antecedent stimulus. Thus, auto-shaping is an effect of the Pavlovian conditioning paradigm that differs from the classical effects observed by Pavlov and later investigators. Auto-shaping is not the only behavior of this type (cf. Rescorla & Solomon, 1967).

V. Concluding Comments The preceding review of response-independent reinforcing effects showed that reinforcement has multiple influences on the behavior of children. Some types of behavior are elicited by response-independent reinforcing stimuli, other forms of behavior are strengthened because a responseindependent reinforcing stimulus follows them. It is this latter behavior that is referred to as superstition since the term “superstition” usually refers to behavior that occurs as if it influences environmental consequences but in fact does not. The emphasis on superstition, though, should not obscure the fact that reinforcement has multiple effects on behavior; it controls behavior scheduled to precede it, it controls behavior that is not scheduled but happens to precede it, it produces stimulus control over behavior both when discriminations are deliberately arranged and when they occur adventitiously, and it elicits various types of behavior. The complexity of the reinforcing event becomes even more evident when it is recognized that all of these different effects may occur simultaneously. The operant conditioning paradigm describes a dependency between a specified response and a consequent stimulus, and operant discrimination describes a dependency between an antecedent stimulus, a specified response, and a consequent stimulus. But superstitious responses occur when a reinforcing stimulus is presented without reference to either an antecedent stimulus or a response, and superstitious discriminations occur when a reinforcing stimulus occurs independently of antecedent stimuli. What superstitious behavior illustrates is that in the absence of a response specification, responses which happen to precede reinforcement increase in probability, and that in the absence of stimulus specification, the stimulus present when reinforcement occurs develops control over responding. Superstition shows that the essential process involved in operant behavior is the temporal contiguity among response and stimulus events.

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REFERENCES Antonitis, J. J. Response variability in the white rat during conditioning, extinction, and reconditioning. Journal of Experimental Psychology, 195 1, 42, 273-28 1. Appel, J. B., & Hiss, R. H. The discrimination of contingent from noncontingent reinforcement. Journal of Comparative and Physiological Psychology, 1962, 55, 37-39. Brown, P. L., & Jenkins, H. M. Auto-shaping of the pigeon’s key peck. Jorrrnal of the Experimentai Analysis of Behavior, 1968, 11, 1-8. Bruner, A., & Revusky, S. H. Collateral behavior in humans. Journal of the Experimental Analysis of Behavior, 1961, 4, 349-350. Catania, A. C. Glossary. In A. C. Catania (Ed.), Contemporary research in operant behavior. Glenview, Ill.: Scott-Foresman, 1968. Pp. 330-33 1. Catania, A. C. On the vocabulary and the grammar of behavior. Journal o f the Experimental Analysis of Behavior, 1969, 12, 845-846. Catania, A. C., & Cutts, D. Experimental control of superstitious responding in humans. Journal of the Experimental Analysis of Behavior, 1963, 6, 203-208. Dews, P. B. Free-operant behavior under conditions of delayed reinforcement. I. CRF-type schedules. Joirrnal of the E.uperimenta1 Analysis of Behavior, 1960, 3, 221-234. Ferster, C. B., & Skinner, B. F. Schedules of reinforcement. New York: Appleton, 1957. Herrnstein, R. J. Superstition: a corollary of the principles of operant conditioning. In W. K. Honig (Ed.), Operant behavior: Areas of research and application. New York: Appleton, 1966. Pp. 33-51. Herrnstein, R. J., & Morse, W. H. Some effects of response independent positive reinforcement on maintained operant behavior. Journal of Comparative and Physiological Psychology, 1957, 50, 461-467. Kelleher, R. T. Schedules of conditioned reinforcement during experimental extinction. Journal of the Experimental Analysis of Behavior, 1961, 4, 1-5. Lander, D. G. Stimulus bias in the absence of food reinforcement. Journal of the Experimental Analysis of Behavior, 1968, 11, 71 1-714. Lane, H. Operant control of vocalizing in the chicken. Journal of the Experimental Analysis of Behavior, 1961, 4, 171-177. Long, E. R., Hammack, J. T., May, F., & Campbell, B. J. Intermittent reinforcement of operant behavior in children. Journal of the Experimental Analysis o f Behavior, 1958, 1, 315-339. Morse, W. H. Intermittent reinforcement. In W. K. Honig (Ed.), Operant behavior: Areas of research and application. New York: Appleton, 1966. Pp. 52-108. Morse, W. H., & Skinner, B. F. A second type of “superstition” in the pigeon. American Journal of Psychology, 1957, 70, 308-3 1 1 . Rachlin, H. Autoshaping of key-pecking in pigeons with negative reinforcement. Jorrrnal of the Experimental Analysis of Behavior, 1969, 12, 521-531. Reese, H. W., & Lipsitt, L. P. Experimental child psychology. New York: Academic Press, 1970. Reid, R. L. The role of the reinforcer as a stimulus. British Journal of Psychology, 1957, 49, 202-209. Rescorla, R. A., & Solomon, R. L. Two-process learning theory: relationships between Pavlovian conditioning and instrumental learning. Psychological Review, 1967, 74, 151-182.

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Reynolds, G. S. Behavioral contrast. Journal of the Experimental Analysis of Behavior, 1961, 4, 57-71. Reynolds, G. S. A primer of operant conditioning. Glenview, Ill.: Scott-Foresman, 1968. Skinner, B. F. The behavior of organisms. New York: Appleton, 1938. Skinner, B. F. “Superstition” in the pigeon. Joitrnal of Experimental Psychology, 1948, 38, 168-172. Spradlin, J. E., Girardeau, F. L., & Hom, G. L. Stimulus properties of reinforcement during extinction of a free operant response. Journal of Experimental Child Psychology, 1966, 4, 369-380. Staddon, J. E. R., & Simmelhag, V. L. The superstition experiment: A reexamination of its implications for the principles of adaptive behavior. Psychological Review, 1971, 78, 3-43. Webster’s new world dictionary. (College ed.) Cleveland: World, 1968. Weisberg, P., & Kennedy, D. B. Maintenance of children’s behavior by accidental schedules of reinforcement. Journal of Experimental Child Psychology, 1969, 8, 222-233. Williams, D. R., & Williams, H. Auto-maintenance in the pigeon: sustained pecking despite contingent non-reinforcement. Joitrnal of the Experimental Analysis of Behavior, 1969, 12, 5 1 1-520. Zeiler, M. D. Fixed and variable schedules of response-independent reinforcement. Journal of the Experimental Analysis of Behavior, 1968, 11, 405-414. Zeiler, M. D. Other behavior: consequences of reinforcing not responding. Joirrnal of P s y ~ h o l ~ g 1970, y, 74, 149-155.

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LEARNING STRATEGIES IN CHILDREN FROM DIFFERENT SOCIOECONOMIC LEVELS'

Jean L . Bresnahad and Martin M . Shapiro EMORY UNIVERSITY

I. INTRODUCTION ........................................... A. VARIABLES ........................................... B. OUTLINE OF EXPERIMENTS ........................... 11. CONCEPT FORMATION .................................... A. EXPERIMENT I-CONCEPT ACQUISITION IN HIGHERAND LOWER-CLASS CHILDREN ........................ B. EXPERIMENT 11-PARTIAL REINFORCEMENT OF AN OBVIOUS DIMENSION .................................. C. EXPERIMENT 111-CHAOTIC REINFORCEMENT . . . . . . . . . D. EXPERIMENT IV-PRETRAINING TO CRITERION . . . . . . E. EXPERIMENT V-PRETRAINING WITH A FIXED NUMBER OF TRIALS ............................................ F. DISCUSSION OF CONCEPT FORMATION . . . . . . . . . . . . . . . .

111. REWARD PREFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. EXPERIMENT VI-AMOUNT AND PROBABILITY OF REINFORCEMENT ....................................... B. EXPERIMENT VII-REINFORCEMENT WITH AND WITHOUT SIGNALS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. DISCUSSION OF REWARD PREFERENCES . . . . . . . . . . . . . . IV. INSTRUCTIONS AND TRAINING . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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1This research was supported in part by Contract B89-4613 from the Office of Economic Opportunity to M. M. Shapiro, J. L. Bresnahan, and I. J. Knopf. The authors express their appreciation to I. J. Knopf for his contributions to the program of research. 2 Present address: Department of Psychology, Lehman College, City University of New York, New York, New York. 31

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V.

A. EXPERIMENT VIII-EXTINCTION AFTER INSTRUCTIONS AND TRAINING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. DISCUSSION OF INSTRUCTIONS AND TRAINING . . . . . . .

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I. Introduction There has been much interest in the characteristics of children from different socioeconomic backgrounds. Many writers have described in detail the differences in the environments of children who come from the extremes of the socioeconomic dimensions in the United States, referred to here as high and low socioeconomic status (SES) . Comprehensive reviews of the topic can be found in the Review of Educational Research (1965) and in Education in Depressed Areas (Passow, 1963). The lower-class homes are typically depicted as overcrowded, noisy, disorderly, and lacking in many of the items associated with the development of learning skills, such as books, magazines, records, and educational toys (e.g., Gordon, 1965). Many of the authors emphasize the nature of the children’s interactions with their parents, and consider this variable to be even more crucial than the material aspects of the homes. In particular, much attention has been devoted to the differences in the verbal communication in homes of high and low socioeconomic levels, and the consequent language development of the children (Bernstein, 1961; Hess Rr Shipman, 1965; McCarthy, 1954; Raph, 1965). The general findings have been that lower-class parents speak to their children in short simple sentences, usually commands, and rarely use language to elaborate or explain concepts. The differences in the behavior of higher- and lower-class children have likewise been observed and reported. It is well documented that lower-class children perform less successfully than higher-class children in many diverse kinds of experimental, academic, and vocational situations (e.g., Karp & Sigel, 1965). Children from lower socioeconomic levels are considered deficient in reading, number concepts, time concepts, auditory discrimination, visual discrimination, and symbolic representation (e.g., Deutsch, 1963; Montague, 1964; Riessman, 1964). Their intellectual functioning has been described as more concrete and inflexible than that of more privileged children (McCandless, 1952). They are depicted as being restless and prone to physical activity, and having a short attention span. They are said to be motivated only by short-term goals, incapable of postponing imme-

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diate gratifications, nonresponsive to symbolic or verbal incentive, and lacking in aspirations consistent with middle-class values (e.g., Gordon, 1965). These descriptions of environmental and behavioral differences among socioeconomic levels have been voluminous and encyclopedic. Attempts have been made to quantify the observations and obtain correlations among several categories of variables. Unfortunately such work suffers from the limitations of all similar endeavors; it is exceedingly difficult if not impossible to separate phenomena from epiphenomena, relationships from artifacts. The question still remains, “What are the necessary or sufficient environmental conditions for the establishment of identifiable patterns of behavior?” Fortunately, the available correlational data do provide the bases for intuitions and guesses. At the start of this research socioeconomic level was the principal independent variable. However, the ultimate goal was to replace this vague and confounded construct by a set of scientifically more manageable variables. A. VARIABLES

Socioeconomic level was defined in terms of the occupation, income, and education of the parents. This gross and impure subject variable of socioeconomic level was combined with manipulations of the more clearly definable independent variables of reinforcement schedule and reinforcement contingency. From the information obtained in the first few studies multiphase experimental procedures were designed in which pretraining conditions were manipulated. In the process, socioeconomic level became less and less interesting and the pretraining became more and more interesting. Instead of assuming that social class was correlated with childhood training, the pretraining was manipulated. A similar evolution occurred in the choice of dependent variables. At first two stimuli were presented to the subject and he was asked to choose one of them in a concept acquisition task; later subjects were asked to choose between two reinforcement schedules. Subsequently, rates of responding to several different stimuli were measured. Additionally, the sequence of choices bctween two stimuli or between two responses was analyzed.

B . OUTLINE O F EXPERIMENTS In the first set of cxperirnents to be presented, concept formation procedures were used. Higher- and lower-class children were trained to select one of two stimuli either on the basis of size or on the basis of number.

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I . L. Bresriahari urid M. M.Shapiro

The discrepancy between the results on the size and number tasks was subsequently interpreted and investigated as a difference between obviousness of stimulus dimensions. A pretraining procedure was then introduced into the design to determine the conditions under which the performance of higher- and lower-class subjects would be equalized. Following this study, subjects from middle range schools were studied to test the hypotheses generated with respect to the acquisition of strategies during concept formation. In the second set of experiments reward preferences of children from high and low socioeconomic levels were investigated. The subjects were allowed to choose between two keys, one of which resulted in a fixed reinforcement schedule and one of which resulted in a variable reinforcement schedule. To investigate further the differences found in the behavior of the two groups, an experiment was designed to study the effect of the magnitude of the previous reinforcement and the effect of a signal predicting the magnitude of the next reinforcement. In the final experiment the rate of responding was considered, first as a function of social class and second as an interaction between social class and training.

11.

Concept Formation

A. EXPERIMENT T - C O N C E P T ACQUISITION IN HIGHERAND LOWER-CLASS CHILDREN

The Board of Education of Cobb County, Georgia, provided the names of schools which had children from either the highest or the lowest socioeconomic levels in the county. The following information was obtained from the school records: name, address, date of birth, occupation of parents, education of parents. Children who had repeated the first grade were excluded from the study. In Experiment I, a previously unpublished study, the following indices were used to determine socioeconomic level: location and quality of residence, occupation of parents, education of parents, grooming of the child. For the residence requirement only houses in very good condition and not too small in size qualified for the high level. The houses in the low level were quite deteriorated and in need of repair, and were often very small in size. The houses for the high and low levels corresponded to Warner, Meeker, and Eells’ (1949) house types 1 and 2, and 6 and 7, respectively. Similarly the occupations of the high and low levels corresponded roughly to Warner, Meeker, and Eells’ classes 1 and 2, and

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6 and 7, respectively. In the former were professionals, semiprofessionals, and proprietors of large businesses; in the latter were craftsmen, semiskilled workers, and unskilled workers. In the high level most fathers were college graduates. In the low level most parents had a seventh to tenth grade education. [In this paper the label “high” is used to describe a socioeconomic level which is typically called “upper-middle’’ in the United States. “High” is therefore broader than the category “upper,” which in some classifications refers to a very small percentage of the population; for instance, the upper class includes only 3% of the population in the Warner et al. (1949) system.] The schools chosen were either predominantly higher or lower class, and any one school was used as a source of only one of the groups, not both. That is, deviant children in these schools were not considered for the opposite group, e.g., a physician’s daughter in a lower-class school would not have been included in the higher group. Since socioeconomic level was of interest as a possible index of early training, the groomed appearance of the child was rated on a five-point scale. A rating of 1-3 was required for inclusion in the lower group and a rating of 3-5 was required for inclusion in the higher group. The measure of grooming proved to be cumbersome and of dubious value. In subsequent studies the criteria of grooming and quality of residence were nct used. It was anticipated that the discrepancy in the performance of the two groups would be reduced if reinforcers and tasks appropriate to the lower group were utilized. An even stronger prediction was that under some conditions there would be no difference in performance or that the lowerclass children might surpass the higher-class children. To investigate the kinds of situations which produce equal or differential success between higher and lower groups, therefore, an experiment was designed to manipulate tasks and incentives. All other factors such as the stimuli and apparatus were chosen or designed with the intent of maximizing performance for the lower group. The experimental task was one of concept acquisition (used interchangeably in this context with concept formation, concept attainment, concept utilization, concept identification). Because “concept” is a word psychology has borrowed from the vernacular, there is no consistent use of the term in the research literature. In this experiment the number of stimuli exceeded the number of possible responses, and concept formation was meant to imply simply the acquisition of common responses to dissimilar stimuli. It was necessary to choose stimuli with which children are familiar. Items that are assumed to be familiar include the common varieties of food, household objects, and clothing. Buttons were chosen for several

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J . L. Bresriahan and M . M . Shapiro

reasons. It was possible to use actual ones as stimuli; for large objects it would have been necessary to resort to either small facsimiles or pictorial representations, either of which would probably have placed higherstatus children at an advantage. Similarly, the fact that the subjects would be able actually to touch and handle the stimuli was considered to be a desirable feature. Buttons were also convenient as stimuli because they vary along many dimensions. For the experimental task itself, the use of buttons allowed the testing of a concept which all children learn by themselves at a very early age. Moreover, the buttons were also appropriate for a concept which is more dependent on specific teaching by others, or at least more related to previous training. These concepts are, respectively, size and number. The size and number tasks differed in difficulty in another important aspect which is related to the functional-conceptual classification. From infancy, size is a relevant and pervasive dimension for all children. It is a variable which they encounter in countless ways. Even more specifically, the attribute of “bigness” itself comes to have positive value for them. In the case of buttons, size can be considered the most obvious and most functional dimension. It was expected, therefore, that the task of choosing the larger of two different sizes of buttons would be extremely easy. Choosing the button with the greater number of holes, however, has very little relevance to experience in an ordinary environment. The utility of number of holes with respect to the usual function of buttons is trivial. When contrasted with the dimensions of size and color, the number of holes is a rather obscure dimension. It seemed desirable to include incentive conditions which were expected to result in different levels of performance. These conditions were knowledge of results only, knowledge of results plus social reinforcement, knowledge of results plus social reinforcement plus a tangible reward. All testing was done in the school. Ninety-eight first-grade girls were used in this first study. Each subject was brought by the experimenter from her classroom into the experimental room. She was seated directly in front of a table on which rested two plywood panels. One of the panels was used for all three reinforcement conditions. For the mechanical reinforcement condition, a large second panel was attached to the first. For the social and tangible reinforcement conditions, a much smaller second panel was attached to the first. Figure 1 shows the experimental apparatus for the mechanical reinforcement condition (knowledge of results only). All panels were painted with diagonal red and white stripes. Two cartoon faces were inserted in the first panel; the top face was a smiling one, the bottom face a sad one with tears. A royal blue plywood tray rested on the table within the opening at the bottom of the first panel. A lid

Learning Strategies in Children

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Fig. I . Apparatus panels f o r mechanical reinforcement condition in Experiment I . T h e subject has taken a hiitton f r o m the blrte tray and is putting it into the green chute. I f the biittorr is the correct one, the happy face will light rip and a bell will sound. I f the button is the incorrect one, the sad face will light rip and a buzzer will sound; the subject will then pick rip ihe other button in the blue tray and place it in the green chute, resrilting in the happy face and bell.

on the tray allowed it to be completely covered or opened, with the subject not being able to see the experimenter when the lid was in either position. Each of the second panels had a dark green chute. The buttons were presented in the royal blue tray and the subject responded by picking up one of them and dropping it into the dark green chute. All events were programmed electronically. For the mechanical reinforcement condition the experimenter merely served as the transducer, translating the subject’s response to an electrical impulse by pressing a push button switch. An easily discriminable 6 V bell and buzzer were mounted on the rear of the apparatus panel. The Peabody Picture Vocabulary Test was administered when the subject was brought from her classroom into the experimental room. Following the completion of the intelligence test, the subject was told that she was going to play a game. She was told that two things would be dropped into the blue tray and that one of them was right and the other was wrong. She was asked to pick up the one she thought was right and put it into the green chute. The procedure was demonstrated to the subject as well as the consequences for right and wrong responses. If the right response was made, the happy face lit up and the bell sounded. If the wrong response was made, the sad face lit up and the buzzer sounded. To make certain that there was no ambiguity for the subject as to which

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J . L. Bresnahan and M . M . Shapiro

stimulus was correct on any trial, a correction procedure was used. The subject was instructed to make the correct response on those trials in which the original response was incorrect. All demonstrations were done with practice stimuli distinct from those used in the actual experiment. Within each socioeconomic group there were three reinforcement conditions (mechanical, social, tangible) and two tasks (size, number) for a total of twelve independent groups. In the mechanical reinforcement condition the larger second panel was used and the experimenter sat behind the panel completely concealed from the subject. After each trial the only feedback the subject received for the response was the lighted face and bell (or buzzer). In the social reinforcement condition the smaller second panel was used. The subject could see the experimenter and after a correct response, the happy face and bell were accompanied by generous verbal support, such as “Good,” “Very good,” “Fine,” “You’ve been getting them all right.” After a wrong response, in addition to the sad face and the buzzer, the experimenter commented, “That one was wrong,” “You picked the wrong one,” etc. On a correction response, the experimenter said, “Okay,” “All right,” “Yes, that was the right one,” etc. In the tangible reinforcement condition the small second panel was used again, and in addition to the verbal support, the subject was given n penny for every correct response (pennies were not given for correction responses). Whenever the subject’s original response was correct, the experimenter put a shiny new penny into a glass dish in front of the subject. Extraneous conversation between the experimenter and the subject was minimized in all conditions. All trials were paced by the subject; as soon as she responded, the experimenter pressed the “right” or “wrong” push button, and if it was the former, the experimenter then immediately presented the next two stimuli. All subjects received 60 acquisition trials on each of which two buttons were presented in the tray. The experimenter tossed the buttons into the tray to make it apparent to the subject that location of the stimuli in the tray was not a variable. Before each trial began, the lid on the tray was closed, but it was raised as soon as the buttons were tossed into the tray. Immediately after the correct button was placed in the chute, the lid was again closed. One-half of the subjects from each reinforcement condition had the size task; the other one-half of the subjects had the number task. On both tasks, the buttons differed in color, size, and number of holes. There were four colors, four sizes, and four “numbers of holes.” For both the size and number tasks, color was an irrelevant dimension. For the size task, the correct button was always the larger of the two. There were twelve pairs of buttons presented five times each. In six pairs size and number were positively correlated, i.e., the larger button was also the button with more holes. In the other six pairs, the larger and

Learning Sirategies in Children

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smaller buttons had the same number of holes. Size and number of holes were not negatively correlated in any pairs. For the number task, the correct button was always the one with the greater number of holes. In six pairs the number of holes was positively correlated with size, and in the other six pairs the buttons were the same size. After trial 60, each subject was asked to guess which button was right without the face, bell, or buzzer (or pennies) being presented. Two buttons were then presented in the usual manner and after the subject had dropped one in the chute, the experimenter removed the remaining button from the tray and in its place immediately presented the next pair, without giving any feedback to the subject. For this transfer task, there were ten trials. Five pairs of buttons were presented twice in the same order. These buttons differed in color, size, and number of holes, but the colors were different from those of the acquisition trials. For the transfer trials after the size problem, both buttons of the pair were the same color and equal in size but differed in number of holes. For the transfer trials after the number problem, both buttons of a pair were the same color and had an equal number of holes, but differed in size. This transfer task could be viewed as an incidental learning problem. The transfer test was designed to determine whether there was differentiai attending or selective responding to the stimuli by the two socioeconomic levels. A control group of seven subjects from each socioeconomic level was run under the mechanical reinforcement condition on the size task. The procedure was identical to that used for the experimental group with the exception of changes in stimuli on three correlated trials. The set of buttons for the control group contained three pairs of buttons with size and number of holes positively correlated. six pairs in which these variables were uncorrelated, and three pairs in which these variables were negatively correlated. The transfer trials for the control group were the same as for the experimental groups. The results from this first experiment were most encouraging. The first useful finding was that IQ could be ignored as a variable. The mean IQ for the higher class was 103.52 with a standard deviation of 11.93, and the mean IQ for the lower class was 88.84 with a standard deviation of 14.51, This difference was significant.3 Correlations and partial correlations between I Q and the dependent variable yielded insignificant results in all cases. Therefore, it was concluded that although the two groups differed significantly in IQ, I Q was not related to the performance of the subjects on the concept formation task. The 60 acquisition trials were divided into 10 blocks of 6 trials each. :I Throughout this paper statistical significance implies a probability less than or equal to .05.

J . L. Bresnahan and M . M . Shapiro

40

The acquisition curves for each of the 12 experimental groups are plotted in Fig. 2. Size was significantly easier than number as a task; the acquisition curves for the two tasks are plotted in Fig. 3. There was no significant effect of socioeconomic level. On the number task the higher-class group made fewer errors, and on the size task the lower-class group made fewer errors; this reversal was reflected in a .06 probability for the interaction between SES and Task. There was a significant Trials effect and a significant interaction between SES and Trials. This interaction is shown in

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Fig. 4; in the first two blocks of trials the errors for the higher class exceeded those for the lower class, but the curves reversed and diverged in later blocks of trials. The curve for the lower class reached asymptote quite early and remained elevated. Since the results of an analysis of variance are relatively unspecific, attention was directed to a more detailed analysis of errors on trials with and without size and number correlated. It was considered possible that both the interaction between SES and Trials and the reversal between SES and Task resulted from different strategies used by the two socioeconomic groups. Since the lower group performed better on the size problem, the question arose as to whether the lower group was using size differences in their attempt to solve the

1. L. Bresrtahart atid M . M . Shapiro

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Fig. 4. Curves f o r rirrmber of errors by higher- arid lower-class groups plotted iri blocks of six acqrrisitiori trials irz Experimerit I . The higher- arid lower-class ciirves are iridicated by solid arid broker1 lines, respectively.

number problem. In view of the fact that size was positively correlated with number on one-half of the pairs and uncorrelated with number on the other one-half, responding according to size would have produced approximately 75 % correct, whereas guessing would have produced approximately 50% correct. As seen in Fig. 2, the size curves for the lowerclass subjects showed fast acquisition while the number curves for the lower-class subjects showed very little acquisition. The latter never exceeded a level superior to that which would have been attained had the

Leurning Strategies in Children

43

stimuli been chosen on the basis of size (correlated chance). They remained at a level between correlated chance and random selection of the stimuli (uncorrelated chance). The errors for the correlated and uncorrelated trials for the first two blocks of trials are shown in Fig. 5. On the abscissa the numbers 1, 4, 5, 7, 9, and 11 represent correlated trials and the numbers 2, 3, 6, 8, 10, 12, uncorrelated trials. As expected, only the number problem for the lower group (Fig. 5D) showed the uncorrelated trials to be more difficult. There is no overlap whatsoever in the number of errors on correlated and uncorrelated trials for the three subgroups of lower-class subjects trained on the number task. This relationship holds even when the group is further subdivided by reinforcement condition and the group size is thereby reduced to one-third. As seen in Fig. 5A and B, the hypothesis was supported that the higher-class subjects did not select the stimulus on the basis of the partially reinforced dimension. For the size problem the lower-class subjects selected the larger stimulus, which was the correct stimulus, thus yielding no difference between the curves in Fig. 5C. To determine whether there was any natural bias in the selection of the buttons, the number of errors prior to each subject’s first correct response was calculated. If no bias was present, the expectation was a geometric distribution ( p 1S ) for the number of errors to the first correct response. Neither the observed frequencies of the total group nor the subgroups differed significantly from the expected frequencies. The fit was good. The analysis of number of errors to the first correct response did not contradict the interpretation expressed in the previous paragraph on the correlated and uncorrelated trials. There are several possible explanations for the fact that the preference of the lower-class subjects to select the larger of the two stimuli did not operate prior to the first correct response. One is that the subjects did not form hypotheses on the first few trials, which would not be surprising since on the practice trials buttons were not even used and size was not a dimension. Another possibility is that the preference of the lower-class subjects for selecting the larger buttons did not operate until it had been reinforced. The data from the control groups were inconclusive because of the small number of subjects. The next experiment is devoted to contrasts with an adequately large control group. An analysis of the transfer task showed a significant effect of Task and an interaction between socioeconomic level and Task. For both socioeconomic groups the transfer test for size was easier than the transfer test for number, i.e., the test trials after the number problem were easier than the test trials after the size problem. The interaction between socioeconomic level and Task was in the same direction as the means for

J . L. Bresnahan and M . M . Shapiro

44 15. 14-

13. 12. (A)

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.

.

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2 3 4 5 6 7

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TRIALS L O W SES

Fig. 5 . Number of errors on correlated (solid curves) and itncorrelated (broken curves) trials in the first two blocks of trials for ( A ) high socioeconomic subjects on size task, ( B ) high socioeconomic subjects on number task, ( C ) low socioeconomic subjects on size task, ( D ) low socioeconomic subjects on number task in Experiment 1. Trials 1, 4, 5, 7, 9 , 1 1 are correlated trials; Trials 2, 3, 6 , 8, 10, 12 are uncorrelated trials.

Learriirrg Strategies in Children

45

the acquisition trials, and in the case of the transfer task, the interaction was significant. The striking result of the experiment, therefore, was that the lowerclass children maintained a partially successful size hypothesis on thc number problem. It is generally considered that on a concept formation problem the subject selects an hypothesis and retains it until he makes an incorrect response, at which time he rejects the hypothesis and samples a new one. If the hypothesis produces the correct response he stays with it. If the hypothesis produces an incorrect response, he shifts to a new hypothesis. This strategy is known as “win-stay, lose-shift’’ (Goodnow & Pettigrew, 1955). The lower-class subjects did not display this win-stay, lose-shift behavior, but continued to perseverate on a partially reinforced hypothesis. On the number task the size hypothesis produced approximately 75 % reinforcement and the subject persisted with the size hypothesis.

B. EXPERIMENT 11-PARTIAL REINFORCEMENT OF AN OBVIOUS DIMENSION The purpose of the next experiment was to replicate Experiment I, using an adequate control group. Since the interesting result of Experiment I was the behavior of the lower-class subjects on the size and number tasks, only lower-class children were sampled for this study. The apparatus and instructions given to the subject were identical to the mechanical reinforcement condition of Experiment I. The failure to obtain a significant result for reinforcement conditions in the previous study was sufficient justification for the discontinuation of that variable. The subjects in Experiment I1 were 64 children, 54 to 65 years of age, sampled from a Head Start program. All children had met the program’s economic criteria for eligibility. The subjects were sampled such that one-fourth were white boys, one-fourth black boys, one-fourth white girls, and one-fourth black girls. The experiment was conducted by Sandra Ivey (Bresnahan, h e y , & Shapiro, 1969). All subjects received 60 acquisition trials, on each of which the stimuli were two plastic clothing buttons presented in the tray. One-half of the subjects had the size task, and one-half had the number task. For both tasks, the buttons differed in color, size, and number of holes. For each of the two tasks, there were twelve different pairs of buttons which were repeated in the same order five times. For both tasks, color was a random dimension. For one-half of the subjects run on the size task, a correlated size procedure was used, and for the other one-half of the subjects, a control size procedure was uscd. Likewise, one-half of the number task subjects had correlated number, and one-half control number.

46

1. L. Bresirohuii uiid

M. M. Shupiro

For either size task, the correct button was always the larger of the two. In six of the twelve pairs for the correlated-size task, size was related positively to number of holes; that is, the larger button was also the button with more holes. In the remaining six pairs the larger and smaller buttons had the same number of holes. In no pairs, therefore, were size and number of holes negatively related. A trial on which size and number were positively related is a “correlated trial.” A trial on which the numbers were equal is an “equated trial.” In three of the twelve pairs of buttons for the control-size task, size was related positively to number of holes; that is, the larger button was also the button with more holes. In three of the pairs size was negatively related to number of holes; that is, the larger button was the button with fewer holes. In the remaining six pairs, the larger and smaller buttons had the same number of holes. The overall correlation between size and number was zero. The presentation order of correlated trials and equated trials was the same for both the correlated task and the control task. For the number tasks the correct button was always the one with the greater number of holes. In six pairs for the correlated-number task, the number of holes was positively related to size, and in the remaining six pairs, the buttons were the same size. In three pairs for the control-number task, number and size were positively related; in three pairs, number and size were negatively related; and in the remaining six pairs, the buttons were the same size. The subject in all conditions paced himself; as soon as he responded the experimenter pressed the “right” or “wrong” push button, and if it was the former, the experimenter then immediately presented the next two stimuli. If the response was “wrong,” the subject was required to make a correction response. The duration of the session was recorded and varied little among subjects. The dependent variable was the number of errors on the two types of trials within each block of six trials. For the correlated-size task and the correlated-number task, there were, within each block of six trials, three on which the two variables were positively related and three on which the irrelevant dimension was equated in value for the two stimuli. Therefore, two points were obtained for each block of six trials, one for the correlated trials and one for the equated trials. For the control size and number tasks, the identical trial separation was considered. For the control groups half of the correlated trials had size and number positively related and half had them negatively related; the equated trials were the same as in the other tasks. Figure 6 shows the total number of errors in each subset of three trials for the correlated-number task and the controlnumber task. An inspection of Fig. 6 shows that the two sets of trials

Learning Strategies in Children C O R R E L A T E D NUMBER

CONTROL

1

41 NUMBER

5L L CORRELATED T R I A L S

0

0

2

4

6

8

1

0

0

2

4

6

8

1

0

BLOCKS OF SIX TRIALS

Fig. 6 . Total number of errors f o r correlated-nrrmber and control-nrrmber tasks showing correlated and eqrrated trials in blocks of six trials in Experiment 11. (Each point represents the sirin of rhree trials. Size is a cite on the correlated trials of the correlated-nrrmber task.) From Bresnahan et al. (1969).

were undifferentiated on the control-number task, but on the correlatednumber task there were more errors on the equated trials than on the correlated trials. Figure 7 shows the results for the correlated-size task and the control-size task. It is evident that there was very little difference between the two groups in total number of errors, and very little differ-

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TRIALS

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k3 15

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2

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2

4

6

8

1

0

0

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4

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Fig. 7 . Total nrimber of errors f o r correlated-size and control-size tasks showing correlated and equated trials in blocks of six trials in Experimerit 11. (Each point represents the sum of three trials. Nrrrnber is a cue on the correlated trials of the correlated-size task.) From Bresnahan et al. (1969).

48

J . L. Bresriahan arid M . M . Shapiro

ence in either group between the equated trials and the correlated trials. The analysis of variance of the data in these two figures showed a significant difference between size and number Tasks and between correlated and equated Trials. There was also a significant interaction between size-number task and correlated-equated trial. Equally of interest, the interaction between correlated-control task and correlated-equated trial was significant. The last meaningful significant effect was the triple interaction among sizenumber task, correlated-control task, and correlated-equated trial. Therefore, all hypotheses were confirmed. There were no significant effects or interactions due to the race or sex of the subjects except the quadruple interaction with size-number task and correlated-control task, which had no readily apparent interpretation. The results of the experiment indicated that use of appropriate size and number tasks produces the same effects as an experimental manipulation of stimulus discriminability (Archer, 1962). The selection of size and number tasks for this population of subjects produced the interaction of obviousness X partial reinforcement that can be obtained in studies which manipulate the stimulus variables (Abraham, Gormezano, & Wiehe, 1964). Therefore, one has an experimental confirmation and elaboration of the fact that size comes earlier in development than number, and that the effects of this difference extend to more complex phenomena of learning. The results of Experiment I1 served as a replication of Experiment I. Young lower-class children did not adopt a win-stay, lose-shift strategy in concept formation tasks. They tended to perseverate on a dimension high in their hierarchy when the hypothesis relevant to that dimension was partially reinforced. Young higher-class children adopted a win-stay, loseshift strategy which ultimately resulted in nearly perfect performance even when the 100% reinforced hypothesis corresponded to a dimension low in their hierarchy. The results of the present study showed that partial reinforcement of size led to the adoption of a size hypothesis by the lower-class subjects when a number hypothesis would have been reinforced 100% of the time. There was n o effect of unequal number during a size task, but unequal size during a number task resulted in poorer performance. The subjects in a size task did not respond differentially to stimuli equated or unequated on the number dimension; the subjects on the number task did respond differentially to stimuli equated or unequated on the size dimension. To paraphrase, the subjects were more responsive to size than number. When number was relevant there was no effect of correlated trials on the control task, but on the correlated task there were fewer errors on correlated trials than on equated trials. This interaction did not occur when size was relevant.

Learuing Strategies in Children

49

C. EXPERIMENT 111-CHAOTIC REINFORCEMENT The previous two experiments showed that lower-class children did not adopt a win-stay, lose-shift strategy in a concept acquisition task. It was hypothesized from these data that lower-class children performed less successfully in concept attainment problems because of their inconsistent reinforcement histories. William Blum conducted Experiment I11 to investigate whether the introduction of chaotic reinforcement into the histories of higher-class children would lead to a comparable decrement in their performance (Bresnahan & Blum, 197 1 ) . The subjects were 60 first graders, with a mean age of 7 years. One-half of the subjects were from a high socioeconomic level and one-half from a low level. In each group one-half were boys and one-half were girls. The selection of subjects and the indices used to determine socioeconomic level were the same as those cmployed in Experiment I, with the previously noted exceptions of grooming and quality of residence. In this third experiment the first n trials were randomly reinforced. After the y1 random trials with no clues given to the subjects, the actual concept acquisition trials began and consistent reinforcement continued thereafter. The apparatus was a Lehigh Valley Electronics human intelligence panel. Mounted on the panel were a dual, multistimulus response key apparatus and a 1-cent reinforcement delivery system. The experimental procedure was automated. The subjects were individually seated in front of the Lehigh Valley console on which two different figures on two different color backgrounds were presented on each trial. A finger press against the stimulus activated a microswitch. Each correct response was rewarded with a penny. The use of a correction procedure required the subject to press the correct key if his initial response did not result in a reward. No penny was given for a response correction. The subject was told that he was going to play a little game with lights in each of the two openings. It was demonstrated to him that if he selected the correct light he would get a penny, and that if he selected the incorrect light he would then have to press thc correct one, although he would not get a penny. In any case, he was asked to leave the pennies in the dispenser until the completion of the game, at which time he would be allowed to keep them. The subject was requested to wait until the lights changed before beginning to play the game. He was allow to use only one hand. The first trial consisted of two stimuli that were never again used. This served as a check on the subject’s ability to follow directions. The actual experimental stimuli consisted of a triangle and a circle, one on a red background and the other on a green background. The four permutations of form and color, GT-RC, RC-GT, GC-RT, RT-GC, appeared with equal frequency in an unsystematic order. The 30

1. L. Bresnahan and M . M . Shapiro

50

subjects in each socioeconomic group were divided into three subgroups of ten subjects each. One-third of the subjects began immediately on the concept acquisition task in which the triangle was always reinforced; one-third had 6 trials in which the triangle and circle were randomly reinforced prior to the beginning of concept formation; and one-third had 12 trials in which triangle and circle were randomly reinforced prior to the beginning of concept formation. The red or green color and the positions of the circle and the triangle were never relevant stimuli. All subjects were given at least 42 trials. If the criterion of 12 correct responses in succession was not reached within the first 42 trials, the run was continued until the criterion was reached, up to a maximum of 120 trials. The number of errors in the first 42 trials, divided into 7 blocks of 6 trials each, can be seen in Table I. An analysis of variance yielded three significant main effects: SES, number of Random Reinforcements, and Trials. The higher-class children made fewer errors than the lower-class children on all tasks combined. Errors increased with an increase in the number of random reinforcements. Errors decreased over the seven blocks of trials. The interaction between SES and Number of Random Reinforcements was partitioned into two orthogonal comparisons, 12 and 6 vs. 0, and 12 vs. 6; only the former was significant. This significant result can be seen in Fig. 8; with 6 or 12 random reinforcements the subjects from a high socioeconomic level became progressively more similar in performance to the subjects from a low socioeconomic level. There were almost identical results from the TABLE I NUMBER OF ERRORS IN FIRST42 TRIALS OF CONSISTENT REINFORCEMENT

High SES

Low SES

Total:

No. of Random Reinforcements

1

2

3

4

5

6

7

Total

12 6 0

33 29 18

31 26 13

20 26 13

19 18 6

24 17 2

24 23 3 50

28 12 1 41

179 151 56 386

22 25 20

69

24 16 16 56

67

180 172 145 497

112

106

108

883

12 6 0

Blocks of six trials

-

-

-

-

-

80

70

59

43

43

31 25 24

27 28 16

24 25 25

22 25 22

-

-

-

80

71

77

30 25 22 77

160

141

136

120

From Bresnahan and Blum (1971).

-

-

Learning Strategies iri Children

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Fig. 8. Mean number of errors f o r each group of I0 subjects f o r 42 iriuls in Experitnetit 111. The high arid low socioecotiorriic lei~pls(ire iridicuted b y solid uiid opeti circles, respeciively. (The broketi litre deriote.r cliuticr level of perforr~inrice.)Fro171 Brestialiari arid B l i ~ t i i (1971).

higher- and lower-class subjccts given 12 prior random rcinforccments. It can be seen in Table I that a significant interaction between SES and Trials resulted from the fact that the higher-levcl children improved more than the lower-level children over trials. [Nonparametric statistical tests (Wilcoxon, 1947) of the numbers of trials to criterion yielded the same general results.] T h e number of errors for each of the 6 groups shown in Fig. 8 was significantly less than the chance level of 21 errors per subject; the smallest z value obtained was 2.93. T h e experiment demonstrated that the introduction of random reinforcement produced typically lower-class behavior in higher-class subjects. It was shown that this result was not a simple conscquence of all concept acquisition degenerating to a chance level. Both number of errors and trials to criterion revealed that the performance of the higher-class childrcn progressively approached and ultimately equaled the ineffectual lower-class performance. T h e data add credibility to the hypothesis that the inferior performance of lower-class children is a function of their chaotic or inconsistent reinforcement histories. Experiments IV and V were designed to investigate the conditions under which subjects will change their hypotheses during concept acquisition. I n both experiments there was pretraining on a concept and subsequent shifting to partial confirmation of that concept. In Experiment 1V the

52

J . L. Bresriahan arid M .M . Shapiro

degree of overlearning was manipulated prior to the shift to partial confirmation. In Experiments I and I1 lower-class subjects did not shift from a partially reinforced hypothesis which was high on their hierarchy. In Experiment I11 higher-class subjects, after random reinforcement, demonstrated similarly inferior concept acquisition behavior. Experiment IV was designed to invesitgate the conditions under which subjects would or would not shift from a nonconfirmed hypothesis as a function of the degree of original learning and the frequency of nonconfirmation.

D. EXPERIMENT IV-PRETRAINING

TO

CRITERION

The subjects in Experiment IV, a previously unpublished study, were 90 first-grade children, one-half boys and one-half girls. The subjects were randomly sampled from schools which had been identified as being located in areas which were neither predominantly high nor predominantly low socioeconomically. The experiment was conducted in a mobile laboratory parked outside each school. The Lehigh Valley human intelligence panel of the previous experiment was used. The previously employed task was simplified. On each trial a red and a green light were presented and the position of the two lights was an irrelevant dimension. The subject was shown the two lights and instructed to press one of the keys. If he made the correct response, a trinket was presented by a Universal feeder. The tray, into which the assortment of trinkets was delivered, had a closed clear plastic top. The subject was told that he would be allowed to keep the trinkets after the experiment. The intertrial intervals and stimuli were automatically controlled. Each subject was individually brought into the laboratory and told that he was going to play a game with the two push buttons. He was shown that pressing the correct button would turn off both lights and cause a toy to fall into the tray. When the lights came back on again, he was instructed to press one of the buttons. If the lights blinked and no toy was obtained, the response had been incorrect and the subject was instructed to press the correct button in order to turn out the lights and get another turn. The red key was always the correct key. If the subject chose the red key first, a toy was received and the lights went off for 3 seconds. If he pressed the green key the lights blinked for 30 msec and a nonreinforced correction response was required to turn the lights out for 3 seconds before the next trial began. In this first phase of the experiment, the subjects received trinkets on a 100% schedule until a criterion run was completed. For onethird of the subjects, the criterion run was defined as 6 correct responses in succession; for one-third, criterion was 12 responses; and for one-third, cri-

53

Learning Strategies in Children

terion was 18 responses. Following completion of the criterion run, partial reinforcement of the response to the red key was introduced without any indication to the subject. The partial reinforcement was 90% for one-third of the subjects, 80% for one-third, and 70% for one-third. The partial reinforcement schedules were run for 60 trials. During partial reinforcement a response to the red key was unreinforced on some trials. Since a correction procedure was employed, the subject was required to terminate these trials with a response to the green key. Following the introduction of partial reinforcement for the red key press, the subjects were expected to shift from the red key to the green key. An initial choice of the green key on any trial was categorized as an error. The dependent variable was the number of errors (initial green key responses) during the 60 trials of partial reinforcement. The results are shown in Fig. 9. An analysis of variance demonstrated that the number of trials required to reach criterion before the shift to partial reinforcement had a significant effect upon the number of errors during partial reinforcement.

I-

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90

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1 6

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I I 12 18 CRITERION

Fig. 9. Mean number of errors per subject during the partial reinforcement test as a function of the training criterion and the testing percentage of confirmation in Experiment I V . T h e number of errors is the number of response shifts during the last 60 trials on which the original response confirmation was 70%, 80%, or 90%. The right-hand figure shows the result as a function of the percentage of reinforcement to which the subjects were shifted. T h e left-hand figure shows the result as a function of the original number of trials to criterion, 6, 12, or 18.

54

1. L. Brestiuhari orrd M. M. Shapiro

The percentage of partial reinforcement also had a significant effect upon the number of errors. This difference was attributable to the discrepancy between the 70% condition and the 80% and 90% conditions combined. No other components of the analysis were significant. The results clearly demonstrated that although concept formation is considered an all-or-none process, there was a cumulative effect. The longer the criterion run in the first phase, the less likely the subject was to shift after a nonconfhnation during the second phase. The results also demonstrated that, if the proportion of nonconfirmations became sufficiently high (30% ) in the second phase, there was an increased tendency for the subjects to shift from their previously reinforced hypothesis. E. EXPERIMENT V-PRETRAINING

WITH A

FIXED NUMBER OF TRIALS

Experiments IV and V differed only in the pretraining of the first phase. In Experiment IV, the groups were defined by the number of criterion trials, irrespective of total number of trials; in Experiment V, another previously unpublished study, the groups were defined by a fixed number of trials, independent of the subject’s performance. The subjects for Experiment V were 90 first-grade children. The schools from which the subjects were sampled, the apparatus, and the instructions were the same as used in Experiment IV. One-third of the subjects received 12 trials before the shift to partial reinforcement, one-third received 24 trials, and one-third received 36 trials. After the 12, 24, or 36 trials, the subjects were shifted to 70%, 80%, or 90% partial reinforcement. Each of the nine groups were composed of one-half boys and one-half girls. The values 12, 24, and 36 in Experiment V were selected because they represented the number of trials required to reach the criteria by approximately 50%, 7 0 % , and 90% of the subjects in Experiment IV. The dependent variable was the number of errors during the 60 trials of partial reinforcement. An error was defined as any initial choice of the green key. The results are shown in Fig. 10. An analysis of variance yielded no significant effects. With partitioning, however, the discrepancy between the 80% and 90% conditions combined and the 70% condition was significant; but the 12-trial condition compared to the combination of the 24- and 36-trial conditions was not significant. In Experiments IV and V the percentage of nonconfirmations was a significant variable when that percentage was sufficiently high. In Experiment IV the number of trials to criterion was a significant variable. Once the subject had learned the correct hypothesis, the number of subsequent trials affected the probability of shifting after a nonconfirmation of the correct hypothesis in the second phase. In Experiment V the procedure did

Learning Strategies in Children 18 17 k 16

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24 36 TRANINO

Fig. 10. Mean number of errors per subject during the partial reinforcement test as a function of the number of training trials and the testing percentage of confirmation in Experiment V . T h e rirmber of errors is the number of response shifts during the last 60 trials on which the original response confirmation was 70%, 80%, or 90%. T h e right-hand figure shows the resiilt as a function of the percentage of reinforcement t o which the subjects were shifted. T h e left-hand figitre shows the resiilt as a function of the original number of training trials, 12, 24, or 36.

not guarantee that the subjects had learned the correct hypothesis and the number of trials was not a significant variable.

F. DISCUSSION OF CONCEPT FORMATION Theoretical accounts of concept formation have turned from response strengthening to hypothesis testing (Krechevsky, 1932; Lashley, 1929, p. 135). The subject has been viewed as formulating an hypothesis and retaining the hypothesis if his response is called “right” and rejecting his hypothesis and formulating a new one if his response is called “wrong.” This strategy has been referred to as “win-stay, lose-shift” (Goodnow and Pettigrew, 1955). Various models have been constructed to account for the method of shifting. All have involved the random selection of a new hypothesis from some subset of the population of all possible hypotheses. [See Levine, Yoder, Kleinberg, and Rosenberg (1968), or Gregg and

56

J . L. Brestiahari arid M . M . Shapiro

Simon (1967). for a description of the specific models.] Elaborate mathematical models have been constructed to formalize and quantity predictions generated by win-stay, lose-shift. Variables such as the numbers of errors prior to the first correct response and the stationary probability of the correct response have been investigated (e.g., Suppes & Ginsburg, 1963). In spite of occasional failures (e.g., Erickson, 1968), the basic notion of hypothesis sampling has been retained. The results of Experiments I and I1 clearly demonstrate that lower-class subjects do not display the expected behavior. They form an hypothesis which governs their selection of the larger stimulus; nonconfirmation of this hypothesis does not result in their shifting to a new hypothesis. Instead of displaying the win-stay, lose-shift behavior, they display a win-stay, losestay behavior. The results of Experiments 111, IV, and V provide some insights into this tendency to perseverate on a partially reinforced hypothesis. A procedure previously employed by Levine (1962) was used in Experiment 111. Random reinforcements at the beginning of training produced a devastating effect upon the performance of the higher-class subjects. This effect raises the possibility that inconsistent, if not random, reinforcement contingencies in the experiential history of lower-class subjects is at least partially responsible for their performance on concept acquisition tasks. When higher-class subjects received as few as six random reinforcements, they performed almost as poorly as lower-class subjects on a subsequent concept task. When higher-class subjects received as many as 12 random reinforcements, they performed as poorly as lower-class subjects on a subsequent concept task. There is no question that relatively little chaos can produce a large degradation of concept acquisition. Experiment IV yielded results which implicate another possible factor in the performance of lower-class children. Experiment IV was conducted with children from the middle socioeconomic range. The results demonstrate that overlearning can result in resistance to changing of behavior. Subjects were trained on a concept until they satisfied the requirement of 6, 12, or 18 correct responses in succession. Since all the subjects learned the correct hypothesis at the beginning of the criterion run, the procedure may be viewed as a manipulation of the number of overlearning trials, 6, 12, or 18. The subjects were then shifted to a partial reinforcement (confirmation) schedule of 70%, SO%, or 9 0 % . The results show that the greater the number of overlearning trials the fewer the number of shifts during partial reinforcement. Although concept acquisition is normally thought of as all-or-none, it is clear that, the greater the number of confirmations after learning has occurred, the less readily the subject shifts from the learned hypothesis. To paraphrase, the greater the number of win-stay occurrences, the less apt the subject is to shift after a loss. In Experiments I and I1

Learliing Strategies

iri

Children

57

lower-class subjects did not adopt a win-stay, lose-shift strategy of concept formation. The results of Experiment 111 raised the possibility that this failure to display the win-stay, lose-shift strategy could result from a chaotic reinforcement history. The results of Experimcnt 1V raised the possibility that this failure to display the win-stay lose-shift strategy could result from overlearning. In Experiment V the number of training trials was manipulated independently of the subjects’ behavior; the number of training trials had no effect upon response shifting during the subsequent partial reinforcement. In Experiment V it was demonstrated that the effect is attributable to the number of confirmations after learning has occurred and not to the total number of opportunities for confirmation, that is, the result of Experiment IV is produced by overlearning. A third possible factor may account for the failure of the lower-class subjects to display win-stay, lose-shift behavior in Experiments I and 11. Perseverating on an incorrect hypothesis enabled the subjects to obtain 75% reinforcement, a percentage which may be higher than the level to which they are accustomed. A direct test of this hypothesis would be very difficult, but the results of Experiments IV and V both demonstrate that the tendency to shift after a nonconfirmation is a function of the relative frequency of nonconfirmations. Shifting is more frequent with 70% confirmation than with 80% or 90% confirmation. The following picture emerges: lower-class subjects do not adopt a winstay, lose-shift strategy displayed by higher-class children and by adults. They perseverate on a hypothesis high in their hierarchy possibly because ( 1 ) they have had a great deal of overlearning on that hypothesis and ( 2 ) the rate of partial reinforcement is sufficiently high. The net result is that lower-class subjects are not only slow in learning new solutions but are conversely slow in giving up old solutions. This general theme will be repeated with respect to both reward preferences and observing responses.

111.

Reward Preferences

A. EXPERIMENT VI-AMOUNT

AND

PROBABILITY OF REINFORCEMENT

Experiment VI was concerned with children’s preferences for different reinforcement schedules which were equated for average quantity of reinforcement. The procedure for investigating reward preferences has been employed extensively with lower animals. There have been studies of children’s preferences with equalized mean reward for the choices but they have incorporated the additional factor of risk (e.g., Cohen, 1960; Kass, 1964).

58

1. L. Bresriahari and M . M . Shapiro

The subjects were 60 white, male, preschool children. Their ages ranged from 43 years to 53 years. One-half of the subjects constituted the lowerclass subgroups and one-half constituted the higher-class subgroups. The experiment was conducted by Stephan Silverman (Silverman & Shapiro, 1970). The experimental apparatus was a specially constructed peanut vending machine. It was a two-choice key-press device with a blue light and a “Mr. Peanut” bank. Doors in front of the keys allowed the experimenter to make either or both of the keys available to the subject on any particular trial. The experimenter sat behind the apparatus panel, operating the doors and delivering peanuts to the subject. The subject was told that he was going to play with a peanut machine. He was instructed to watch for the blue light and to press an available key when the light came on. He was shown how the key presses would turn off the lights and how peanuts would sometimes be delivered. The peanuts came down a transparent delivery tube and into a transparent covered dish. The subject was told that he could have the peanuts at the end of the experiment. Within each socioeconomic level there were three experimental groups. For one of the groups, one key was programmed to deliver one unshelled peanut 100% of the time, and one of the keys was programmed to deliver two unshelled peanuts 50% of the time. For the second group, one key produced one peanut 100% of the time, and the other key produced four peanuts 25% of the time. For the third group, the choices were between four peanuts 25% of the time and two peanuts 50% of the time. Within each group, the key assignments were counterbalanced for the right- and left-hand sides. All subjects were given 80 trials. At the beginning of each block of eight trials, the subject was free to choose between the two keys. Forced trials were instituted after the subject had chosen one of the buttons four times. Trials were forced by dropping the guillotine door over the key that first accumulated four responses. Therefore, the subject had four to seven free-choice trials and one to four forced trials within each block of eight. The probabilities were preprogrammed by using all possible permutations. On a reinforced trial, a bell was sounded and “Mr. Peanut” flashed with the delivery of each peanut. The intertrial interval was 4.5 seconds. It is clear from the experimental design that there was no right or wrong strategy. Any pattern of responses by the subjects yielded the same expected value, 80 peanuts in 80 trials. The intrusion of forced trials, within each block of eight trials, prevented any consistent perseveration of response choice by the subject. There is much discussion in the observational literature of the discrepancy between the reinforcing characteristics of the higher- and lower-class environments. This experiment represents our first

59

Learning Strategies in Children

objective attempt to determine the reinforcement schedule preferences of the two socioeconomic levels and to determine their strategies following reinforcement and nonreinforcement. As shall be seen, the sequence of choices proved most interesting. The proportion of choices to each key was computed for the free trials. Both the high- and low-socioeconomic-level subjects showed a significant preference for the higher probability alternative. They chose 100% over 5 0 % , or 100% over 2 5 % , or 50% over 25%. In the 100% vs. 50% and 100% vs. 25% conditions, the lower-class subjects exhibited a steady acquisition of preference. The mean choice proportions within each set of 16 trials are shown in Figs. 11 and 12. An analysis of the choice proportions showed that Trials was significant. It was clear that the only meaningful trends occurred in the two previously mentioned lower-class curves. The data for the four subgroups which had 100% as an alternative were analyzed to determine the frequency with which the subject remained on the 100% side from Trial n to Trial n 1. Each of these subjects’ free-choice data were submitted to a 1 x 2 chi-square test for goodness of fit. The expected proportion of n 1 trials on which the subject remained on the 100% key was .5. Since the square root of a chi-square with one degree of freedom is equal to z, a standard score frequency distribution was constructed for each subgroup. Positive or negative signs were attached to the

+

+

.9

r

L *

23

r nc L .=a,

o w

C

.a

L

2%

0

1

2

B L O C K S OF

3 SIXTEEN

4

5

TRIALS

Fig. 1 1 . Mean proportion o f free-choice trials to higher probability alternative f o r the three subgroups of higher-class subjects in Experiment VI (Silverman & Shapiro, 2970).

60

I . L. Bresnahan and M . M . Shapiro

100% vs. 25%

I 0

1 BLOCKS

2

I 3

1 4

I 5

OF S I X T E E N T R I A L S

Fig. 1 2 . Mean proportion of free-choice trials to higher probability alrernarive f o r the three srcbgroups of lower-class subjects in Experiment V l (Silverman & Shapiro, 1970).

z’s to denote greater than expected frequencies of staying or switching, respectively. Both socioeconomic levels displayed a larger proportion of responses to the 100% alternative. The z values were summed over subjects and divided by the square root of 10 (the number of subjects) to give an overall z for each s ~ b g r o u p Lower-class .~ subjects yielded z values of 11.97 for the 100% vs. 25% choice and 11.48 for the 100% vs. 50% choice. The z values for the higher-class subjects were 5.30 and 6.27, respectively. Each of the four z’s was significant in the direction of staying with the 1. The response to the 100% reinforced side from Trial n to Trial n difference between two z’s divided by the square root of 2 is also equal to z . ~The lower-class subgroups revealed a significantly greater tendency to 1 after reinforcement on Trial n than did the higher-class stay on Trial n subjects, z = 4.72 for the 100% vs. 25% subgroups, and z = 3.68 for the 100% vs. 50% subgroups. There were 112 possible response patterns that a subject could produce

+

+

4The sum of k independent normal distributions has a normal distribution with a mean equal to the sum of the k means, and a variance equal to the sum of the k variances. 5 The difference between two independent normal distributions has a normal distribution with a mean equal to the difference between the means and a variance equal to the sum of the variances.

61

Learning Strategies in Children

TABLE I1 OBSERVED AND EX~ECTED FREQUENCIES OF RESPONSE SEQUENCES~ Stereotype Group

High ( % )

Low ( % )

Low SES

141 (122) 103 (122) 244

75 (57) 39 (57) 114

High SES Total

Single alternation 0 (13)

26 (13) 26

Other

Total

84 (108) 132 (108)

300 300

-

-

216

600

Figures in parentheses are expected frequencies. From Silverman and Shapiro (1970). a

in the four to seven free trials within each block of eight. The frequencies of occurrence of each pattern for each subject were recorded. Table I1 shows the frequencies for the two stereotypic patterns (four consecutive responses to either one of the alternatives) and the single alternation pattern (ABABABA). The frequencies of all other patterns were pooled into a fourth category. It was clear that the higher-class subjects used the single alternation pattern more often than did the lower-class subjects. The use of a statistical test on these data would not be valid because of the lack of independence between entries pooled over subjects and trials; however, these data provided a rough demonstration of socioeconomic differences. The greater variability of the higher-class patterns was also indicated by the more frequent occurrence of the miscellaneous pattern category. In summary, Experiment VI explored the effects of allowing preschool children to choose between two alternatives that yielded the same mean reinforcement but differed in the amount and probability of reinforcements. For each of the socioeconomic groups, it was found that higher probabilities and lower magnitudes were preferred to lower probabilities and higher magnitudes. The finding of preference for continuous reward was in agreement with the results from studies using rats. The results were also in accord with the finding that young children prefer predictable to nonpredictable reinforcement (Lewis, Wall, & Aronfreed, 1963). When the data were analyzed for differences between the socioeconomic levels, clearly there were different approaches to the task. The two lowerclass subgroups receiving 100% as an alternative showed a significantly stronger tendency to perseverate on that response than did the higherclass subgroups. This finding is logically consistent with the data for response sequences, which revealed a tendency of the lower-class subjects to use stereotyped patterns to both the generally preferred 100% alternative and the generally nonpreferred 25% and 50% alternatives. The higher-class subjects used a greater variety of response patterns.

62

J . L. Brestiuhati arid M . M . Shapiro

Several inferential explanations may be applied to the differences in response modes used by the two socioeconomic groups. It can be speculated that the responses of the lower-class subjects generally reflected the effect of the just previous trial. They responded, perhaps, in a simple instrumental manner, for the most part, seeing success as consistent reinforcement (Wycoff & Sidowski, 1955). In a related study using a threechoice discrimination problem, Gruen and Zigler ( 1968) showed that lower-class subjects used fewer sequences of responses than did higher-class subjects. Many of the higher-class subjects’ response sequences, especially single alternation responses, may be considered as strategies. They may have 1 committed the “gambler’s fallacy” assuming that a payoff on Trial n is less likely on the same alternative that paid off on Trial n. Other investigators have found that their subjects preferred to predict correctly the less likely event than the more likely one (Brackbill & Bravos, 1962; Siegel, 1959). This preference may have been operative in the present study. It was clear that the higher-class subjects more frequently employed “cognitive” strategies than did the lower-class subjects. The lower-class subjects were bound by the outcome of the just previous trial, while the higher-class subjects were more able to discriminate between the overall contingencies. The behavior of the higher-class subjects was, therefore, less stereotyped.

+

B. EXPERIMENT VII-REINFORCEMENTWITH WITHOUT SIGNALS

AND

To pursue further the findings of Experiment VI, Experiment VII was designed to investigate the behavior of 48 third-grade children from higher and lower classes under three percentages of reinforcement. The reinforced trials were either signaled or unsignaled. A simple manual task was chosen to minimize the effcts of intelligence or previous learning. Other investigators (Espenschadi, 1946; Moore, 1941, 1942; Rhodes, 1937) have not found significant differences in children from high and low socioeconomic levels or between black and white children on manual dexterity and eye-hand coordination tasks. In Experiment VII the rate of performance on a simple motor task was measured as a function of the reinforcement on Trial n and the presentation of a signal for reinforcement on Trial n 1. The experiment was conducted by Jomary Hilliard (1970) as part of an undergraduate Honors Thesis. Twenty-four subjects were selected from the third grade of a school in a higher-class neighborhood, of whom one-half were white girls and

+

Learning Strategies in Childreti

63

one-half were white boys. Twenty-four subjects were also sampled from the third grade of a school in a lower-class area of the city. One-fourth of the children were white girls, one-fourth black girls, one-fourth white boys, and one-fourth black boys. The mean age of the higher-class subjects was 8.91 years and the mean age of the lower-class subjects was 8.95 years. The apparatus consisted of a plywood cabinet with an upright rear panel. When placed on a desk top at a comfortable height for the seated subject it formed a flat work area with the panel screening the activities of the experimenter from the subject’s view. On the right-hand side of the work area there was an opening under which was mounted a 400hole, square plexiglass pegboard. Ten individual pegboards were made of masonite with metal handles. These were fitted into the opening in the cabinet over the 20 X 20 pegboard matrix. Each individual board had 20 holes, arranged randomly with one corresponding to each row and column of the matrix. When the individual test board was in place, brightly colored banana plugs or pegs could be inserted through the holes in both boards to make electrical contact with 40 brass rods mounted beneath the rows of the matrix. These rods were wired so that insertion of the first peg, anywhere in any row, activated a timer located behind the panel facing the experimenter. With the insertion of the twentieth peg all the rows were filled and the timer was shut off automatically, giving an accurate measure of the time taken to fill the board. Above the pegboard area on the panel were a slot for dispensing and receiving pegboards and a tray for dispensing pegs. Pegs were fed into this tray manually at regular intervals by the experimenter. A coin dispenser was mounted on the right-hand side of the p a n d Two red signal lights of different diameters were mounted above the coin dispenser. The area of the cabinet directly beneath the coin slot was left clear for the child to place his rewards out of his way but in plain view. There were six groups of four subjects within each socioeconomic level. One-third of the children received a nickel on 80% of the trials, onethird received a nickel on 50% of the trials, and one-third received a nickel on 20% of the trials. For one-half of the subjects during each trial there was a signal which indicated the subsequent reinforcement or nonreinforcement; for one-half of the subjects there was no signal. The three reinforcement percentages (80, 50, 20) and the two signal conditions (signal and no signal) resulted in six independent groups. The subjects were tested in a small, quiet, well-lighted room within the school building. Each child was familiar with both the room and the experimenter. The experimenter was visible to the subject and could pass a board through the slot. The subject was told that it was a pegboard

64

J . L . Bresrrohort niid M . M . Sliapiro

game and to take the board and fit it into the hole. The subject was instructed to fill the board with pegs from the tray. I t was explained that after he finished he should pull the board out and pass it back through the slot. He was told that something would happen, sometimes a loud noise (coin dispenser) and sometimes the same loud noise and a prize (dispensed coin). He was asked to take the nickel prize and to put it down on the table. He was told that every time he was given a new board he should start again. For the signal group an addition was made to these instructions. The child was informed that if the little signal light was on there would only be a loud noise when he finished; if the big signal light was on there would be the same loud noise and a nickel prize would be given when he finished. Work with pilot subjects showed that it was necessary to insure that the subjects actually looked at the signal lights. Subjects were instructed to start the next trial only after they saw the signal light. In practice the subjects were not paced by the light; it was turned on simultaneously with the dispensing of the board. Subjects worked steadily, completing 20 trials. Between each trial the experimenter recorded the time, reset the timer, dispensed reinforcement. changed the signal light when appropriate, and provided a new board. After Trial 20, the child was allowed to keep his nickels. Only trials involving a change in reinforcement were analyzed. The signal and no-signal groups were compared for the pairs of successive trials for which Trial n was reinforced (or not reinforced) and Trial n 1 was not reinforced (or reinforced). The signal and no-signal groups were compared for the pairs of trials for which the groups had the same change in reinforcement and for which the groups had the opposite change in reinforcement. An analysis of variance for each of the four possible combinations was computed using the time taken to complete each trial as the dependent variable. For the 20% reinforcement groups, there were four trials on which a nickel was given, and, for the 80% groups, there were four trials on which no nickel was given; for these two sets of groups, the trials to be analyzed were predetermined. Within each block of five trials, the position of the one reinforced trial or the one nonreinforced trial was randomized, all subjects receiving a different order. For the 50% reinforcement groups there were ten reinforced and ten nonreinforced trials in random order; the successive pairs of reinforced and nonreinforced trials used in the analyses were randomly sampled from the first, second, third, and fourth sets of five-trial blocks. Each of the analyses, therefore, considered high vs. low socioeconomic level, signal vs. no signal, percentage of reinforcement, Blocks 1, 2, 3, 4, and Trials n VS. n 1. It should be noted that these four analyses were not completely independent but they were chosen because of our interest in the trials

+

+

65

Learning Strategies in Children

on which reinforcement changed. The no-signal groups were expected to show an effect of the reinforcement or nonreinforcement of Trial n upon performance on Trial n + 1 . The signal groups were expected to show an effect of the signal during the same trial on which the signal appeared. One question of interest was the relative effectiveness of a previous reinforcement or nonreinforcement upon the higher- and lower-class subjects. Another question was the effectiveness of a signaled expectation of a subsequent reinforcement or nonreinforcement upon the two socioeconomic groups. Figure 13 shows the mean time for completing the task for the higher and lower-class children on the pairs of trials for each of the four blocks of trials. The results are graphed for the three reinforcement percentages. Figure 14 depicts the difference in time for completing the task between 1 for the signal and no-signal groups as a function Trial n and Trial n

+

50

05 LOW

HIGH

LOW

HIGH

50

\

49 48 47 46 45 44 43 42 41 40 39

38

4

37

36

~

351 I

2

3

4

I

2

3

4

I

_ 2

3

4

% _

1

2

3

4

BLOCKS

Fig. 13. Mean time to complete task during a pair of trials (one reinforced and one notireinforced) taken from each of the four blocks. The curves denote the performance of higher- arid lower-class subjects with 80, 50, and 20% reinforcement in Experiment VII.

1. L. Bresnahan and M . M . Shapiro

66

05

50

HIGH

z

9 Z

LOW

LOW

HIGH

s.

-5 -6

-7

er CI

SIGNAL NO SIGNAL

-a 1

2

3

4

1

2

3

4

1

2

3

4

I

2

3

4

BLOCKS

+

Fig. 14. Mean difference in time to complete task during Trial n and Trial n 1 of a pair of trials (one reinforced and one nonreinforced) taken f r o m each of the four blocks. The curves denote the performance of higher- and lower-class subjects with and without signals f o r reinforcement in Experiment V l l .

of socioeconomic level, reinforcement change from Trial n to Trial n f 1, and blocks of trials. In each of the four analyses the mean time to complete the task de1). creased significantly over the four blocks of two trials ( n and n In general, the decrease in task time over blocks was relatively homogeneous for both socioeconomic groups, both signal and no signal, both sexes, and all three reinforcement schedules. Furthermore, there were no significant main effects or interactions among these variables. The difference between task time on Trials n and n 1 proved interesting. When there was no reinforcement on Trial n and reinforcement on Trial n 1 for both the signal and no-signal groups, there was no significant difference between n and n 1. There was a significant interaction between signal vs. no signal and n vs. n 1. With a signal, the task time decreased from a nonreinforcement on Trial n to a reinforce1 (Fig. 14); in the signal condition, the response time ment on Trial n

+

+

+

+

+

+

67

Learning Strategies in Children

was a function of the signaled (expected) reinforcement. With no signal, the task time increased from a nonreinforcement on Trial n to a reinforce1; in the no-signal condition, the response time was ment on Trial n a function of the previous reinforcement. These results were replicated in the comparison of signal and no-signal groups when there was reinforcement on Trial n and no reinforcement on Trial n 1. Task time increased from the signaled reinforcement on Trial n to the signaled non1. Task time decreased from the unsignaled reinforcement on Trial n reinforcement on Trial n to the unsignaled nonreinforcement on Trial n 1. The interaction between signal vs. no-signal 2nd Trial n vs. n 1 was again significant. These results were supported by statistically significant results in the other two analyses. The important and expected finding of Experiment VII was that the subjects were controlled by the anticipated reinforcement when reinforcements were signaled and by the previous reinforcement when reinforcements were unsignaled. There were no meaningful or consistent effects of socioeconomic level or sex. The particular schedules of reinforcement, 80, 50, and 20%, had occasional but weak effects.

+

+

+

+

+

c. DISCUSSION OF REWARDPREFERENCES Experiment VI was designed to investigate choice responding for two reinforcement schedules which produced equal mean reward. Both higherand lower-class subjects chose the schedule with the higher reinforcement probability and lower reinforcement magnitude significantly more often; the proportion of such choices was significantly greater for the lowerclass subjects than for the higher-class subjects. Furthermore, the lowerclass subjects showed a greater tendency to retain a choice which had just previously been rewarded. Experiment VII was designed to investigate further the effects of a previous reinforcement or nonreinforcement. In Experiment VI the subject was confronted with a choice between two simultaneously presented response keys; in Experiment VII a single response was measured during successive trials. The results of Experiment VII showed that, without a signal, response time was a function of the previous reinforcement or nonreinforcement but there was no interaction between the effects of the previous trial and socioeconomic level. Subjects from both high and low socioeconomic levels took more time to complete the task on a trial following a nonreinforcement than on a trial following a reinforcement. Some groups in Experiment VII were given discriminative stimuli (signals) which changed the paradigm from a mixed reinforcement schedule to a multiple reinforcement schedule. One signal was presented during trials in which responses were to be reinforced and

68

J . L. Brestiahaii arid M . M . Shapiro

another signal was presented during trials on which responses were not to be reinforced. For these groups, the time taken to complete the task was controlled by the signal (excepted reward) rather than the previous reinforcement. The time taken to complete the task was shorter when a reinforcement was signaled than when a nonreinforcement was signaled. Again there was no interaction with socioeconomic level. A general conclusion is that higher- and lower-class children differ in their choice behavior when simultaneously confronted with two reinforcement schedules, However, the response rates of higher- and lower-class children are not differentially affected by successive reinforcements and nonreinforcements. Particularly interesting is the finding that lower-class subjects can use the discriminative stimuli of the multiple schedule as effectively as the higher-class subjects.

IV.

Instructions and Training

A. EXPERIMENT VIII-EXTINCTION AFTER INSTRUCTIONS AND TRAINING Experiment VIII was designed and conducted by Anthony Epworth ( 1969) to determine whether different conditions of reinforcement main-

tained responding in children from high and low socioeconomic levels. There were three related procedures. Two variables were of specific interest: expectations of reinforcement produced by instructions and expectations of reinforcement produced by prior training. The purpose of the initial procedure was to compare the response rates of the two socioeconomic groups without either prior experimental training or instructionally produced expectations. In another sense, the procedure can be viewed as a determination of activity rates confounded with the ability to follow instructions. This procedure constituted the control condition for the ensuing experiments. The subjects in the first procedure were four-year-old white children, 13 boys and 11 girls enrolled in preschool programs. The higher-class subjects attended private nursery schools in Fulton County, Georgia, and the lower-class subjects were enrolled in Head Start programs in Decatur, Georgia. The Head Start program was limited to children from families with less than a $3,000 annual income. All children were tested within their school setting. The apparatus was set at a 30" angle within a three-sided acoustically shielded screen. A square panel was located in the center of the apparatus.

Learning Straiegies in Children

69

Behind the plexiglass panel was a box with milk glass on top and a twoway mirror inside. A 15 W bulb was located above the mirror and a 60 W bulb was located below the mirror. A line drawing of a smiling face was placed in the bottom portion of the box. One bulb illuminated the empty box above the two-way mirror. The other bulb illuminated, with equal intensity, the smiling face below the mirror. The 24 subjects were tested individually for 15 minutes. Four subjects from each socioeconomic level were assigned to the three conditions: (1 ) Panel press produced a counter noise, ( 2 ) panel press produced the top light and counter noise, and ( 3 ) panel press produced the lighted smiling face and counter noise. All feedback was presented for approximately 0.25 second immediately following each press. Verbal instructions and demonstrations were given preceding testing. Each subject was told to press the plexiglass panel as quickly and as often as he could. The experimenter told him to continue until he was asked to stop. Each press was counted as a response. Cumulative totals were recorded at one-minute intervals. There was no significant difference between the two socioeconomic groups, nor among the three Conditions, nor an interaction between SES and Conditions. The six mean cumulative response curves for the two socioeconomic groups in each of the three procedures were all linear. This procedure constituted a control condition. I n the ensuing experiments, any differences in responding between the two socioeconomic groups will not be attributable to base rate differences or the ability to follow directions. The purpose of the second procedure was to measure response rates for the two socioeconomic groups with instructionally produced expectations of reinforcement. Nine boys and seven girls were drawn from the same populations used in the first procedure. The apparatus was also the same and the 16 subjects were again tested individually for 15 minutes. Four subjects from each socioeconomic level were assigned to the two conditions: (1) the smiling face never appeared, and ( 2 ) the smiling face appeared for approximately 0.25 second after each press. The instructions and demonstrations of the first procedure were repeated with one modification. Each subject was told that a light would come on every time he pressed the panel and that sometimes he would be able to see a smiling face. The instructions were designed to produce an expectation of partial reinforcement. The mean cumulative response curves are shown in Fig. 15. If the subjects were told that they might see a smiling face and the face was presented after each press, both higher- and lower-class subjects responded

70

J . L. Bresnahan and M . M . Shapiro

0

10 MINUTES

20

Fig. 15. Mean number of cumulative responses f o r both higher- and lower-class groups with the instrrrctionally produced expectation of partial reinforcement and either with continuous reinforcement (squares) or without reinforcement (circles), in the first and second procedures of Experiment VIII. The solid lines indicate higherclass groups and the broken lines indicate lower-class groups.

at high steady rates. If the smiling face was never presented, the higherclass response rate was high but the lower-class rate declined during the test period. An analysis of variance demonstrated significant effects of Socioeconomic Status, Reinforcement Contingency, and an interaction between SES and Reinforcement Contingency. The main effect of Time (minutes) was statistically significant, as well as the interaction between SES and Time, the interaction between Reinforcement Contingency and Time, and the triple interaction among Time, SES, and Reinforcement Contingency. All differences were due to the group of lower-class subjects who received no reinforcement. The purpose of the third procedure was to create different expectations of reinforcement by training. The dependent measure was the number of responses during subsequent nonreinforcement. Eleven boys and 13 girls were drawn from the same populations used previously. The apparatus was also the same and the children were tested individually. The instructions and demonstrations were identical to those used in the second procedure. Four subjects from each socioeconomic level were assigned to the three experimental conditions: ( 1 ) smiling face available for 5 minutes, ( 2 ) smiling face available for 10 minutes, and ( 3 ) smiling face available for 15 minutes. Extinction immediately followed the training. Subjects were run in extinction until they reached a criterion of 2 minutes without a response. The mean total number of nonreinforced responses for each group is plotted in Fig. 16. The number of nonreinforced responses was a mono-

Learning Strategies in Childrerz

71

l5OOr

7 50

.

c

150

5

10

15

MINUTES OF PRIOR CONTINUOUS REINFORCEMENT

Fig. 16. Mean nrcmber of resporises to extinction f o r both higher- (solid line) and lower-class (broken line) grorips follou'ing 5-, lo-, and 15-minrrte periods of coiitinriorrs reinforcement in the third procedrrre of Experiment VIII.

tonic function of the length of the preceding continuous reinforcement sequence. For the lower-class subjects the function was a positive monotone. For the higher-class subjects the function was a negative monotone. The analysis of variance indicated a significant effect of Socioeconomic Status, Prior Reinforcement, and an interaction between SES and Prior Reinforcement. The results of the third procedure were of sufficient interest to warrant a replication with a larger sample. The subjects were 48 junior first-grade and kindergarten white boys between 53 and 63 years of age. The 24 lower-class subjects were enrolled in the Decatur, Georgia, Junior First Grade, a program with standards similar to those of Head Start. The 24 higher-class subjects were enrolled in private nursery schools. Eight subjects from each socioeconomic level were assigned to each of the three procedures. Only boys were tested to control for sex. The apparatus was functionally similar to that used previously, but it was placed inside a square metal box. The procedure was identical to that used previously with the exception that four subjects were tested at a time. Instructions were given individually and immediately preceding testing. Figure 17 shows the mean total number of responses during extinction. The results of the third procedure were replicated. The number of nonreinforced responses was a negative monotonic function of the length of the preceding period of continuous reinforcement for the higher-class group and a positive monotonic function for the lower-class group. All lower-class subjects who had received 5 minutes of continuous reinforcement stopped responding by the sixth minute of nonreinforcement. Figure 18 shows a minute-by-minute graphic analysis of the number of nonreinforced responses made within each of the first 6 minutes. The temporal development of the phenomenon can be seen. The analysis of variance demonstrated an effect of Socioeconomic Status, Prior Reinforce-

J . L. Bresnahan and M . M . Shapiro

12

0 z

s

1500

wl

Y

U

‘’ z z

4,

450 5

10

x z z z

15

5

10

15

zwl

MINUTES OF PRIOR CONTINUOUS REINFORCEMENT

4

MINUTES OF PRIOR CONTINUOUS REINFORCEMENT

Y

(Bl

(A)

Fig. 17(A). Mean number of responses to extinction f o r both higher- (solid line) and lower-class (broken line) groups following 5-, lo-, and 15-minute periods of continuous reinforcement in the replication of the third procedure of Experiment VIII. ( B ) Mean number of responses made during the first six minutes f o r both higher(solid line) and lower-class (broken line) groups following 5-, lo-, and 15-minute periods of continuous reinforcement in the replication of the third procedure of Experiment VIM.

ment, and Time in 1-minute blocks. There were significant interactions between SES and Prior Reinforcement, SES and Time, and Time and Prior Reinforcement. The triple interaction was also significant.

B.

DISCUSSIONOF

INSTRUCTIONS AND

TRAINING

Holland (1958) demonstrated that the schedule of signal detections controls the rate of observing an instrument. His procedure required a report of all detections. Frankmann and Adams (1962) suggested that a procedure without detection reports would limit the stimulus control found by Holland. They hypothesized that two responses occurred. The first response made a detection possible by making the display visible and the rate of this response was controlled by subject variables. The second response was a sense receptor orientation and its rate was controlled by the schedule of signals. The instructions in the first procedure of Experiment VIII emphasized the first response of making the display visible without any mention of the importance of the feedback. The task and instructions were simple and both socioeconomic groups were able to perform equally well. No reinforcement contingencies were mentioned and, presumably, there were no explicit expectancies of a specific reinforcement. The second procedure was the “zero” condition for the third procedure. The same instructions were used in these experiments. They differed primarily in that the second procedure employed zero minutes of experimental

73

Learning Strategies in Childreri Minute

1

Minute 2

/--*

45 15

Minute 3

150

r

Minute 4

Minute 5

r

15

L

5

5

10

I5

Minute 6

,

d’

10

I5

M I N U J E S OF P R I O R A € I N F O R C f h l f N l

Fig. 18. Meari tiurnher o f responses made dirring each of the first six minutes for hotli hrgher- (solid lines) und lower-cluss (hroken linesj groiips following 5 - , lo-, and 15-minrrte periodr of coritinuoirs reirijorcement in the replication of the third procedirre of Experimerit V l l I .

training and the third procedure employed 5. 10, and 1.5 minutes of training. There was a discontinuity in the results from the zero training to the 5-, lo-, and 15-minute training conditions. The lower-class group made fewer responses in the second procedure than did the higher-class group. With this procedure the lower-class group behaved more pragmatically. The subjects had been told that they would sometimes see a face. When no faces appeared the lower-class subjects soon stopped responding. This situation was most likely a very familiar one for them. However, the lowerclass behavior became relatively less pragmatic as the length of training increased. The performance of the two socioeconomic groups differed in the third procedure when a discrimination between initial reinforcement and subsequent extinction was possible. The lower-class responding was apparently based on the number of times the response had been reinforced. The higher-

J . L. Bresnahan and M . M . Shapiro

74

class group appeared to discriminate between reinforcing and nonreinforcing situations. In the second procedure, the ability to distinguish between different situations was not relevant since for any one subject there was only continuous reinforcement or continuous nonreinforcement. The two socioeconomic groups did not differ in the first procedure or under continuous reinforcement in the second procedure. The reinforcement was consistent and unchanging. There was a significant difference between the two socioeconomic groups under nonreinforcement in the second procedure. The lower-class response, which had never been followed by reinforcement in the test situation, extinguished. The higher-class response did not extinguish within the test period. Reinforcement had been described as forthcoming within the test situation but there was no reinforcement shift (contrast) in the procedure. The results of the third procedure suggested that higher-class subjects were affected by the shift in reinforcement while lower-class subjects were affected by the previous number of reinforcements. If it is assumed that higher-class children reacted to the change from reinforcement to extinction, then it follows that the longer acquisition periods made this change more obvious and the extinction more rapid. If it is assumed that the lower-class children responded on the basis of the number of reinforcements, then it follows that they stopped responding more quickly following the shorter acquisition periods.

V.

Summary and Conclusions

In this section the results reported in this paper will be reviewed first, and then some of the authors’ subsequent research and thinking on the problem will be discussed. In concept acquisition, lower-class children do not adopt the win-stay, lose-shift strategy employed by adults and higher-class children but perseverate on an incorrect hypothesis. The failure to adopt this strategy can also be established in other subject populations by experimental manipulations. In Experiments I and I1 it was hypothesized that the perseveration of the lower-class subjects occurred because the rate of partial reinforcement was sufficiently high and the incorrect hypothesis had been greatly overlearned (high in their hierarchy). Accordingly, in Experiment TIT the effects of prior partial reinforcement were examined, and in Experiments IV and V the effects of prior overlearning and partial reinforcement were examined. After a relatively small number of random reinforcements, higher-class subjects learned as poorly as lower-class subjects. When sub-

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jects were shifted to partial reinforcement after overlearning, they also did not adopt the win-stay, lose-shift strategy. In the experiments in which the subjects did not employ the win-stay, lose-shift strategy, they perseverated on a behavior which was partially reinforced. Since they retained the partially reinforced behavior, it can be said that they utilized the win-stay aspect of the strategy but not the loseshift component. In a situation in which reinforcement is continuously available f o r some alternative behavior, this perserveration is clearly disadvantageous. Conversely, in a situation in which no reinforcement is available for an alternative behavior, this perseveration maximizes reinforcement (Gruen & Zigler, 1968). The success of a subject in an experiment is not unlike the role of a person in real life. His task is to discriminate among the possible contingencies. H e must determine whether he is faced with a concept acquisition task, a simple discrimination problem, a probability learning task, extinction, an unsolvable (random) problem, etc. Certainly no one suggests that a person typically makes this decision in an orderly verbalized manner but, nevertheless, his task is to match his behavior to the contingency. A person is most able to conform to those contingencies with which he has had the most recent experience or the most extensive experience. People who have overlearned one contingency d o not readily shift their behavior when the contingency or the nature of the task is shifted. I n the reward preference studies there is also a difference in the behavior of higher- and lower-class subjects. In Experiment VI lower-class subjects more often chose consistency than did higher-class subjects; the former perseverated more than the latter. More specifically, the lower-class children showed a tendency to retain a just previously reinforced choice whereas higher-class children were more likely to shift away from a choice following reinforcement. The task is one on which only the pattern of reinforcements, but not the expected number of reinforcements, is contingent on the choice behavior. There is no “correct” or “better” strategy and yet the lower-class children exhibit highly stereotyped response patterns. T h e data from the mixed and multiple schedules of reinforcement in Experiment VII show no difference in performance between the two socioeconomic levels. Thus, when successive reinforcements are externally signaled, higher-and lower-class subjects use the information with comparable efficiency. O n the mixed schedule in which no discriminative stimuli are available, response times are a function of the previous reinforcement. 0 1 1 the multiple schedule in which discriminative stimuli are available, response times are a function of the expected reinforcement. Children from both socioeconomic levels appear equally capable of determining the nature of these particular contingencies. With these schedules there are no choices

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to be made; the dependent variable is the time required to complete the task on each trial. These schedules are probably less sensitive to differences between socioeconomic levels. In the last study there was an interaction between socioeconomic level and the experimental conditions: Lower-class children perseverated more than higher-class children under one procedure but less than higher-class children under another procedure. In Experiment VIII response rates were measured during extinction. It was found that when reinforcement is not promised and not delivered, higher- and lower-class children respond equally. When reinforcement is promised and not delivered, lower-class children exhibit much faster extinction than higher-class children; lowerclass children do not perseverate as much as higher-class children in this situation. However, when reinforcement is promised and actually delivered, lower-class children exhibit much slower extinction than higher-class children, provided there is sufficiently long prior reinforcement training. The longer continuous reinforcement is maintained prior to withdrawal, the faster the higher-class subjects exhibit extinction of the response and the slower the low SES subjects exhibit extinction. Again, it is important to note that these differences between the behavior of higher- and lower-class subjects are not always instances of the higher-class children doing “better” than the lower-class children. Some of the differences are favorable to the lower-class children, such as when these children stop responding when promised reinforcements are not forthcoming. Several training procedures were designed to encourage response shifting. None of these procedures has proven to be completely satisfactory. In one of these procedures conducted by William Blum the subjects were given a series of discrimination problems before being tested on a concept acquisition task. Each group received a different sequence of four problems, of which one to three were solvable and the rest insolvable. The results of the experiment were somewhat encouraging but not readily interpretable because of the apparently complex sequence effects. In another one of the procedures which Joan Tritschler has already employed, subjects were allowed to choose between five equally reinforced alternatives. After the choice behavior had become stereotyped, reinforcement was made contingent upon the subject’s shifting responses. The equipment was programmed so that only more complex patterns of choice behavior were reinforced. All subjects adopted the more complex patterns which had been used by the higher-class subjects in our previous experiment on reward preferences. The question of how this training would transfer to new situations requires extensive further investigation. The possibility was also considered that differences in response strategies might best be investigated as a function of personality variables rather than

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as a function of socioeconomic level. This approach was prompted by the concepts of internal and external control which had been proposed by Rotter (1966). External control was defined by Rotter in the following manner: “When a reinforcement is perceived by the subject as following some action of his own, but not being entirely contingent upon his action, it is typically perceived as the result of luck, chance, fate, as under the control of powerful others. or as unpredictable because of the great complexities of the forces surrounding him.” Conversely, internal control was defined as, “When a person perceives that an event is contingent upon his own behavior, or his own permanent characteristics . . . .” The possible relationship to our findings is almost inescapable. Mary McNair, with the help of Russel Penrod, conducted an extensive study of all 89 fourth-grade students at Sagamore Hills Elementary School, DeKalb County, Georgia. This school is in a uniformly upper-middle-class neighborhood. Measures on the following tests were obtained from each subject: ( 1 ) Bialer Locus of Control Scale (Bialer, 1961), ( 2 ) Level of Aspiration Board (Rotter, 1942), ( 3 ) the reward preference procedure using the 25% and 100% choices described in Experiment VI of this report, ( 4 ) Otis Lennon Mental Ability Test, Elementary 11 Level, Form J, ( 5 ) Stanford Achievement Test, Intermediate I Level, Form W, and ( 6 ) the Adjective Check List (Gough & Heilbrun, 1965) filled out by each teacher. Using all subtest scores, the alternative scoring techniques of the behavioral data, several composite test score differences, and subject categories such as sex and age, a 43-variable correlation matrix was obtained. The results were unfortunately not very informative. Locus of Control correlated significantly (r = .24) with the Achievement Scale of the Adjective Check List. A dependent variable, defined as the difference between the Otis Lennori I.Q. score and the Stanford Achievement Test score (underachievement) was significantly correlated with the Defensiveness ( r = - . 3 4 ) , Self-control ( r = -.38), Achievement (r = -.32), and Succorance ( r = .27) Scales of the Adjective Check List. Performance on the two behavioral tasks, reward preference and Level of Aspiration Board, did not correlate with any other variables. The search is being continued for procedures to alter learning strategies. The goal is to design training techniques that teach specific learning strategies without producing perseveration on one strategy. REFERENCES

Abraham, F. D., Corrnezano, I . , & Wiehe, R. Discrimination learning as a function of prior relevance of a partially reinforced dimension. Jourtlal of Ewprrimrnfal Psychology, 1964, 67, 242-249.

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Archer, E. J. Concept identification as a function of obviousness of relevant and irrelevant information. Jorrrnal of Experimental Psychology, 1962, 63, 616-620. Bernstein, B. Social structure, language, and learning. Educational Research, 1961, 3, 163-176. Bialer, I. Conceptualization of success and failure in mentally retarded children and normal children. Jorrrnal of Personality, 1961, 29, 303-320. Brackbill, Y., & Bravos, A. Supplementary report: The utility of correctly predicting infrequent events. Journal of Experimental Psychology, 1962, 64, 648-649. Bresnahan, J. L., & Blum, W. L. Chaotic reinforcement: A socioeconomic leveler. Developmental Psychology, 197 I , 4, 89-92. Bresnahan, J . L., Tvey, S. L., & Shapiro, M. M . Developmentally defined obviousness in a concept formation task. Developmental Psychology, 1969, 1, 383-388. Cohen, J . Chunce, skill, and /rick. Baltimore: Penguin, 1960. Deutsch, M. The disadvantaged child and the learning process. In A. H. Passow (Ed.), Education ii7 depressed areas. New York: Teachers College, Columbia University, Bureau of Publications, 1963. Pp. 163-179. Epworth, A. The effect of socioeconomic level during extinction. Unpublished master’s thesis, Emory University, 1969. Erickson, J. R. Hypothesis sampling in concept identification. Journal of Experimental Psychology, 1968, 76, 12-1 8. Espenschadi, A. A note on the comparative motor ability of Negro and white tenth grade girls. Child Development, 1946, 17, 245-248. Frankmann. J . P., & Adams, J. A. Theories of vigilance. Psychological Brillefin, 1962, 59, 257-272. Goodnow, J. J., & Pettigrew, T. F. Effect of prior patterns of experience upon strategies and learning sets. Journal of Experimental Psychology, 1955, 49, 38 1-389. Gordon, E. W. Characteristics of socially disadvantaged children. Review of Edrrcational Research, 1965, 35, 377-388. Cough, M. G., & Heilbrun, A. B. The adjective check-list manual. Palo Alto: Consulting Psychologists Press, 1965. Gregg, L. W., & Simon, H. A. Process models and stochastic theories of simple concept formation. Journal of Mathematical Psychology, 1967, 4, 246-276. Gruen, G., & Zigler, E. Expectancy of success and the probability learning of middleclass, lower-class, and retarded children. Jorrrnal of Abnormal Psychology, 1968, 73, 343-352. Hess, R. D., & Shipman, V. C. Early experience and the socialization of cognitive modes in children. Child Development, 1965, 36, 869-886. Hilliard, J . Response time as a function of reinforcement and cue. Unpublished honor’s thesis, Emory University, 1970. Holland, J. G. Human vigilance. Science, 1958, 128, 61-63. Karp, J. M., & Sigel, I. Psychoeducational appraisal of disadvantaged children. Review of Educational Research, 1965, 35, 401-412. Kass, N. Risk in decision-making as a function of age, sex, and probability preference. Child Development, 1964, 35, 577-582. Krechevsky, I. “Hypotheses” in rats. Psychological Review, 1932, 39, 516-532. Lashley, K. S. Brain mechanisms and intelligence: A quantitative study of injuries to the brain. Chicago: University of Chicago Press, 1929. Levine, M. Cue neutralization: The effects of random reinforcements upon discrimination learning. Journal of Experimental Psychology, 1962, 63, 438-443.

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Levine, M., Yoder, R . M., Kleinberg, J., & Rosenberg, J. The presolution paradox in discrimination learning. Journal of Experimental Psychology, 1968, 77, 602-608. Lewis, M., Wall, A. M., & Aronfreed, J. Developmental changes in the relative values of social and nonsocial reinforcement. Jorrrnal of Experimental Psvclrology, 1963, 66, 133-137. McCandless, B. Environment and intelligence. American Jorrrnal of Mental Deficiency, 1952, 56, 674-691. McCarthy, D. Language development in children. In L. Carmichael (Ed.), Manria/ of child psychology. New York: Wiley, 1954. Pp. 492-630. Montague, D. 0. Arithmetic concepts of kindergarten children in contrasting socioeconomic areas. Elementnry School Jorirna/, 1964, 64, 393-397. Moore, J. E. A comparison of Negro and white children in speed reaction on an eyehand coordination test. Jorrrnal of Genetic P~yclrology,1941, 59, 225-228. Moore, J. E. A comparison of Negro and white preschool children on a vocabulary test and eye-hand coordination test. Child Development, 1942, 13, 247-252. Passow, A. H. (Ed.) Edrrcation i n depressed areas. New York: Teachers College, Columbia University, Bureau of Publications, 1963. Raph, J. Language development in socially disadvantaged children. Review of Edrrcalional Research, 1965, 35, 389-400. Review of Edrrcational Research, 1965, 35, 377-440. Rhodes, A. A. A comparative study of motor abiilties of Negroes and Whites. Child Development, 1937, 8, 369-37 1 . Riessman, F. The overlooked positives of disadvantaged groups. Jortrnal of Negro Edrrcation, 1964, 33, 225-23 1. Rotter, J. B. Level of aspiration as a method of studying personality. Jortrrral of Experimental Psychology, 1942, 31, 410-433. Rotter, J . B. Generalized expectancies for internal versus external control of reinforcement. Psychological Monographs, 1966, 80( 1 , Whole No. 609). Siegel, S. Theoretical models of choice and strategy behavior in the two-choice uncertain outcome situation. Psychometrika, 1959, 24, 303-3 16. Silverman, S. M., & Shapiro, M. M . Magnitude-probability preferences of preschool children from two socioeconomic levels. Developniental Psychology, 1970, 2, 134-139. Suppes, P., & Ginsburg, R. A fundamental property of all-or-none models, binomial distributions of responses prior to conditioning, with application to concept formation in children. Psychological Rertiew, 1963, 70, 139-161. Warner, W. L., Meeker, M., & Eells, K. Social class in America. Chicago: Science Research Associates, 1949. Wilcoxon, F. Probability tables for individual comparisons by ranking methods. Biometrics, 1947, 3, 119-122. Wycoff, L. B., & Sidowski, J. B. Probability discrimination in a motor task. Jortrrial of Experirnental Psychology, 1955, 50, 225-23 1.

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TIME AND CHANGE IN THE DEVELOPMENT OF THE INDIVIDUAL AND SOCIETY'

Kluus F . Riegel UNIVERSITY OF MICHIGAN

I.

INTRODUCTION

..........................................

11. THE CONCEPT O F TIME . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. THE CONCEPT OF TIME IN THE NATURAL SCIENCES . . B. T H E ANALYSIS OF PSYCHOLOGICAL TIME IN DEVELOPMENTAL STUDIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. SUMMARY AND CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . .

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83 83 87 95

111. DEVELOPMENTAL CHANGES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

96 A. PROPERTIES OF QUALITATIVE GROWTH MODELS . . . . . 97 B. APPLICATIONS OF QUALITATIVE GROWTH MODELS . . . 99 C. RELATIONS BETWEEN QUALITATIVE AND QUANTITATIVE GROWTH MODELS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 D. APPLICATION OF A QUANTITATIVE GROWTH MODEL 103 E. INTERACTIONS BETWEEN CHANGES IN THE INDI107 VIDUAL AND SOCIETY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F. SUMMARY AND CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . . 109

REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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1 This paper was presented on June 2, 1970 at a colloquium at the Laboratory of Psychology, National Institute of Mental Health, Bethesda, Maryland upon the invitation by Dr. Jacob Gewirtz. The author gratefully acknowledges the continued support by Dr. Gewirtz as well as the encouragements and critical comments by Donna Cohen, Clinton Fink, William Gekoski, Wilbur H a s , William Looft, and Ruth Riegel.

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I.

Introduction

Any discussion of time and change is bound to be entangled in philosophical difficulties. Indeed, since the beginning of philosophy, these topics have been at the center of speculations, in that some philosophers emphatically denied time and change as essential attributes of the universe (Parmenides, Melissus of Samos, Zeon of Elea) , while others regarded them as the most basic properties (Heraclitus, Empedocles, Democritus) . The distinction implied here, that between an idealized universe (of which the observable world af changes is an incomplete reproduction) and phenomenal changes (from which idealized systems are but empty abstractions), still permeates our thinking and is expressed, one way or the other, in all modern systems of philosophy and sciences. Locke, for instance, considered substance, space, time, causality, etc., as universal, primary qualities which (in contrast to the views of the earlier “naive realists”) are supplemented by secondary qualities of psychologically and socially dependent interpretations. With this distinction, Locke reintroduced the option for a study of perception of time (as well as substance, space, causality, etc. ) but, independently, maintained that there are substances, space, causality, time, etc., that these are not mere inventions. On the contrary, through their existence they make perception possible at all. Locke’s successors, step by step, reduced and modified the list of primary qualities. Hume explained causality as a regular succession of spatial events in time. Kant considered these qualities as a priori forms of the mind rather than as physical properties of the universe. Finally, the positivism of the early 19th Century (Comte) and its various representatives in the late 19th Century (PoincarC, Mach, Avenarius) denied the necessity for such “metaphysical” entities altogether by reemphasizing that all our knowledge is derived from the senses and is perceptual. The “real” world, which hitherto had been regarded as providing the foundation and cause for these sensations, now was being seen as a construct and an abstraction from the sensory information given. Statements concerning the “true” nature of the “real” physical world were being considered as metaphysical and, therefore, as unscientific. Among the basic attributes of the “real” world, i.e., the primary qualities of Locke, causality was already reduced by Hume. Space was not seen any longer as a metaphysical whole into which perceptions are cast nor as a prerequisite of an absolute and universal type for the study of all natural processes (see Jammer, 1954). Prior to this conceptual shift, the analysis of events was restricted to Euclidean space and geometry. Now, the concept of space became relative and dependent upon the direction of

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the research undertaken; a researcher could operate within the space model of Euclid, Riemann, Loboschevsky, or any others. Similarly, the concept of substance as representing the smallest building blocks of the universe gave way to relativistic views alternating between interpretations in terms of particles, waves, quanta, or combinations of these (see Cassirer, 1910). While, increasingly, philosophers and scientists realized the dependency of concepts like causality, space, substance, and time on sociocultural conditions (see Sarbin, 1968), they did not abandon these concepts altogether but proposed basic reformulations. Their preservation can be observed in the explication of measurement systems, e.g., the cgs system. Among these reformulations, vigorously promoted by Reichenbach ( 1958) and translated into developmental sciences by Reichenbach and Mathers (1959), the concept of time is of greatest interest for our present purpose.

Time is born out of my relationship to things - Merleau-Ponty

11.

The Concept of Time

A. THECONCEPT

OF

TIMEIN

THE

NATURAL SCIENCES

In his famous First Scholium of the Principiu, Newton (1687) described, closely in line with Locke’s viewpoints, the space and time concepts appropriate to his physics, which, subsequently, dominated the sciences so thoroughly that it has been hard for anyone ever since to form independent concepts for himself (Park, 1967). He started with the idea of a particle, defined as a body small enough that its internal structure can be ignored but as occupying a definite region of space at a given time. Extended bodies are made up of infinitesimals and their laws are derived by summation. The concept of time, as introduced by Newton, is by no means the simplest one possible. He burdened it further by distinguishing between “absolute” and “relative” time, a distinction which refers to the dichotomy between time as a primary and secondary quality. Absolute real and mathematical time, in itself and in its very nature, proceeds or flows steadily without relation to anything external you care to mention, and to give it another name, is called “duration.” Relative, apparent and common time is a perceptible, external form of measurement of some sort of duration derived from movements, either regular or uneven, which the layman uses instead of real time, such as an hour, a day, a month, or a year [Newton, 1687, Definition VII, Scholium Mathematical Principles].

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1. Zero points Time in the natural sciences has an absolute zero point which, nevertheless, is arbitrarily determined by the initiation of a particular process, for instance by the activation of a watch. Absolute zero points are not given by “nature” but are delineated through the development of scientific theories and techniques. They are, ultimately, dependent upon the observers’ perceptions and choices. Only a few theories elaborate rationales for absolute “natural” zero points, for example, those for temperature, electrical conductivity, as well as for such complex variables as saturation, using absolute black as its zero point. In regard to the time dimension, modern cosmologies (e.g., the “Big-Bang’’ theory) have proposed a rationale for an absolute, “natural” zero point, implying also the notion of an absolute, “natural” upper limit, represented by the speed of light. When considering psychological and social processes, zero points in time are always arbitrarily defined. In experimentation, zero points are defined by the start of the clock; in development analysis, zero points represent the moments of birth or the commencement of schooling; in historical-sociological analysis, zero points are the founding of Rome, the Birth of Christ, the beginning of the French or Russian revolution, etc. Since behavioral and social sciences are unlikely to advance sufficiently far to provide rationales for absolute, “natural” zero points in time, it is reasonable to turn our attention to less ambitious attempts and to discuss time measurements along scales with relative zero points.

2 . Intervals and Cycles If we ask ourselves whether time is primarily and originally experienced as a continuum or as periodicity, we will have to conclude that the latter represents the information immediately given. For instance, a child alternating from a state of hunger or thirst to one of drive satisfaction. then back to hunger or thirst, will develop some notion about the periodic up and down in his conditions. The experience of the changes from day to night, from lunar month to lunar month, or around the annual seasons all impress upon the child a notion of periodicity. For this reason it is not surprising that until modern ages the concept of time was intimately tied to this notion. Greek philosophers and scientists, especially of the Pythagorean, Platonic, and Stoic schools, rarely viewed time as a continuous dimension but emphasized its wavelike and cyclic nature. The same has been shown for Indian and various “primitive” cultures on the basis of linguistic analyses (see Nakamura, 1966; Whorff, 1956). By defining its units, the periodicity of time represents the basis for time measurements. These units could be the solar year, the lunar month, the terrestrial day, etc. Practical measurements rely on the isomorphism between these astronomical units and those more directly accessible for

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our manipulations, such as the swing of the pendulum or the vibration in quartz molecules. Further on in this chapter, we will have to examine how we might define time units of psychological and sociological processes.

3 . Order and Direction If we take one step further down in the hierarchy of measurement, we are considering systems in which order and direction play a role but not the periodicity and intervals of measurements. Commonly, our recordings of time and change in psychology are more ambitious. But all that these measurements imply is a blind adaptation of the periodicity of physical systems. Whenever less ambitious attempts are made by restricting judgments to ordered sequences of earlier and later events or to developmental interpretations in terms of stages and periods, they are considered with less esteem. Scientific knowledge, it is argued, ought to progress to the more advanced levels of observations. The concepts of order and direction can best be demonstrated by an example from physics frequently used for this purpose. Let us assume that we record a physical event, such as the movement of a billiard ball, by taking a film strip with a camera mounted above the pool table. If we cut the frames apart and randomize them, we could, thereafter, reconstruct the order of the event but would not be able to determine the direction of the move. In other words, we can line up the frames in a systematic manner, but we do not know which one of the two end points of the reassembled film strip is the first and which one is the last frame of the sequence. In such considerations, as in the “classical natural sciences” in general, time does not imply direction and irreversibility. For instance, the free fall of a body can be viewed as proceeding in either direction (whereby, of course, the reversal of the fall represents the throwing of the body). The law that describes these processes, i.e., the law of gravitation, is the same in both instances; only the signs have been changed from plus to minus. The development of “modern natural sciences” is characterized by the attempt to deal with the problem of directionality and irreversibility of time. The reorientation brought about can best be explained by extending the example given before. Let us assume that many balls are moving randomly within a confined area, such as a pool table, bouncing off from one another and from the edges, and that, moreover, two equal subareas are sectioned off by a bar placed across the table, one containing a greater number of balls than the other. If we remove the bar, the balls, after a lapse of time, will be completely mixed, i.e., will be equally distributed over the whole table. If, after the removal of the bar, we had taken pictures again and separated the frames, we could now reconstruct the sequence of the frames as well

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as the direction of the event. The condition in which the two sets of balls are separated is less likely than the one in which they are mixed. The former will precede the latter in time. The separate states can be recreated only through the intervention of some external, ordering forces. During the normal course of events the separate states will merge into a mixed one but not vice versa. Our example implies the notion expressed in the second law of thermodynamics providing a new conception of time. Eventually, time is reduced to probable sequences of spatial conditions. By enumerating some properties of these conditions, for instance the distribution of balls in the two sections of the table, estimates of time can be obtained. Of course, such a procedure relies again on extrinsic periodic systems, in this case the regular exposure of film material in the camera. However, the periodicity of the camera is not a necessary but only a convenient prerequisite. Time estimation could be based on randomly selected frames. Any two of them allow for inferences about the direction of the process. Of course, the fewer observations there are, the less reliable these estimates will be. Provided that a sufficiently large sample of frames is given, we can put them into the proper order, and by chopping off equal segments of frames beginning at the less likely end, we redefine our time measure on the basis of the sequence of spatial states. 4. Simultaneity The modern concept of time began to emerge with the development of thermodynamics and through the works of Boltzmann and Clausius. Whereas Newton postulated particles, space, and time as independent and necessary properties of the universe, modem natural science has reduced time to succession of spatial conditions of particles, for instance the molecules of an enclosed ideal gas. Similarly, Maxwell described electromagnetic fields in terms of amplitudes of space-time instances. Here, in comparison to the reduction of the time variable in thermodynamics, the particle substance loses its place. In his attempt to harmonize electromagnetic field theory with Newtonian mechanics, Einstein in his relativity theory introduced the concept of a space-time compound measured in terms that refer to the observer as well as to the object observed. In further extension, Planck consolidated the notion of particle with its counterpart, the notion of wave, which, like for Einstein, is depicted in a space-time system. Thus in all these theories, the three basic units of classical natural sciences-particles, space, and time-are compounded or reduced to one another and their relativity is stressed. In spite of all these modifications, the properties of order and direction remain essential parts of the time concept. To abandon these properties

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would lead to systems of unrelated classes. Although time without order and direction seems unthinkable, its discussion raises the problem of simultaneity which is of central importance for relativity theory as well as for developmental studies in the behavioral and social sciences. When, for instance, can we consider two children as being equal (simultaneous) in psychological age? Can comparable reaction time measures be obtained from the same individual but (therefore) at different times? Questions like these reveal some of the difficulties with which we are faced in a psychological analysis of time and change. Therefore, it may seem disillusioning as well as surprising that some modern natural scientists feel compelled to consider psychological knowledge rather than physical and, perhaps, formalized systems as fundamental for their analysis of time, space, and substance. The following quotation from Milne, as well as Einstein’s inquiry with which we begin our next section, reveals this orientation quite clearly. The reason why it is more fundamental to use clocks alone rather than both clocks and scales or than scales alone is that the concept of the clock is more elementary than the concept of the scale. The concept of the clock is connected with the concept of “two times at the same place,” whilst the concept of the scale is connected with the concept of “two places at the same time.” But the concept of “two places at the same time” involves a convention of simultaneity, namely, simultaneous events at the two places, but the concept of “two times at the same place” involves no convention; it only involves the existence of an ego [Milne, 1952, p. 461.

B. THEANALYSIS OF PSYCHOLOGICAL TIMEIN DEVELOPMENTAL STUDIES Several years ago, Einstein raised the questions “Is time immediate or derived?” and “Is it integral with speed from the very outset?” Piaget ( 1946), to whom these questions were addressed, tentatively suggested that the notions of speed and distance are psychologically most basic, without denying, of course, that theories of physics might be more readily formulated when time rather than speed or movement is regarded as its fundamental unit (Piaget, 1946). Nowadays, with our increasing preference for cognitive and phenomenological interpretations, Piaget’s reply seems to warrant few further explanations. During earlier periods of philosophy and science, however, such viewpoints would have caused consternation. Kant, for instance, maintained firmly that space and time are a priori givcn whereas the concept of motion is derived through experience. In contrast to Kant, many psychologists have argued that our perceptions of substance, space, and time are not direct but derived. Thus, an individual

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needs the experience of many different spatial clues before he recognizes the organziation of a display and before he develops an adequate notion of space. Similar arguments have been made for the perception of substance, mass, and weight. In particular, it has been argued that these notions develop only under conditions of change, i.e., through temporal variations. We do not gain full knowledge of weight unless pressure is changed and comparisons become possible. Similarly, static space is insufficient for its perception. Only movements through space and changes of space make its appreciation possible. Thus, while time and change are intimately tied to the perception of space and substance, the latter two, nevertheless, are directly accessible through the senses of touch and vision. Time perception, in contrast, has to rely on memory. We perceive one event, then a second event, and compare the second with the memory image of the first. Thus, we do not experience time itself but events and their successive changes, i.e., we experience transformations. Time is an abstraction from immediate experience and the conception of changes is prior to that of time. The psychological investigations of time have proceeded from several different angles (Cohen, 1964; Fraisse, 1963; Ornstein, 1969; Wallace & Rabin, 1960). First and oldest, the perception of time has been analyzed by comparing one interval with others slightly longer or shorter in duration. Second and comparable to the threshold of detection, the shortest noticeable intervals have been determined, i.e., intervals experienced as “unitary.” None of these laboratory explorations is of direct interest for our analysis. They will not be reviewed here nor will we discuss the work by Piaget (1946, 1955) and Fraisse (1963) on the development of time concept in children. Of greater interest for our present purpose are the studies in which subjects are asked to recollect events of the past. Studies of this type are concerned with much longer periods than those on the perception of time. They use a retrospective methodolgy which, though rarely applied in developmental research, represents a naturalistic form of inquiry in which individuals are engaged at all times, i.e., when they compare their present experiences with those of the past. Undoubtedly, retrospective retrievals are not only crucial for clinical and historical explorations, but also for experimental studies of learning and memory in which subjects receive some stimulus material and then, after the passage of time, are requested to recollect the information given. Of course, these experiments differ from clinical-historical studies in that the stimuli and the intervening passage of time are controlled by the experimentcr; they differ more sharply from developmental investigations, however, in which, predominantly, enactive methodologies have been applied.

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In these enactive studies, the states of individuals differing in age are either cross sectionally assessed o r individuals are longitudinally followed through portions of their lifespans. In both cases the here-and-now of subjects is evaluated. Rarely has it been attempted to have subjects recollect events of the past. I n three recent studies, the present author used a retrospective methodology; these studies may serve to demonstrate some of the theoretical issues raised, especially ( a ) on the compatibility of retrospective and enactive time estimates, ( b ) on the steadiness of the flow of psychological time. and ( c ) on its periodicity and zero points. 1, Psvchologicnl Time In the first study, 26 undergraduate students in psychology wrote down as many names of persons (relatives, friends, acquaintances) as they could recall during a six-minute session. After the completion of this task, they indicated the years at which they had first met each of the persons named. Furthermore, they recorded their birth date and the years during which they attended the various types of schools. I n Fig. 1 , the number of persons recalled is plotted as a function of school ages. The results resemble a serial position curve whereby the serial order represents subjects' school age. Recency has a strong effect, i.e.. persons met in very recent years are recalled much more often than those met earlier in life. A primary effect is also revealed, i.e., persons met during the first years of life are recalled more often than those met during the intermediate years (but not as often as those met during the very recent years). The results shown in Fig. 1 raise some questions on the congruence be-

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tween such retrospective data and the enactive data commonly obtained. In order to answer these questions, we ought to obtain “objective” records on the number of persons whom an individual meets during the various periods of his life: during the preschool years, at home, in the elementary school, in the high school, etc. Although such data are not available to us, it seems reasonable to speculate about the reconstructions of these “objective” contingencies without access to records. As shown in Fig. 2, an individual born at time to faces a social environment with aO persons (parents, siblings, friends, neighbors). During the early years the rate of physical-psychological mobility ( a o ) will be small. The individual is bound to the immediate environment of his home and to the social interactions provided there. During the following years, when the child is entering the various types of schools, successive ecological expansions (ai)occur at times ti. Also his rate of mobility aiincreases. Instead of sticking close to his home, he explores his street block, goes to different parts of the city, travels to the neighboring towns and through the country. While, thus, the rate of mobility increases with age (ai to a,) the ecological expansion also progresses in ever bigger steps ( a , to a , ) . At first, in the nursery or kindergarten, he finds himself among few other children. The group size increases from the elementary to the junior high to the senior high school. He enters college with several hundreds or thousands of other freshmen, all of whom he can potentially meet. Figure 2 depicts the changes in the social possibilities of what we might call the “official child,” i.e., the child regulated by educational policies and laws. Aside from this role, the growing individual is exposed to various other social contingencies. He might engage in religious, political, recreational, and occupational activities. Each of these settings will provide for

10

11

l2

l3

l4 years

Fig. 2. Hypothetical model of the expansion of the social environment during the school years.

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other, partially independent expansions. In conjunction, these settings will smooth the stepwise progression shown in Fig. 2 and transform it into an exponential function ( y = 2” a,,) which, on another occasion, was suggested as one potential model of historical growth, a “branch structure model” (Riegel, 1969). Thus far we discussed the growth of the environmental potential for social interactions. Any event or any person entering into the growing repertoire of an interacting individual is subjected to forgetting. Using the simplest interpretation possible, we propose a linear decay, drop out, or forgetting of the persons encountered. We also stipulate that at a particular point in time the number of persons retrieved by their names will amount to 50% of the names accumulated at any point earlier in life. This point, measured in years, might be called the “half-life” of the specific social contingencies. According to this assumption the later in life an event is experienced, the faster the rate of forgetting will be. Figure 3 shows several forgetting lines originating at those points in time at which individuals enter new educational settings. Extrapolating these lines beyond the “half-life” provides for an inference congruent with Ribot’s law which states that items learned last during the period of growth are forgotten first; childhood experiences are best retained, adulthood experiences least. More important for our present considerations, the free recall task of our subjects can be represented by the cross-section at ti, indicated by a heavy vertical line in Fig. 3. If we plot, in a noncumulative manner, the

+

Point of R e c a l l ( t , )

:I;

’S

ES Jt

TIME PERSONS MET

Fig. 3 . Hypothetical model of the expansion of the social environment during the school years and of the recall of persons during the life span.

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average number of persons predicted to be recalled at t , , we obtain the curve shown in the upper right part of Fig. 3. This curve is closely similar in shape to that for the empirical data plotted in the upper section of Fig. 1 . Our predictions fit our empirical data almost perfectly. The preceding discussion served the purpose of contrasting subjective, retrospective recall data with those that might have been obtained through more “objective,” enactive inquiries into social contingencies and their changes with the age of subjects. The suggested mechanisms for forgetting and retrieval together with our interpretations on the changes of the social environment with the age of subjects seem to predict the observed recall surprisingly well. Therefore, it seems justified to make some comparisons between the flow of psychological and chronological time. Such an analysis will be based on another study in which subjects from three different age groups were engaged in the same task described above. 2. Age Differences in Psychological Time Twenty subjects each from three consecutive generations wrote down as many names of persons as they could recall during a 10-minute session. Most members of the youngest group (average age z 23.1 years) belonged to the same kin, the middle group (average age z 50.0 years) included their parents, aunts, and uncles; the oldest group (average age = 73.3 years) included their grandparents, grandaunts, and granduncles. Increasingly from the youngest to the oldest generation, the groups had to be supplemented by persons unrelated to the kin. After the completion of the recall task, subjects listed behind each name the years at which they had met these persons for the first time. An analysis of the results is shown in Fig. 4. Here, the ordinate indicates the number of persons recalled. The abscissa indicates the years at which these persons were met for the first time. Since the average age of the three groups, I, 11, and 111, were related in ratios of about 3:2: 1, the scales were compressed accordingly. Thus, along the abscissa, three different age scales are used. As in the preceding study, the youngest group (111) shows a very strong recency effect and a less strong primacy effect; the curve is J-shaped and the data points are almost bisected by the influence of these two factors. The middle-aged group (11) reveals a strong recency effect but the primacy effect has disappeared; the curve has the shape of a boomerang. For the oldest group ( I ) , the primacy effect reappears slightly, while the recency effect has almost disappeared; the curve resembles a straight line. Thus, in their retrospective perception the oldest subjects attend to all five time periods most evenly; the names of persons recalled are almost equally spread over the full age range. The retrospections of the middle-aged group

Time and Charige arid the Individual

I

93

Young

(m)

Middle

p:

(In

W

a LL

0

20

Old (I)


1930-39 1940-49 1950-59 1960-69 1950-54 1955.59 1960-64 196569

[II] IIUl

TIME PERSONS MET

Fig. 4 . Average riuniber of persons recalled by three age groups plotted against time of first acqrrairrtarice.

as well as those of the youngest group are dominated by persons recently met. The youngest group also pays considerable attention to persons encountered very early in life. According to our results, retrospective perception varies with age. If we consider the number of persons recalled per chronological time period as an index for the intensity of time experience, we would have to conclude that psychological time flows faster for the young and the middle-aged subjects, the closer the period recalled is to the time of testing. The further backward in time these subjects go in their search, the more often events and persons seem to have faded away. The oldest subjects, however, live more intensely with their intermediate and their remote past; recently met persons are of lesser significance. Youiig subjects split their attention between the very early and the very late periods of their lives; the intermediate years are experienced with low intensity; time seems to flow slower here. All these interpretations are based upon subjective recall scores. Since the number of persons recalled will also be a function of the number of persons met, and since this number, as we have already discussed in Study I, might vary systematically with the age of subjects, the present data and interpretations need to be supplemented by “objective,” enactive records of changes in the social environment over the life span (more specifically, in the number of new persons encountered).

3. Historical Time In a third experiment, we asked 16 undergraduate students in psychology to write down as many names of historical figures (politicians, artists,

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scientists) as they could recall during a 6-minute session. An advanced graduate student in psychology, in cooperation with the author, assigned a most characteristic historical date to each person listed, which would, most frequently, represent the midpoint of their active career. When the average number of persons recalled was plotted against historical time, far fewer responses than in the first experiment were observed. Of course, the recall of historical figures differs from the recall of personal acquaintances in several important ways. There is, for instance, no zero point in historical time corresponding to the birth of the recalling subject. Subsequently, no primacy but only a recency effect was produced. However, politicians, historians, and teachers seem to indoctrinate their listeners with artificial zero points. Subsequently, we find an accumulation of names at such times as the discovery of America or, as shown in Fig. 5 , at the time of the American Revolution. Although the span of history covers a much longer period than the life of an individual, subjects become acquainted with historical figures during very short sessions only. In spite of the scarcity of exposure, the progression is likely to proceed in the natural order, i.e., early events are reported first and later ones last. But as the accumulation of names at the times of the discovery of America and of the American Revolution have already shown, politicians, historians, and teachers tend to chop the “stream” of historical events into digestible chunks. In particular, they seem to prefer an apocalyptic view of history. As shown in Fig. 5, large numbers are accumulated at the times of major wars: The War of Independence, the Civil War, the Spanish-American War, World War I, and World War 11. Our statement on the normative effects of historical teaching is not meant

I800

1900

TIME

Fig. 5 . Average trrrmber of historical figrires recalled, plotted against historical rime.

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to be unreasonably critical (after all, students of developmental psychology are subjected to similar treatment when they are exposed to the all too popular stage theories of growth). However, this statement raises the question on the accuracy with which our retrospective data, as well as the books, treatises, and teachings by historians, represent “objectively” the enacted “stream” of historical events. Do these events accumulate in leaps and bounds as our data reveal and as, presumably, history is being taught, or does “real” history flow continuously and represents a smooth process of growth and expansion? Are there historical mutations or does natura non facit saltus? In order to make possible an analysis of the recall processes of historical perceivers (including the politicians, historians, and teachers), we need to reconstruct history in a manner similar to our construction of the socialenvironmental contingencies of the growing individual. Similar to the shift from school type to school type and similar to the growth in physicalpsychological mobility, shown in Fig. 2, the history of man may be interpreted, for example, as a stepwise progression through social systems of ever increasing size, a,, and with ever increasing communicative mobility, ai (Rashevsky, 1968). Perhaps the first increase in modem times occurred during the vast migrations at the end of the Roman Empire, the next during the opening of the sea trade by the Hanseatic League in the north and by the Crusaders in the Mediterranean, the next during the worldwide explorations by the Spaniards and Portugese, the next during the colonization by Britain and France, etc. As the size of the system for social and economic exchange increased, the rate of mobility, the speed of travel, the degree of communication grew abruptly through inventions and technical improvements. This development was not restricted to physical modes but applied to intellectual and cultural growth as well. As suggested on a different occasion (Riegel, 1970b), the growth of knowledge in a society and the history of sciences can be successfully explained by models of information exchange which are based on the very same assumptions as those implied in the model of individual development of Figs. 2 and 3.

C. SUMMARY AND CONCLUSIONS Our retrospective analyses of individual and historical time have been based on psychological recall data. Because personal recollections are not only dependent upon the amount and sequencing of the “actual” events, but are also affected by processes of forgetting, the results vary when plotted along either physicakhronological or psychological-developmental time scales. This conclusion does not depreciate the value of the data. It makes us realize, however, that nobody, not even the careful historian, is able to

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reconstruct “objectively” the “actual” sequences of past events. The historian’s recollections too are dependent upon the drop-out and selective survival of documents and reports. Thus, time and change as idealized abstractions may make the physicist’s theories simple and eloquent but, in these forms, they are much less relevant for behavioral and social scientists. When recollecting the past, psychological, phenomenal time flows faster the closer the period of observation is to the observer. Older persons perceive past events more equally distributed than young (and, parenthetically, men more than women). Units or cycles are strongly determined by social regulations, such as school ages, religious conventions, voting ages, promotion by seniority, and retirement. Historical units or cycles (as well as historical zero points) reflect the biases of politicians, teachers, and scholars. They are dominated by apocalyptic interpretations. All our explorations have focused upon retrospective analyses of past events and led us to the derivation of developmental-psychological time scales. In contrast to these attempts, almost all investigations in developmental psychology have preferred the study of enacted changes applying chronological time scales in an uncritical manner. While such an approach needs urgent reappraisal, future psychological investigations, as convincingly shown by Ahammer (1970), Ahammer and Baltes (1972), and Baltes and Goulet (1970, 1971), also ought to be concerned with the perception (rather than the external recording) of changes in the individual and in the society, i.e., with their anticipations and intentions.

Time

. .

.

does not

changes -Aristotle

exist without

111. Developmental Changes The retrospective time scales discussed in the preceding sections did not correspond directly and simply with the chronological measures normally applied in developmental studies. This mismatch is likely to hold for crosssectional comparisons, where the here-and-now of subjects belonging to different age groups is investigated, as well as for longitudinal comparisons, where the same group of subjects is followed over an extended enacted period of their lifespan. All these investigations have resulted in an accumulation of large masses of data in which differences or changes in variables have been plotted against chronological age, revealing the various growth trends reported in texts and handbooks, such as those edited by Mussen (1970) on child psychology or by Birren (1959) on aging, In spite of the wealth of data collected, the records are insufficient for at least three

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reasons: ( a ) Almost none of the reports has been addressed to the question of why organisms grow and change, but have remained descriptive and prescientific; ( b ) the uncritical application of physical time scales has been harmful for the development of theoretical interpretations of growth; and (c) without exception, individual and cultural changes have been confounded. In the following section we will analyze these three issues by discussing qualitative and quantitative growth models as well as the interaction between individual and historical developments. Throughout, the focus will be on changes, i.e., on systematic modifications of behavior, rather than on time, which, as we have seen, represents an abstraction from experienced changes. The following presentation modifies the innovative proposals made by van den Daele ( 1969). A. PROPERTIES

OF

QUALITATIVE GROWTHMODELS

Most models of qualitative developmental changes assume an invariant order of some sets of behavior. A model, stated in such a general form, fails to account for individual differences in the development of these sets as well as for variations within individuals between different modes of behavior. It also disregards the question of how much of an early form of behavior is retained, transferred, or transformed into the operations of the succeeding stage. In spite of these limitations, the property of an invariant order is a necessary prerequisite for all of the more complex models. If we define an ordered collection, D, which contains the sets U , V , and W , the “single sequence model” implies that the features or structures studied emerge in fixed order:

u+v+w

(1)

This model does not consider any inter- or intraindividual variations except in rate of progression. Differences in the rate of progression would imply comparisons between these ordered sets and a metric time scale upon which an evaluation of the rate of progression would have to be based. Logically, such a match between different types of scales is inappropriate. If we want to allow for inter- or intraindividual variations in developmental progression, we need to specify that D may contain single or several subsets , i.e., U 3 u,, . . . ; V 3 v l , v2, . . . ; W 3 wl,w q ,w : ~W, J , . . . . If these subsets are mutually exclusive, i.e., w 1# w q ,. . . , we may generate three types of multiple progression, a divergent branch structure, a convergent root structure, and parullel seriation. Most likely, the three types of combinations will be confounded into partially convergent and partially

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divergent progressions. The digraph for a divergent progression, for the “multiple sequence model,” is given below (Digraph 2 ) .

If, as above, there is more than one subset for some set of D and if some of these subsets are not mutually exclusive, i.e., are intersecting or correlated, we are accounting for differences between traits within persons or within trait compounds. For instance, trait compounds might represent linguistic skills (including phonetic, semantic, and syntactic components) , mathematical skills (including analytic and synthetic modes of thinking), but also, in a more general way, perceptual storage, and motor aspects. If we allow that a behavior of an individual may represent a composition of traits different from that of another individual but with an equal overall effectiveness characterizing the particular developmental stage attained by both, we would have to delineate these differences by specifying the elements a, b, c, . . . , of the subsets ui,vi, wi. If intersections occur also in the transition between stages, i.e., through an accumulation of behavior or trait components over time, we posit within persons alternatives, namely that more than one stage might characterize the behavior or traits of a person at a given time. Subsequently, a person at one occasion might regress and respond in a more primitive manner; at another occasion he might progress and respond in a more mature manner. Similarly, a complex performance might be predominantly related at one point in time to one trait, such as linguistic skill, at another point in time to another trait, such as mathematical skill. The fluctuations within as well as between stages are seen in the “complex sequence model” (Digraph 3 ) .

Here, the element a, intersects across all three stages; the elements 0, and b2 intersect across the last two stages only. There are many modes of such sequential intersections or accumulations; the intersection can be

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partial or can extend over the whole range of stages. Also some withinstage interscctions are depicted in Digraph 3. Element a, connects all the different branches at the last two stages; elements 6, and bz connect two branches each at the third stage only. A pure, sequential intersection or accumulation across stages is possible for parallel seriations only. In most other cases, as in the example above, both sequential (between stages) and parallel (within stages) intersections cooccur. B. APPLICATIONS OF QUALITATIVE GROWTHMODELS The single sequence model of Digraph 1 represents Piaget’s theory of cognitive growth as well as many other interpretations emphasizing developmental stages, such as the popular distinction of infancy, childhood, adolescence, maturity and old age. It excludes alternative progressions and alternative organizations at the same stages. However, Piaget (1963) has discussed the issues of transition and transformation across stages. Therefore, our assignment oversimplifies his contribution. If, in the study of history we rely on such distinctions as pre-Socratic, Socratic, and post-Socratic periods or if we compare the Greek-Roman with modern Western philosophy without specifying the transitional influences, we are applying the single sequence model. Recently, Kuhn (1962) has emphasized such an interpretation in his discussion of the history of sciences. As he suggests with sufficient precaution, science progresses through successive paradigms which do not merely represent ever more comprehensive and parsimonious systems but, to some extent, are nonoverlapping and distinct in their emphases. Within these paradigms, such as within “Ptolemaic astronomy.” “Copernican astronomy,” “corpuscular optics,” “wave optics,” science proceeds as if complex jig-saw puzzles were to be solved, and thus a supplementary model for the progressions within stages is suggested. The multiple sequence model of Digraph 2 implies alternative developmental progressions originating from each node. The developmental branches may represent different persons as well as different traits or behaviors within a single person. Both possibilities might be confounded. Thus, Erikson (1968) allows at each stage for mutually exclusive binary choices, such as between trust vs. mistrust, identity vs. identity confusion, integrity vs. despair, etc. The progression results in increasing individual as well as developmental differentiations. The application of the multiple sequence model to the history of sciences has been elaborated previously (see Riegel, 1969). The description of divergent lines of thinking, the “branch structure model” or Heraklitean model, represents but one possible system of multiple progression which needs to be supplemented by the converging “root structure model” or

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Hegelian model as well as by noninteracting “seriations” through which ideas are preserved in an unmodified manner. Most reasonably, history (as well as an individual’s development) represents a complex compound of all three of these paradi-ms. The preceding two models did not consider interactions between persons or between traits of a trait compound either within or between developmental stages. The complex sequewce model of Digraph 3 takes account of such variations. In order to provide a convincing application of this model to psychology, we will describe a modified version of Piaget’s theory of cognitive development as proposed by McLaughlin ( 1963). McLaughlin’s brief outline is even more ambitious than Piaget’s theory because he equates successive stages of cognitive growth with increases in immediate memory span. But his interpretations are also simpler because he reduces the intellectual operations of children to logical operations of classes. If classes are distinguished by a number of attributes or dimensions ( N ) , then each class can be characterized by the binary choice on the presence or absence of these attributes. Each value of N specifies a unique logic ( 2 s ) which McLaughlin equates with successive levels in cognitive development. 1 concept at a time. This period correAt level 0, the child is able to process 20 sponds to Piaget’s ser~sorirnotor ir7tel/i,qence. During this time the child learns to attend to objects and to develop a notion of object constancy but is unable to operate logically with concepts since he lacks a basis for comparisons. The selection of a particular object is not based on a specific attribute or dimension, but the child seems to focus his attention upon items which happen to be in his reach and available for manipulations. At level 1, the child is able to retain 21 = 2 concepts simultaneously and, thus, to classify objects according to the presence or absence of the attribute. This period corresponds to Piaget’s preopemtional iritelliperrce. At this level the child cannot yet perform seriations since this would involve the simultaneous retention of at least three concepts. For instance, a child may start by aligning a small item with a larger one but, then, may shift to the attribute of form, even though size is a transitive criterion but, now, would require the simultaneous comparison of three objects, i.e., large, medium, and small. At level 2, the child is able to process 22 = 4 concepts simultaneously. This period corresponds to Piaget’s concrete operatioiinl iirtelligeuce. Now, a child is able to consider not only the attribute of the classes A and A’, but also to form a third concept, that of their sum, B . By accommodating a fourth concept, the complement to B , called B , he is able to perform class additions. Such performance is evident when the child combines items into superordinate classes or when he orders items into extended series on the basis of a transitive criterion. At level 3, the child is able to process 23 = 8 concepts simultaneously. This period corresponds to Piaget’s formal operafional irltrlligence. An individual retaining u p to eight concepts and distinguishing up to three attributes at one time can perform logical operations in conformity with the intellectual demands of everyday situations. Conceivably, at level 4 a person would be able to categorize items on the basis of four attributes. This would require the simultaneous consideration of 16 concepts. For all practical purposes such operations are not only beyond scientific needs but

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can be reduced to successive performances o r more limited operations or can be transcribed into a formal language which will facilitate greatly their execution.

McLaughlin’s interpretation of cognitive development represents the complex sequence model. Each stage develops its logic by embedding those preceding it. At level 0. the child merely focuses upon objects; at level 1, he distinguishes items along one dimension; at level 2, he superimposes a second dimension; at level 3 a third, etc. Since each categorization system is conceptually implied in the following system, with one new dimension added, therc is transitivity between the stages, i.e., Digraph ( 3 ) is applicable. The conzpIex sequence model is also implied in some empirical studies of the history of sciences. For instance, Garfield, Sher, and Torpie (1964) relied on such a model in their cross-refercnce analysis of the history of the genetic code. Similarly, the present author compared eight books on the history of psychology and eight books on the history of philosophy. By implying the same model of qualitative changes, it became possible to provide systematic interpretations for the observation that historical writers allot disproportionally larger numbers of pages to early figures in the history, i.e., to persons who had no or only a few competitors. As the number of scientists increases with historical time, the number of pages allotted to them decreases. Therefore, the number of pages devoted to different time periods remains about constant; during the early periods few persons received much attention; during the late periods many persons received little attention.

C . RELATIONBETWEEN QUALITATIVE AND QUANTITATIVE GROWTH MODELS Piaget has assigned chronological age boundaries to the successive stages. Thus, by superimposing the interval scale of time upon the ordinal scale of stages without providing a rationale other than empirical evidence, he has gone beyond the theoretical possibilities of his model. Of course, Piaget (and, to a lesser extent, the majority of developmental psychologists) does not take these chronological boundary markings too seriously. Primarily, he attempts to satisfy the practitioner’s need and curiosity. McLaughlin’s interpretations have the advantage of allowing for a more succinct analysis of the relationship between qualitative models of stages and quantitative models of age changes. McLaughlin reduces the progression across stages to increases in immediate memory span. When averaged over several subjects or over repeated measurements, such tests show a smooth increase with age in the number of

Klairs F . Riegel

I02

items retained. The ages at which, on the average, 0, 2, 4, or 8 items are retained correspond reasonably well with the suggested age boundaries for the successive levels of logical operations, i t . , 2, 7, and 11 years (see Wechlser, 1958). But, while an individual’s performance will fluctuate intraindividually around a fractional average (which is characteristic for his capacity at a particular chronological age), in any given testing situation he reports only a whole number of items, His concrete performance is always of an all-or-none type; he reports either 3, 4, 5, or 6 items but never 4.58. Correspondingly, his mode of logical operations shifts back and forth between the more and less advanced levels. His assignment to a developmental stage represents a best estimate of his performance during a certain period of time but always remains artificial. Stated generally, qualitative growth models imply temporal order but not temporal distances; quantitative models imply both. Since the choice of the measurement unit is arbitrary (although often dependent on technological refinements), the differences between the two approaches are often less marked than they appear to be at first glance. Even within a system of continuous changes, measurement will always be taken in discrete steps, e.g., in hours, minutes, seconds, or milliseconds, depending on the precision requested and/or the instruments available. In the matrix of Table I, for instance, each row and each column represents one discrete measurement. Theoretically, there can be as many rows and columns as desired. Table I represents Digraph 3 of the complex sequence model rewritten in matrix form to demonstrate the relationship between qualitative and quantitative growth models. Each row stands for one discrete element in uir v,, or w , ;the same is true for the columns. Dependent upon the number of branches (or roots), most qualitative growth models have several cell entries for single rows (or columns). In comparison, continuous growth models have only one entry per row and one corresponding, i.e., functionally related, entry per column. Moreover, the rows, with few exceptions, represent a different type of variable from the columns. The columns often depict chronological age, the rows the dependent, psychological variable. Since the entries in continuous growth models usually represent the set of all real numbers, their magnitude can be decreased infinitely. Without providing a precise description of the properties of continuous TABLE I MATRIXREPRESENTATION OF DIGRAPH 3 a1

bl

b,

C1

a1

1

1

1

1

b, b*

1

1 0

0

1 0

1

1

c2

c3

c4

1 1

1

0

1 0

0

1

1

Time arid Change arid the Individual

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growth models, a system of relations (qualitative model) is functional (quantitative model) if each member of the domain of the (independent) variable is paired with one and only one member of the range of the other (dependent) variable. Although this statement can be accepted for most practical purposes, important exceptions exist in form of multiple value functions. In this case, each member of a domain is paired with several members of the range. This possibility is implied when we consider intraindividual differences (e.g., task differences) and interindividual differences (e.g., group differences) in developmental trends, as well as the important problem of the spread of growth functions along the time continuum, i.e., the problem of the interaction between changes in the individual and the society. Before we discuss some of these implications, we describe a concrete example of a quantitative growth model.

D. APPLICATIONS OF QUANTITATIVE GROWTHMODELS In the past, several attempts have been made to depict changes in word variability with length of a text and/or age. A model discussed by Carroll (1938), Chotlos (1944), and Herdan (1960) assumes a frequency distribution of the items incorporated, represented by Zipf's (1935) standard curve of the English language. In a large universe of items, such as words, some occur at very high frequencies, e.g., articles, auxiliaries, prepositions, and conjunctions, and others occur less often. When such considerations are applied to the analysis of language acquisition, the individual is assumed to draw successive samples at a constant rate and to incorporate any new items into his repertoire, i.e., items that have not occurred to him before. Subsequently, common items are likely to be acquired early in development. Later in life, only rare items will not have occurred and, therefore, the accumulation will proceed at a slower pace. Because of its better fit with empirical data, the present author (Riegel, 1966, 1968) selected a simpler version of such a continuous growth model which does not consider variations in word frequency but only in the range of different items. This model is similar to one on verbal fluency proposed by Bousfield and Sedgewick (1944) and assumes that the increase with age, t , in word variability, D , is proportional to the number of different words in a language universe that have not yet occurred to the subject. Thus, if L is the total number of different words in the language universe and D is the number of different words that have occurred up to a certain point in time, the differential equation reads as follows: dD/dt =m ( L - D) D = L(l - e-mt),

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The negatively accelerated growth curve, thus derived, provides estimates of language acquisition time or “language age” which are at variance with the traditional measures of chronological age. If for the purpose of obtaining such estimates we assume that the occurrence of an equal number of new items represents equal time units, we would have to conclude that language age progresses faster during the early than during the later periods of development. As shown in Fig. 6, this inference can be well supported by research data on the growth of the synonym vocabulary and other psycholinguistic skills (Riegel, 1970a). but deviates from the results on the retrospective recall of events discussed in the preceding sections. What most individuals seem to experience at any particular moment in their life is an increasingly faster progression of events the closer the retrieved time period is to the time of observation. For all practical purposes, the language universe from which vocabulary items are sampled is infinitely large and the acquisition of any one item represents an exceedingly small step in the development which, thus, might be described by a continuous function. The growth of the vocabulary, representing one example out of a set of psychological performances, is frequently contrasted with the acquisition of sensorimotor skills which follow different developmental trends. A comparison of various growth curves, all sharing the same origin, represents an example of multiple value functions. For any individual at any particular age, there exists a set of different scores characterizing different psychological skills. In such an analysis of differential changes, the vocabulary, generally, shows a fairly slow rate of growth and a zero or very small rate of decline. Skills dependent upon sensorimotor capacities and their coordinations show a fast rate of growth and a fast rate of decline coupled with short lasting periods of peak performances. As shown in Fig. 6, even within the narrow range of verbal skills differential changes have been observed.

Synonyms Antonyms

8 8 Selections

s9

Classifications

7

15-19

30-34

s - ~ m - w e - m r n - ~75+ ~

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Fig. 6. Differential trends f o r four verbal tests.

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The continuous differential changes of verbal skills, depicted as a case of multiple value functions, are analogous to the qualitative differentiations described by the multiple sequence model of Digraph 2. Another example relates to differential changes of a particular skill as a function of interindividual differences. As shown in Fig. 7, superior subjects d o not only exhibit higher average performance along the whole age continuum but a

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-

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c

75 %

30 -

-

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20

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Fig. 7 . Top: Chunges in the Matrices Test percentile poitiis as age advances. Bottoni: Changes iri the Vocubrrlury Test perceritile poitits as age advatices ( f r o m Raveti, 1948).

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faster growth rate during the early years and a slower rate of decline during the later years of life. Inferior subjects show a slow rate of growth and a fast rate of decline. Observations like these have been reported for nonverbal intelligence tests and for vocabulary tests (see Raven, 1948) but have not been accepted unequivocally (see Baltes & Nesselroade, 1972; Riegel & Riegel, 1972; Schaie, 1972). They depict the dependency of changes upon the (original or average) level of performance. The examples of Figs. 6 and 7 describe intraindividual differentiations (differences between skills within subjects) and interindividual differentiations (differences between subjects in one skill). As recent evidence has shown (Riegel & Riegel, 1972), both components interact during development, e.g., superior subjects retain their lead only on tests requiring complex cognitive organizations but not on recognition vocabulary tests. Thus, the complex sequence model of Digraph 3, which also takes into account interdependencies between skills or persons or both, represents the more appropriate analogy for the continuous differential changes presently discussed. We will not pursue this issue in detail, but we have to take notice that all our examples of qualitative and quantitative developmental trends share the origin or zero point. Important modifications involve cases in which the points of origin are scattered along the time or age axis. Strictly speaking all developmental observations are of this type, i.e., no two subjects are precisely of the same age, but for reasons of simplicity we pool our subjects into groups “equal” in chronological or school age. While such an adjustment or averaging seems reasonable for short time periods, serious problems arise if these points of origin are spread out widely over historical time, i.e., if we compare subjects belonging to different cohorts or generations. Figure 8 shows an hypothetical example of the results which we might expect. Since an increase in intelligence with historical time has been documented in the literature (e.g., Tuddenham, 1948), each of the last two of the three curves shown will be elevated in comparison to the earlier ones. Because of improvements in the quality and availability of education, the rate of growth during the early years might also be assumed to have increased with historical time, i.e., intellectual growth might have been accelerated. Finally, improvements in communication, adult education, and health care might have prevented a fast deterioration of the performance during the later years of life, i.e., the rate of decline might have decreased with historical time. Without exception, developmental psychologists have disregarded the results as well as the problems shown in Fig. 8 and have pretended that a child born in 1900 would have to reveal the same developmental changes as a child born in 1970. Contradictory evidence, such as reported by

Time arid Change arid the Individual

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1875

1900

1925

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1950

Fig. 8. Hypothetical developrnerital trends for three cohorts.

Tuddenham ( 1948) on the differences in intelligence between draftees of the first and the second world wars, have been noticed with bewilderment but have not led to any basic reformulations of the developmental analyses. Extensive further evidence and interpretations by Ryder (1 965) have been disregarded. Only when Schaie (1965) proposed a theoretical extension of developmental research designs did at least the psychological gerontologists become seriously concerned about this problem. None of the qualitative developmental models presented in the present paper takes into account the problem that the growth of different persons always originates at different points in historical time and that this growth, therefore, is subjected to sociocultural influences which change as well and, perhaps, at a faster rate than the individual. Changes in the individual and in the society have been kept confounded by developmental scientists. The research designs proposed by Schaie (1965) allow for an unconfounding of these changes. Since we have maintained throughout this paper that the models described are equally applicable to the study of changes in the individual as well as changes in the society, it is reasonable to conclude our presentation with a brief review of this problem.

E. INTERACTIONS BETWEEN CHANGES IN

THE

INDIVIDUAL AND SOCIETY

As shown in an insightful manner by Baltes (1968), certain variables, for instance the amount of physical mobility and intellectual communication, may yield developmental gradients increasing in magnitude from generation to generation. If these increases are linearly related to age and if, furthermore, we were to assess age differences by the traditional crosssectional method, i.e., by testing at one time samples from different age groups (thus representing different generations or cohorts), results like those indicated by the heavy line in Fig. 9 might be obtained. Curves like this one are all too familiar to developmental psychologists but represent mere artifacts because neither the generation nor the time of measurement effects thave been eliminated as contributing factors. Following Baltes’ discussion of Schaie’s (1965) model, the problems of our analysis can best be explicated in reference to Table 11. This table lists

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AGE

Fig. 9 . A hypothetical example for the effects of generation differences ot1 the results of a cross-sectional study. Broken line, generations; solid line, cross section 1960 ( f r o m Baltes, 1968, Figure I , p. 1 2 ) .

the age of seven cohorts, born between 1880 and 2000, over eleven times of measurement, between 1880 and 2080, five within each of the seven cohorts. Comparisons within the columns of the table represent crosssectional designs; those within the rows represent longitudinal designs. Most surprisingly, a third basic design, the time-lag design, has not been discussed by developmental psychologists. This design compares cohort differences across various times of measurements within specific age groups and is represented by arrays of cells running along the diagonals from the upper left to the lower right corners of Table 11. As one of his major conclusions, Schaie emphasized that none of these three basic developmental designs measures in an unconfounded manner either age, cohort, or historical time differences. An inspection of Table I1 will, indeed, reveal that results from cross-sectional designs (CSD) confound age differences (AD) and cohort differences (CD); those from longitudinal designs (LOD) confound age differences (AD) and historical SUBJECT'S AGE AS Cohort 1880 1900 1920 1940 1960 1980 2000

A

TABLE I1 FUNCTION OF COHORTS AND TIMEOF MEASUREMENTS"

1880

1900

1920

1940

1960

0

20 0

40 20 0

60 40 20 0

80 60

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From Baltes (1968, Table 11, p. 154).

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80 60 40 20 0

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2040

2060

2080

80 60 40 20

80 60 40

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80

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time differences (TD); those from time-lag designs (TLD) confound historical time differences (TD) and cohort differences (CD). In terms of equations given by Baltes (1968, p. 156), these conclusions can be summarized as follows: CSD = AD + CD LOD = AD + TD TLD = TD + CD

Solving these equations for any one of the three terms in the right-hand parts yields the following results : AD = $ (CSD - TLD + LOD) CD = 5 (TLD - LOD + CSD) TC = 1 (LOD - CSD + TLD)

While it is, thus, in principle possible to obtain estimates of the “pure” effects of age, cohort, or historical time differences, such attempts will always have to rely on the joint utilization of all three basic designs. The remaining problem, therefore, is to derive complex designs which incorporate the three basic designs in different manners, optimizing the precision with which estimates of either age, cohort, or historical time differences can be obtained. Consequently, Schaie has proposed three strategies which he has called cohort-sequential, time-sequential, and cross-sequential methods. Because of their far reaching consequences it is surprising that these issues of developmental research designs have still not reached the majority of psychologists, especially child psychologists. Gerontologists, in contrast, have been engaged in further reaching explorations (see Baltes & Labouvie, 1972; Riegel & Riegel, 1972; Schaie, 1972). Thus, the foundation of the variance analyses models of Schaie and Baltes has been questioned (CICment, 1969; Palmore, 1969; Riegel, Riegel, & Meyer, 1967, 1968) by showing that factors of selective test participation influence the composition of different age samples in a systematic manner. Subsequently, the homogeneity of the samples across rows and columns of Table I1 can no longer be assumed. However, any conclusions concerning selective test participation have to be derived from considerations other than those of the designs themselves. They have to be based on biological or sociocultural observations and theories of growth and development rather than on formal properties of the strategies for their analysis.

F.

SUMMARY AND CONCLUSIONS

As our knowledge of developmental processes advances and as the field of developmental studies matures, we need to become more fully aware that

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this area, as well as any other area or discipline, does not emerge within a vacuum but is intimately dependent upon general sociocultural conditions (Riegel, 1972a, b). Studying history as a developmental sociology (by drawing generalizations from research and theories in developmental psychology) (Riegel, 1972c) and studying developmental psychology as a systematic inquiry into individuals’ histories (by analyzing retrospectively their pasts) might help to accelerate such an awareness (Riegel, 1972a). Subsequently, developmental psychologists ought to give up their antiquated views of time and change. They ought to divorce themselves from separated studies of cross sections of the population, e.g., of infancy, childhood, adolescence, adulthood, or old age. Only functional changes over time ought to be of concern to them. If this were not the case, they would be concerned with static condition rather than with dynamic modifications during individual and historical time, i.e., the dependency of later changes upon earlier ones. With these claims we neither propose an uncritical progression to longitudinal studies nor do we abandon qualitative growth models at the benefit of quantitative models. We do not recommend the adaptation of a simple longitudinal strategy because such a methodology would fail to unconfound the changes in the individual and in the society. Only the more advanced and complex developmental designs enable us to solve this problem. At the same time these designs direct our attention once more to the dialectic interactions between the individual and the society. They make us recognize that the human being (like any living organism) is a changing organism in a changing world, which he creates and by which, at the same time, he is created. To separate out static conditions would be as useless for the study of development as would be the abstraction of universal, unchanging dimensions of time, space, substance, causality, etc. The differences between qualitative and quantitative growth models are related to the type of measurements obtained. If time measurements represent sets of ordered relations, a qualitative model is all that can emerge. If time measurements represent real numbers, we develop models of continuous changes. In practice, however, we cannot obtain time measures of infinitesimal magnitude but always chunk the continuum in technically manageable units. The outcome is a time scale of concrete steps which, as the example of McLaughlin’s theory of cognitive development has shown, is also psychologically reasonable. The differences between qualitative and quantitative models of change are conceptually clear but they do not reflect “real” differences of a nature independent of the scientific observer. As convincingly argued by Reese and Overton ( 1970), they reflect viewpoints projected by the observer upon nature; they represent his way of constructing “reality.” Therefore, he

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should aim at developing psychological interpretations which, at the same time, determine the type of measurements taken. Only when interpretations and observation are seen in their dialectic interactions can knowledge be gained. REFERENCES khammer, 1. M. Alternative strategies for the investigation of age differences. Paper presented at the Southeastern Conference on Research on Child Development, Athens, Georgia, April, 1970. Ahammer, I. M., & Baltes, P. B. Objective versus perceived differences in personality: How do adolescents, adults, and older people view themselves and each other. Jortrfial o f Geroiitology, 1972, 27, 46-5 1. Baltes, P. B. Longitudinal and cross-sectional sequences in the study of age and generation effects. Hirniati Deivlopnwnt, 1968, 11, 145-17 1. Baltes, P. B., & Goulet, L. R. Status and issues of a life-span developmental psychology. In L. R. Goulet & P. B. Baltes (Eds.), Life-span developmental psychology: Research and Theory. New York: Academic Press, 1970. Pp. 3-21. Baltes, P. B., & Goulet. L. R. Exploration of developmental variables by manipulation and simulation of age differences and behavior. Hitman Developmerit, 1971, 14, 149-170. Baltes, P. B., & Labouvie, G . V. Adult development of intellectual performance: Description, explanation, modification. In C. Eisdorfer & M. P. Lawton (Eds.), A PA task force oii aging. Washington, D.C.: American Psychological Association, 1972, in press. Baltes, P. B., & Nesselroade, J. R. The developmental analysis of individual differences o n multiple measures. I n J. R . Nesselroade & H. W. Reese (Eds.), Lifespari develop~ne~rtal psycholo,qy: Methodological issires. New York: Academic Press, 1972, in press. Birren, J. E. Haridbook of agirig and the imfividiral. Chicago: University of Chicago Press, 1959. Bousfield, W. A., & Sedgewick, C . H. W. An analysis of sequence of restricted associative responses. lorrrnal of Geiieral Psychology, 1944, 30, 149-1 65. Carroll, J. B. Diversity of vocabulary and the harmonic series law of word-frequency distribution. Psychological Records, 1938, 2, 279-386. Cassirer, E. Sirbstarizbegriff rcrid Firriktioiisbegriff. Berlin: Cassirer, 19 10. Chotlos, J. W. Studies in language behavior: 1V. A statistical and comparative analysis of individual written language samples. Psychological Monographs, 1944, 56, 75-111. CICment, F. Du prognostic de mort B partir de diverses mesures. Paper presented at the 8th International Congress of Gerontology, Washington, D.C., August, 1969. Cohen, J. Psychological time. Scierifific American, 1964, 211, 116-124. Erikson, E. H. Identity, yoirth arid crisis. New York: Norton, 1968. Fraisse, P. The psychology of time. New York: Harper, 1963. Garfield, E., Sher, I. H., & Torpie, R . J . The ii.se o f citatiori data in writing the history of scierice. Philadelphia: Institute for Scientific Information, 1964. Herdan, G. Type-token tnnthemntics: A textbook of mathematicul lingrristics. The Hague: Mouton, 1360. Jammer, M. The concepts of space. New York: Harper, 1954.

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Kuhn, T. S. The strrrctrtre of scieritific revolrrtioris. Chicago: University of Chicago Press, 1962. McLaughlin, G. H. Psycho-logic: A possible alternative to Piaget’s formulation. British Jorrrrial of Edrrcational Psychology, 1963, 33, 61-67. Milne, E. A. Modern cosmology and the Christian idea of G o d . London and New York: Oxford University Press (Clarendon) , 1952. Mussen, P. H. (Ed.) Carmichael’s marirtal of child psychology. (3rd ed.) New York: Wiley, 1970. 2 vols. Nakamura, H. Time in Indian and Japanese thought. In J. F. Fraser (Ed.), The voices of time. New York: Braziller, 1966. Pp. 77-91. Newton, I. Philosophiae natrcralis principia mathematics. London: Straeter, 1687. Ornstein, R. E. On the experience of time. Baltimore: Penguin, 1969. Palmore, E. B. Physical, mental, and social factors in predicting longevity. Geroritologist, 1969, 9, 103-108. Park, D. The changing role of concepts of space and time in physics. Strrdirrm Generale, 1967, 20, 10-14. Piaget, I. Le dfveloppemeiit de la riotion de temps chez I’enfarit. Paris: Presses Universitaires de France, 1946. Piaget, J. The development of time concepts in the child. In P. H. Hoch & J . Zubin (Eds.), Psychopathology of childhood. New York: Grune & Stratton, 1955. Pp. 34-44. Piaget, J. The origins of intelligerrce in children. New York: Norton, 1963. Rashevsky, N. Lookirig at history throitgh mathematics. Cambridge, Mass.: MIT Press, 1968. Raven, J . C. The comparative assessment of intellectual ability. British Joirrrinl of PSychology, 1948, 39, 12-19. Reese, H. W., & Overton, W. F. Models of development and theories of development. In L. R. Goulet & P. B. Baltes (Eds.), Life-ypan developme/rtal pyychology: Research and theory. New York: Academic Press, 1970. Pp. 115-145. Reichenbach, H. The philosopky of space arid time. New York: Dover, 1958. Reichenbach, M., & Mathers, R. A. The place of time and aging in the natural sciences and scientific philosophy. In J. E. Birren (Ed.), Handbook of a g i r ~ arid the itrdividiral. Chicago: University of Chicago Press, 1959. Pp. 43-80. Riegel, K. F. Development of language: Suggestions for a verbal fall-out model. Human Development, 1966, 9, 97-120. Riegel, K. F. Some theoretical considerations of bilingual development. Psychological Bulletin, 1968, 70, 647-670. Riegel, K. F. History as a nomothetic science: Some generalizations from theories and research in developmental psychology. lourrial of Social Issues, 1969, 25, 99-127. Riegel, K. F. The language acquisition process: A reinterpretation of selected research findings. In L. R. Goulet & P. B. Baltes (Eds.), Life-span developmental psychology: Research and theory. New York: Academic Press, 1970. Pp. 357399. ( a ) Riegel, K. F. A structural, developmental analysis of the Department of Psychology at the University of Michigan. Hitrnari Development, 1970, 13, 269-279. ( b ) Riegel, K. F. Developmental psychology and society: Some historical and ethical considerations. In J. R. Nesselroade & H. W. Reese (Eds.), Lift-spatr developmental psychology: Methodological issrtes. New York: Academic Press, 1972. Pp. 1-23. ( a )

Riegel, K. F. The influence of economic and political ideology upon the development of developmental psychology. P.vycholo,yical B i f / / e / i r l ,1972, in press. (b) Riegel, K. F. On the history of psychological gerontology. In C. Eisdorfer & M. P . Lawton (Eds.). A P A tosk forcc o r i rr,~irt,q.Washington, D.C.: American Psychological Association, 1972, in press. ( c ) Riegel, K. F., & Riegel. R. M. Development, drop and death. Dr,i,c,lopr?iPrit(il Psvchology, 1972, 6, 306-3 19. Riegel. K. F.. Riegel, R. M., & Meyer, G. A study of the drop-out rates in longitudinal research on aging and the prediction of death. Jourrial of P u s o m l i l y arid Social Psyclrology, 1967, 4, 342-348. Riegel, K. F., Riegel, R. M.. & Meyer. G. The prediction of retest-resistance in longitudinal research o n aging. Joiirticrl of Gerorrtolo,yy, 1968, 23, 370-374. Ryder, N. The cohort as a concept in the study of social changes. Arrirricari Sociological Revieit., 1965, 30, 843-86 I . Sarbin, T. R. Ontology recapitulates philology. A riicricari Psycliologist, 1968, 23, 4 1 I418. Schaie, K. W. A general model for the study of developmental problems. Psycholo,~icalBirlletiri, 1965, 64, 92- 108. Schaie. K. W. Limitations on the generalizability of growth curves of intelligence: A reanalysis of some data from the Harvard Growth Study, Ifirrncrrr Df,i.e/oprtlcJrif, 1972, 15, 141-152. Tuddenham. R. D. Soldier intelligence in World Wars I and 11. Ainericari Psychologist, 1948, 3, 149-159. van den Daele, L. D. Qualitative models in developmental analysis. Developrtrrrrtal Psyckology. 1969, 1, 303-310. Wallace, M., & Rabin, A. I. Temporal experience. Psychological Birllctin, 1960, 57. 2 13-236. Wechsler, D. The rueusiiremc~/ittrrtd apprriisrrl of adirlt irifelligrJrice. Baltimore: Williams & Wilkins, 1958. Whorff, B . L. (Collected writings) In J . B . Carroll ( Ed .) , Lnri,qiiagc~,//iorr,g/it rrrrd rerrlity: Selecirvf bt,rifirix of Br/ijcirtiiri Let, WliorfT. Cambridge, Mass.: M IT Press, 1956. Zipf, G . K. The p.ryc/io-l>iologyof /trri,girrigr. Boston: Houghton, 1935.

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THE NATURE AND DEVELOPMENT OF EARLY NUMBER CONCEPTS'

Rochel Gelman UNIVERSITY OF PENNSYLVANIA

I . INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A . BASIC CONCEPTS: ESTIMATOR AND OPERATOR . . . . . . .

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I1. ESTIMATORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A . METHODOLOGICAL CONSIDERATIONS . . . . . . . . . . . . . . . . B . REVIEW O F THE LITERATURE . . . . . . . . . . . . . . . . . . . . . . . . C . THE ROLE O F COUNTING IN ESTIMATION . . . . . . . . . . . . D . AN EXPERIMENTAL INVESTIGATION OF ESTIMATORS

120 120 123 128 131

111. ESTIMATOR CONFIDENCE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

143

IV . OPERATORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A . MORE ABOUT OPERATORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. METHODOLOGICAL CONSIDERATIONS . . . . . . . . . . . . . . . . C . EXPERIMENTAL INVESTIGATIONS O F OPERATORS . . . .

147 147 148 152

V . SUMMARY AND DISCUSSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . REFERENCES

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162 165

1 The research reported in this paper and the preparation of the manuscript were supported by NICHHD Grant No . 04598 . The author wishes to thank the staffs of the Garrettford Elementary School. Upper Darby. Pennsylvania. Trinity Nursery School. Paoli. Pennsylvania. and the Melrose Hall School for Boys and Girls and YWCA Chestnut House of Philadelphia. Pennsylvania; Marsha Freifelder and Denise

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Rochel Gelmari

I. Introduction The purpose of this paper is twofold: (1) T o provide a conceptual framework within which to study the early development of concepts of quantity; and ( 2 ) to demonstrate how this framework can be used to gain insight into the young child’s conception of number. Particular emphasis is placed on the problem of studying number concepts in preschool children. Although much of the paper will deal with the development of the concept of number, it is thought that the general approach can serve as a working model for an understanding of the acquisition of other quantity concepts. A. BASICCONCEPTS: ESTIMATOR AND OPERATOR We begin by drawing a distinction between the process of extracting an estimate of a given quantity and the process by which one judges the consequences of transforming a quantity. The cognitive processes by which people determine some quantity, such as the numerosity of a set of objects, are termed estimators. The cognitive processes by which people determine the consequences of transforming a quantity in various ways are termed operators. Thus, the distinction is between processes that are used to determine how many items there are in an array or the relative numerosity of two arrays as against the processes used to determine whether transformations performed on a set affect its numerosity. There are several reasons for distinguishing between operators and estimators. First, estimators may be thought to involve a “lower” level of processing than operators. Estimators are closely tied to perceptual input, operators are not. Operators can, at least in principle, specify the outcome of applying a particular operation to a given amount whether or not the amount is actually present. For example, adults assume that pouring a quantity of water from one container to another will not change the quantity, whether or not they are actually witnessing such a transformation of some quantity of water. I n contrast, they cannot estimate accurately some quantity of water unless water is actually present to be estimated. Second, operators may be thought to be “more cognitive” than estiWeinberg, who collected the data; and Justin Aronfreed, C . R. Gallistel, Ellen Markman, Dan Osherson, and Burton Rosner who carefully read eai-lier versions of this manuscript. 1 a m particularly grateful to my husband, C . R. Gallistel, who took the time to help elucidate some of the concepts in the paper and translate foreign manuscripts.

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mators. Operators provide integrative links between successive estimates. Thus, f o r example, a perception that five rabbits went into the hat, in conjunction with the perception that only two rabbits came out of the hat, provides surprise through the mediation of a cognitive operator which specifies that placing arrays in hats and taking them out again are not transformations that alter number. In this case, two successive estimates of number are integrated by means of a cognitive operator. A third reason for regarding the distinction between estimators and operators as important is that operators are more central to a mature conception of number. Consider the category of transformations which involve displacements or rearrangements. Adults, who treat number operationally, d o not believe that the numerosity of a set is altered by such transformations, no matter how great the perceptual changes produced by them. And, as Piaget (1952) has shown, young children give evidence of believing that such transformations alter the quantity. In Piaget’s view it is the presence of operators in the adult that enables him to judge numbers as invariant under such transformations. Similarly, Piaget argues that young children fail to judge number as invariant under such transformations because they lack the appropriate operators. And because they lack the appropriate operators they are said to have not yet developed a concept of number. The centrality of operators in Piaget’s theory can be seen from the fact that children are said not to have a concept of number until they pass the operator task, i.e., conservation. Yet most children can accurately estimate smaller numbers by counting well before they pass the conservation test. Piaget’s assumptions are reflected in several scalogram analyses of the number concept which assign a higher developmental ranking to operational tasks than estimation tasks (Siegel, 197 1 ; Wohlwill, 1960). Consideration of experiments designed to investigate the development of operators highlights a fourth reason for distinguishing between operators and estimators. It appears that the way in which an individual estimates at any given time influences the way he behaves in such experiments, in particular, whether he uses operators. This observation leads to the thesis that the use of the two types of processes is related in a complex fashion, and that a consideration of how a particular estimation strategy process influences the use of operators would provide guidelines for studying the development of number concepts in young children. To illustrate that the use of one estimation strategy as opposed t o another is related to the use of operators, we start by considering a hunter who sees a flock of ducks spread out in the sky. When h e first sees the flock, he estimates the number of ducks at 150. After watching the same

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flock land close together on the small pond nearby, he changes the estimate to 75. In this particular situation, the ducks simply rearranged themselves. No ducks flew away. Yet the effect of the rearrangement led the hunter to say there were fewer ducks. Why? One explanation is that he thought the number actually changed. Yet questioning the hunter would probably show he did not think this. Instead, he would say that his original estimate was a guess based on the extent of the array and that the landing of the ducks led him to alter his initial guess. Further, he would argue that this was a reasonable thing to do since he had no reason to be confident about his initial estimate. However, had the hunter reason to be confident about his initial estimate, he would not have changed it. Thus, for example, if he could have counted the ducks or been told by someone what the actual number of ducks was, he would not have suggested that there were fewer ducks after they rearranged themselves. The example serves to illustrate that whether operators are revealed in behavioral reactions to transformations depends on the type of estimator invoked. When an estimate is based on a property that is not invariant across transformations of a set, the individual may treat each distribution of the set as an independent estimation trial. When the estimate depends upon numerosity per se then rearrangements may be ignored or deemed irrelevant. In this case, the use of invariance operators can be inferred. Thus, a consideration of estimation processes is central to our interpretation of the behavior of an observer who witnesses transformations of an array. Failure to consider these may lead one to conclude that the hunter lacked number invariance operators or that he treated rearrangement as a transformation that is relevant to number. These considerations point to the possibility that, to a large extent, the apparent absence or presence of number invariance operators may depend upon the absence or presence of the ability to estimate number with precision and confidence. If one does not estimate on the basis of number per se, then one cannot utilize the operator part of his number scheme. Rather, one may treat the successive presentations of different arrangements of the given quantity as separate occasions for estimating. This argument suggests several hypotheses with respect to the develop ment of number concepts. First, the quality of estimation strategies may determine whether a child reveals a competence for treating number operationally. Second, as processes for estimating number with precision develop, so may the use of operators. Related to both of these hypotheses is the possibility that a study of processes which contribute to a child's confidence in his estimates may aid our understanding of developing quantity concepts.

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In order to assess these hypotheses it is necessary to study the development of estimators as well as operators. In general, these two processes have not been considered together in investigations of developing number concepts. The interest in the development of number concepts can be traced back to the end of the nineteenth century. Initially, psychologists tended to investigate processes that are classified as estimators in this paper. Thus, much of the early work focused on how children count, perceive, and discriminate numbers. Although there was some discussion of operations, particularly by McLellan and Dewey ( 1896), Piaget’s treatise on number ushered in a concerted effort to investigate operations. The earlier work did not place questions of what children knew about addition and subtraction into the framework of assessing development of operators but rather into a catalogue of number facts which children of various ages knew. Thus, for example, Brownwell ( 194 1) assessed children’s knowledge of number combinations such as ( 1 2 ) or (5 - 3 ) and provided normative charts showing which of these number facts children knew. The studies were not designed to determine the operations which children thought did or did not change number. Piaget shifted the framework from one in which the child’s responses to number were thought to indicate mastery of number facts to one in which the child’s responses to number were thought to reveal the functioning of underlying cognitive operators. Thus, further studies of children’s comprehension of addition and subtraction (e.g., Smedslund, 1966a, 1966b, 1966c; Wohlwill, 1960) were placed in the context of Piaget’s treatment of number as a manifestation of logical thinking. Although most of the research that is relevant to the discussion of estimators predates Piaget’s work, some work in this area has continued (e.g., Beckwith & Restle, 1966; Potter & Levy, 1968). And, as indicated below, some of the current research on the pre-conserver’s notion of number is relevant to the discussion of estimators (e.g., Gelman, 1969a; Mehler & Bever, 1967; Wohlwill, 1960; Zimiles, 1963, 1966). Still, there has been little tendency to consider the two problems together and to take into account possible interactions. The body of this paper begins with a review of the literature that pertains to estimators and a consideration of methodological problems in determining the properties upon which the child’s estimate is based. There then follows a report of research on estimators from our own laboratory. Then we take up the problem of confidence in estimates. Finally, there is a selected review of previous research on operators and a summary of our current studies on operators that have been designed in light of the results of our estimation studies.

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11. Estimators A. METHODOLOGICAL CONSIDERATIONS

Estimator tasks are those tasks which were designed to determine under what conditions subjects can abstract the precise or approximate numerosity of a perceptual array. In such tasks, subjects are asked to judge, construct, or compare arrays which vary in numerosity and other attributes. Various tasks of this kind have been used with children. For present purposes, it is necessary to decide whether the child’s responses in these tasks were based on the numerosity or on other distinctive cues in the array(s). Knowing which cues determined the responses will help one determine what estimation processes the child utilized. Therefore, the question is what methodologies can or cannot be used to assess the extent to which young children respond to numerosity per se. An analysis of the tasks used by various investigators to study number concepts in children helps answer the question. Some investigators use a discrimination paradigm, in which children are to respond differentially to two arrays of equal or unequal number. In some of the number discrimination studies, children are required to learn to pick the larger array (e.g., Long & Welch, 1941; Wohlwill, 1962). In others, they are asked to decide whether the arrays contain the same number or if one has more or less than the other (e.g., Rothenberg, 1969; Russell, 1936; Zimiles, 1966). Generally, the above discrimination tasks do not indicate which attribute of the arrays was responded to by the child. Consider what interpretations can be made of “correct” responses to differences, i.e., reaching a learning criterion of choosing the array which has more (or less) objects. Figure 1 presents schematic samples of pairs of arrays that have been used in various experiments. In some cases these are placed side by side (e.g., Long & Welch, 1941; Russell, 1936); in other cases one above the other (e.g., Rothenberg, 1969; Zimiles, 1966). The actual numbers in each stimulus pair have been varied, e.g., 3 vs. 5 , 6 vs. 10, 1 vs. 6, etc. Figure 1 shows that each pair of arrays always has at least one other difference redundant with the difference in numerosity. This is necessarily so when only two stimuli are used. Consider the Pairs A and B in Fig. 1 where the two arrays each have different numerosities but no differences in size, shape, or color of the objects or the pattern of dispersal. If the two arrays are of equal length (Pair B) , then they must vary in density and the more dense stimulus must be the more numerous. Conversely, if density is held constant (Pair A ) , length varies with numerosity. In stimulus pairs C and D length and density are in conflict, respectively, with numerosity (cf. Zimiles, 1966) ;

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12 1

Fix. 1 . Schematic illustration of representative arrays used in discrimination of number tasks wliere the numbers differ.

however, density and length, respectively, are redundant with numerosity. Thus, for example, if Stimulus 2 in Pair C is chosen as "more," one cannot be certain as to whether density or numerosity prevailed over length. Thus, children may score correctly without responding to number. A related problem occurs when the numbcr of objects in both arrays is equal. Figure 2 shows eight stimulus pairs. Each array in a pair has the same number. Inspection makes it clear that many stimulus pairs can be judged "same" on grounds other than number. Only the arrays of Pair H are alike on number alone; and this is true only if the child responds to the whole array as opposed to parts of arrays. If he does the latter, he could judge Pair H the same because they both contain a small black circle. Thus, in many cases a child could again score correctly without responding to number. Other cues are available. The presence of redundant non-numerical cues confounds the interpretation of performance in other number tasks as well. A child required to reproduce a given set of objects for number (Brownwell, 1941; Buckingham & MacLatchy, 1930) may simply pair off each object without assessing the number (Piaget, 1952). Or a child required to identify, for example, which of three arrays contains 10 objects (Brownwell, 1941; Grant, 1938; Woody, 1931) may solve the problem by remembering that 1 0 means a lot and by looking for the biggest array (Brownwell, 1941). Although both

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122 ~

_

_

Stimulus I

-

Number, Size, Shape.Cobr

Number. Size. Shape, Color

Numbef, Lenqth. Size, Density. Color Number. Length, Dens*. Shape Color Number, Length, Size.Density.Area Shapa. Color

*I

Number. Sire. Shape. Color

Number 7

Fig. 2 . Schemutic illustration of representative arrays used in discrimination of number tasks where the numbers ure the same.

of these strategies are “quantitative” to some degree, neither reveals the unambiguous use of number alone. The difficulty in inferring whether a child responds to number in the preceding tasks is reduced or disappears when other response criteria are included. For example, verbal protocols may serve this end. The child might be asked why x has more, why x equals 10, or why x is the winner. In a study described later, the child’s ability to respond to number was assessed with a modified discrimination task. Children aged 3-5 years were shown two arrays of toy mice differing in number ( 2 vs. 3 ) and length or density. The child had to determine which array was the “winner” and which the “loser.” During the learning, children were asked why they identified the winner or loser as such. The majority of the children said that one had 3 or the other hand 2 or both. No child said that one was longer or more bunched up. The use of verbal protocols is not the only way to render a response unambiguous in a number task. Baldwin and Stecher (1925) noted that children who could construct a set equal in number to that in a sample, counted extensively. Observations of this sort also serve to remove ambiguity. Not all estimation experiments present a problem of interpretation. Many have been carried out in such a way that number was the only possible cue for consistent responding. For example, Beckmann (1924) used

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a number production task in which the children took out N marbles (or other objects) from a box. Since the experimenter in this task did not first make a similar sample, the child had no set to match. Therefore, it is unlikely that the children could have succeeded in this task without responding to the numerosity per se. Beckmann (1924) also used a simultaneous discrimination task with repeated trials. This involved presenting different examples of two numbers over a series of trials. The configurations and materials within and between the sets varied but thg numbers did not. He scored children as having mastered the task only if they answered correctly regardless of configurations or materials. Thus, consistently correct responses must have been based on number, the only cue which was the same in all arrays. A repeated trials design has also been employed in recognition expenments in which children have to identify the number of dots in arrays with varying patterns of dots (e.g., Brownwell, 1941; Freeman, 1912). Buckingham and MacLatchy (1930), in what they called a number identification task, instructed their testers to cast a given number of objects on the table before the child and then to ask how many there were. They reasoned that doing this three times for each of 1,356 children on each of nine numbers would serve to control for the use of any non-numerical cue. This methodological discussion highlights the criteria used in selecting for review, in the next section, studies from the literature on the child’s use of number. The review concentrates on those studies which reveal with some certainty whether or not the children were responding to numerosity. The experiments had to satisfy either of the following criteria: ( a ) the task was designed so that a correct response had to be based on the use of number, and ( b ) verbalizations or some other behavior of the child made it possible to decide which cues controlled the child’s response. B. REVIEWO F

THE

LITERATURE

1. Studies with Preschool Children Monographs by Beckmann (1924) and Descoeudres (1921) contain some of the most extensive data on the ability of 2- to 6-year-old children to estimate number accurately. Baldwin and Stecher (1925) used Descoeudres’ procedures with an American sample of 3- to 5-year-olds. Unfortunately, their data are reported in a way that makes it impossible to determine how closely these studies agree. Beckmann used four different tests of the child’s ability to estimate number. The easiest was the number production task described in the preceding section. Despite its simplicity, it required a child to respond to number in order to succeed. Descoeudres also tested children with a number production task. However, in her test,

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the experimenter always constructed samples against which the child could compare his own. Despite some resulting ambiguity, her results are strikingly similar to Beckmann’s. It seems safe to assume that the children in Descoeudres’ study were in fact responding only to number. Together, these two studies surveyed 663 children. Beckmann deliberately attempted to include children from all social strata and environments in and around the city of Gottingen. His sample included children from orphanages and day-care centers for working mothers as well as children from private kindergartens and nursery schools. Although Descoeudres does not give details of her sample, it apparently included a considerable range. The normative data from these two studies on the ability to produce a specified number accurately are shown in Table T. The percentages in these tables represent minimum figures, not average performance. In order for a given child to be counted as capable of reproducing 2, for example, the child had to perform perfectly over several trials with a variety of materials. Table T clearly shows that children between the ages of 2 and 3 years can generally produce the number 2 with considerable reliability. They seem, however, unable to produce the number 3 reliably. At some time between the age of 3 and 4 most children become capable of producing the number 3. But it is not until they are 4+ or 5 years old that they can produce larger numbers. The similarity in the results of these two studies serves to emphasize another theme that emerges from the Descoeudres monograph : Numerosity is a very salient feature of an array for a child, provided the array is sufficiently small so that the young child can accurately estimate its TABLE T OF CHILDREN I N THE BECKMANNAND DESCOEUDRES STUDIES ABLETO PERCENTAGE REPRODUCE EACHNUMBER CONSISTENTLY Number Sample Size Ba D 20 20 46 25 41 42 56 60 155

5 19 21 30 36 31 27 15 14

1

Ape 2-0 2-6 3-0 3-6 4-0 &6 5-0 5-6 6-0

Bb

3

2

D 40 79 100 100 100 100 100 100 100

5

B

D

B

D

B

D

B

D

30 70 70 84 90 99 100 100

40 74 100 97 97 100 100 100

0 0 20 20 63 83 82 93 96

0 16 19 67 78 87 96 100 100

0 0 4 12 39 55 64 87 92

0 4 13 25 61 81 73 100

0 0 0 4 17 36 45 70 74

-

100

B and D stand for the authors of each study. b Dash indicates data not collected.

a

4

0 4 0

11 32 33 14 93

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numerosity. Descoeudres went to great lengths to avoid any mention of number, yet she obtained very much the same results as Beckmann, who required the children to produce a specified number. When the children reproduced the experimenter’s arrays for Descoeudres, they did so on the basis of numerosity even though their attention was not specifically directed to this property. Thus, it appears that a young child will attend to numerosity as opposed to other cues in an array if he has the capacity to estimate the number represented. Both Beckmann and Descoeudres demonstrate that the ability to estimate number in these and other tasks is not stimulus or task specific. Beckmann, for example, trained some children to estimate reliably the number they first failed on in the normative task. Although the children were trained with a single type of stimulus material, such as marbles, their estimating ability generalized to a wide range of other objects, including objects portrayed in pictures. Descoeudres found that the ability to discriminate arrays consistently on the basis of number is closely related to the ability to produce numbers. Table I1 shows a notable drop in discrimination performance when numbers greater than 3 are represented in the arrays to be discriminated. A similar effect was found in the production tasks in Descoeudres’ and Beckmann’s studies (see Table 1 ) . Thus, young children can differentiate sets on the basis of number if the numerosities displayed fall within a range they can estimate. The effect shown in Tables I and TI, a sharp drop in preschooler’s performance when numbers greater than 3 are used, was found throughout the Beckmann and Descoeudres studies. The generality of this effect led Descoeudres to refer to what she callcd the “1, 2, 3 , beaucoup” phenomena in preschool children. She used this description to indicate that the preschool child’s ability to estimate number breaks down rather abruptly at TABLE I1 PERCENTAGE OF CHILDREN WHOCONSISTENTLY DISCRIMINATED ON THE BASIS OF NUMBER I N DESCOEUDRES SAMPLE^ Age in years 2-6 Discrimination (13)b 1 vs. 2 2 vs. 3 3 vs. 4

23 23 0

3 (17)

(IS)

4 (25)

4-6 (17)

5 (13)

59 41 0

67 67 13

76 64 8

100 100 5

77 77 38

3-6

5-6 (8) 100 100 75

From Descoeudres (1921, p. 278). With permission of author’s publisher. Number in brackets indicates the size of each age group. c Dash indicates data not collected.

0

h

6 (2) -C

100

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some number between 2 and 5, most typically after 3 in children younger than 4 years of age. A typical pattern of performance for a 34-year-old child was as follows: The child could estimate the numbers 1, 2, and 3 with reliability in a variety of tasks; he could estimate the number 4, but only imprecisely and unreliably, e.g., the child sometimes produced five or three objects instead of four. For numbers greater than four the child was grossly inaccurate and unreliable. Descoeudres introduced verbal protocols and other observations to demonstrate that the children regarded the larger numbers as equal to “a lot” and therefore undifferentiated from one another. The generalization regarding the abrupt breakdown of performance at some number between 2 and 5 was true for all tasks in Beckmann’s and Descoeudres’ studies. However, the percentages of children passing a task for a given number varied considerably from task to task, particularly in Beckmann’s studies. Many of the failures were due to extrinsic factors. For example, performance on Beckmann’s most difficult task clearly depended on the child’s ability to focus on one array of small dots shown on a paper with 11 other dot patterns. Because of these extrinsic factors, Beckmann’s four estimation tasks were not scalable. The order of task difficulty for individual children could not be predicted from the group data. Beckmann’s data somewhat underestimate the preschool child’s ability to estimate small numbers. Since each of his tasks was an unambiguous test of the child’s ability to respond to number per se, success on any one task indicated some such ability. Beckmann, however, does not give composite data indicating the percentage of children in each age group who passed at least one of the tests. 2 . Studies with School-Aged Children Several studies with school-aged children contained estimation tasks which allow one to determine whether children did or did not abstract numerosity from an array. Counting was discouraged in some of these studies but not in others. The latter type is emphasized in this section. Buckingham and MacLatchy ( 1930) tested 6- to 6&-year-old children who were just entering the first grade and who had no previous instruction in arithmetic. They used a variety of number knowledge tasks, one of which required the children to estimate the number of objects thrown randomly on a table. Sets of 5 , 6, 7, 8, and 10 objects were each thrown three times. Another task with the same numbers was like Beckmann’s production task and required the children to hand an N = x to the experimenter. Seventy percent of the children successfully estimated 10 objects on at least one of the three trials. The respective percentages for the numbers 8, 7, 6, and 5 , were 72, 74, 75, 81. However, the ability to estimate these numbers

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reliably was considerably less. Thus, only 42, 45, 46, 52, and 63% of the children correctly estimated the numbers 10, 8, 7, 6, and 5 on all three trials. Similar results were reported for the production task; for example, 85% of the children produced the number 5 at least once, but only 64% produced it all three times. Brownwell (1928) tested first graders on their ability to indicate how many dots were present in arrays varying in number from 3-12. A given number of dots was arranged in five different two-dimensional patterns and one linear pattern. The average percentage of correct responses for the numbers 3-12 is given in Table 111. Freeman (1912) had children report the number of dots they saw in a briefly exposed array. The arrays also varied in number and pattern. Freeman reported that his younger subjects (6- to 7-year-olds) could grasp the number in an array as well as older children and adults when the number represented was 4 or less. As the number increased “beyond the scope of attention” performance fell off markedly for the younger children but not for the older children and adults. He attributed this difference to the older subjects’ propensity to group the objects, even when no obvious pattern was present. The older subjects used more sophisticated estimation strategies. The 6- to 7-year-old subjects did not do as well as Brownwell’s subjects of the same age, probably because Brownwell’s subjects were not discouraged from counting whereas Freeman’s were-a point to which we will return. Brownwell (1941 ) used tasks comparable to those of Buckingham and MacLatchy and obtained similar results. Thus, for example, 54% of 631 6-year-old school entrants were able to put “tails on nine of the rabbits” TABLE 111 AVERAGE PERCENTAGE CORRECT RESPONSES GIVEN TO THE NUMBERS 3-12 BROWNELL’S (1928) SUBJECTS Number 3 4 5 6 7 8 9 10 11 12

BY

Average percentage correct5 98 95 93 91 85 81 78 78 70 69

the computations summarized here were made by the present author and are based on the data given for two-dimensional patterns. Insufficient information was given for the linear arrays.

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in a picture displaying many rabbits and 80% were able to draw five marbles on an answer sheet. When instructed to give the experimenter a particular number of objects, 85, 80, 81, 80, and 77% of the children could produce 5 , 6, 7, 8, and 10 objects. This finding is almost identical to that reported by Buckingham and MacLatchy for the first trial of a comparable production task. Together these data suggest that first- and second-grade children can abstract the numerosity of arrays of 5 with no difficulty and can do so with considerable accuracy for numbers up to 9 or 10. Their ability to estimate accurately does decline as the number becomes still larger; however, this decline is not nearly so abrupt as that described for younger children. A review of the literature on number estimation in young children has revealed two points that will reappear in subsequent sections: ( 1 ) Young children, particularly preschoolers, have difficulty estimating accurately, i.e., abstracting the numerosity of an array when the numerosity is greater than 3-5. When the numerosity is 3 or less even 24-year-olds can frequently abstract it. (2) Provided the numerosity of an array falls within the range that a child can estimate, the numerosity is a very salient property of the array. That is, the child will attend to this property in comparing arrays even when many other readily perceived cues are also presented by the arrays. It would seem, then, that studies of the young child’s ability to use number operators should involve small numbers.

c.

THEROLE OF

COUNTING IN

ESTIMATION

A considerable amount of evidence supports the hypothesis that counting‘ is the preeminent mechanism used by young children to estimate numbers of all sizes, with the possible exception of 1 and 2. It might be expected that the ability to apprehend small numbers is mediated by a “perceptual” mechanism and that this mechanism is the initial estimating process used by young children. This perceptual mechanism might rest on some apprehension of the geometric properties of the configurations made by small arrays or some at yet unexplicated process. Direct apprehension of the numerosity of small arrays without the mediation of counting is common in adults. In the literature on adult performance, it is referred to as subitizing (Beckwith & Restle, 1966; Neisser, 1966). The ability to subitize small numbers also appears in preschool children. But, as shown in Table IV, it 2 A number of investigators have distinguished between the ability to repeat a number sequence by rote and the ability to coordinate the numerals with successive items. The term counting has the latter meaning here.

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TABLE IV PERCENTAGE OF CHILDREN I N BECKMANN’S STUDYWHO COUNTED OR SUBITIZED WHEN ESTIMATING NUMBERS~ Age of children

2 3 4 5

6 0

Count Subitize Count Subitize Count Subi tize Count Subitize Count Subitize

25 75 71 29 80 20 100

-

100 -

17 83 33 67 80 20 88 12 96 4

11 89 35 66 71 29 76 24 90 10

4 96 21 79 52 48 61 39 64 36

2 98 5 95 17 83 33 67 41 59

From Beckmann ( 1924, Table 8, p. 28). Number in brackets indicates the size of each age group.

appears to develop after children have learned to estimate a number by counting. Table IV shows the results of Beckmann’s analysis of the way in which children arrived at an accurate estimate of the number of items in an array. Depending on their behavior during the task and their explanations of how they reached an answer, Beckmann categorized the children as counters or as subitizers.:’ Children classified as counters were observed to count before giving their answer and said they counted when asked how they knew an answer. Children classified as subitizers responded very quickly without giving any indication of counting and said they could see when asked how they knew the answer. Thus, for example, children said “It looks like two,” “I can see it’s two.” It can be seen in Table IV that the younger the child, the greater the tendency to count for all numbers. Furthermore, the larger the number, the greater the tendency for all children to count. Together these results support the conclusion that children estimate a number by counting before they can subitize the same number. The same pattern of developmcnt from counting to subitizing appears in Beckmann’s production task. In this task children had to produce a designated number of marbles from a box. Beckmann reported that the children used three strategies in this task: ( 1 ) Children counted as they removed one marble at a time; ( 2 ) childrcn lookcd at the marbles and then pulled out 3

The term subitize is used as a translation of Beckmann’s term Erkennen.

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TABLE V PERCENTAGE OF CHILDREN I N BECKMANN’S PRODUCTION TASKWHO USED THE DIFFERENT STRATEGIES~ Age level Strategy Count Look and take Group 0

3-0/3-6 58

33 8

4-0

4-6

5-0

5-6

6-0

57 25 18

46 30 24

39 30

43 30 27

48 32 20

31

From Beckmann ( 192 I , Table 6, p. 25).

the appropriate number; ( 3 ) children constructed the sum taking two groups of marbles, e.g., a child asked to produce five marbles first took two marbles and then another three. The percentage of children who used each of the strategies appears in Table V. Counting was the prevalent strategy used by children of all ages. The older children used the grouping strategy more than the younger children. Brownwell (1928) and McLaughlin (1935) reported a similar effect. As indicated above, Brownwell tested children in grades 1 through 5 for their ability to identify the number of elements in arrays of 3-10. The arrays were presented for five seconds each, allowing sufficient time to count some of the displays. Brownwell reported that the younger children almost always counted and seldom took advantage of the patterns in the display. McLaughlin indicated that 3- to 6-year-olds typically counted in order to determine the number of objects in an array, even when the numbers were small. As the number of items a child could count increased, so did the ability to estimate. Good counters made high scores. A comparison of performance in experiments in which children might have counted with those in which they might not have, adds support to the hypothesis that young children initially estimate by counting. We have already described Brownwell’s ( 1928) and Buckingham and MacLatchy’s (1930) work on estimation. Brownwell used a dot recognition task. The comparable Buckingham and MacLatchy test involved showing children the result of a random throw of objects. In both of these studies, children were not prevented from counting. As indicated, Brownwell reported that the 6-year-olds did count. Douglass (1925) used three number tasks with children of different ages, including 6-year-olds. Two of his tasks were similar to Brownwell’s and Buckingham and MacLatchy’s. In one, children saw 1-10 blue dots arranged in a row on cards; in the other, children had to identify the number of pennies (1-10) held in an open hand. The third task involved choosing the one of ten cards displaying the number of dots which corresponded to a spoken word between one and ten. In all three tasks, stimulus exposure was brief and the children were discouraged from

Early Number Concepts

13 1

counting. Although the three studies had samples of varying ages, all included a 6-year-old group. A comparison of Douglass’ 6-year-olds with equally old children in the other two studies reveals a large discrepancy. In the studies in which the children were allowed to count, approximately 70% accurately estimated nonlinear arrays of ten on at least one trial. And although children in Brownwell’s study were less likely to estimate linear arrays of 9, 10, and 11 accurately, 54% did SO.^ I n general, these studies give the impression that 6-year-old children can estimate arrays of ten items with reasonable accuracy. In contrast, in Douglass’ study in which children were not allowed to count, only 8% of the children could estimate the numerosity of ten element arrays. Such a low score means the children did poorly on all three of Douglass’ tasks, including the two which appear comparable to those used in the other studies. Although the studies differed in a variety of ways, some of the discrepancy in estimation scores may reasonably be attributed to the presence or absence of counting. Errors in estimation may reflect errors in counting. Russell (1936) reports that some children erred because of counting mistakes when asked to judge which of two groups of blocks had the “most.” Thus, for example, a child counted an 8 vs. 9 display of blocks as 8 vs. 8 and accordingly reported the displays had the same number. Counting may not only be the first mechanism used in estimation but may also be the basic mechanism used when children begin to add and subtract. Various investigators report that the initial stages of adding and subtracting involve counting (e.g., Beckmann, 1924; Brownwell, 1941; Ilg & Ames, 1951; Reiss, 1943). Thus, for example, a child may add 8 and 3 by counting “8, 9, 10, 11” or may even count to 8 first and then proceed to 11. To summarize, a child’s ability to abstract number seems related to his ability to count. Young children tend to count even when estimating small numbers. The ability to subitize and group elements within arrays develops later. D. AN EXPERIMENTAL INVESTIGATION OF ESTIMATORS 1. Introduction The research considered above indicates whether or not a child can abstract number and provides some evidence as to how he estimates on the basis of number. It does not, however, allow one to determine the nature of estimators used by the child who does not abstract number per se. This question is of some theoretical interest. 4 The manner in which data were presented for the linear arrays allows computations of a composite score only for the numbers 9-1 1.

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One source of this interest is Piaget’s writings (Piaget, 1952, 1968). These contain the hypothesis that there are four stages in the development of estimators, and that at each of these stages children use different information in the array. Piaget provides a description of the first two stages in his interpretation of Mehler and Bever’s (1967) study of the ability of 2- to 6year-old children to compare the number of objects in two rows before and after the rows are transformed. His account of the stages in the conservation of number provides a description of the last two stages. Piaget suggests that Mehler and Bever’s work shows that very young children estimate on the basis of density, judging which row is more “heaped” or “crowded,” while somewhat older children estimate with length cues, judging which row is longer. According to Piaget, the early use of density cues derives from a topological intuition; and the subsequent use of length cues derives from an ordinal comparison of how far each of two rows extend. This explanation is derived from research on space concepts (Laurendau & Pinard, 1970; Piaget & Inhelder, 1956), which shows that topological notions of space develop before Euclidean ones.5 Piaget formulates three stages in the development of number conservation. In the first stage, children center on a perceptual cue that changes with transformations, and fail to conserve; in the second stage, they begin to consider both the length and density of arrays, and sometimes conserve. However, if a perceptual change introduced by a transformation is too great, they will focus on it and fail to conserve. Finally, in the third stage, the child recognizes the compensatory relationship between the density and length of an array and can conserve number. This account suggests that in the first stage of conservation children use length or density; then they begin to use both; and finally they can abstract number. Combining the consideration of Mehler and Bever’s data on very young children and Piaget’s own account of the stages in conservation in 5 - to 7-year-old children, we arrive at the hypothesis that there are four stages in the development of estimators. In the first, children use density; then they use length; then length and density; and finally, number alone. A related hypothesis has been advanced by investigators who suggest that failure on a conservation task reflects lack of a set to respond to number (e.g., Bearison, 1969; Gelman, 1969a; Zimiles, 1963, 1966). According to Zimiles and Gelman young children think of number in a multidimensional fashion. The hypothesis is that there is a hierarchy of cues controlling the young child’s attention to the numerosity of an array. Included

5 However, Piaget’s definition of topology appears to differ from the mathematical system of topology in which the concept of density does not appear.

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in such a hierarchy are cues like length, density, arrangement features, and the numerosity of an array. With development or experience, number is assumed to become differentiated from the other cues, and thereby more salient in the hierarchy. This position implies that experiences which serve to set young children to attend to the number and not to other features of an array will increase the likelihood of their abstracting number. Another implication is that as children develop better skills for attending to number, the size of the hierarchy controlling number estimators decreases and number per se becomes dominant. Older children should use number more in estimating than younger children. To evaluate these hypotheses, one needs a method that yields the likelihood of children responding on the basis of number as well as other features of the array. One possibility is a choice procedure. However, as indicated in Section I1 A, two-choice procedures are problematic in that they often yield ambiguous data. To circumvent the problem of interpretation presented by a two-choice paradigm, a three-choice procedure was used. In previously assessing whether children were most likely to attend to the length, orientation, or number in a row of elements, the writer (Gelman, 1969b) employed the modified method of triads used by Suchman and Trabasso ( 1966a, 1966b) to study color-form preferences. Children were shown a series of triadic stimulus arrays. Each triad was constructed so that every pair of arrays in a triad was alike on a value of one binary dimension (e.g., number) and different on values of two other dimensions (length and orientation). Children had to judge which two arrays in the triad were the same. Since they received no feedback, there were no right or wrong answers. It was assumed that a child’s choice of a particular pair of stimuli reflected the cue to which he attended on that trial. By considering the overall frequency of number, length, and orientation responses, it was possible to determine the likelihood that each of the cues-length, number and orientation-affected a judgment. The study reported here also involved the triad technique. The concern was to study the development of estimators and the use of length, density, or number in an estimation task. Thus, the instruction to the children was to select the two of three stimulus arrays that had the “same number.” An example of triads shown to the children is given in Fig. 3. It can be seen that each pair of arrays in a triad was alike on only one value of either a number, length, or density variable. Thus, a choice of a particular pair of arrays in response to the question of which two arrays had the same number had to be based on that variable. For example, if a child chose stimulus pair A and B it would be inferred that he responded to number. If he chose stimulus pair A and C, it would be inferred that he responded to length.

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Fig. 3. Schematic representation of triadic stimulus array which varies values of only length, number, and densiiy.

2. Subjects Children who participated in this experiment were drawn from nursery and elementary schools in the Philadelphia area. Although some black middle- and lower-class children attend the nursery schools, all schools serve a predominantly white middle-class population. The design originally included 3-, 4-, 5- and 7-year-old groups. After testing fifteen 3-year-olds, who responded primarily on the basis of position, we decided to drop this age group. In all, 37 nursery schoolers (median age = 4-6 years); 45 kindergarteners (median age = 5-8 years); and 30 second graders (median age = 7-8 years) were tested. Seven of the nursery school subjects ( S s ) were dropped because of their tendency to respond to place cues. An equal number of the remaining children from each age group was assigned to one of three independent stimulus conditions. An effort was made to counterbalance sex. 3. Triad Construction There were three sets of 72 triads, one for each of three independent stimulus conditions. A triad consisted of three 12.70 x 20.32-cm cards, each containing a row of red (or green) .64-cm circles (or stars). The items in the row on each card were spaced equidistantly. Cards within each triad were placed to form a triangle. The choice of values for the critical dimensions of length, number, and density was governed by three considerations. First, we wanted to vary systematically the values of these attributes. Second, we wanted to include comparisons of numbers as small as 2 vs. 3 in order to set our results against those of others who have studied estimation in young children. Third, we wanted to generate stimulus triads that contained one pair of arrays with an equal number, another pair with equal lengths, and a third pair with equal densities.

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The former considerations present a design problem since the critical dimensions are not independent. For example, a variation in the number of an array effects a simultaneous variation in length, density, or both. To facilitate the description of the way in which this problem was handled, Table VI presents a summary of the length, number, and density relations selected to generate the triads within each stimulus condition. As stated previously, three independent groups of subjects were assigned to each of three conditions. The values used to generate the triads within each condition are summarized under the columns labeled with Roman numerals. The three conditions differed in terms of which of the three dimensions (number, length, density) took on a fixed pair of values for all triads used in that condition and which dimensions took on the permissible combinations of four values. Thus, in Condition I, the children saw a series of triads that all displayed the same pair of number values but varied in the pair values of length and density. Children in Condition I1 saw triads that all displayed the same pair of density values but varied with respect to the pair values of number and length. Children in Condition 111 saw triads that all displayed the same pair of length values but differed with respect to the pair values of number and density. Within each condition there are only three permissible combinations of the number, length, and density values selected. The three permissible combinations are shown in Rows A, B, and C of Table VI. Any other combination violates the requirement that one pair of arrays in each triad should have an equal number, another an equal length, and another an equal density. Note that basic triad B was used in all three conditions. To construct the basic triads represented by the combination of value pairs shown in the rows, the smaller number of each number pair was used in two arrays, the larger number in one array. The length and density values which were used twice were dictated by this constraint. Then each of the basic triads was prepared with two colors (red or green), two shapes (circles or stars), and the six possible positional permutations of the three constituent stimuli. This yielded 24 versions of a triad. With three basic triads per column of Table VI, 72 triad versions resulted for a given stimulus condition. In order to make the results of this triad generating procedure more concrete, Table VII presents the actual lengths and densities of the triads in the first column of Table VI. 4. Procedure The experiment involved three phases spread out over two days. The first phase was a pretest, the second the triad test, and the third a counting test. A child’s participation each day took 15 to 20 minutes. The 12-trial pretest was an oddity task described elsewhere (Gelman, 1969a). The stimuli

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TABLE VI DESCRIPTION OF BASICTRIADS IN ESTIMATION EXPERIMENT Combination of value pairs in each conditiona Condition I1

Condition I

Basic triad

Condition 111

~~

A

B

C

3,5 L, 2L hD, t D 3,5 BL, L 1D,D 3,5 tL, 1L D, 2 0

2,3

2,3 BL, L :D, &D 3,s &L,L fD, D 5,9 1L, L D, 2 0

i L , 4L &D,D 3,5 1L, L D,D 5,9 L, 2L iD,D

a L = 9.0 cm as measured from the center of end items of each row; D =1 /2.25 cm where 2.25 cm represents the distance from the center of one element to the next.

were small plastic toys glued on 6.35- x 7.62-cm masonite blocks. The children were asked which of the stimuli were the same, on half the trials, and which was different on the other half of the trials. Verbal feedback was given. As found in a previous study (Gelman, 1969a), this was an easy task for the children. The triad test always began on the same day as the pretest. In this session a child was tested on 36 of the triads. The remaining 36 triads were administered in the second session. The children were given the counting test at the end of triad testing on the second day. The order in which the triads appeared was randomized for each child. Each child experienced only one of the three stimulus conditions. TABLE VII STIMULUSVALUESIN CONDITIONI BASICTRIADS IN ESTIMATION EXPERIMENT^ Stimulus 2

3

.11

3 9 .22 3

.22

4.5 .44 3

5 18 .22 5 9 .44 5

1 A

B

C

Number Length Density Number Length Density Number Length Density

3 18

3 9

3 4.5

.44

2.25 39

4.5

.89

a Lengths are measured in centimeters between the centers of the end items in each row. Density values are the reciprocals of distances in cm from the center of one element to the next; smaller values reflect lesser densities.

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137

The triad test began by telling the child, “This game is like the toy game we played. Now you will be looking at cards which have stars or dots on them instead of toys. I want you to point to or give me the cards that have the same number.” Specific responses were not reinforced; however, at random times, the experimenter told the child he was doing very well and offered general warm support. The counting test consisted of asking the child to count to 10 and then select six of ten objects. The experimenter interrupted the counting if and when the child had counted as far as 10. All but one of the children could count to 10.

5 . Results a. Overall proportion of number, length, and density choices. The data were initially analyzed to yicld the overall proportion of length, number, and density choices made by all Ss within a condition. Table VIII presents these proportions for each age group and each triad subset within a condition. Children in Condition I responded primarily to number. Only the nursery school group showed any tendency to respond to length, and there were virtually no density choices in all three age groups. Condition I reveals no effect of varying the values of length and density. Given fixed number values ( 3 and 5 ) , the children were equally likely to estimate on the basis of number for all three subsets. In Condition 11, the pair values for density were the same throughout and the values for length and number varied. In Condition 111, the pair values for length were the same throughout and the pair values for number and density varied. Variations in the pair values of the number dimension affected both nursery and kindergarten Ss but not second grade Ss. No matter what values number had in Conditions TI and 111, second grade children always estimated on the basis of number. In contrast, the tendency for younger children to estimate on the basis of number varied depending on the numbers shown in the arrays. When the number values were 2 and 3 (Triad A in Conditions I1 and III), they always responded to number. When number values were 3 and 5 (Triad B in Conditions I1 and 111) , they still responded predominantly to number but not as consistently. When the number values were 5 and 9 (Triad C in Conditions I1 and I I I ) , even fewer choices were coded as number responses. Increasing the magnitude of the number values was more disturbing for the nursery school Ss than for the kindergarten Ss. When children did not estimate on the basis of number, they primarily responded to length as opposed to density. Thus, for example, with arrays of 5 vs. 9 (Conditions 11 C and 111 C ) , nursery school children responded to length on 62% of the trials, and to density on only 9.5% of the trials.

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TABLE VIII PROPORTION OF LENGTH,NUMBER, AND DENSITYCHOICESIN FOR EACHAGE GROUPI N EACHCONDITION ESTIMATION EXPERIMENT Triad subset and summary of value pairs in each condition Condition 1 3,5:L,2L:

Age Group Nursery ( N = 10)

Kindergarten ( N = 15)

Number Length Density

.88 .12

.oo

Number Length Density Number Length Density

.84 .16

.98 .02

.87

.97 .03

Number Length Density Number Length Density

.96 .04 .o1 .75 .24 .01 .32 .57 .ll

Chosen dimension

.oo

.oo .12 .01

.99

.o 1

.oo

.oo

Condition N

Number Length Density Condition Ill

.96 .02 .02 .90 .08

8 .07

.99

Number Length Density

.98 .01

.o1

.o 1 .oo

Number Length Density Number Length Density

.72 .24 .04

.9 1 .07 .02

.25 .67 .08

Grade 2 ( N = 10)

-

1 .oo

.oo .oo 1 .oo .oo .oo

1 .oo

.oo .oo

1.oo

.oo .oo 1.oo .oo .oo 1.oo .oo

.oo

1.oo

.oo

.oo 1 .oo .00

.oo

1 .oo

.oo .oo

The data reveal an effect of varying the values of length and density. The nature of this effect was most pronounced in the kindergarten groups in Conditions I1 C and I11 C in which the pair values of number were the same but the pair values of length and density differed. These conditions are circled in Table VIII. The Ss in Condition I1 C responded to number more than length. In contrast, the same age Ss in Condition 111 C responded more to length than number. The description of these conditions shows that the average density of the element in the I11 C triads was greater than that in the I1 C triads, and that the rows in I11 C were shorter than those

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in TI C. Thus, an increase in densities accompanied by a decrease in lengths led the children to base their response more on length than density. The same conditions for the youngest group yielded a similar effect. A chi-square comparison of the frequencies from which the proportions were derived 2 )6.4, p < .05). yielded a significant effect of condition ( ~ ~ ( = A comparison of all three stimulus conditions reveals in the younger groups an effect of keeping constant the values of a dimension. In Condition I, with constant values of number in all three subsets, younger children were more likely to estimate on the basis of number than were children in Conditions I1 and 111, who saw different values of number in each subset. On the triad subset common to all three conditions, i.e., Subset B, in Condition I nursery school children responded to number on 84% of the trials; in Conditions I1 and 111, they chose number on 75 and 71% of the trials. Similarly, kindergarten children estimated on the basis of number on 98% of the Condition I B trials as opposed to 90% of the Condition TI B and I11 B trials. Thus, there seems to be a tendency for younger children to estimate less consistently on the basis of number when they are shown variations within this dimension. The import of this finding is discussed in Section I11 on estimator confidence. b. Analysis of individual tendencies. Individual differences were examined to determine whether individual children estimated primarily on the basis of one dimension, and, if not, what combination of dimensions controlled their judgments. For a given subset of 24 trials, a child whose choices were based on one dimension for at least 16 of the 24 trials was judged dominant on that dimension. If no one dimension was chosen 16 or more times but two of the dimensions between them accounted for 22 of the 24 choices, a child was scored as a length-number, length-density or numberdensity responder. Otherwise, he was scored as a mixed responder. The percentage of children who met these various criteria is shown in Table IX. These percentages are given for each condition and age level. Number-density and length-density percentages are not entered in the table because no child showed the length4ensity response pattern and only one child showed the numberdensity response pattern. This child was in kindergarten Condition TI1 and he gave this response pattern only in Triad C. A comparison of Tables VIII and IX shows that the group and individual data analyses yield the same pattern of results. Furthermore, no child estimated only on the basis of density in any condition. The density responses given in Table VIII are attributable to the mixed choice patterns in Table IX. Since the mixed choice pattern can be taken to mean no consistency in the way these children estimated, we may conclude that no children in this experiment estimated on the basis of density.

TABLE IX PERCENTAGE LENGTH,NUMBER,DENSITY,NUMBER-LENGTH, OR MIXEDRESPONSEPATTERNSIN EACHCONDITIONFOR EACH AGE GROUP IN ESTIMATION EXPERIMENT Triad subset and summary of value pairs in each condition

Age Group

__..

Response oattern

Nursery ( N = 10)

Mndergarten (N

= 15)

Grade 2 (N

= 10)

Condition I Number Length Density Number-Length Mixed Number

90 10

100 0

100

0 0 0

0 0 0 0

80

100 0

100 0

0 0 0

10

Density Number-Length Mixed Number Length Density Number-Length Mixed

0 10 0 90

Number Length Density Number-Length Mixed Number Length Density Number-Length Mixed Number Length Density Number-Length Mixed

100

Number Length Density Number-Length Mixed Number Length Density Number-Length Mixed Number kngth Density Number-Length Mixed

100 0

10

0 0 0

0 0 0 100 0 0 0 0

0 0 0

100

0 0 0 0

Condition I1

0 0 0

0 70 20 0 0 10 20 50 0 10 20

93 0 0 0 7 93 0 0 0 7 60 14

0 0 26

100 0 0

0 0

100 0 0 0 0 100

0 0 0 0

Condition 111

3,5:hL,L:

(&D,D

)

100

0 0 0

0 0 0 0

50

100

0 0 20 30 0 50 0 30 20

0 0 0 0 26.6a 53.3 0 0 13.3

100 0

0 0

0 00 0 0 0 0 00 0 0 0 0

& O n e child (6.7% of the group) gavc the number-density pattern; this pattern is not included in the table, and therefore the kindergarten I11 C percentages d o not sum to 100.

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6. Discussion This study was conducted to determine the extent to which young children estimate on the basis of the actual number of elements in an array. It also explored the nature of the cues to which children respond when they do not estimate on the basis of numerosity. As in the Descoeudres and Beckmann studies, it was shown, that 4-yearolds consistently respond to number when the arrays contain two or three items. When the arrays contain three or five items, they still respond primarily but less consistently to number. Similarly, 5-year-olds always choose on the basis of number for 2 vs. 3 triads, but sometimes do not when confronted with 3 vs. 5 triads. With arrays of still larger magnitudes ( 5 vs. 9), 4-year-olds no longer estimate on the basis of number; and whether 5-yearolds do depends on the length and density of the displays. Second-grade children always abstract number in all conditions. Thus, 4- and 5-year-olds can abstract the numerosity of small arrays and have difficulty doing so with larger arrays. Several features of the results indicate that children who do not respond to numerosity use length instead. First, as shown in Table IX children do not use density exclusively nor in combination with another dimension. Second, in conditions in which children sometimes respond to number and at other times do not, they shift between using number alone, length alone, and number and length alternatively. Thus, for example, in the 5 vs. 9 condition, a decrease in length and an increase in density shifted responding by kindergarteners away from number to length. The failure to find children estimating on the basis of density or density and length in any age group or condition is surprising in the context of Piaget’s theory. Perhaps still younger children would respond to density. The 3-year-old sample was originally included to provide a test of this hypothesis; however, the children of this age responded primarily on the basis of place, in spite of concerted experimenter efforts to break this set. Apparently, the task was too difficult for children this young, and some other procedure will have to be used to test the hypothesis that density is the dimension that children initially use in estimation. Still, the finding that children responded to length and number as opposed to length and density suggests that density is not a primitive dimension in the child’s concept of number whereas length and number are. Perhaps when children begin to use density, they treat it as a derived attribute in their conceptual scheme of number. If so, older children should more readily respond to density than younger children. Some evidence for this hypothesis comes from a recent dissertation by Henry (1971). In a study of kindergarten and thirdgrade children’s number concepts, Henry used a triad choice task much like that described here. Children had to choose the two of three rows of

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chips (where each chip in each row was placed one above the other) that were the same. The magnitude of the arrays was greater (7 vs. 14) and children were not specifically asked about number. Still, Henry found, in agreement with the present results, that older children were more likely to choose on the basis of number and younger children on the basis of length. Further, both groups made relatively few density responses. Probe questions designed to assess whether children had the other dimensions ‘‘available” revealed that it was primarily the older children who referred to the relative densities of the rows (e.g., “these are closer together”). Younger children in the 5 vs. 9 conditions responded more to length than number when the arrays were shorter and denser. This suggests that when number is large and the array is spread out, young children can keep track of the number. As a result, they estimate on the basis of number, either by counting or grouping the elements. If the elements are too close to each other, however, young children can no longer use number-based estimators and shift to estimating number on the basis of length. Unfortunately, the data collection method does not allow a determination of whether the children tended to count the less dense arrays more often, but subjective impression is that they did so. Attention studies which vary the relative salience of dimensions (e.g., Trabasso & Bower, 1968) suggest that an increase in density and decrease in length would highlight density for young children and therefore increase the likelihood of their responding to it. The actual responding more to length suggests that the children attend to variations in dimensional salience only if their concept of number utilizes that dimension. If so, accounts of the development of number concepts in terms of attention alone (e.g., Gelman, 1969a) are inadequate and must include the possible nature of the child’s conception of number. It appears that the cues to which a child attends depend on his prevailing concept of number. In sum, this experiment shows that the older a child is the more likely he is to estimate linear arrays on the basis of number. As the number values of an array increases, so does the tendency for younger children to estimate on the basis of length. Finally, 4-to 7-year-old children do not estimate on the basis of density. These results suggest that the young child’s concept of number is initially based on length and number and that the understanding of density as an attribute that is relevant to number develops later. This hypothesis derives neither from a consideration of the writer’s own work nor from Piaget’s theory. Indeed, it differs markedly from Piaget’s formulation of the development of number concepts, which treats the notion of number as a derivative of the child’s initial use of length and density.

Early Number Concepts

111.

143

Estimator Confidence

One finding in the estimation study deserves attention before operators are discussed. Young children tended to use number less consistently when presented a series of triads that varied in the values of number than when presented a series of triads that had all values of number fixed at 3 and 5. Thus, in Condition I where the values of number were consistently 3 and 5 , 4-year-olds responded to number on 86% of the trials. In Conditions I1 and 111 where the value of number varied, children of the same age estimated on the basis of number less often (73.5% of the trials). A similar but smaller effect appeared in the 5-year-olds, whereas no such effect occurred for the oldest children. The question is, what might account for such a finding? In the earlier example of the hunter, it was suggested that he changed his estimate after the ducks rearranged themselves, in part because he was not confident about his first estimate. Given this lack of confidence in his initial estimate, he altered his answer as his attention was drawn to new information. The question now raised is whether lowered confidence also accounts for the tendency of younger children to respond less consistently to number when this attribute varies across trials. To show that a young child’s performance on number tasks may sometimes reflect a lack of confidence more than a lack of cognitive ability two effects need to be demonstrated. The first is that the child behaves as if he lacks confidence. The second is that altering the child’s confidence by varying conditions that affect it changes the likelihood of his meeting the criterion of task success. Assume that an individual lacks confidence in his ability to deal with a task. How might this show itself in behavior? The person might vacillate in his choice of a solution, he might change his answer with repeated questioning, or he might be inconsistent in his responses to a sequence of related questions. Thus, evidence that a young child is inconsistent in responses to quantity tasks or that he changes his answers with repeated questioning may indicate his lack of confidence in his own performance. A study by Rothenberg (1969) reveals that young children are inconsistent in the way they answer a pair of questions about the effect of a transformation in a number conservation task. Rothenberg classified the pattern of responses of children who failed to conserve as consistent or inconsistent. Pre-kindergarten and lower-class children were classified as inconsistent more often than kindergarten and middle-class children. Rothenberg’s data seem to show that children scored as inconsistent were so classified because of errors o n the second question. Thus, it might be

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argued that the younger children were more likely to change their answers with repeated questioning because they lacked confidence in their initial response. This possibility points to the need for research designed to assess the consistency of responses to a series of repeated questions. As indicated above, a child who lacks confidence should be influenced by manipulations which enhance or decrease confidence. If a child is not sure he has answered a question correctly, then he should be influenced by external sources which suggest that there is another answer or that he has misinterpreted the question. An hypothesis related to this argument holds that children interpret the transformations and subsequent requestioning in the second phase of conservation tasks as a challenge to their original answer and this misperception leads the children to think that the experimenter expects them to say that the quantities are different (Gelman, 1969a; Zimiles, 1963, 1966). In this regard, Russell (1936) found children tend to focus on differences if asked a question that could be interpreted as implying a difference. Russell reported two experiments on number discrimination abilities in kindergarten through second-grade children. Children were shown two sets of blocks, varying in color both within and between the sets. The number combinations used in each experiment are shown in Table X. The main variable differentiating between the two experiments was the form in which the number discrimination question was asked. In the first (Experiment A ) , children were asked several questions about two sets of blocks, including “Which pile has the most blocks?” If they appeared to have difficulty with this question, they were then asked, “Are the piles of blocks the same?” “Does one pile have more blocks than the other?” “How many blocks does this pile have?” Scoring was based on the child’s ability to indicate which pile had more when there was a number difference and to say that neither had more when each set had the same number. In the second experiment (B) , children were asked, “Are the piles of blocks the same? Are the piles of blocks equal in number?” A correct response involved saying that they were equal if in fact they were, or saying that they were not equal when each pile had a different number of blocks. Table X gives percentage errors for the different number combinations in Experiments A and B. As might be expected, the children were more accurate the smaller the numbers, no matter how the question was asked. However, the form of the question did alter performance accuracy. For the combinations of different numbers, the children were more often correct when asked which combination had more; and for the combinations of identical numbers, they were more often correct when asked whether the combinations were equal. Russell concluded that when the numbers are identical, asking the child which has more focuses his attention on irrelevant

Early Nirmber Concepts

PERCENTAGE ERRORSFOR

THE

145

TABLE X NUMBERCOMBINATIONS USEDB Y RUSSELL" Question type

Number combinations

Which has more? (Experiment A ) *

Are they equal? (Experiment B)

86 72 86 66 66 52 28 14 14 10

48 52 48 48 48 24 16 4 0 0

31 10 24 3 14 28 3 14

52 28 48 12 12 28 4 40 18 32 13

Identical 10-10 9-9 8-8 7-7 6-6 5-5 4-4 3-3 2-2 1-1

Different 9-10 8-10 8-9 7-10 1-9 7-8 6-8 6-7 5-7 5-6 4-5 3-5 3-4 2-4 1-5

-

10 I 3 3 3 3

3 -

-

0 Based on Russell (1936, Table 7 and 8, p. 206). With permission of author and publisher. '1 Dash indicates data not collected.

differences between the sets, e.g., color. The few errors made even for the 3-3, 2-2, and 1-1 combinations add support to the notion that some children took the question to mean they should focus on the differences. T o the extent that a child's performance reflects a lack of confidence, feedback should either improve or depress performance, depending on the nature of the feedback. Training studies that have investigated the effects of feedback lend support to the hypothesis that failure on a conservation task may be attributed in part to a lack of confidence. Children who failed to conserve on a pretest were more likely to conserve on a posttest given after a training phase which involved feedback to focus their attention on relevant features of the conservation problem (Bruner, Olver, Greenfield,

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et af., 1966; Gelman, 1969a). Similarly, training procedures which provide explanations of the conservation principle also enhance the posttest probability of conserving (Beilin, 1965; Smith, 1968). The estimation study described in Section 11, D may also be interpreted as showing that external sources which suggest another answer will influence children who lack confidence. Younger children in this experiment were les!j likely to respond to number in a 3 vs. 5 triad if they also were tested on 5 vs. 9 triads. Since younger children tend to judge the latter triads on the basis of length, those trials may serve to suggest length as the “correct” cue. A child who is not sure that the task requires responses based on number might shift his basis of responding in the face of such an experience. Older children are apparently more confident; the eflect of varying the magnitude of the arrays decreased with age, and second-grade children were not influenced at all by this manipulation. Where confidence is an issue, the opportunity to succeed at the beginning of a series of questions should affect subsequent performance. Without external feedback, the initial performance might set the pattern of responding. Zimiles (1966) found that the way in which children began to answer a series of related conservation tasks influenced the mode of responding to subsequent tasks in the series. If children were given first a number conservation task with three items in each array and then one with a larger number of items, they were more likely to conserve with both small and large arrays than if they were initially tested with large arrays. In the context of the present discussion, it can be argued that the small-large sequence maximized the likelihood of the children being confident that they were to respond to number per se. The previous section showed that 5-year-old children firmly base their estimates of arrays with three elements on number per se; however, arrays of nine tax their ability to do so consistently. Accordingly, children of this age should be more confident when confronted with small arrays than larger ones. Thus, starting a child on small arrays should increase his chances of confidently answering the initial question correctly. If so, this should increase his chances of continuing to do so for larger numbers, which, in isolation, present some problem for the child. Even though young children can be quite successful with smaller arrays, Zimiles found that they will not show even this limited capacity as readily on a problem that might shift their attention away from number. This suggests that the children have yet to develop complete confidence in their ability to work with even small numbers. Russell’s (1936) data are in agreement with this hypothesis. Table X shows that variations in Russell’s question form influenced performance. It can be seen that, in general, the larger the arrays, the greater the effect of the question variable. Still, even with small arrays, variations in the question form influenced performance, particularly for identical number combinations.

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This discussion of confidence is particularly relevant to the next section on operators. As will be seen, a test of operational knowledge involves repeated questioning over time. It has already been suggested that children fail to pass conservation tests because they lack confidence in their initial response. In considering alternate tests of operational knowledge, it would seem advisable to take steps that might maximize the young child’s confidence in his judgments. In summary, young children may “fail” number tasks because they lack confidence in their ability to negotiate the tasks. However, this factor may be of less importance in tasks involving small numbers, reinforcing our earlier suggestion to focus on the use of small arrays in studies of young children’s number operating abilities. Furthermore, in experiments in which it is desirable that children give a consistent performance, feedback techniques that buttress confidence can help serve this end.

IV.

Operators

Thus far, attention has been concentrated on the young child’s ability to abstract numerosity from an array of elements. At the beginning of the paper a distinction was made between operators and estimators, in part because it appears that the way a child estimates number may determine whether he shows competence for treating number operationally. It was suggested that whether or not a child behaves as if he has an invariance scheme for number will first depend on whether or not he estimates on the basis of number in a given situation. The research reported in this section was designed to assess whether children who estimate on the basis of number also possess number operators or a number invariance scheme. The presentation of this research is preceded by a section which expands the notion of operator that is used in this paper and provides a discussion of the nature of an operator test in conjunction with the relevant literature. A. MOREABOUT OPERATORS In general, the intervention of operators is inferred if an individual behaves as if he has considered an object or event in relation to the outcome of manipulations that can be or are performed on the object or event. With respect to number, we assume that operators mediate the ability to: ( a ) classify transformations of a set as relevant or irrelevant; ( b ) anticipate whether and how a particular manipulation will or will not change number; and ( c ) integrate perceptions from two or more successive presentations of a set (or sets) of elements through inferences about manipulations that change or do not change number.

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In general then, when an individual classifies events according to their effect on number, we postulate the use of operators. Further, we take as the fundamental feature of this classification the ability to distinguish between those events or manipulations which are relevant to number and those which are not. The presence of number operators not only leads to t’he classification of transformations and manipulations that are irrelevant: they also specify a complementary class of transformations and manipulations that are relevant to number, i.e., change number. Thus, for example, the operations of addition, subtraction, multiplication, and division belong to this complementary set because they are thought to change number. In contrast, the operations of rearrangement and displacement are classified as irrelevant because they are thought not to change number; the number of objects in a set is assumed to be invariant despite such manipulations. As Piaget has pointed out, a mature concept of number may be mediated by higher order operations which specify the relations among lower order operators. For example, the inverse operator specifies that subtraction reverses addition and vice versa. The reason for postulating the inverse operator is that adults can anticipate the effect of addition followed by subtraction and vice versa and can specify the manipulation required to reverse sorne previous transformation. Of the several manifestations of operators, the classification of transformations as relevant or irrelevant seems the most fundamental. Thus, the question of experimental interest is whether young children who estimate on the basis of number classify manipulations of sets as either relevant or irrelevant to number. Piaget (1957) and Flavell and Wohlwill (1969) acknowledged the possibility that very young children have some operators. Thus far, there has been no statement of what these might be and very little research that would help provide such a statement. The literature holds some suggestion that young children may understand the effects of addition and subtraction (see Section IV, B ) . But it is not known whether this understanding is part of an invariance scheme which classifies operations as relevant or irrelevant. One reason for the limited understanding in this area seems to be that tasks used to study operators are not suitable for preschool children. The following section takes up this problem in more detail.

B. METHODOLOGICAL CONSIDERATIONS Implicit in the above discussion of operators is an assumption that an individual can or does think about number in terms of transformations that are performed over time. This specifies the nature of the class of behaviors that can be used to support the postulation of operators: Those that indicate

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a subject is thinking about a given quantity at time? in terms of its status at time, and the events that have occurred in the interval. If, on a given test he behaves as if the events at time, and time? are independent, it cannot be determined whether he has taken into account the manipulations that have occurred in the interval. Thus, in order to infer operators one needs behavioral evidence that the subject is treating numerosity over time and in conjunction with what has happened or might have happened to the relevant set during the interval. A consideration of Piaget’s conservation tasks is in order here. They are the most widely used tests of the young child’s quantity operators and appear to meet the above criterion. In the number conservation task a child is initially (timel) shown two rows, one above the other, of N objects placed in one-one correspondence. The child is asked if the display represents an equivalence relationship with respect to number (e.g., “Does your row have as many as my row?”). Having acknowledged the numerical equivalence, the child watches as one row is transformed, e.g., lengthened, such that the perceptual relationship between the rows but not the numerical equivalence is altered. Then (time?) the child is asked if numerical equivalence still holds. Thus, the task structure seemingly meets the criterion outlined above for the assessment of operators. In fact, the child’s behavior may or may not be used to infer the presence of operators. He could treat the examples at time, and time? independently and take two estimates of the quantities. As has been argued above, the likelihood of his doing so may depend partly on the way he judges at time,-i.e., whether he does it on the basis of number-and on his confidence in his ability to negotiate the task. Further, as other investigators have argued, he may misinterpret the questions (Braine, 1959) or be distracted by various features of the task (Bruner et al., 1966; Gelman, 1969a; Wallach, Wall, & Anderson, 1967). All these considerations can be taken as forms of the general argument that the child might say that the quantities are different at time? because he takes the task to be two independent trials. If he does so, then we cannot decide whether or not he has operators. Failure to adopt the desired form of the task may or may not reflect his ability to operate on quantities. The suggestion of so many factors that could confound the assessment of young children’s operative knowledge implies that the task may be too complex and that simpler procedures might better assess the question of interest. Before considering what these may be, there is a further issue regarding the conservation task. What if the child does say the numbers are the same at timey? Can the presence of operators be inferred unambiguously? It appears not. The child could still treat both examples of the relationship as independent estimation trials. Or the child may be stating that the elements of the sets

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are identical rather than asserting a belief in the continued equivalence of the sets (Elkind, 1967). Insofar as the interpretation of the judgments is ambiguous here, further criteria are necessary for the positive inference of operators. In this light, the reason for Piaget’s insistence on verbal explanations becomes obvious. The child who says “They used to be the same,” “YOU haven’t added any,” or “You just moved them around” is clearly thinking of the original displays and the manipulations performed on them. T o the extent that a child can provide such statements, his data meet the criteria for inferring operators. Thus, good explanations become excellent data. The problem, however, is that the child must have sufficient verbal facility to give the investigator interpretable explanations. Young children may not be able to verbalize their understanding of the effect of transformations (Gelman & Weinberg, 1972). This simply adds to the variables already considered which confound the interpretation of the conservation task. It thereby lends support to the position that different operational tasks are needed for studies with younger children. Since children who pass conservation tasks often offer the explanation that no amount has been added or subtracted since time,, it can be concluded that these children possess addition and subtraction operators. The child who says that the amount is the same because neither addition nor subtraction has occurred is by implication telling us that he knows that the occurrence of these operations would indeed alter the quantity. Note that this type of assessment of addition and subtraction operators depends on the child’s saying what has not occurred. It points to the possibility that children might better display their understanding of addition and subtraction operations in tasks which involve actual demonstrations of them. Several studies show that children can respond correctly to the effects of addition and subtraction before they conserve (e.g., Smedslund, 1966b; Wohlwill, 1960). In a study designed to permit a scalogram analysis of number concepts, Wohlwill included addition and subtraction as well as conservation items. The former involved adding or subtracting a button from a row of buttons in front of the child, scrambling the resulting row, and asking the child to match the result with one of three test cards. Children passed this test more readily than the conservation task, which involved merely scrambling. Smedslund analyzed the ability of kindergarten and first-grade children to take account of the effects of addition and subtraction operations. He also assessed the children’s ability to conserve number. The addition/subtraction tasks involved establishing the equivalence of two sets placed side by side, covering the sets with boxes, and putting another element into one of the boxes or taking one out. After each addition or subtraction the child had to indicate whether both boxes had equal amounts or whether the left or right box had more. Each trial involved a series of

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three successive additions and/or subtractions performed on either the left or right box. Almost all children responded correctly to the first addition or subtraction on a three-item trial. That is, children could say which box had more after they witnessed either an addition or subtraction. In contrast, of 81 children, only 33 and 16, respectively, met the pre- and posttest conservation criteria of correct judgment and adequate explanation. The conservation training literature provides further evidence that children can pass direct tests of addition and subtraction operators before they solve conservation problems. Various investigators have postulated that children who fail to conserve benefit from training that involves addition and subtraction (e.g., Smedslund, 1961, 1966b; Winer, 1968). These procedures do not always induce conservation and are open to alternative interpretations (Beilin, 1971 ); but it is still of interest that the nonconserver, as assessed by pretests, is able to respond accurately during the training phase. This implies that addition and subtraction tasks which involve the clear demonstration of these operations are easier for young children than is the conservation task. Thus, the evidence suggests that children who d o not conserve still have some capacity to respond correctly to instances of operations of addition and subtraction. The research on addition and subtraction operators has been limited to children of four years and older. In fact, most of the subjects in the reported studies are five and older. Could the previously employed paradigms be used with still younger children to determine the developmental course of such operators? A consideration of the techniques shows the inherent difficulties of doing so. These techniques typically involve a child’s responding to a relationship between two arrays. Thus, for example, Smedslund’s procedure requires the child to keep track of the nature of the quantitative relationship and to indicate whether two arrays are equal or if one is more (less) than the other after addition or subtraction has occurred. Rothenberg’s (1969) work emphasizes the difficulty of such a procedure. The children are unlikely to use the critical words consistently. Some of Smedslund’s writings (Smedslund, 1966b) reveal the same problem. Wohwill’s procedure does not present the child with the semantic problem, but it involves a complex matching technique which frequently may be too difficult for very young children. The foregoing considerations led to a search for a task that would not require young children to keep track of a quantitative relationship and yet would meet the criteria outlined above in the discussion of what constitutes a test of operators. The use of surprise reactions as an index of cognitive capacity (Achenbach, 1969; Charlesworth, 1969; Shantz & Watson, 1970) seemed promising. In surprise studies, it is assumed that a surprise reaction occurs when a subject’s perception fails to conform with his expectations.

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Presumably, the expectation derives from and is camed over from previous experiences that are related to the unexpected perception. If so, behaviors which indicate a violation of expectancy might also indicate a subject’s efforts to integrate past and present experiences in terms of events that apparently must have intervened to produce the discrepancy. To the extent that this can be shown to be the case, reactions that reflect violations of expectancy are in the class of behaviors that can be used to assess operators. Magic shows suggest how to design a procedure that elicits surprise in order to study number operators. Magicians often perform tricks that involve violating invariance rules to produce surprise and mystification. Various reactions could be elicited if a magician worked with number. T o begin with, he would have to establish an expectancy for a number of objects, just as he does for a particular colored scarf. Then he would begin covering and uncovering the objects. Sometimes he might simply rearrange them. In this case, the change should go unnoticed or should be explained in terms of an hypothesized intervening event (e.g., “The objects s1ipped”)i and/or should be said not to matter because it did not alter the number. On another occasion he might surreptitiously change the number. He then would wait for the audience to notice the change, express surprise, and even say that he must have done something to the original display. Occurrence of these differential reactions would show the audience’s capacity to classify correctly operations that are relevant and irrelevant to number. These considerations led the writer to develop a number “magic” task which involves two phases. In the first, the expectancy phase, the child is given experience with a set of objects. In the second phase, the child is shown a transformation of this set, one produced by a surreptitious addition., subtraction, or displacement. It was reasoned that number operators could be inferred if the children were surprised by transformations produced by addition and subtraction but not displacement, and if the children gave concomitant responses postulating the intervention of some unperceived event. The procedure was deliberately designed to take into account the variables discussed throughout this paper. The procedure does not involve instructions that rely on the child’s comprehension of quantity words or phrases such as “same” or “same number”; it involves feedback and the child’s active participation in setting up trials in order to build the child’s confidence in his understanding of the task; and it involves small numbers so as to maximize the likelihood of the child attending to numerosity.

C. EXPERIMENTAL INVESTIGATIONS OF OPERATORS The studies reported here were designed first to determine whether young children have number invariance operators and second, whether the way

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in which a child estimates number affects his tendency to use number operators. The magic paradigm briefly described above was used. In some experiments children were tested with very small arrays whose numerosity they should be able to estimate; in other experiments the arrays were large enough that the children might not be able t o estimate on the basis of number. Two classes of surreptitious changes were introduced in Phase IT of all experiments. These were ( 1 ) the addition or subtraction of one element, and ( 2 ) the lengthening or shortening of a row. The question is how children react to these different classes of operations as a function of the magnitude of an array. In particular, will they treat the effects of these operations as relevant or irrelevant to number when they can estimate on the basis of number but not when they cannot make such estimates? 1. General Procedure of the Magic Experiment A detailed description of the procedure and design used in all of the following experiments can be found in Gelman (1972). In outline, the procedure involved two phases. The first built expectancies for two arrays of objects; the second assessed the child’s reaction to surreptitious changes in one of the arrays. The expectancy phase began with showing a child two plates, each of which had a row of toy green mice. The number of mice on each plate differed (e.g., 2 vs. 3 ) . The rows were either: ( a ) the same length, in which case a difference in density is redundant to the difference in number; or ( b ) the same density, in which case a length difference is redundant to the difference in number. While the child was looking at both plates and without mentioning the difference in number, the expcrimenter pointed to one of the plates (e.g., the 3-mouse plate) and said, “This plate is the winner.” Then the child was told that he and the experimenter would take turns hiding the plates under two large cans and mixing them up. After each covering and shuffling, the child was asked to guess which can was hiding the winner plate. He lifted that can and answered the question “1s that the winner?” If the child chose correctly and confirmed his choice, he was told so and given a prize. A new trial of covering and shuffling then began. If, however, he selected the loser and said so, he was then asked where the winner was and was allowed to look under the remaining can. A correct identification at this point was reinforced. A new trial then began. Whenever a child erred in response to the question about whether he had uncovered a winner, he was corrected, the display was covered, and the can were reshuffled. Each lifting of a can was counted as a trial in order to control for total exposure of the arrays.‘; On three of the trials the child was asked why a plate is a winner or loser. The essential features of the “ N o t e that this was not a shell game and the child was not required to keep track of the winner. Indeed, shuffling wits extensive to prevent this.

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procedure described so far were: (1 ) The child was never asked a question about number on the identification trials; ( 2 ) the child set up half the trials and therefore was involved directly in the game; ( 3 ) the child saw the equipment and both stimulus arrays, a condition designed to reduce the likelihood of children appealing to some unseen feature of the apparatus in Phase 11; and (4) the child was given feedback in order to induce confidence in his judgments. In most of the experiments, Phase I1 began after 10 or 11 trials (depending on whether the child uncovered a loser or winner on Trial 10). From the experimenter’s point of view, this involved covertly changing the winning display either by adding or subtracting a mouse or lengthening or shortening the row. From the child’s point of view, the onset of this phase was just another trial. The phase was brief. As soon as the child uncovered the altered display, be it on the first or second trial, he was asked if it was the winner. Overt surprise reactions were noted. The child was then asked why the display was a winner or loser; whether anything had happened, and if so, what; and how many mice were present now and before. Finally, he was asked if the game could be fixed and how. This was done to determine whether the children could undo or reverse any noticed changes. 2. Studies with Two- and Three-Item Arrays In the estimation study described in Section 11, D it was found that preschool children could consistently estimate on the basis of number when shown arrays with two and three items. Therefore, arrays of this magnitude were used in the lirst three “magic” studies. Two of these involved 3- to 6-year-old children and are reported elsewhere (Gelman, 1972). The third, with 28-year-olds was done after the reported studies were completed. The first two studies are summarized here to provide continuity in the more detailed description of the subsequent research. In all of the 2 vs. 3 studies the main design variable was the nature of the surreptitious change introduced in Phase 11. Half the children in each experiment witnessed the effect of surreptitious suhtraction or addition; the other half saw the effects of surreptitious displacement. The design also counterbalanced for the nature of the dimension (length or density) that was redundant in Phase I and for the locus (end, middle) of the addition or subtraction introduced or for whether the displacement consisted of lengthening or shortening. a. Experiment 1 . In Experiment 1 , 32 children at each of three age levels (3, 4, and 5 years) were assigned to one of two of the basic conditions, subtraction or displacement. In Phase I, the 3-mouse array was designated the winner and the 2-mouse array the loser. The surreptitious operations were performed on the winner plate.

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The answers to probe questions in Phase I indicated that children chose number as opposed to length or density as the relevant attribute of the sets. Almost all children in each age group gave number descriptions of the plates either in response to probe questions in Phase I or as soon as they saw the altered array. In Phase 11, 94% of the displacement children continued to identify the 3-mouse plate as the winner even though it was shorter or longer than it had been. In contrast, 69% of the subtraction children said the transformed plate lost; and the others either would not answer-the question as to whether the uncovered plate was a winner or vacillated between saying “yes” or ‘‘no.’’ These findings confirm the hypothesis that the children would abstract numbers of the magnitudes used. The critical question of interest is whether they reacted to Phase I1 as if they treated number as invariant. This question is answered by analysis of the reactions and verbalizations for the particular transformation a child saw. Ninety-four percent of the subtraction subjects were judged to show surprise.? Only 27% of the rearrangement children were so judged. All children in the subtraction condition noticed the change and 80% searched. I n contrast, only 52% of the displacement children noticed the change and none searched. The children’s verbalizations reveal that these differential reactions indexed an understanding of what relevant or irrelevant operation must have intervened. Of the children in the displacement condition who did notice the change, almost all suggested that the mice moved. Still, they said they won because the plate had three mice on it. Thus, even though they noticed and accounted for changes in length or density, they acted as if these changes were irrelevant. In contrast, when subtraction children who appeared doubtful about winning were asked what had happened, they said the plate now had two mice instead of three. Further, the majority of these children went on to say that a mouse had been removed. Thus, the children behaved as if subtraction changed number but displacement did not. Finally, an analysis of children’s responses to questions about how the game might be fixed showed that 77% of the children knew that addition reversed subtraction or that elongation and shortening reversed each other. Thus, not only can subtraction and displacement operators be inferred, but so can higher order inverse operations. b. Experiment 2. Children in Experiment 1 could reverse the effect of subtraction, suggesting that they knew that addition is an operation that is relevant to number. To provide direct evidence for this hypothesis the 7 Criteria for scoring surprise, noticing, search, and verbalizations can be found in Gelrnan ( 1972). As indicated there, the scoring was highly reliable.

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first experiment was modified by simply designating the 2-mouse plate the winner and replacing the subtraction condition with an addition condition. This experiment included 3- and 4-year-olds. Half the children were assigned to displacement conditions and half to addition conditions. Thus, in Phase 11, children either saw the row of mice on the winner plate displaced or they saw an extra mouse on the winner plate. The Phase I results were comparable to those reported for Experiment 1. The children identified the winner and loser on the basis of number. The Phase I1 results were also comparable. Surprise reactions occurred predominantly in the addition groups. All addition children noticed the change as opposed to only 38% of the displacement children. Children who noticed the changes could explain the nature of the operation that might have intervened; they postulated the operations of addition or displacement, depending on the condition they experienced. The children were also very likely to suggest or execute the relevant operation for undoing changes they noticed. Together, Experiments 1 and 2 provide evidence that children as young as 3 years of age have number invariance operators and can use the operators on small numbers which they can estimate. c. Experiment 3 . Experiment 3 was the same as Experiment 1 except that the subjects were 23-year-olds. Children were assigned to either a subtraction or displacement condition. The transformations were performed on the 3-mouse plate. A total of 21 subjects (median age, 2.7 years) was tested; 5 were excluded for failure to reach criterion in Phase I, leaving 8 children in each of the two basic conditions. The reason for working with children of this age derives from Descoeudres’ findings. As reported in Section 11, B, Descoeudres tested the ability of 29-year-olds to discriminate consistently between 2 and 3 item arrays on the basis of number. Only 26% of the 24-year-olds could do so; whereas 41-67% of 3-year-olds and 67-100% of 4-year-olds passed this test. On the basis of this finding, it was expected that 2i-year-olds would be less likely than the children in Experiment 1 to use number operators. Descoeudres’ finding can be interpreted to mean that 2+-years-olds are unable to estimate number on the basis of numerosity. As already indicated, a failure to estimate on the basis of number would predict a failure to use number operators. The Phase I data from the children in these experiments confirmed Descoeudres’ results in two ways. First, children in Experiments 1 and 2 seldom made an identification error in Phase I; they seldom failed to identify accurately an array as the winner or loser. When they did err, they always did so in the first half of the Phase I trials. In contrast, eight of the twenty-one 2+-year-olds in this experiment failed to reach a criterion of

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5 correct out of 6; and five of these children failed to do so again on a second day and were dropped from the experiment. Second, only five of the sixteen remaining children could accurately describe the winner and/or loser with respect to number. One of the nine who failed to refer to number did talk about the winner having a “middle.” The rest either gave irrelevant answers (e.g., “It just does”) or no answer at all to probe questions. The Phase I1 reactions of the 23-year-olds were like those of the older children in some respects but not others. Seven of eight subtraction children said the altered array did not win or expressed doubts about its status, whereas 6 of 8 displacement children continued to identify the 3-mouse plate as the winner. Further, six subtraction children as opposed to one displacement child were surprised by the change. The Phase I1 results differed from those reported for the older children in many ways. Only one subtraction child said there used to be three mice but there were only two now. None of the displacement children said they won because of the number. Of the 13 subjects who were judged to have noticed the change, only five made any kind of reference to an operation and none was able either to indicate how to undo the change or actually to undo it. The five children who gave some indication of attributing the change to an operation were all subtraction subjects. They included three of the five children who used number in Phase I and the one who talked about the winner as having a middle. They were also the only subtraction children who searched in Phase 11. The data from the estimation phase of the experiment (Phase I ) show that it is difficult for 24-year-old children to estimate the numerosity of arrays of two and three objects. Some children had to be dropped from the experiment without proceeding to the test of their operators (Phase 11). The test of operators in those children who solved the estimation task yields ambiguous data. It cannot be said with any confidence that these children possess number invariance operators. However, those children who showed the strongest evidence of utilizing number invariance operators were the best estimators in Phase I. In other words the data suggest that behavioral manifestations of the use of number operators are closely tied to the ability to estimate the numbers involved accurately and confidently. The less accurate and the less confident the child’s estimate of the numbers, the less evidence the child gives of using number invariance operators to integrate his perceptions of numerosity and manipulations of arrays. It might be thought that the ambiguous behavior of the 24-year-old children is attributable mostly to a general lack of verbal facility in children this young. Experiments with larger numbers and older children may indicate whether it is lack of verbal facility or lack of estimation ability that

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produces these results. Earlier research has shown that 3- and 4-year-old children have the verbal facility to give unequivocal evidence for the use of operators when shown arrays of two and three. If older children were found to respond to larger arrays as the 2&-year-olds did to 2 vs. 3 item arrays, the effect would seem to be attributable to number estimation difficulties rather than lack of verbal facility.

3. Experiment 4: A Study with Three- and Four-Item Arrays Beckmann’s and Descoeudres’ findings indicate that 3- and 4-year-old children may estimate arrays as large as 3 items on the basis of number, but have difficulty doing so with 4-item arrays. This happened particularly in 3-year-olds. Experiment 4 consequently included 3- and 4-year-old groups and 3- and 4-item arrays. Equal numbers of children from each age level were assigned to either a displacement or an addition condition. The 3-mouse plate was designated the winner. In Phase 11, the experimenter surreptitiously added 1 mouse to the 3-mouse plate or displaced (inward or outward) the original 3-mouse display. In all, thirty-two 3-year-olds and twenty-two 4-year-olds were tested, but sixteen of the 3-year-olds and six of the 4-year-olds were dropped from the experiment for failure to reach Phase I criterion (correct identification of the winner). The median age of the subjects dropped was 3.3 and 4.1 years in the respective age groups. The median ages of the retained subjects was 3.5 and 4.4 years. The need to drop some children indicates that the children in this experiment had difficulty learning to identify the winner and loser. It should be noted that before any children were dropped for failure to reach criterion, an attempt was made to train them in two stages. Stage I involved an extra 10 identification trials. Stage I1 involved what was thought might be an easy-to-difficult transfer situation (Lawrence, 1952). Children who failed to reach criterion after Stage I were brought back another day and tested on a 2 vs. 3 identification task. If they succeeded on this, they were once again given the 3 vs. 4 task for 10 or 1 1 trials. All children who succeeded after Stage I or I1 of extra training remained in the experiment; they were tested in Phase 11 as soon as they met the identification criterion. The training was effective to some extent, in that two of the 4-year-olds and nine of the 3-year-olds in the final sample had received some training. The responses to probe questions in Phase I corroborated the impression that the much greater difficulty of the 3 vs. 4 task reflected the children’s difficulty in estimating the numerosity of these larger arrays. With arrays of 2 vs. 3, 91% of the children in the previous experiments accurately described the winner and loser in terms of number. In the present experiment, only 62% of the 32 children in the final sample described the winner

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and loser in terms of number. Of the 10 who did not meet this criterion, 6 gave no answer to the probe questions or gave an irrelevant answer; 3 used number inaccurately (e.g., “One, two wins”); and 1 described the arrays with respect to their relative lengths. The difficulty with the identification task seems related to the ability to estimate on the basis of number. Of the 20 children who used number accurately in Phase I, only two needed extra training. Of the 12 who did not use number at all, or did so erroneously, 10 required extra training. Table XI provides a breakdown of children in the addition and displacement conditions in terms of the type of response they gave in Phase I. Eleven children in each condition gave accurate responses to number and five children in each condition did not. For the children in the addition and displacement conditions who used number accurately in Phase I, the effects were like those reported for Experiment 2 (2 vs. 3 arrays). All 11 addition subjects said the altered array was a loser or expressed doubt on this point. When asked why they lost or were not sure, they all said that there were four mice and there should be three. Nine of 11 said either that there was an extra mouse or that a 4-mouse plate had been substituted for a 3-mouse plate. For example, one 3-year-old said “There’s four, should be three. . . . We don’t need this mouse. . . . Take one off and make three.” As indicated in this protocol, these children could tell or show how the noticed transformation could be reversed. In contrast, all 11 displacement children who used number accurately in Phase I said they won. Nine said they did so because the array had 3 mice, although most of the children who seemed to notice the change (7 of 9) said that the mice had moved (together or apart). Finally, 7 of the 9 who noticed the change reversed it. These data, then, indicate that displacement children who estimated on the basis of number treated the operation of displacement as irrelevant to number. The protocol of D.L. (4.8) and E.B. (4.1) clearly illustrate this. In response to the question as to whether the transformed plate was the TABLE XI NUMBER OF CHILDREN I N ADDITION AND DISPLACEMENT CONDITIONS WHO DID OR DIDNOT USE NUMBER IN PHASEI ~~

~~~~~~

~~~

~

Phase I1 assignment Phase I response type Number: Accurate Number: Inaccurate Length Other

Addition

Displacement

11 1 1

11 2

3

3

0

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winner D.L. said, “Ya.” (“How do you know?”) “Cuz it has 3. . . . It’s too far back cuz I saw; The first time I saw it closer than it is. Like this.” (“How did that happen?”) “I think we shook them . . . .” And E.B. said, “Even if it’s mixed up it’s still 3.” (“How do you know?”) “Cuz 1-2-3.” Several analyses of the Phase I1 reactions of the 10 children who did not use number at all in Phase I, or did so inaccurately, indicate that these children did not treat number operationally. First, none of the five addition children in this group was surprised by the transformation, whereas two of the displacement children were. Second, whether children in the addition condition thought they won seemed to depend on whether the length changed. The two children in this condition who said they had won were in a condition in which one mouse was added to the middle of the row; two of the three children in conditions which involved adding a mouse to the end of the row said they did not win. Tn fact, one of the latter children said he did not win because “Both are the same size.” Third, although four of these five displacement children said the transformed plate was a winner, these children indicated that they thought length changes were relevant. For example, two children who saw shortened arrays said there were fewer mice: One 4-year-old said she was looking for another mouse and one 3-year-old said, “Maybe one went away.” Fourth, of these 10 children, only one clearly suggested the intervention of an operation that was relevant to the condition he was in. Fifth, none of the children was able to reverse, even those who seemed to suggest irrelevant operations to account for perceived changes between Phase I and IT. Finally, none of the children referred to numbers when asked why a display was the winner or loser in Phase 11. In sum, children who gave clear evidence of accurately estimating the numerosity of the initial arrays behaved as if they knew that the operation of addition and its reverse were relevant to number and that the operation of displacement was irrelevant. In contrast, children who failed to estimate on the basis of number or did so inaccurately failed to treat the operations of addition and subtraction as relevant or irrelevant to number. If anything, they may have behaved like Piaget’s subjects who failed to conserve and treated changes in length as critical to number. The results of this study support the hypothesis that whether or not a young child estimates on the basis of number predicts whether or not he will reveal the use of number operators. 4. Spontaneous Counting The protocols of children who treated number as invariant in the last experiment showed that a considerable number of them tended to coun’t

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out loud spontaneously. This led to a consideration of the possible role of counting in the magic experiments. As indicated in Section 11, B, Beckmann found that young children count more than older children when estimating. Further, there is a greater tendency of children to count when confronted with large as opposed to small arrays. On the basis of these findings, children might be expected to count in order to estimate the number of mice on the winner and loser plates in Phase I. Moreover, more counting should occur in children shown 3 and 4 item arrays than in those shown 2 and 3 item arrays. Aside from serving as an estimator in Phase I, counting might also be the process by which children determine whether their expectancy for a given number has been violated. Children who notice transformations may count in order to classify them as irrelevant or relevant with respect to number or in order to confirm a decision to do so. To assess these hypotheses, the protocols of children in Experiments 2 and 4 were examined. These experiments were selected for the analysis since the designs were the same with the sole exception that children in Experiment 2 saw 2 and 3 item arrays and children in Experiment 4 saw 3 and 4 item arrays. In both experiments, the covert operations of displacement or addition were performed on the array that contained fewer items. The age sample (3 and 4 years) was also comparable. When children described arrays in terms of number, they either labeled or counted. Labeling involved the use of a number name (“It’s got three”); counting involved the use of a sequence of number names (“One-twothree”). If a child who used number descriptions spontaneously counted out lound at least once within a phase, he was scored as a counter for that phase; otherwise he was scored as a labeler. A child who labeled and counted was scored as a counter for this analysis. Note that the assessment of the amount of counting is probably conservative in that a child was classified as a counter only if he counted out loud. Table XI1 shows the proportions of children in Experiments 2 and 4 TABLE XI1 PROPORTION OF CHILDREN I N EXPERIMENTS 2 A N D 4 WHOUSEDNUMBER ACCURATELY A N D EITHER LABELED O R COUNTED

Phase Experiment Experiment 2: 2 vs 3 Experiment 4: 3 vs.4

Type of Response

I

I1

Count Label Count Label

.42 38 .64 .36

.65

.35 .86 .I4

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who used number accurately and who were classified as counters or labelers in Phases I and 11. A comparison of the proportion of children who counted at least once during Phase I of Experiments 2 and 4 confirms Beckmann’s finding. There is a greater tendency to count given 3 vs. 4 item arrays than 2 vs. 3 item arrays. Table XI1 also shows that children in both experiments were more likely to count in Phase I1 than in Phase I. This suggests that children do count especially when confronted with information that may constitute a discrepancy from an expectation. This result is relevant to the hypothesis of Wohlwill ( 1966) and Bearison (1969) that measurement operations mediate the development of conservation. As Bearison pointed out, the child who is able to measure quantities can then determine on his own whether or not a transformed quantity is conserved. Insofar as measurement involves counting, the present results are consistent with the positions of Wohlwill and Bearison.

v. SUMMARY AND DISCUSSION This paper has dealt with some of the variables that must be taken into account in order to understand the nature of number concepts in very young children. The distinction between operators and estimators served to organize the research and discussion of these variables. Particular emphasis has been placed on the way in which the child’s ability to estimate accurately and with confidence interacts with his ability to understand quantity words, to attend to relevant or irrelevant features of a number task, and to use number operators. It was argued that one has to maximize the likelihood of a child’s estimating on the basis of number in tasks designed to study operator processes. Given the finding that young children estimate very small numbers consistently, magic studies to assess whether young children have invariance operators for numbers in this range were conducted. The results of the magic experiments show that, under some conditions, children as young as 3 years of age-and possibly 29 years-behave as if they know that a small number of items in an array remains invariant through the operations of displacement but not addition and subtraction. Moreover, given the same range of numbers, children this young can understand the inverse relationship between addition and subtraction. Still, it appears that young children apply this invariance scheme only to small numbers. These findings raise two questions. The first is whether these children have a concept of number. The second concerns the role estimators play in the development of mature number abilities. Do young children have a concept of number? They can abstract number

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from small arrays. They can infer that a change of number from 2 to 3 or vice versa must involve the addition of one item. They can classify the effects of a displacement operation as irrelevant to number. Surely, to some extent, they have a concept of number. These abilities indicate a complex categorization, one in which numbers are ordered, the numbers in a series are separated sequentially by a unit of 1, and sets that vary in length or density but contain the same number of units are classified in the same category. Moreover, the operators that treat addition and subtraction as relevant and displacement as irrelevant to number, and which assign an inverse relationship to addition and subtraction, constitute a number scheme that has some of the essential properties of axioms in the formal developments of arithmetic. Despite these conclusions, the young child’s notion of number has definite limits. One is that the invariance scheme applies only to numbers that are small enough for the child to estimate accurately and confidently. And, as reported elsewhere (Gelman, 1972), young children do not necessarily pass a number conservation task with three items. It has been suggested that the number conservation task is failed, not so much because the child lacks a number invariance scheme, but because he fails to understand the questions, lacks confidence, is readily misled, or shifts attention as he watches the transformations. But, since older children and adults do not have these difficulties with the task and are able, for example, to integrate their understanding of quantitative phrases with their number scheme, it still must be said that the number capacities of young children are limited. These, and other examples in Piaget’s work, reveal the limits of the young child’s application of the number scheme. There seem to be two possible interpretations of these discrepancies. The child may be said to have a complete concept of number but to fail to use it in most situations because of his limited estimating abilities. He thus may have a number scheme which, in principle, could be applied to larger numbers. This position implies that the child knows there are numbers which he cannot estimate. Alternatively, the young child’s number scheme may actually be incapable of dealing with numbers beyond a certain limit. The child may know only those numbers he can estimate, at least to some extent, and not recognize the existence of numbers beyond that limit. The writer is inclined to favor the second of these hypotheses. As Descoeudres reported, young children apparently fail to differentiate between numbers beyond a certain limit and instead classify them as “many.” Whichever interpretation is accepted, one faces the question of how the young child extends his concept of number to a wider range of situations. Our speculations on this issue derive from four observations about young children: ( 1 ) they know the effects of addition, subtraction, and displace-

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ment on a small set; ( 2 ) they know the specific effect of adding or subtracting one element to (from) small sets; ( 3 ) they tend to count when estimating numerosity; and (4) if they accurately estimate the numerosity of a set, they apply invariance operators to the same set. These abilities could serve as a base for the broader development of number. Children at a young age realize that 3 is generated from 2 by the addition of 1, and that 4 is generated from 3 by the addition of 1 . This points the way to the realization that larger and larger numbers can be generated by the continued iteration of the addition of 1. Since the child seems to realize that his number scheme can be applied to what he counts, the realization that he could count indefinitely large numerosities should lead to the generalization of his number scheme. This is not to say that the child actually has to learn to count indefinitely large numbers. Rather, what he must grasp is the principle that numbers are constructed by the continued addition of units and are in principle countable. This position is congruent with that of Gal’perin and Georgiev (1969), who postulated that “The concept of the unit has a special place in the formation of elementary arithmetic. All other numbers are built from the unit (by the formula n -+ 1) . . . [p. 891.” It also reaches its most general expression in the principle of mathematical induction. The above hypothesis suggests that an understanding of the development of estimators is central to an understanding of the development of number abilities. The ability to treat numbers operationally appears to depend on the ability to estimate numbers. What has been suggested about the way children expand their use of a number invariance scheme to larger numbers has implications for the more general problem of how children form other quantity concepts. In principle, all quantities may be rendered countable through measurement. Thus, for example, the application of a ruler to a length is a process that translates length into a countable number of units. Similarly, liquid quantities can be measured with a cup. T o the extent that quantities are rendered countable they may be handled by the number invariance scheme. Such considerations suggest that the number scheme is a central quantity scheme which facilitates the development of other quantity concepts. Further, it may be that the processes which enable the child to apply the number scheme in general are essentially those which render quantities countable. Insofar as the logic underlying measurement hinges on the under-. standing that quantities can be translated into units, the problem in development becomes one of learning to measure (cf. Wohlwill, 1966). The finding that children come to conserve number before other quantities (Inhelder & Sinclair, 1969) is consistent with this suggestion. So is the fact that Bearison (1969) was able to teach children to conserve liquid quantities by teaching them to measure liquids.

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As indicated at the beginning of the paper, the present approach to the analysis of the development of number concepts can, hopefully, be extended to other quantity concepts. On the basis of the foregoing, it can be suggested that insight into the nature of other quantity concepts may be gained from investigations of how children come to estimate or measure quantities and whether the operators children use to deal with other quantities are comparable or identical to the operators in their number scheme. REFERENCES Achenbach, T. M. Conservation of illusion-distorted identity: Its relation to MA and CA in normals and retardates. Child Development, 1969, 40, 663-679. Baldwin, B. T., & Stecher, L. I. The psychology of the preschool child. New York: Appleton, 1925. Bearison, D. Role of measurement operations in the acquisition of conservation. Developmetital Psychology, 1969, 1, 653-660. Beckmann, H. Die Entwicklung der Zahlleistung bei 2-6 jahrigen Kindern. Zeitschrift fiir Angewandte Psychologie, 1924, 22, 1-72. Beckwith, M., & Restle, F. Processes of enumeration. Psychological Review, 1966, 73,437-444. Beilin, H. Learning and operational convergence in logical thought development. Journal of Experimental Child Psychology, 1965, 2, 3 17-339. Beilin, H. The training and acquisition of logical operations. In M. F. Rosskopf, L. P. Steffe, & S. Taback (Eds.), Piagetian cognitive development research arid mathematical education. Washington, D.C.: National Council of Teachers of Mathematics, 1971. Braine, M. D. S. The ontogeny of certain logical operations: Piaget’s formulation examined by nonverbal methods. Psychological Monographs, 1959, 73, No. 5, Whole No. 475. Brownwell, W. A. The development of children’s number ideas in the primary grades. Supplemeritary Educational Monographs, 1928, No. 35. Brownwell, W. A. Arithmetic in grades 1 and 11: A critical summary of new and previortsly reported research. Durham, N.C.: Duke University Press, 1941. Bruner, J. S., Olver, R. R., Greenfield, P. M., ei al. Studies in cognitive growth. New York: Wiley, 1966. Buckingham, B. R., & MacLatchy, J. The number abilities of children when they enter grade one. In F. B. Knight (Ed.), Report of the society’s committee on arithmetic. Tweriry-ninth yearbook of the riatiorial society f o r the study of edrrcation. Bloomington, Ill.: Public School Publishing, 1930. Charlesworth, W. R. Surprise and cognitive development. In D. Elkind & J. H. Flavell (Eds.), Studies in cognitive development: Essays in honor of Jean Piaget. London and New York: Oxford University Press, 1969. Descoeudres, A. Le dhveloppement de I’enfarit de deux d sept ans. Paris: Delachaux & Niestlt, 1921. Douglass, H. R. The development of number concepts in children of pre-school and kindergarten ages. Journal of Experimental Psychology, 1925, 8, 443-470. Elkind, D. Piaget’s conservation problems. Child Developmenf, 1967, 38, 15-27. Flavell, J. H., & Wohlwill, J. Formal and functional aspects of cognitive development.

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In D. Elkind & J. H. Flavell (Eds.), Studies in cognitive development: Essays in honor of Jean Piaget. London and New York: Oxford University Press, 1969. Freeman, F. N. Grouped objects as a concrete basis for the number idea. Elementary School Teacher, 1912, 12, 306-314. Gal’perin, P. Y., & Georgiev, L. S . The foundation of elementary mathematical notions. In J. Kilpatrick & I. Wirszup (Eds.), Soviet studies in the psychology of learning and teaching of mathematics. Vol. I . Chicago: University of Chicago Press, 1969. Gelman, R. Conservation acquisition: a problem of learning to attend to relevant attributes. Journal of Experimental Child Psychology, 1969, 2, 167-187. ( a ) Gelman, R. The development of number concepts. Paper presented at the meeting of the Society for Research in Child Development, Santa Monica, Calif., March 1969. ( b ) Gelman, R. Logical capacity of very young children: number invariance rules. Child Development, 1972, 43, 75-90. Gelman, R., & Weinberg, D. H. The relationship between liquid conservation and compensation. Child Development, 1972, 43, 371-383. Grant, A. An analysis of the number knowledge of first-grade pupils according to levels of intelligence. Journal of Experimental Education, 1938, 7 , 63-66. Henry, D. E. Attention and cardinal-ordinal factors in the conservation of number. Unpublished doctoral dissertation. University of Minnesota, 197 1. Ilg, F., & Ames, L. B. Developmental trends in arithmetic. Journal of Genetic P ~ y c h o l ~ g y1951, , 79, 3-28. Inhelder, B., & Sinclair, M. Learning cognitive structures. In P. H. Mussen, J. Langer, & M. Covington (Eds.), Trends and issues in developmental psychology. New York: Holt, 1969. Laurendau, M., & Pinard, A. The development of the concept o f space in the child. New York: International Universities Press, 1970. Lawrence, D. H. The transfer of a discrimination along a continuum. Journal of Comparative and Physiological Psychology, 1952, 45, 51 1-5 16. Long, L., & Welch, L. The development of the ability to discriminate and match numbers. Journal of Genetic Psychology, 1941, 59, 377-387. McLaughlin, K. Number ability of preschool children. Child Education, 1935, 11, 348-3 53. McLellan, J. A., & Dewey, J. D. The psychology of number and its application to methods of teaching arithmetic. New York: Appleton, 1896. Mehler, J., & Bever, T. G. Cognitive capacity of very young children. Science, 1967, 158, 141-142. Neisser, U . Cognitive psychology. New York: Appleton, 1966. Piaget, J. The child‘s conception of number. New York: Norton, 1952. Piaget, J. Logique et tquilibre dans les comportements du sujet. In L. Apostel, B. Mandelbrot, & J . Piaget. Logique et tquilibre. Etudes dhpistitnologie ghnhtique. Vol. 2. Paris: Presses Universitaires de France, 1957. Piaget, J. Quantification, conservation, and nativism. Science, 1968, 162, 976-979. Piaget, J., & Inhelder, B. The child’s conception of space. London: Routledge & Kegan Paul, 1956. Potter, M. C., & Levy, E. I. Spatial enumeration without counting. Child Development, 1968, 39, 265-273. Reiss, A. An analysis of children’s number responses. Harvard Educational Review, 1943, 13, 149-162.

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Rothenberg, B. Conservation of number among four- and five-year old children: some methodological considerations. Child Development, 1969, 40, 383-406. Russell, N. M. Arithmetical concepts of children. Journal of Educational Research, 1936, 29, 647-663. Shantz, C. U., & Watson, J. S. Assessment of spatial egocentrism through expectancy violation. Psychonomic Science, 1970, 18, 93-94. Siegel, L. The sequence of development of certain number concepts in pre-school children. Developmental Psychology, 1971, 5 , 357-361. Smedslund, J. The acquisition of conservation of substance and weight: 11. External reinforcement of conservation of weight and the operations of addition and subtraction. Scandinavian Journal of Psychology, 1961, 2, 71-84. Smedslund, J. Microanalysis of concrete reasoning. I. The difficulty of some combinations of addition and substraction of one unit. Scandinavian Journal of Psychology, 1966, 7 , 145-156. (a) Smedslund, J . Microanalysis of concrete reasoning. 11. The effect of number transformations and non-redundant elements and some variations in procedure. Scandinavian Journal of Psychology, 1966, 7 , 157-163 ( b ) Smedslund, J. Microanalysis of concrete reasoning. 111. Theoretical overview. Scandinavian Journal of Psychology, 1966, 7 , 164-167. (c) Smith, I. The effects of training procedures upon the acquisition of conservation of weight. Child Development, 1968, 39, 5 15-526. Suchman, R. G., & Trabasso, T. Color and form preference in young children. Journal of Experimental Child Psychology, 1966, 3, 177-187. ( a ) Suchman, R. G., & Trabasso, T. Stimulus preference and cue function in young children’s concept attainment. Journal of Experimental Child Psychology, 1966, 3, 188-199. ( b ) Trabasso, T., & Bower, G. Attention in learning: Theory and research. New York: Wiley, 1968. Wallach, L., Wall, A. J., & Anderson, L. Number conservation: the roles of reversibility, addition-subtraction, and misleading perceptual cues. Child Development, 1967, 33, 153-167. Winer, G. A. Induced set and acquisition of number conservation. Child Development, 1968, 39, 195-205. Wohlwill, J. F. A study of the development of the number concept by scalogram analysis. Journal of Genetic Psychology, 1960, 97, 345-377. Wohlwill, J . F. The learning of absolute and relational number discriminations by children. Journal of Genetic Psychology, 1962, 101, 2 17-228. Wohlwill, J. F. Vers une riformulation du role de I’exptrience dans le dtveloppement cognitif. Psycliologie et Ppi.\tPmologie RPnltiques. TliPnies PiagPtians. Paris: Dunod, 1966. Woody, C. The arithmetical backgrounds of young children. Journal of Educational Rcsearch, I93 1, 24, 188-20 1. Zimiles, H. A note of Piaget’s concept of conservation. Child Development, 1963, 34, 691-695. Zimiles, H. The development of conservation and differentiation of number. Monographs of the Society f o r Research in Child Development, 1966, 31, No. 6.

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LEARNING AND ADAPTATION IN INFANCY: A COMPARISON OF MODELS'

Arnold J . Sameroff UNIVERSITY OF ROCHESTER

I . INTRODUCTION

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11 . INFANT CONDITIONING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A . CONDITIONING O F THE BABKIN REFLEX . . . . . . . . . . . . . B. CONDITIONED HEAD TURNING . . . . . . . . . . . . . . . . . . . . . . . C. CONDITIONED SUCKING BEHAVIOR . . . . . . . . . . . . . . . . . . .

170 171 171 177 181

I11 . PARAMETERS OF CONDITIONABILITY . . . . . . . . . . . . . . . . . . . . . A . ORIENTING REACTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. PREPAREDNESS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C . SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

191 192 195 201

IV . MODELS OF DEVELOPMENT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A . ORGANISMIC AND MECHANISTIC MODELS . . . . . . . . . . . . B . MODELS OF INFANT BEHAVIOR . . . . . . . . . . . . . . . . . . . . . . . C . GENERAL SYSTEMS THEORY . . . . . . . . . . . . . . . . . . . . . . . . . . D . OVERVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

202 203 204 207 209

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'Research reported in this paper was supported by grants from the Office of Education ( N o. 2-710381) and the National Institute of Mental Health (MH-16544) . The author wishes to thank Marshall Haith and Michael Davidson for their helpful editorial comments . 169

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I. Introduction The study of the infant has been often justified as an attempt to study the beginnings of behavior. Understanding the simple processes that one hoped to find in newborn behavior would put one on the road to understanding the more complex processes found in the adult. The reality of the situation has proved to be quite the opposite. No process found in the young infant has lent itself to an easy explanation. Infant behavior has proven to be as difficult to study and comprehend as adult behavior and researchers have been consistently perplexed at making sense of these complexities (Kessen, 1963). However, the complexity found in the newborn’s world works to the ultimate advantage of behavioral research. It acts as an important deterrent to the view that there is anything simple in psychological functioning, for the adult as well as for the infant. A basic flaw in the common sense view of the infant has led to the unfulfilled expectation of simple functioning. This erroneous view has been that infancy represents a beginning. Indeed, the case is quite the opposite. Infancy is not a beginning but only a transition from a predominantly physiological mode of functioning to a psychological one. To the extent that the psychological functioning of the infant has been isolated from its physiological context, to the same extent have researchers failed to make any sense of infant behavior. A clear example is the increasing importance that researchers have given to behavioral state as an overriding consideration in any study of newborn behavior (Hutt, Lenard, & Prechtl, 1969). The specific issue to which this paper will address itself is the learning abilities of young infants. An attempt will be made to show that the difficulties of research in this area stem from a faulty reductionism which tends to isolate the learning process from its complete behavioral context. The physiological context has been ignored in studies in which arousal state has not been controlled (Hutt et ul., 1969) and even the psychological context has been ignored in studies in which the nature of stimulation has not been taken into consideration (Sameroff, 197 1). Piaget (1960) has made a case for the unity of process of psychological and biological functioning. Rather than postulate new functional principles which suddenly come into play with the beginning of psychological behavior in infancy, Piaget extends the usc of processes already at work in the biological sphere. These “functional invariants” are the co-processes of assimilation and accommodation which are bound together in the organism’s adaptation to his environment. General systems theorists (Boulding, 1956; von Bertalanffy, 1967) have developed an approach which allows the behavior of the individual human

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to be viewed in the context of all living things. Organismic theorists (Werner, 1948) have continually made a case against isolating behavior, since out-of-context has proven equivalent to out-of-understanding. The general principles that govern the psychological functioning of human infants are not unique to either humans, infants, or for that matter, living systems (Gerard, 1957). Infant and especially newborn behavior represents only one point on a continuum of behavioral organization, anchored at one end in the initial biological activity of the single germ cell and leading to the group activity found in social organizations. The individual’s life itself is only one point in the broader scale of evolution. The overriding principle which regulates functioning in both the individual and the species is adaptation to its environment. Understanding any specific process, such as learning, will not be successful if the broader context is ignored (Seligman, 1970). On the following pages, the research on learning in early infancy will be reviewed. A contrast will be made between those studies which have proven successful and those which have led to questionable findings. The infant’s ability to perform separate components of the conditioning process will be discussed with special attention to stimulus variables. In the final sections, a theoretical position will be developed which places infant behavior in the broader context of the adaptation of living systems to their respective environments.

11.

Infant Conditioning

Sameroff ( 197 1 ) reviewed much of the literature on infant learning and raised serious questions about the newborn’s ability to be classically conditioned. The clearly negative results were concentrated in studies of aversive conditioning (Marum, in Lipsitt, 1963; Wickens & Wickens, 1940). More recent experiments with appetitive situations have yielded successful conditioning and these studies will be reviewed below. A. CONDITIONING OF THE BABKINREFLEX

Attempts at classical conditioning took a novel turn when Kaye (1965) reported conditioning of thc Babkin reflex in newborns. The Babkin reflex is a reaction to the simultaneous pressing of the palms of the hands of the infant (Babkin, 1960). It consists of opening of the mouth or gaping, turning the head toward the midline, and raising or flexion of the head (see Fig. 1 ) , It can also bc accompanied by closing of the eyes and flexion of the forearm. The response is viewed as a rudimentary reflex and has

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Fig. 1 . Babkin’s reflew in the newborn: Pressure on the palm causes opening o f the mouth (from Lippmann, 1958 with permission).

been observed in premature infants as small as 580 grams (Parmelee, 1963). Humphrey (1969) has elicited the reflex in utero as early as 14 weeks of gestational age. Kaye (1965) chose to use an arm-raise as a CS. He raised thc infant’s arms from the extended to the flexed position and then pressed the palms to elicit the gaping response. When the conditioned group was compared with a US control group that received only palm presses, the conditioned group showed more responses to the arm-raise during an extinction period when no palm presses were administered. Encouraged by these findings, Connolly and Stratton (1969) replicated Kaye’s study. In addition they went a step further and attempted, apparently successfully, to condition the Babkin to an auditory CS instead of the arm-raise. A number of my students became concerned that certain experimental issues were not fully dealt with in the Babkin conditioning studies and so resolved to investigate the phenomenon further (Sostek, Sameroff, & Sostek, 1972). The unresolved issues related to the nature of appropriate control groups, the neutrality of the arm-raise CS, and the effect of the infant’s behavioral state on the response. Kaye did not systematically control for responding to the CS alone, and did not control for pairing by the use of a noncontingent CS-US control group. While Connolly and Stratton did use a CS control, they also omitted a noncontingent CS-US control group. A random CS-US control seemed important in order to control for the total amount of stimulation provided in the paired CS-US group (Rescorla, 1967). In newborns the total stimulus picture assumes even greater importance

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because of the evanescent quality of the infant’s behavioral state. State has come to be seen as an important determinant of behavior patterns in the human newborn (Prechtl, 1969; Wolff, 1966). Neither of the Babkin conditioning studies recorded state throughout the experimental session although Connolly and Stratton took it into consideration for their auditory study. State changes in the neonate may play a large part in the acquisition of conditioned responses. Lenard, von Bernuth, and Prechtl ( 1968) found that-the Babkin reflex can be elicited only during irregular sleep or wakefulness. Papousek ( 1969) has noted the reciprocal relationship between state and stimulation during the course of conditioning. Sostek et al. (1972) repeated the Babkin conditioning study with the arm-raise CS using modifications designed to answer some of the unresolved issues. They included a random CS-US control group in addition to the traditional CS- and US-only controls. Both CS and US baseline measures were also taken to test for initial response to the arm movement as well as the palm press. In addition, systematic observations of state were made before each trial to investigate the effect of state changes on the infant’s responsivity and conditionability. The newborns were seen within 40 minutes after they began a feeding as in the earlier studies. Each infant received 60 trials divided into blocks of 5 with a 10-second intertrial interval. The difficulty in getting alert subjects at this age can be seen in that 24 infants were dropped from the study because of digestive problems, fussing, crying, falling asleep, or lack of Babkin response before 30 infants were found who could complete the procedure. The results did not replicate either the Kaye (1965) or Connolly and Stratton (1969) findings. In no subject was the rate of responses to the CS during extinction higher than the rate to the CS during the baseline period. Figure 2 shows the Babkin reflex responses to the stimuli given by the various groups. The decline in responding was the opposite of the result expected for learning and could be better explained as habituation or fatigue to the US. In the contingent CS-US group, the CS-only control, and the US-only control, the infant could only respond once per trial, but in the random CS-US group the subjects could respond twice, once to the US and once to the unpaired CS. Figure 2 shows responses to the CS in the random condition in a separate curve from the responses to the US. As a further test of the possibility of finding conditioned responses, two additional groups of subjects were tested for comparison with the paired CS-US group which received 40 conditioning trials. One of the new groups received 20 trials followed by a 5-trial extinction period, and the second group received 10 trials followed by a 5-trial extinction period. It was

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Fig. 2. Percentage responses f o r the contingent CS-US group and control groups. The responses to the C S in the random CS-US condition are indicated by a dashed line. Each point is an average of 5 trials f o r 5 Ss ( f r o m Sostek ei al., 1972; courtesy of the Society for Research in Child Development).

hypothesized that the more training trials, the stronger would be the conditioning effect. The conditioning-extinction cycle was repeated in the new groups until the last extinction period was the same as that for the 40-trial group in terms of total previous trials. Figure 3 shows that the number of training trials had no effect on the number of responses during extinction. There were no differences in number of responses in the extinction period following 10, 20, or 40 conditioning trials nor were there reliable differences between the three groups after the 40 trials. In addition, no

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subject in the new groups responded to the CS more during extinction than during the baseline trials. The increased responding to the CS found when “training” trials are compared with baseline trials is usually attributed to the effect of some kind of learning. However, in the typical newborn study, as can be clearly seen in Fig. 3, there is no incremental process in the increase in response rate, rather it appears immediately within the first block of training trials and remains relatively constant or decreases during the training period. The decrease in responding seen in Fig. 2 was associated with a decline in level of arousal from the first to last trial blocks. The behavioral state of the infants did play a role in their responsiveness. As a further indication of the relation between arousal and responsiveness the rate of response decrement was different for each of the treatments. Although somewhat obscured in Fig. 2, the response rates were directly related to the amount of stimulation inherent in each condition, the paired condition having the highest rate and the CS-only condition having the lowest. Classical conditioning of the Babkin reflex to arm movements was clearly not demonstrated in the Sostek et al. (1972) experiment. Contrary to the findings of Kaye (1965) and Connolly and Stratton (1969), no differences were found between the experimental and the control conditions during extinction. Response levels during extinction were generally lower than the baseline rates. The recording of behavioral state showed that response decrements found during the course of the experiment were related to changes in the infant’s state. In addition, those infants who received the most stimulation during training, the paired and random CS-US groups, produced the most responses, while those infants who received the least stimulation, the CS-only control group, produced the least. One of the striking results of this study was the finding that the arm movement was not a neutral CS for the Babkin reflex. Large individual differences in responding to the arm raise were found in the newborns. Since Connolly and Stratton did not include arm movement baselines, the lower level of responding they found in their CS control group may be accounted for by individual differences. Many infants were found who responded to the arm movement alone, and those who responded during baseline trials continued to gape during extinction. The fact that arm movements can elicit gaping is not surprising when it is realized that there is a close relationship between the innervation of the hand and the mouth (Peiper, 1963). In describing the development of hand-mouth reflexes, Babkin himself noted that the reflex that follows the Babkin reflex at about four months of age involves mouth opening to movements of the arm toward the mouth (Babkin, 1960). Although the exact nature of the subsequent reflex has not been clearly elaborated,

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raising the arms toward the head appears to be very similar to moving the hand toward the mouth. Babkin, in fact, paired palm pressing with raising the arms in order to elicit gaping during the period of transition between the two responses at about three months of age. The association between arm movements and mouth opening suggests a more general question : What is neutral stimulation for a developing organism? A stimulus which appears to be neutral at two days but which is linked with a specific response at four months cannot properly be used as a neutral CS. The developmental sequence of behaviors to be conditioned must be carefully studied before appropriate stimuli can be chosen for testing the learning abilities of newborns. Connolly and Stratton ( 1969) were aware of this problem in their study. They questioned whether the administration of the arm-raise CS might not have components of the palm-press US, resulting in a lack of functional independence. T o use a stronger test of conditioning they changed from the arm-raise CS to a white-noise CS, thereby separating more completely the modalities of the auditory CS and the proprioceptive US. They reported that they were as successful in conditioning the Babkin response to the white noise as they were to the palm press. Since Sostek et al. (1972) did not attempt to replicate the auditory conditioning portion of the Connolly and Stratton study, there can be no direct evidence to contradict their findings. However, Sostek et a / . did point out that as in the Connolly and Stratton arm-raise study, the auditory CS study did not contain the random CS-US control group nor a measure of CS baseline responses. Thus, as in the arm-raise study, their positive results might be due to differences in the baseline responsivity of the two groups or differences in the total amount of stimulation received by the two groups. Also their white-noise, CS-only control group gave virtually no responses during the conditioning trials, whereas in the previous palmpress study, the CS was able to elicit responses, further raising questions about the neutrality of the palm-press CS. Some issues emerge from the above discussion of recent attempts to condition the Babkin response. It is extremely difficult to defend a null hypothesis, such as that newborn infants cannot be classically conditioned. However, defense is made much easier by the fact that there are so many plausible alternative explanations which remain in studies of young infants where appropriate controls have not been used. The difficulties inherent in subject recruitment, finding subjects in appropriate arousal states and keeping them there, are so overwhelming that the investigator continually finds himself in the position of eliminating one group or another or continuing a simple study for a number of years to obtain a bare minimum of data.

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In order to make a strong case for any newborn behavior a study needs t o be replicated at least once before a base level of confidence in the results can be obtained. Connolly and Stratton were apparently faced with these issues since in each of their studies they found that they needed to change some of their experimental parameters. I n their last white-noise conditioning study, ( 1 ) they decided that the state variable had to be taken into account, ( 2 ) they cut the number of conditioning trials from 35 to 25, and (3) they presented the US immediately after CS onset instead of after 3 seconds, as in previous studies. Their change in CS-US interval is relevant to a persistent question in infant research. Although work with animals and human adults has traditionally found half a second to be the optimum CS-US interval, no one has used this interval in newborn research. The rationale has been that the newborn requires a longer time to “absorb” the stimulus. Perhaps, in shortening their CS-US interval Connolly and Stratton have demonstrated that the half-second interval is appropriate for newborns as well. i.e., that previous failures at conditioning have resulted from inappropriate CS-US intervals. Only further parametric investigations, however, will provide clarification of this point.

B. CONDITIONED HEADTURNING Attempts to condition head turning in infants have led to some of the most successful research on infants’ learning abilities but have also led t o confusion in judging the significance of these findings. The head turning paradigm was first described by Papousek in 1959 (Papousek, 1959). The US was a tactile stimulus to the side of the mouth; the U R was head turning, commonly called the rooting reflex. Typically, a n auditory stimulus has been used as a CS and paired with the tactile US. If the procedure ended at that point, it would be an example of a classical conditioning paradigm. However, when the infant turned his head to the US, he received a milk reinforcer. The addition of the reinforcer brings this procedure close t o an instrumental conditioning paradigm and converts the significance of the auditory stimulus from a conditional stimulus to a discriminative stimulus. To confuse the picture further. if the infant learned to turn his head to the auditory stimulus the tactile stimulus was not administered at all. Despite all these variations on standard themes, the essential bit of data is that the procedure seems to work (Papousek, 1961. 1967, 1 9 6 9 ) . Papousek was primarily interested in studying the course of the conditioning rather than the speed. His procedure called for the administration of tcn trials a day until the infant reached a criterion of five successive “correct” responses within a session. A correct response was defined as a head

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turn in the appropriate direction to the auditory stimulus. In newborns the criterion was reached in an average of 177 trials over three weeks of conditioning. The subject who conditioned most quickly required only one week of training (Papousek, 1967). Siqueland and Lipsitt (1966) adapted the Papousek procedure and did three studies to determine whether conditioning would occur in a single session during the newborn period. Initially, head turning will occur about one-fourth of the time to a perioral tactile stimulus. In their first study a buzzer presentation was followed by the tactile stimulus and a dextrose reinforcer. In the experimental group the dextrose reinforcer immediately followed a head turn to the tactile stimulus. In a control group the dextrose was given 8-10 seconds after the tactile stimulus, irrespective of response. In the control group the head turning rate remained at about 25% while in the experimental group, the rate increased after 30 trials to about 8 0 % . Papousek (1967) similarly reported that only 3 of 14 infants responded to the tactile stimulus in the first trial, while 3 to 22 trials were necessary before the remaining subjects would respond. Siqueland and Lipsitt ( 1966) found no evidence that the buzzer had any effect on the responding. The infants did not turn their heads to the presentation of the auditory signal but waited until after the tactile stimulus had been delivered. In their second experiment they used two auditory stimuli which signaled a tactile stimulus to either the right or left side of the mouth. The positive auditory stimulus was paired with a tactile stimulus eliciting head turning to one side, while on alternate trials the negative auditory stimulus was paired with tactile stimulation eliciting head turning to the other side. After training by reinforcing the response to the positive stimulus with dextrose solution, these investigators were able to show an increase of head turning to the stroke on the positive side and a decrease of head turning to the stroke on the negative side. Again, however, there was no evidence that the auditory stimuli played any role in the learning since the infants responded only after the differential stroking of the cheek to one side or the other. In the third experiment some evidence for differentiation of the auditory stimuli was demonstrated. They again used the buzzer and tone as positive and negative stimuli, presented alternately as in the previous experiment; but this time both were paired with a tactile stimulus eliciting head turning to only one side. When the positive stimulus sounded, the tactile stimulus was applied and if a head turn occurred the infant was reinforced with dextrose solution. When the negative stimulus sounded, the infant was stroked on the same side, but a head turn did not result in reinforcement. In this situation the infant increased his responding to the tactile stimulus following the positive auditory stimulus, while the stroke associated with

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the negative stimulus did not increase in effectiveness to eliciting head turns. The Siqueland and Lipsitt (1966) studies are interesting in that the last one showed the beginning ability of the infant to use auditory stimulation discriminatively, although in none of their studies was the infant able to make the response to the auditory stimulus alone. The auditory stimulus supplemented the tactile stimulus but could not replace it. Papousek (1969) attempted to use two auditory cues as discriminative stimuli as in the second Siqueland and Lipsitt study, but the auditory stimuli were both positive, signaling tactile stimuli to opposite sides. He found this procedure extremely difficult for newborns. At the rate of 10 training trials a day, it took the subjects an average of 814 trials to reach a criterion of S successive correct responses to the auditory stimuli. By that time they were four months old. In follow-up studies on the Siqueland and Lipsitt ( 1966) work (Clifton, Meyers, & Solomons, 1972a; Clifton, Siqueland, & Lipsitt, 1972b) several confounding factors were found in the original studies. As in the Babkin conditioning studies, a primary nuisance variable was the behavioral state of the newborn. Clifton et al. (1972a) used the head turning technique in an attempt to assess effects of medication during delivery on the infant's conditionability during the newborn period. They were surprised that they could not replicate the increase in responding to the tactile stimulus found by Siqueland and Lipsitt (1966). The experimental groups in their study never reached a response rate much over SO% and even this rate tended to taper off toward the end of the 30-trial session. Clifton et al. attributed the differences between their results and those of Siqueland and Lipsitt to a number of differences in cxperimental procedure. Instead of using spontaneously awake subjects as Siqueland and Lipsitt had done, Clifton et al. used a wake-up procedure and included initially drowsy infants in their study. They found that the infants that had been awakened tended to fall back asleep, depressing the average response rate of the group in the later part of the session. In addition, although Siqueland and Lipsitt used a perceptible head turn (So-10') as their criterion, Clifton et al. used a more stringent IS" as their criterion. Clifton c t al. felt that the stricter criterion might not permit an adequate shaping of the response and might be beyond the capability of newborn infants. To resolve the discrepancies between the two studies Clifton et al. (1972b) ran a third study with only spontaneously awake infants, in two different criterion conditions, a S o and a 15" head turn. Although the subjects in this last study were selected for being awake, many of them fell asleep or drifted in and out of drowsiness during the experiment. The results showed a clear relationship between state of wakefulncss and the probability of obtaining a positive response to the tactile stimulus. The

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difference in response criterion did not make a significant difference in the training. The investigators concluded that their results provided reliable evidence of conditioned head turning in newborn infants. However, it should be noted that their data (see Fig. 4) indicate that the differences in response rate between the experimental and control groups in their study appear during the first block of training trials and remain relatively constant across the rest of the conditioning blocks. As in the Sostek et al. (1972) study discussed earlier, the high level of response to the CS in the experimental group seemed to be already present in the first few trials. Sameroff (1968) found similar results in his attempt to condition components of sucking. He attributed this type of phenomenon to already built-in response systems rather than conditioning. What the Clifton et al. study seemed to demonstrate was that this built-in head turning response to the tactile stimulus is very sensitive to state variables. Prechtl (1958) made the point that only if the infant is awake and alert can the response be reliably elicited. Reinforcement does affect head turning, but the effect seems to be related more to maintaining the built-in reflexive behavior rather than to establishing it. The next section, on conditioned sucking studies, provides further elaboration of this point. Another study by Siqueland (1968) has shown how head turning can be manipulated. After going through all the complexities of working with the Papousek head turning paradigm, Siqueland (1968) simplified the procedure and attempted to use head turning as a free operant. Whenever a subject turned EXP. AWAKE

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his head 10" or more in any direction, Siqueland reinforced the response by giving the infant a nonnutritive nipple to suck on for 5 seconds. After 25 reinforcements a group of infants that had been reinforced for every head turn had increased its rate of response from 5 to over 18 responses per minute. In a second group that had been started on continuous reinforcement but shifted to a 3 : l schedule (every third response reinforced) for the last 15 reinforcements the head turning rate increased to over 25 responses per minute. As expected from the operant literature the intermittent reinforcement group showed slower extinction rates than the continuous reinforcement group. Siqueland included a third group of subjects who were given reinforcement only when they had held their heads still for 20 seconds. This last group showed a small decrease in the number of head turns during the training period. The success in getting the last group to reduce their head turning rate argues against the possibility that the results obtained in the first two groups could be a simple excitation effect of the nipple administration.

C. CONDITIONED SUCKING BEHAVIOR Among the problems of research with young infants has been the lack of reliable response measures that can be easily observed. One of the more commonly used measures has been sucking behavior. Since feeding is one of the more necessary animal functions, it is easily understood why it is considered to be the most highly organized behavior of the young infant. Kessen, Haith, and Salapatek (1970) have written a general review of newborn behavior. 1 . Classical Conditioning of Sucking Marquis (1931) observed 10 infants in conditioning sessions during the first 10 days of life. During each session a 5-second buzzer was followed by the insertion of the milk bottle into the baby's mouth. This procedure was followed throughout the feeding. Marquis felt that conditioning had occurred in that many of the infants were responding to the buzzer with sucking and mouth opening responses within five days. Wenger (1936) criticized the study because Marquis did not report any statistical analyses, used a subjective response scoring procedure, and omitted appropriate control groups. Using only two infants, he was unable to replicate Marquis's findings. More recently, Lipsitt and Kaye (1964) again attempted to study classically conditioned sucking behavior in newborns. The infants were seen for only one session within the first four days of life. For the experimental group a tone CS was followed after 1 second by insertion of a nipple into

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the infant’s mouth. After every 4 paired presentations, the US was omitted to test for the development of the conditioned response to the tone. A control group in which the tone and nipple were presented, but unpaired for each trial, was used as a comparison. Lipsitt and Kaye’s results are confusing because during the training period when the CS and US were paired the experimental group did not respond more frequently than the control group during CS-only test trials. The control group gave as many sucking responses to the tone as the experimental group (see Fig. 5 ) . Only during extinction did the groups begin to show a difference in responsivity to the CS. A fuller report of this study might be helpful in understanding these findings since it is possible that temporal conditioning could have occurred. Something seems to have happened to the infant’s performance related to the administration of the tone, even though it was not a clear cut conditioning phenomenon. Siqueland and Lipsitt (1966) had also found puzzling effects of auditory stimuli which their infants seemed to be able to sense yet could not respond to directly. Again, as in the Marquis (193 1 ) success followed by the Wenger (1936) failure to replicate, Lipsitt and Kaye’s (1964) complex findings were followed by more complex findings in a study by Clifton (1971). Clifton attempted to classically condition sucking to a tone CS. For an additional response she measured heart rate in her infants and tested for a conditioned heart rate response to the tone at the same time. She found no evidence of conditioned sucking responses during training nor during extinction. However, the course of the heart rate response showed a dramatic change. An 75 80 EXPERIMENTAL

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initial accelerative response to the tone CS dropped off during the training trials. By the last conditioning trial, there was no heart rate response to the tone CS. However, on the first extinction trial, when the CS was not followed by nipple insertion, a large heart rate deceleration occurred. It was as though the infants had learned to “expect” the US to follow the CS and were surprised when it was omitted. Clifton interpreted the heart rate response to be an orienting response to the absence of a stimulus. A summary of the attempts to classically condition the sucking response would not give strong support to the success of these attempts. Of the two studies that yielded positive results, the Marquis (1931) study seems the more clear cut. That she continued training for many sessions over 10 days would have given her subjects training equivalent to Papousek’s (1 967) infants who learned to turn their heads. The Lipsitt and Kaye (1964) and Clifton ( 197 1) studies require more complex interpretations, which will be left to a later section. It has been argued that because sucking is such a highly organized response in the newborn (Kessen, 1967), it is difficult to manipulate by experimental intervention. Seligman ( 1970) has described a number of prepared responses which are extremely conditionable because of their biological significance to the organism. In a later section it will be argued that sucking may already be conditioned to environmental stimuli in the human newborn. Therefore, all studies in which sucking on a nipple was the UR and anticipatory sucking without a nipple was the CR have some questionable aspects because of the prepotency of the sucking response in the hungry infant. Jensen (1932) has reported onset of sucking to squeezing the infant’s toe or pulling his hair. More recent evidence calls into question the neutrality of auditory stimulation in sucking studies since an unconditioned sucking response to onset of auditory stimulation has been found (Keen, 1964; Semb & Lipsitt, 1968). The prepotency of this response and the inability of the investigator to decide conclusively what elicited the response, when it occurs, was it the infant’s touching his tongue to his lips or merely touching the two lips together makes sucking a response requiring complex controls in studies of classical conditioning. 2. Instrumental Conditioning of Sucking The attempts to classically condition sucking behavior to novel conditional stimuli have led to complicated results. Studies of sucking in which reinforcement contingencies have been manipulated have led to more traditional outcomes and placed sucking in the category of operant behaviors that can be modified in the newborn period. Lipsitt and Kaye (1965) had noted that different oral stimuli varied in effectiveness in eliciting sucking behavior. Specifically, a nipple was a

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better elicitor of sucking than a rubber tube. Lipsitt, Kaye, and Bosack (1966) speculated that reinforcement of the weak sucking response to the tube should enhance its value as an elicitor of sucking. In an experimental group the tube was inserted into each infant’s mouth during IS-second trials, in the last five seconds of which dextrose was delivered through the tube. A control group received the tube insertion for the same period of time but no nutrient was delivered. Instead, an amount of dextrose equal to that received by the experimental group was inserted into the infant’s mouth during the intertrial interval. It can be seen in Fig. 6 that giving the dextrose increased the effectiveness of the tube as an elicitor of sucking. However, it can also be noted that the increased sucking occurred almost immediately in the first block of trials. During extinction the effects of the reinforcement procedure were immediately washed out. The same results were obtained during a reconditioning and second extinction period. Given the great difficulty found in attempts to classically condition responses in newborns, what can be said about conditioning that occurs so rapidly? It is not clear whether anything was indeed learned. The Lipsitt et al. data seem to show that the newborn infant has a great capacity for moderating his sucking behavior. The next series of studies reported below (Sameroff, 196Sa, 1968) attempted to separate out some of the variables involved in the infant’s sucking behavior and to determine which components lend themselves to the most rapid modification, that is, are most sensitive to reinforcement contingencies, and

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which components are less sensitive, that is, require prolonged training periods before they are modified.

3 . Conditioned Components of Sucking The operant conditioning paradigm offers an opportunity to observe how the infant is able to respond to the consequences of his behavior. T o the extent that he modifies his behavior, one gains information about both the infant’s ability to perceive the reinforcement and about the adaptability of the particular response system in question. Whereas most of the attempts to condition the sucking response, described above, have dealt with the total response, a better approach might be to make more detailed analyses of the infant’s sucking behavior and then attempt to modify specific components of the behavior (Sameroff, 1968). The more specific one becomes in defining a response measure, the greater the possibility of accurately identifying changes in performance. Two responses have been described for getting milk out of a nipple, “expression,” the squeezing of the nipple between tongue and palate (Ardran. Kemp, & Lind, 1958), and “suction,” the generation of negative pressure in the mouth (Colley & Creamer, 1958). These two components seemed to offer the opportunity to attempt differential conditioning within the organized sucking response. Bruner ( 1969 ) has subsequently relabeled the components positive and negative pressure. The new labels lose the important distinction between the positive physical pressure of the lips and tongue squeezing the nipple during the expression component, as opposed to the negative pneumatic pressure when the floor of the mouth is lowered creating a partial vacuum in the oral cavity during the suction component. However, there is some compensation in not having to make the confusing phonetic distinction between the suction component and the sucking response. An apparatus was devised to provide nutrient either when the baby performed the positive pressure (expression) component of sucking or when he performed the negative pressure (suction) component (Sameroff, 1965a). The recording of the negative pressure component and consequent delivery of nutrient were based on an earlier apparatus designed by Kron, Stein, and Goddard (1963). A nipple was constructed to record positive pressure and negative pressure independently. The nipple was attached to a milk delivery system which permitted the delivery of nutrient through the nipple as a consequence of either positive or negative pressure (see Fig. 7 ) . The delivery apparatus could be sct to operate in one of three modes. ( 1 1 A direct suction condition permitted nutrient to be delivered as a direct consequence of negative pressure applied to the nipple. The level of nutrient was adjusted so that no pressure differential developed. The

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amount of nutrient delivered was in direct proportion to the amount of negative pressure applied to the nipple and independent of squeezing pressure on the nipple (Kron et al., 1963). The nutrient delivery tube could be attached to a liquid pump which was operated whenever pressure exceeded an adjustable threshold. ( 2 ) In an expression threshold condition the pump operated whenever the positive pressure exceeded the threshold, 25 mm of Hg in the first study. ( 3 ) A suction threshold condition functioned similarly but the threshold was for the negative pressure component. Three studies were completed which included a variety of contingencies to evaluate the infant's ability to modify his behavior (Sameroff, 1965b, 1968). In each session, the first minute of sucking was nonnutritive, i.e., no milk was delivered through the nutrient delivery tube. During the next S-minute period, the infant was given milk under the appropriate response condition, direct suction or expression threshold in Study 1, high and low expression threshold in Study 2, and high and low suction threshold in Study 3. In Study 1 this 6-minute cycle was repeated, while in Studies 2 and 3, after the first nonnutritive minute the infant was fed throughout the session. The negative pressure component appeared to be almost invariably tied to the positive pressure component of sucking, i.e., the negative pressure component rarely occurred without a corresponding positive pressure component. In an examination of more than 25,000 responses, only two instances were found in which the negative pressure component appeared in

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the absence of the positive pressure component. In contrast, the positive pressure component was not so strongly tied to the negative pressure component. Exclusive of mouthing (the irregular, low-frequency, low-amplitude manipulation of the nipple in the mouth that appears as positive pressure in records of the sucking responses), a number of sucking responses occurred in which the negative pressure component was absent. If it were assumed that the infant functioned in the direction of maximizing the ratio of nutrient obtained to effort expended under the various conditions, certain expectations could be stated for the directions in which the components of the sucking response would be changed. In the direct suction condition one would expect the infants to use a greater negative pressure amplitude than in the expression threshold condition. Similarly, in the expression threshold condition one would expect the infants to use a greater positive pressure than in the direct suction condition. The question of whether the expected changes in response components would be the result of learning or the adaptation of already existing response abilities could be examined through several comparisons. Evidence for learning would be ( 1 ) greater difference between the direct suction and expression threshold conditions in the second feeding session than in the first, ( 2 ) greater differences between the direct suction and expression threshold conditions in the nonnutritive sucking period following the training period than in the one preceding the training period, ( 3 ) greater differential effect of restarting nutrient delivery during the second feeding cycle than during the first, or (4) increasing differences between the direct suction and expression threshold conditions during the feeding period. Evidence for adaptation would be ( 1 ) equality of differences in the second feeding session and first, ( 2 ) no differences between the direct suction and expression threshold groups during the nonnutritive periods, ( 3 ) no increase in differences during the second feeding cycle as compared with differences in the first feeding cycle, and (4) immediate occurrence of differences between the direct suction and expression threshold conditions, i.e., during the first minute of feeding, and no alteration by subsequent feeding experience. Most of the data did not lend themselves to a learning interpretation, i.e., ( 1 ) the differences between the two conditions were not greater in the second feeding session than the first, ( 2 ) the differences between the two conditions were not greater during the second nonnutritive minute than the first, and ( 3 ) there was no greater differential effect of restarting nutrient delivery in the second feeding cycle than during the first. However, there were some differences between the direct suction and expression threshold conditions which increased during the feeding period. For the expression threshold group a trend developed across the 5-minute

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feeding period in the ratio between the positive and negative pressure components. During the feeding period 90% of the expression threshold infants made some responses without a suction component, none did in the direct suction condition. Figure 8 shows the change in the ratio of number of negative pressure responses to the number of positive pressure responses as a percentage during the first 6 minutes of each session. In the second study infants were fed in an expression threshold condition for two feeding. During one feeding, a positive pressure threshold of 25 mm of Hg was required to obtain nutrient; during the other feeding, a threshold of 50 mm of Hg was required. Half the infants had the low expression threshold condition at the first feeding and half had it at the second feeding. The infants exhibited greater positive pressure amplitude in the high expression threshold condition than in the low expression threshold condition (see Fig. 9 ) . Although there was no initial difference between the positive pressure amplitude in the high expression threshold and low expression threshold conditions, the amplitude of the infants in the low expression threshold condition decreased during the feeding period, and the amplitude of the infants in the high expression threshold condition was maintained at the initial levcl. As in the expression threshold condition of Study 1 an analysis of the ratio between the negative pressure and

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positive pressure components of the sucking response showed that the ratio declined during the feeding period (see Fig. 8 ) . The third study (Sameroff, 1965b) was performed to test whether the infant is as sensitive to threshold requirements in negative pressure as he is in positive pressure. Infants were fed in two conditions, a high suction threshold condition where the required pressure was 100 mm of Hg and a low suction threshold condition where only a 50 mm of Hg response was required. Although the data were in the appropriate direction, they were not sufficiently reliable for strong conclusions (see Fig. 10). A different choice of threshold level might have produced larger differences between the conditions. The results of these investigations demonstrated that the newborn human infant can change his sucking behavior as a function of the consequences of his activity. Study 1 showed that the components of the sucking response can be influenced by varying the relation of the components of sucking to the delivery of nutrient. If nutrient delivery is directly contingent on the performance of the negative pressure component of sucking, the newborn uses more negative pressure than when nutrient delivery is not contingent on this component. If nutrient delivery is contingent on the positive pressure component, the ilzwborn performs the now unnecessary negative pressure

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component less often. Study 2 was designed to investigate further the positive pressure component of sucking. Again it was demonstrated that the infant exhibits a relatively high amplitude of positive pressure. When a When a strong positive pressure is required for the delivery of nutrient, the infant exhibits a relatively high amplitude of positive pressure. When a lower amplitude is sufficient to obtain nutrient, the infant exhibits a lower amplitude of positive pressure. Most of the effects found in the two studies seem to be the result of previously organized abilities of the newborn to adapt his sucking response. The differential training in the first session had no measurable influence on the performance of the sucking response in the second session. In Study 1 when differences between the groups occurred, the differences appeared within the first minute, remained constant until the nonnutritive period, in which they disappeared, and then reappeared during the first minute of renewed feeding. There were, however, two changes in performance that may have been the result of new learning, or new accommodations of the sucking response. In both studies, the linear function shown by the increasing inhibition of the negative pressure component during the expression threshold conditions and in Study 2 the change of positive pressure amplitude in the low expression threshold condition were different from the immediate changes found in the amplitude measures of Study 1. The fact that the response modifica-

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tions in the various studies did not persist from the first session to the second indicates that the new behaviors had not had the opportunity to stabilize adequately. Although longer training was not possible at the time of the present study because infants were available only during their two nighttime feedings, longer experience in the different conditions would seem an appropriate direction for future research.

111.

Parameters of Conditionability

The preceding review of the research on learning in newborns indicated that there were limitations on what could be achieved by the efforts of the investigator. The difference between the studies that have been successful and those that have been unsuccessful seems to lie in a distinction between attempts at instrumental conditioning as opposed to classical conditioning. The successful studies have made use of already existing organized patterns of behavior in the newborn. These patterns have included built-in associations between specific stimuli and responses. In the Lipsitt et al. (1966) study an already existing low sucking rate to an oral stimulus was enhanced. In the Sameroff (1968) studies already existing positive and negative pressure components of the sucking response to oral stimulation were modified. In Siqueland’s (1968) operant conditioning of head turning, an already existing organized component of the rooting-sucking-feeding complex was modified. Sucking and head turning in the human newborn seem to have the characteristics of what Seligman ( 1970) has called “prepared” responses. He hypothesized that the evolution of a particular species has affected the associability of various CSs with various USs, and various responses with various outcomes for that species. This position will be elaborated in a later section. The immediate implications of Seligman’s view, given the evidence of the research reviewed above, is that the infant is prepared for instrumental conditioning but not for classical. What, then, is required for an infmt to be classically conditioned that is not also required in the instrumental paradigm. In both paradigms the initial response to be made is in the repertoire of the organism, but, in the classical situation, the response must be made to a stimulus which has previously not been associated with that response. Herein seems to lie the newborn’s inability to be conditioned, an inability to form associations to a new stimulus. However, prior to the question of the infant’s ability at association is the question of his ability to perceive the stimulus at all, or, more basically, the infant’s ability to respond to changes in stimulation.

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A. ORIENTING REACTION The study of perceptual abilities in the newborn has utilized a series of indicator responses, such as nonnutritive sucking (Haith, 1966; Sameroff 1967) movement (Kessen, 1967), visual orientation (Salapatek & Kessen, 1966), and heart rate (Graham & Jackson, 1970). The single response systems typically used have been given some generality by being organized under the rubric of orienting or defensive reactions (Sokolov, 1963). “Reaction” is used here to describe a complex of separate responses. Orientation has been indexed by a quieting of general behavior which permits the organism to attend to the environment. Typically, the reaction has involved slowing of heart rate and respiration and cessation of gross activity. In addition, there is activation of perceptual systems, i.e., turning of sense organs toward the source of stimulation, and activation of the EEG, i.e., desynchronization (Lynn, 1966). Sokolov (1963) has argued that orienting to a CS is a prerequisite for conditioning to occur. Others (Zeaman & House, 1963) have implicated the ability to attend to relevant stimuli as being necessary for learning. If the human newborn does not orient to the stimuli used in conditioning studies, then the failure of attempts at classical conditioning becomes understandable. Sameroff (1971) reviewed the research on the newborn’s ability to orient and found that in general the evidence was positive. However, one autonomic indicator of orienting, heart rate, seemed to respond in a contrary fashion. Studies of the cardiac response have typically revealed acceleration to stimulation instead of the deceleration which typically accompanies adult orienting behavior. The failure to find heart rate deceleration in newborns has been attributed to a number of causes. Graham and Jackson (1970) have implicated the state variable as one that has been frequently overlooked in studies of orienting behavior. If the subject is asleep, it would be difficult to demonstrate attentional behavior. Lewis, Bartels, and Goldberg (1967) had shown that there were distinct differences in cardiac response in infants, 2 to 8 weeks of age, when their heart rate was measured in different states. A number of the subjects showed some deceleration to a tactile perioral stimulus. The typical response to auditory stimulation is a monophasic acceleration lasting some 3 to 7 seconds (Jackson, Kantowitz, & Graham, 1971). Graham and Jackson suggested that this accelerative curve might be the characteristic newborn response to stimulation when asleep. If awake newborns were used, the typical deceleration heart rate response of adult orientation might be found. Jackson er af. (1971) proposed that in addition to the state variable not enough attention has been paid to the type of stimulus used in these studies. They pointed to both the high intensity and fast rise times of the auditory stimuli used to elicit

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newborn reactions as causes of the acceleratory response. The use of lower intensity and slower rise-time stimuli might lead to the deceleratory response. When the three variables, behavioral state, rise time, and intensity of stimulation, were taken into account in a series of recent experiments, the heart rate deceleratory response typical of orienting behavior was found in human newborns. A beginning success was reported by Jackson et al. (1971), who presented moderate auditory stimuli (50 and 75 db) with relatively slow rise times to awake infants. Using these procedures they did not find the monophasic accelerative heart rate responses typical of earlier studies. However, neither did they find an unambiguous decelerative response. Jackson et al. concluded that the question of newborn orienting was still open. Kearsley ( 197 1 ) studied eye-opening and cardiac responses of awake infants to auditory stimuli which varied in frequency, intensity, and rate of stimulus change. He found that rate of stimulus change was the most potent of the variables. When rise times were instantaneous, the predominant responses were eye-closing and heart rate acceleration. When rise times were long (2000 msec) , the predominant responses were eye opening and heart rate deceleration. Kearsley concluded that level of wakefulness and the dimensions of the stimulus energy were important if the infant were to demonstrate his full range of response capacities. Sameroff (1971 ) argued that in addition to state and intensity variables, the quality of the stimulus is important in determining the infant’s response to it. Orienting should be expected when the infant can make use of cognitive structures, previously organized through experience, in attempts to adapt to the stimulus input. Clearly, sleeping infants could not do this. Nor could infants adapt to high-intensity fast-rise-time stimuli which acted to disrupt ongoing behavior. The defensive reaction characterized by heart rate acceleration can be viewed as an indicator of behavior interference, a disorganization of adaptive mechanisms. Kearsley’s (1971 ) finding of eye closure accompanying heart rate acceleration underscores the defensive nature of the acceleratory response. Sameroff proposed that the decelerative heart rate response might be found if low intensity stimuli that had elicited components of orienting behavior in other studies were investigated. Patterned visual stimuli seem to fit the requirements since visual orientation to these stimuli has been demonstrated in a number of studies (Salapatek, 1968; Salapatek & Kessen, 1966). In a recent study Sameroff, Cashmore, and Dykes (1972) measured the heart rate response to visual stimuli. State of the infants was well controlled since an awake condition was a necessary prerequisite for the visual test. A checkerboard with one-inch squares was presented to newborns in random alternation with a plain white field for 10 trials. Whenever the infant

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opened his eyes a stimulus was presented for 10 seconds. The nature of the stimulus condition was determined by a second experimenter who was unaware of the condition of the infant’s eyes. The results showed a large heart rate deceleration to the patterned stimulus (see Fig. 11 ) and no response to the control stimulus. The monophasic decelerative curve troughed between 5 and 6 seconds after stimulus onset and was similar in shape to that reported for adult orienting reactions (Graham & Jackson, 1970). The time course of the response to the visual stimulus is difficult to relate to that found by other investigators using auditory stimuli. I n the case of the auditory stimulation the point in time when onset occurs is quite definite. For the visual stimuli, onset was determined by the infant’s looking at the stimulus. Open eyes do not necessarily imply looking at the stimulus. As a result onset could be delayed by several seconds so that the averaged time course shown in Fig. 11 could be an overestimate of latency to maximum response. Rise time was also dependent on when the infant looked at the stimulus. Anecdotally, the investigators noted that heart rate decelerations of over 20 beats could often be detected and that these seemed to be related to scanning movements of the infant’s eyes. The combination of an awake infant and a moderately intense, moderately complex, visual stimulus appears to have resulted in the heart rate deceleration characteristic of the orienting reaction. Another example of the role of quality of the stimulus in orientation was described by Malcuit and Clifton ( 197 1 ) . Presenting auditory, vestibular, and tactile stimuli to sleeping or awake infants before and after a feeding, they found complex interactions among these variables. Heart rate deceleration was found under several combinations of the stimulus, state, and feed-

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ing variables. The investigators concluded that, whereas the acceleratory response was quite easy to elicit in newborns, the deceleratory response was limited to a small range of special stimulus and state conditions. Kearsley’s (1971 ) data also showed differences in direction of response when whitenoise was compared with pure-tone stimuli. From the preceding discussion it appears that four factors are associated with the ability of the infant to respond to a stimulus: the intensity of the stimulus, the rate of stimulus change, the quality of the stimulus, and the behavioral state of the infant. With the appropriate combinations of these factors, moderate intensity, slow rise time, and an awake state, the infant can orient to the stimulus. Given the ability for orientation to occur, the next step for the infant being conditioned is to make some use of the stimulus. He must associate it with the required response. There must be a change from a generalized reaction to the stimulus, i.e., orientation, to a specific response to the stimulus, i.e., the conditioned response. The infant’s required differentiation of response from the general to the specific is related to what has been loosely called above the quality of the stimulus. A more specific meaning must now be given to this stimulus dimension. What is meant by quality is a function of previous experience with the stimulus, both in the phylogenetic sense of Seligman (1970) and in the sense of the ontogenesis of the individual infant. This next problem the infant faces in his attempts at association can be related to the distinction between a “neutral” stimulus and a “new” stimulus. Classical conditioning has been defined as the association of a previously neutral CS with the non-neutral US. An additional problem in newborn conditioning is that a neutral stimulus is also a new stimulus. How many newborns have had previous experience with electric shock or acetic acid vapors or even bells or buzzers? Since from the studies described in this section it would seem that the newborn can respond to general changes in stimulation, the first hypothesis related to his inability to be classically conditioned seems disconfirmed. The next hypothesis to explain his inability could be that the newborn is unable to respond differentially to the specific stimuli that have been used in studies of early classical conditioning. To elaborate this hypothesis one must move away from the empirical base of the preceding two sections and explore some theoretical issues in the next section.

B. PREPAREDNESS Seligman (1970), in a discussion of the generality of the laws of learning, described what he called the “general process learning theory.” The basic premise is that “the choice of CS, US, and response is a matter of

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relative indifference, that is, any CS and US can be associated with approximately equal facility [p. 4071.” Seligman then went on to argue against this position, stating that these general laws might be only a subset of the laws of learning, functioning only in very arbitrary situations. Indeed, he proposed that it is not the case that the choice of CS, US, or response are matters of indifference, but rather learning will occur only when the right choices are made. A similar argument against the general process view of learning was made by Breland and Breland (1966). Certain species are more prepared to associate certain stimuli with certain responses, while others are more prepared to associate other stimuli and responses. For each species there is a dimension of preparedness running from responses that can be associated with any stimulus, to those that can be associated with none. Seligman (1970) cited the work of Garcia and his collaborators (Garcia & Koelling, 1966), who found that rats were prepared to associate taste stimuli with illness, but exteroceptive stimuli could not be associated with illness. Pigeons quickly learn to peck lighted keys for food but it is very difficult to train them to peck to avoid shock (Hoffman & Heshler, 1959). Seligman suggested that the associability of various combinations of stimuli and responses among different species is an outcome of each specie’s evolutionary history. The laws of the “general process learning theory” function only in the context of the preparedness dimension for each species, and are, therefore, only a subset of the laws of learning. The phenomenon observed in studies of newborn conditioning can be interpreted within the context of the preparedness notion. Even though the newborn human can orient to stimuli, he may be unprepared to associate them with the required responses. Yet, the difficulties at conditioning do not seem to be a species problem. As the infant gets older he is able to make the associations he was unable to make as a newborn. The head turning which could not be conditioned to auditory stimuli in newborns (Clifton et al., 1972a, 1972b; Siqueland & Lipsitt, 1966) could be conditioned a few weeks after birth (Papousek, 1967). Little (1971) conditioned eye-blink responses to a tone CS in lo-, 20-, and 30-day-old infants. After 50 training trials she was able to increase the level of CRs to 20% in the 10-day-old group. Something must have occurred during the first weeks after birth which permitted the eventual success of conditioning. The infant was more prepared after a few weeks to learn to turn his head in response to an auditory stimulus. This something might best be called experience. If experience is viewed in a larger context than the ontogenetic history of an individual, to include the phylogenetic history of a species, then preparedness can be seen as a function of total experience. According to this

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view, various species are differentially prepared for associating certain stimuli because of differences in the evolutionary experience of the species. Similarly, various infants are differentially prepared for associating certain stimuli because of differences in their life experience. It should be appreciated that the newborn infant has had very little experience with the typical CSs used in conditioning tasks. Although the CS is a neutral stimulus for the adult, it is a new stimulus for the newborn. It is quite possible that the infant must be experientially prepared before he can associate a new stimulus in the typical conditioning studies described earlier. 1. Prerequisites of Conditioning What then is the prerequisite for the classical conditioning of the newborn? The infant must be prepared to associate the CS with the US and response. The preparation takes the form of experience with the stimulus. The existing “unconditioned” bond between the US and the UR can be seen in a broad sense to be prepared by the evolutionary history of the species. The intended bond between the CS and CR must be prepared by the life history of the infant. A program can be devised to test the above formulations about newborn learning. The first stage is to find stimuli that elicit orienting behavior in the newborn. The newborn would then be given experience with these stimuli, after which they would be used as CSs in conditioning tasks. In our laboratory, the search for stimuli to which the infant will orient has led us to visual stimuli (Sameroff et al., 1972). However, the giving of experience has proven to be a more difficult problem. The major difficulty has been to index the experience a newborn has with a given stimulus. Although the numbzr of times a stimulus is presented can be easily determined, the number of times the stimulus is received by the infant is another question. One of the major paradigms for determining the infant’s experience with a stimulus has been the habituation procedure. If some response is monitored while a stimulus is repeatedly presented and a diminution of that response occurs, evidence is obtained that the infant has made some use of his experience with the stimulus. Kessen et al. (1970) and Jeffrey and Cohen (1971 ), in extensive reviews of the literature on habituation studies in infancy, concluded that habituation is not readily obtained in newborns. They suggested that one of the major complicating factors which may be obscuring habituation is the instability of the infant’s state of arousal. In addition, the stimuli used in habituation studies have generally led to responses that appear to have more components of a defensive reaction than an orienting reaction. If the infant is not awake, it would be difficult for him to attend sufficiently to the stimulus to gain experience

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from it. If the stimulus elicits a defensive reaction, then the infant is avoiding it rather than gaining experience from it. Both of these factors would tend to limit severely the infant’s experience with the experimental stimuli.

2. Response Changes in the Newborn Period In an attempt to study changes in the infant’s response to stimulation during the first few days after birth, a group of newborns was observed during the first four days (Sameroff, 1970a). On each day they were stimulated during a 20-minute session with a series of auditory stimuli which varied in intensity and pattern. The four stimuli used were a constant 65 dB tone, a 65 dB tone that was alternately on and off at 500-msec intervals, a 65 dB tone that was alternately on and off at 250-msec intervals, and a constant 75 dB tone. Background sound was approximately 55 dB. The infants were seen for four sessions just before a feeding at 24-hour intervals, the first of which took place about 24 hours after birth. Respiratory and nonnutritive sucking responses were recorded. The infants were awake at this time and generally alert. The state criterion used was that the infant had to be sucking continuously at the nipple. When an infant begins to fall asleep, his nonnutritive sucking declines in amplitude until only slight lip movements are observed and then after about 6 0 seconds the sucking movements stop altogether. If sucking is continuous and of constant amplitude, the infant can be judged to be in a fairly awake state. Because of close ties between sucking and respiration rates (Peiper, 1963), it was important to stimulate the infant each time at the same point in the sucking cycle so that trials with the various stimuli could be compared. Therefore, stimulation was made contingent on the onset of a sucking burst. Nonnutritive sucking occurs in a pattern of bursts of about 5-20 sucks lasting about 7 seconds and followed by a no-sucking interval of approximately equal length (Sameroff, 1967). For each trial, stimulus onset occurred after the first two sucks of a sucking burst. An analysis of the sucking data showed that stimulation tended to shorten the duration of the sucking burst in which it occurred, but there seemed to be no difference in the effect produced by the four stimuli, neither were there any strong changes in response across the four sessions. The respiration data did show differences in response to the stimuli and also changes in response across the four sessions. When the respiratory rate following stimulus onset was compared with the respiratory rate during the preceding sucking burst when no stimulus was presented, an increase in rate was found. However, this increase declined between sessions and by the fourth session had become a decrease (see Fig. 12). When the responses to the individual stimuli were analyzed, differences in direction were found on all days. Increase in respiratory rate occurred to the constant 65 and 75 dB

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tones, while a decrease in rate occurred to the alternating 65 dB, 250-msec tone. The response to the alternating 65 dB, 500-msec tone fell in between (see Fig. 1 3 ) . Sameroff (1971) hypothesized that the differences in direction of change of the respiratory rate could be related to the difference Lynn (1966) had described between the orienting and defensive reactions. If defense was

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associated with increases in respiratory rate and orientation with decreases, then the infants were showing a change across sessions from defense to orientation in their response to the auditory stimulation. The difference in response to the various stimuli also could be interpreted as a difference between defensive and orienting reactions. The greatest increase in respiratory rate was associated with the most intense stimulus, 75 dB. The decrease in respiratory rate was to the alternating 65 dB, 250-msec stimulus. It is difficult to separate out the effects of patterning from intensity in the latter stimulus. It would be appealing to attribute the infant’s orientation to the complexity of the alternating stimulus, but since it was only on 50% of the: time it had a lower total intensity level than the constant stimuli. It would appear, then, that there was some evidence for changes in response in newborns as they get more experience with auditory stimuli in the first days after birth. To investigate further the effect of repeated auditory stimulation Sameroe (1970b) used the same stimuli as in the above study but presented them serially for 120 sec periods. The infants were seen for three sessions, before a feeding at 24-hour intervals while nonnutritive sucking and respiration were recorded. The use of a no-tone 55 dB background noise condition permitted some separation of the effects of intensity and patterning of the randomly presented stimuli. When respiratory rate in breaths per minute was calculated for each stimulus period and averaged across the three sessions, a positive relation was found between intensity and respiratory rate (see Fig. 14). However, when the data were separated for the three sessions, a complex interaction was found. The respiratory rate for the first 12 seconds following stimulus

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change was compared with the rate for the 12-second period preceding the change (see Fig. 15). In the first two sessions, the largest increases in respiratory rate were associated with the quickly alternating stimulus; but in the last session, there was a slight decrease in rate to these stimuli. I n contrast, the response to the more intense 65 and 75 dB constant tones increased across sessions. The second study replicated the earlier one in showing changes in the size and even direction of response after several days of experience with auditory stimuli. More detailed parametric studies would be necessary to evaluate the characteristics of the stimulus to which the infant is most sensitive, especially to separate the patterning from the intensity dimension. The nature of the changes in the infant’s response in these two studies is not clear. They do seem to be in line with what one would expect if the infant were gaining experience with his world, developing competence at differentiating among stimuli, and building the necessary cognitive structures which would allow him to interpret his stimulus inputs. It is possible that only after he has achieved this end with the stimuli to be used as CSs in conditioning studies, will he be able to form the associations necessary for a demonstration of classical conditioning.

C . SUMMARY Review of the research on learning in newborn infants shows no clear demonstration of classical conditioning. Reports of successful classical con-

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ditioning were contaminated by the lack of appropriate controls, especially as related to behavioral state. Most newborn research findings have been strongly influenced by the arousal state of the infants. It would appear that complex behaviors, such as learning and habituation, as well as the simpler phenomenon of orientation, require an awake infant. Studies of learning by Sostek et al. (1972) and Clifton et al. (1972a, 1972b), reviews of the habituation literature by Kessen et al. (1970), Jeffrey and Cohen (1971), and Hutt et al. ( 1969), and studies of orienting by Jackson et al. ( 197 1 ) and Lewis et al. (1967) have shown how state plays a significant role in the final data. Even with an awake infant, capable of orienting to various stimuli, there appears to be an additional parameter which must be taken into account, that of preparedness (Seligman, 1970). Species differ in the extent to which their evolutionary experience has prepared them to associate specific stimuli and responses. Similarly, individuals differ in the extent to which their personal experience has prepared them to associate specific stimuli and responses. For human infants, evolutionary preparedness appears to center around responses associated with feeding, rooting, and sucking. The head turning response (rooting) seems to be prepared for association with perioral stimulation (Papousek, 1967; Siqueland & Lipsitt, 1966), while the sucking response seems to be prepared for association with intraoral stimulation (Sameroff, 1968). The isolation of the “general process learning theory” from the individual’s phylogenetic and ontogenetic development arises from adherence to a particular fundamental model of development, the mechanistic one. The ignoring of the state variable can also be subsumed under the same mechanistic model because, although in its reductionist form it attempts to explain psychological functioning by appealing to physiological processes, in actuality it removes psychological functioning from its physiological context. The next section will explore in greater detail the influence of developmental models on the understanding of infant behavior.

IV.

Models of Development

Overton and Reese (1972) have explored the implications of the two models that have had the largest impact on developmental psychology, the mechanistic and organismic models. In general, a model is used to represent a body of empirical data because it is simpler and better organized than the data. The model aids in understanding and explaining the subject matter. However, in addition to being an aid to understanding the data better, a model causes one to see the data with a specific focus. A model fulfills a

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number of such functions. It establishes the basic categories for interpreting the data, including certain theoretical constructs while excluding others. At the same time a model acts to define the problems that should be investigated. Some areas of interest are legitimate to a particular model while others are irrelevant. Reese and Overton (1970) made the point that it is very important for the scientist to be explicit about his underlying model, at least to himself, since it influences both the selection and interpretation of research problems. AND MECHANISTIC MODELS A. ORGANISMIC

The model of most currency in the recent empirical history of research in infant development has been a mechanistic one. The basic metaphor for this model is that of a machine, with the universe, both inanimate and animate, represented as having machine-like properties. These properties are (1) that there are basic elements, pieces of the machine, whose interrelationships form reality and ( 2 ) that these elements are essentially reactive. The machine is inherently at rest and its activity is externally caused. These basic properties of the mechanistic model lead to certain theoretical consequences. From the developmental point of view, changes in behavior are the result of quantitative changes in the elements. Changes in structure which produce seemingly qualitative changes in function are in reality reducible to quantitative changes in the basic elements. Since the machine operates by external forces, its purpose can be viewed only as derived from the purpose of those external forces. Teleology is denied and is seen only as a confusing epiphenomenon whose mechanistic derivation has not yet been determined. Complete prediction of behavior is possible in principle. Since behavior is a resultant of specific elements responding to specific forces, only the quantification of this relationship need be achieved to permit predictability. The basic metaphor of the organismic model is the biological organism. The first major property that can be derived from this model is that elements cannot be taken out of the context of their organized structure. The function of a structure is neither interpretable from the nature of its constituent elements nor can it be understood in terms of the properties of these elements. The elements subserve the properties of the totality which they constitute, and the totality has properties which cannot be reduced to those of the elements. The second major property of the organismic model is that the organism is seen to operate on its own energy. Activity is inherent in the structure and is not required from external sources. Some of the theoretical consequences of these two properties of the organismic model are that teleology is possible and complete prediction of be-

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havior is impossible. Teleology has continued to be a theoretical bugaboo, even to those who given credence to its usefulness. For example, in genetics the organism’s growth has been seen as a predetermined expression of an inherent plan or purpose contained in the genes, a restatement of early preformistic notions. More recent views express a more clearly defined epigenetic process (Waddington, 1966). Teleology is seen as a compound function of an organism or structure acting in a specific environment which regulates its behavior. The notion of teleological regulation is probably the most difficult to grasp in current theorizing from an organismic viewpoint. If the organism or structures within the organism are seen to have activity as an inherent property, then it follows that complete prediction of behavior is not possible since it would require a knowledge of the internal condition of the organism at any point in time. Since activity means constant change there can be no such knowledge. From the developmental perspective the organismic model admits of qualitative changes in structures and these changes are related to qualitative changes in function. Changes in organization of the elements in a structure result in changes in the function of the structure. In contrast to the mechanistic model, where change can follow only from external causes, in the organismic model, change results from internal causes, ie., the self-organizing activity of the organism. Von Bertalanffy (1968) in his discussion of the open systems which characterize living organisms carried this argument one step further by stating that structural change is an inherent characteristic of any living system. The system is not only active but its activity causes constant reorganization in the structure of the system. The changes in internal organization are basic to the epigenesis found in organismic models of development. The epigenetic point is in strong contrast to the mechanistic view that change is only a consequence of external forces acting on the organism. The contrast between the mechanistic and organismic models is elaborated in much greater detail in the papers of Reese and Overton (1970), and Overton and Reese (1972), as well as in Langer’s (1969) book. B. MODELSOF INFANT BEHAVIOR To concretize the model issues as applied to infant behavior, one can place the experimental findings reviewed earlier in their model context. The mechanistic model has found a clear-cut expression in the behaviorism that had dominated experimental psychology for the first half of this century (Scheerer, 1954). Behavior consisted of basic elements, stimuli and responses, and the complex performances that characterize human activity could be reduced to these basic elements plus a few basic laws describing

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their interrelationship. These laws have found their expression especially in descriptions of the classical and instrumental conditioning paradigms. The assumed generality of these laws was such that the specific stimuli, responses, or organism were effectively irrelevant to their operation. The reactive basis of the mechanistic view would posit the individual as a passive structure which operates on a few basic principles, i.e., the laws of learning. Elements, the stimuli, act on the individual and are then related to other elements, responses, in determined ways. The organism is seen as a routing device for S-R connections (Sperry, 1969). Seligman (1970) has proposed that the generality of these laws of learning may not exist but rather the specificity of stimuli, responses, and species is the primary consideration. For the human infant, Seligman’s views seem appropriate. Only after the specific nature of stimuli and responses are taken into account d o the “laws” of learning come into play. I n the field of physics, Newtonian principles held sway for many decades because those principles provided a good approximation to the true state of affairs in physics. In a similar way, S-R principles have held sway in psychology because the laws of learning also provided a good approximation to the true state of affairs. When Newtonian principles were applied to the limits of the physical domain, the interstices of the atom and the expanse of the universe, they were found to be inadequate to interpret anomalous research data. The result was a fundamental change in physical theory. Kuhn (1970) has traced the history of a number of disciplines and shown how anomalous findings have led to the overthrow of a dominant major theory or “paradigm.” The new paradigm not only could explain the anomalies but in addition provided a better interpretation of the more general phenomena of the field. Segal and Lachman (1972) have suggested that the last decade in psychology might be considered to represent the beginnings of one of Kuhn’s paradigm changes. As researchers have delved into more complicated phenomena than the sensory-motor behavior of primates, they have been unable to interpret their perceptual, physiological, cognitive, or personality data in S-R terms. Each discipline of psychology has its share of anomalous findings. This review has been devoted to the anomalies found in research with human newborns. The emergence of a new paradigm in psychology has been prevented by the lack of an articulated general theory of behavior. Segal and Lachman (1972) note that “the student is not taught the details of the lenses through which he has to look.” They define these lenses as the concepts and methods a paradigm provides to view scientific data. Although they note that a scientist’s research flows from his particular point of view, they do not discuss these points of view in terms of specific

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underlying models of science. One of the factors that may influence the emergence of a new paradigm is a current shift in underlying models. In the last decade, the behaviorist approach to psychology with its underlying mechanistic view has lost much of its momentum, and an organismic model has come to permeate current thinking about development. The work of Werner (1948) and Piaget (1960) has been instrumental in changing the focus from the elements of behavior to the organization of behavior, at least in developmental psychology. Werner in his orthogenetic principle described the organism’s development as proceeding toward higher levels of organization. He pointed to the genetic parallelism in the operation of the principle in biological, cognitive, and cultural spheres. Piaget ( 1960) derived specific laws of operation from biological functioning and related them to psychological functioning. His functional invariants of adaptation and organization offered a model for relating psychological behavior to the principles of the basic biological development that accompanied it. The active organism property of the organismic model, as described by Piaget’s processes of assimilation and accommodation, made it incumbent to consider the specificity of the individual’s organization before predictions could be made about its response to the environment. Infant behavior from the organismic view can be understood only in terms of the level of organization of the infant’s cognitive system, especially as it effects his level of adaptation to his environment. The elements of the cognitive system, schemas for Piaget (1960), permit the infant to make sense of, i.e., assimilate, the stimuli found in his environment. The general schemas of activity, e.g., sucking, looking, and hearing, must become differentiated before the infant can make a differentiated response to specific environmental stimuli, e.g., a bell vs. a buzzer (Sameroff, 197 1) . The differentiation occurs through the infant’s experience with his environment. The similarity shown in the development of human infants can be attributed to the similarity of experiences to be gained from their environments. When novel experiences are created for the infant, major accommodations are necessary before adaption can occur. Such is the case when experimental attempts at classical conditioning occur. Novel, artificial contingencies are established in the environment to which the infant is expected to adapt in a short period of time. It is only after an extended accommodation to these contingencies that “criterion” performance can occur, as seen in Papousek’s (1967) studies. The newborn infant has not yet made the necessary accommodations and manifests an ability only for minor changes in his performance, as seen in the instrumental manipulations by Sameroff ( 1968) and Siqueland ( 1968). These qualifications on S-R theory are generally unnecessary when adult

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animals are studied because most of the major perceptual accommodations have already occurred. The minor ones involved in adapting to the experimental room or maze have been typically ignored as irrelevant to the basic learning situation. The emphasis researchers with an organismic orientation have placed on considering the individual’s level of self-organizing activity has provided an explanation for the newborn’s performance inadequacies not as functional deficits but as part of a developmental series involving a continuing interaction with his environment. The view of the infant shifts from one of incompetence to one of competence (Kessen, 1967) when it is realized that the infant is primarily involved in his own developmental growth and not the artificial situations created by the researcher. Behavioral state, which has been seen as a nuisance variable in much of the research reviewed earlier, is another example of the anomalous data which forces one to consider the limitations of current psychological paradigms. Piaget ( 1960) has shown the parallelism of adaptive functioning in the biological and psychological spheres, but has treated their structural elements independently. To gain an understanding of the state variable forces one to take the further step of studying the structural integration of biological and psychological functioning. A groundwork for such an integration may be found in the formulations of general systems theory.

c. G E N E R A LSYSTEMS THEORY Boulding ( 1 9 5 6 ) has described General Systems Theory as a level of theoretical model building which lies between the generalized construction of pure mathematics and the specific theories of the specialized disciplines of science. The demand for such a general model has primarily risen at the interfaces of the specialized disciplines, where an “interdisciplinary” movement has grown, as expressed in such areas as biophysics, biochemistry, social anthropology, and physiological psychology. One of the main objectives of such a theory would be to allow one specialist to understand relevant communications from another. Boulding suggested two complementary approaches to a generalization of science. The first approach would be to select certain general phenomena found in many different disciplines and to build general theoretical models relevant to these phenomena. The second approach would be to arrange the empirical fields in a “hierarchy of complexity of organization” of their basic units of behavior. Although the notion of hierarchies has generally been associated with an organismic view, the adherents of a theory of general systems base their formulations on a variety of philosophical models.

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The mechanistically oriented theorists have attempted to apply principles found in inanimate systems to animate systems. Rapoport and Horvath (1959), for example, felt that all teleologic phenomena can be reduced to non-teleologic behavior, in principle. However, they did not go beyond a cybernetic, feedback model and had little to say about the self-organizing properties of living systems. Ashby (1962) did focus on the self-organizing properties of systems but his model reduced each reorganization in a system to the action of an external operator on the system, which undercut the self aspect of self-organization. In contrast, organismicly oriented theorists have attempted to view nonliving systems as living systems with certain null parameters. Von Bertalanffy ( 1967) proposed that closed systems, e.g., servomechanisms, are open systems, i.e., self-organizing, with transport terms equal to zero, i.e., nondevelopmental. Von Bertalanffy (1967) has been quite forceful in his organismic interpretation of living systems. In fact, the living system is defined by its selforganizing quality. The hierarchical model applied to the universe of science by Boulding (1956) and von Bertalanffy (1967) argues for new principles of organization and functioning which appear at each level of the hierarchy. Boulding’s hierarchy runs from static frameworks through clocks, thermostats, animals, and social organizations, while von Bertalanffy’s hierarchy of linear, closed, and open systems interweave with Boulding’s units. The hierarchical step of concern to this paper is that from biological to psychological functioning, the dominating aspect of the newborn infant’s behavior. The focus of most recent psychological research has ignored both the biological precursors and context of infant behavior. The view that the simple “beginnings” of psychological functioning can be found has been the major stumbling block to an adequate understanding of newborn behavior. The distinction between biological and psychological functioning is a contrast between an organism which is tied to the “here and now” context of material exchanges with the environment and an organism that can extend itself in time and space to include information as a medium of exchange with its environment. Surprisingly, it has not been psychologists as much as physiologists, psychiatrists, and pediatricians who have posed the appropriate development problem of the newborn (Parmelee & Stern, 1972; Prechtl, 1965). They have addressed themselves to the emergence of wakefulness as a characteristic of human behavior. The research reviewed earlier has shown how investigators have finally come to see that state, and more specifically, wakefulness, which is taken for granted in the adult human, is of paramount importance in newborn behavior.

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One could propose a line of research which would tie these two trends together. It is a safe assumption at this time that an awake infant is necessary for psychological functioning found in learning and habituation. What is not clear is the role such psychological functioning plays in the development of the awake state. Birth represents a transition from an existence where space and time are for the most part irrelevant to the organism’s immediate local adaptation to its uterine environment to an existence where the spatial and temporal extensions of psychological experience become crucial to adaptive functioning. Sperry (1969) has made a strong case for viewing consciousness as an emergent property of neural functioning. Although accused of treating consciousness as a dualistic epiphenomenon (Bindra, 1970), Sperry ( 1970) tried to show the control exerted by conscious experience on neural functioning while at the same time showing the limitations imposed on consciousness by the properties of the neural substrate. Wakefulness in the newborn is the emergent property that will ultimately coincide with Sperry’s consciousness. Sperry saw ongoing central mechanisms as organizing consciousness around the input from the sensory modalities. The newborn stands near the beginning of this organizational process. Research in neurophysiology has sought the physiological basis of complex adult mental processes. The fascination of research on the newborn is that he is on the frontier where these complex mental processes are first emerging from their physiological base.

D. OVERVIEW Research on the human newborn has been devoted to a search for the beginnings of the behavior found in adulthood. The reductionist position of the behaviorist school has argued that the simple paradigms of classical and instrumental conditioning undcrlic all complex behavior (Bijou & h e r , 1961 ) . The search for prototypes of conditioned responses in the newborn has been relatively unsuccessful. Although instrumental behaviors can be manipulated, it appears that the newborn is unable to establish the association between a new stimulus and a response required for classical conditioning. I t can be argued that maturation of the associative process is necessary before classical conditioning can occur, i.e., the S-R connections that will compose psychological behavior. However, if one changes focus from a search for the initial elements of behavior to an investigation of the transition from a physiological organization of behavior to a psychological organization of behavior, other interpretations become available. General systems theory provides a model for relating biological to

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psychological functioning. Although Piaget ( 1960) has limited himself to abstracting the adaptive processes of biological functioning and applying these to cognitive development, systems theorists have fitted psychological processes into a hierarchy extending from atomic nuclei to social institutions. The self-organizing properties of the open systems described by von Bertalanffy (1967) move the organism in both phylogeny and ontogeny to higher levels of internal organization in response to environmental regulation. When newborn behavior is viewed in its biological context, the behavioral state of the infant changes dramatically in significance. Instead of being regarded as a nuisance variable, the differentiation of behavioral state becomes the central developmental characteristic of the newborn. The emergence of wakefulness provides the infant with the opportunity to extend his transactions with his environment from the material to the informational. The human newborn has been prepared by phylogenetic experience to cross the threshold from biological to psychological functioning. The emergent property of consciousness described by Sperry (1969) has its origins in newborn behavior. The psychological ontogeny of the individual infant requires him to make the cognitive adaptations which will eventually lead him to complex adult behaviors. It has been proposed that differentiated cognitive structures must develop before the infant can form the new associations required in classical conditioning (Sameroff, 1971). The way these structures are formed is through the infant’s accommodation to new perceptual experiences. In regard to the conditioning problem, these experiences must include the stimuli to be used as conditional stimuli in the learning procedure. It is only after these stimuli can be assimilated to emerging or existing structures that the coordination required in classical conditioning can occur. Since there are no ultimate truth criteria for the validity of a philosophical position (Reese & Overton, 1970), the choice of a developmental model is left to the individual scientist, The criterion of most relevance in such a choice is the usefulness of the model for interpreting the data in a given area. Viewing the newborn from a reductionist viewpoint would force one to conclude that the newborn is beset by the vagaries of unstable levels of arousal and is maturationally incapable of the associative process. However, when the newborn is placed in his organismic context, the vagaries of arousal are seen as the emergence of psychological from biological functioning, and the evolving associative capacity is seen as the outer aspect of the internal organization of new psychological experiences. T o this investigator, the latter view offers the parsimony and clarity traditionally claimed by the former.

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born infants. In H. W. Reese & L. P. Lipsitt (Eds.), Advances in child development and behavior. Vol. 4. New York: Academic Press, 1969. Pp. 127-172. Jackson, J. C., Kantowitz, S. R., 8: Graham, F. K. Can newborns show cardiac orienting? Child Development, 1971, 42, 107-121. Jeffrey, W. E., & Cohen, L. B. Habituation in the human infant. In H. W. Reese (Ed.), Advances in child development and behavior. Vol. 6. New York: Academic Press, 1971. Pp. 123-176. Jensen, K. Differential reactions to tase and temperature stimuli in newborn infants. Genetic Psychology Monographs, 1932, 12, 361-479. Kaye, H. The conditioned Babkin reflex in human newborns. Psychonomic Science. 1965, 2, 287-288. Kearsley, R. B. Neonatal responses to auditory stimulation: A demonstration of orienting and defensive behaviors. Paper presented at the meeting of the Society for Research in Child Development, Minneapolis, March 197 1 . Keen, R. Effects of auditory stimulation on sucking behavior in the human neonate. Journal of Experimental Child Psychology, 1964, 1, 348-354. Kessen, W. Research in the psychological development of infants: An overview. Merrill-Palmer Quarterly, 1963, 9, 83-94. Kessen, W. Sucking and looking: Two organized patterns of behavior in the human newborn. In H. W. Stevenson, E. H. Hess, & H. L. Rheingold (Eds.), Early behavior: Comparative and developmental approaches. New York: Wiley, 1967. Pp. 147-179. Kessen, W., Haith, M. M., & Salapatek, P. H. Human infancy: A bibliography and guide. In P. H. Mussen (Ed.), Carmichael's manual of child psychology. (3rd ed.) New York: Wiley, 1970. Pp. 2 8 7 4 4 5 . Kron, R. E., Stein, M., & Goddard, K. E. A method of measuring sucking behavior of newborn infants. Psychosomatic Medicine, 1963, 25, 181-19 1. Kuhn, T. S. The structure of scientific revolutions. (2nd ed.) Chicago: University of Chicago Press, 1970. Langer, J. Theories of development. New York: Holt, 1969. Lenard, H. G . , von Bernuth, H., & Prechtl, H. F. R. Reflexes and their relationships to behavioral state in the newborn. Acta Paediatrica Scandinavica, 1968, 55, 177-185. Lewis, M., Bartels, B., & Goldberg, S. State as a determinant of infants' heart rate response to stimulation. Science, 1967, 155, 486-488. Lippmann, C. Uber den Babkinschen reflex. Archiv fiir Kinderheilkunde, 1958, 157, 234-237. Lipsitt, L. P. Learning in the first year of life. In L. P. Lipsitt & C. C. Spiker (Eds.), Advances in child development and behuvior. Vol. 1 New York: Academic Press, 1963. Pp. 147-195. Lipsitt, L. P., & Kaye, H. Conditioned sucking in the human newborn. Psychonomic Science, 1964, 1, 29-30. Lipsitt, L. P., & Kaye, H. Change in neonatal response to optimizing and non-optimizing sucking stimulation. Psychonomic S c i c ~ c e ,1965, 2, 221-222. Lipsitt, L. P., Kaye, H., & Bosack, T. N. Enhancement of neonatal sucking through reinforcement. Journal of Experimental Child Psychology, 1966, 4, 163-168. Little, A. H. Eyelid conditioning in the human infant as a function of ISI. Paper presented at the meeting of the Society for Research in Child Development. Minneapolis, April 197 1. Lynn, R. Attention, arousal and the orientation reaction. Oxford: Pergamon, 1966.

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Malcuit, A,, & Clifton, R. The pursuit of the OR in the human infant. Paper presented at the meeting of the Society for Psychophysiological Research, St. Louis, November 197 1. Marquis, D. P. Can conditioned reflexes be established in the newborn infant? Journal o f Genetic Psychology, I93 1, 39, 479-492. Overton, W. F., & Reese, H. W. Models of development: Methodological implications. In J. R. Nesselroade & H. W. Reese (Eds.), Life-span developmental psychology: Metliodological issues. New York: Academic Press, 1972. Pp. 65-86. Papousek, H. A method of studying conditioned food reflexes in young children u p to the age of six months. Pavlov Journal of Higher Nervous Acfivity, 1959, 9, 136-1 40. Papousek, H. Conditioned head rotation reflexes in infants in the first months of life. Acta Paediatricn (Stockholm), 1961, 50, 565-576. Papousek, H. Experimental studies of appetitional behavior in human newborns and infants. In H. W. Stevenson, E. H. Hess, & H. L. Rheingold (Eds.), Early behavior: Comparative and developmental approaches. New York: Wiley, 1967. Pp. 249-277. Papousek, H. Elaborations of conditioned head turning. Paper presented at the XIX International Congress of Psychology, London, August 1969. Parmelee, A. H., Jr. The hand-mouth reflex of Babkin in premature infants. Developmental Medicine arid Child Neirrology, 1963, 5 , 381-387. Parmelee, A. H., & Stern, E. Development of states in infants. In C. Clemente, D. Purpura, & F. Mayer (Eds.), Maturation of brain mechanisms related to sleep behavior. 1972, in press. Peiper, A. Cerebral function in infancy anti childhood. New York: Consultants Bureau, 1963. Piaget, J . Psycliology o f inrelligcrice. New York: Littlefield, Adams, 1960. Prechtl, H. F. R. The directed head turning response and allied movements of the human body. Bekaviour, 1958, 13, 212-242. Prechtl, H . F. R. Problems of behavioural studies in the newborn infant. In D. S . Lehrman, R. A. Hinde, & E. Shaw (Eds.), Advances in the study of behavior. Vol. 1. New York: Academic Press, 1965. Pp. 75-98. Prechtl, H. F. R. Brain and behavioural mechanisms in the human newborn infant. In R. J . Robinson (Ed.), Brain arid early behavior. New York: Academic Press, 1969. Pp. 115-138. Rapoport, A., & Horvath, W. J . Thoughts on organizational theory. General Systems. 1959, 4, 87-91. Reese, H. W., & Overton, W. F. Models of development and theories of development. In L. R. Goulet & P. B. Bakes (Eds.), Life-span developmental psychology: Research and theory. New York: Academic Press, 1970. Pp. 116-154. Rescorla, R. A. Pavlovian conditioning and its proper control procedures. Psychological Review, 1967, 74, 71-80. Salapatek, P. Visual scanning of geometric figures by the human newborn. Journal o f Comparative and Physiological Psycliology, 1968, 66, 247-248. Salapatek, P., & Kessen, W. Visual scanning of triangles in the human newborn. Journal o f Erperiinental Child PsycholoLyy, 1966, 3, 155-167. Sameroff, A. J . An apparatus for recording sucking and controlling feeding in the first days of life. Psychoriornic Science, 1965, 2, 355-356. ( a ) Sameroff, A. J . An attempt at the modification of the suction component of nutritive sucking. Unpublished manuscript, University of Rochester, 1965. ( b )

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Sameroff, A. J. Nonnutritive sucking in newborns under visual and auditory stimulation. Child Development, 1967, 38, 443-452. Sameroff, A. J. The components of sucking in the human newborn. Journal of Experimental Child Psychology, 1968, 6, 607-623. Sameroff, A. J. Respiration and sucking as components of the orienting reaction in newborns. Psychophysiology, 1970, 7, 213-222. (a) Sameroff, A. J. Response complexity in human newborns. Paper presented a t the meeting of the Society for Psychophysiological Research, New Orleans, Novernber 1970. ( b ) Sameroff, A. J. Can conditioned responses be established in the newborn infant: 1971? Developmental Psychology, 1971, 4, 1-12. Sameroff, A. J., Cashmore, T., & Dykes, A. Cardiac deceleration during visual fixation in human newborns. Developmental Psychology. 1972, in press. Scheerer, M. Cognitive theory. In G. Lindzey (Ed.), Handbook of social psychology. Vol. 1 . Cambridge, Mass.: Addison-Wesley, 1954. Pp. 9 1-142. Segal, E. M., & Lachman, R. Complex behavior or higher mental process: Is there it paradigm shift? American Psychologist, 1972, 27, 46-55. Seligman, M. E . P. On the generality of the laws of learning. Psychological Review. 1970, 77, 406-418. Semb, G., & Lipsitt, L. P. The effects of acoustic stimulation on cessation and initiation of non-nutritive sucking in neonates. Journal of Experimental Child PsyC I I O I O ~ Y , 1968, 6, 585-597. Siqueland, E. R. Reinforcement patterns and extinction in human newborns. Journal of Experimental Child Psychology, 1968, 6, 43 1-442. Siqueland, E. R., & Lipsitt, L. P. Conditioned head turning behavior in newborns. Journul of Experimental Child Psychology, 1966, 3, 356-376. Sokolov, Ye. N . Perception and the conditioned reflex. New York: Macmillan, 1963. Sostek, A. M., Sameroff, A. J., & Sostek, A. J. Evidence for the unconditionability of the Babkin reflex in newborns. Child Development, 1972, 43, in press. Sperry, R. W. A modified concept of consciousness. Psychological Review, 1969, 76, 532-536. Sperry, R. W. An objective approach to subjective experience: Further explanation of a hypothesis. Psychological Review, 1970, 77, 585-590. von Bertalanffy, L. Robots, men and minds. New York: Braziller, 1967. von Bertalanffy, L. General sysferns theory. New York: Braziller, 1968. Waddington, C. H. Principles of development and differentiation. New York: Macmillan, 1966. Wenger, M. A. An investigation of conditioned responses in human infants. University of Iowa Studies in Child Welfare, 1936, 12, 7-90. Werner, H. Comparative psycholngy of mental dcveloprnent. Chicago: Follett, 1948. Wickens, D. D., & Wickens, C. A study of conditioning in the neonate. lournu/ of Experimental Psyclrology, 1940, 25, 94-102. Wolff, P. H. The causes, controls, and organization of behavior in the neonate. Psychological Issires, 1966, 5 , Whole No. 17. Zeaman, D., & House, B. J. An attention theory of retardate discrimination learning. In N. R. Ellis (Ed.), Handbook of mental deficiency. New York: McGraw-Hill, 1963. Pp. 159-223.

Author Index Numbers in italics refer to the pages on which the complete references are listed.

A Abraham, F. D., 48, 77 Achenbach, T. M., 151, 165 Adams, J. A., 72, 78 Ahammer, I. M . , 96, I 1 1 Ames, L. B., 131, 166 Anderson, L., 149, 167 Antonitis, J. J., 19, 28 Appel, J. B., 9, 10, 28 Archer, E. J., 48, 78 Ardran, G. M., 185, 211 Aronfreed, J., 61, 79 Ashby, W. R., 208, 211

B Babkin, C. S., 171, 175, 211 Baer, D. M., 209, 211 Baldwin, B. T., 112, 123, 165 Bakes, P. B., 96, 106, 107, 108, 109, Ill

Bartels, B., 192, 202, 212 Bearison, D., 132, 162, 164, 165 Beckmann, H., 122, 123, 129, 130, 131, 165 Beckwith, M., 119, 128, 165 Beilin, H., 146, 151, 165 Bernstein, B., 32, 78 Bever, T. G . , 119, 132, 166 Bialer, I., 77, 78 Bijou, S. W., 209, 211 Bindra, D., 209, 211 Birren, J. E., 96, I l l Blum, W. L., 49, 50, 51, 78 Bosack, T. N., 184, 191, 212 Roulding, K., 170, 207, 208, 211 Bousfield, W. A,, 103, 1 1 1 Bower, G., 142, 167 Brackbill, Y., 62, 78

Braine, M. D. S., 149, 165 Bravos, A,, 62, 78 Breland, K., 196, 211 Breland, M., 196, 211 Bresnahan, J. L., 45, 47, 49, 50, 51, 78 Brown, P. L., 25, 28 Brownwell, W. A., 119, 121, 123, 127, 130, 131, 165 Bruner, A,, 19, 28 Bruner, J. S., 145, 146, 149, 165, 185, 211 Buckingham, B. R., 121, 123, 126, 130, 165

C Campbell, B. J., 7, 10, 28 Carroll, J. B., 103, 111 Cashmore, T., 193, 197, 214 Cassirer, E., 83, 111 Catania, A. C., 4, 5, 20, 28 Charlesworth, W. R., 151, 165 Chotlos, J . W., 103, I l l CICment, F., 109, 111 Clifton, R., 179, 180, 194, 196, 202, 211, 213

Clifton, R. K., 179, 196, 202, 211 Cohen, J., 57, 78, 88, 1 1 1 Cohen, L. B., 197, 202, 212 Colley, J. R. T., 185, 211 Connolly, K., 172, 173, 175, 176, 211 Creamer, B., 185, 211 Cutts, D., 20, 28

D Descoeudres, A., 123, 125, 165 Deutsch, M., 32, 78 Dewey, J. D., 119, 166 Dews, P. B., 9, 28 Douglass, H. R., 130, 165 Dykes, A., 193, 197, 214 215

Author Index

216

E Eells, K., 33, 35, 79 Elkind, D., 150, 165 Epworth, A., 68, 78 Erickson, J. R., 56, 78 Erikson, E. H., 99, 111 Espenschadi, A. A., 62, 78

F Ferster, C. B., 4, 13, 23, 28 Flavell, J. H., 148, 165, 166 Fleshler, M., 196, 211 Fraisse, P., 88, 111 Frankmann, J. P., 72, 78 Freeman, F. N., 123, 127, 166

G Gal’perin, P. Y.,164, 166 Garcia, J., 196, 211 Garfield, E., 88, I 1 1 Gelman, R., 119, 132, 133, 135, 136, 142, 144, 146, 149, 150, 153, 154, 155, 163, 166 Georgiev, L. S., 164, 166 Gerard, R. W., 171, 211 Ginsburg, R., 56, 79 Girardeau, F. L., 24. 29 Goddard, K. E., 185, 186, 212 Goldberg, S., 192, 202, 212 Goodnow, J. J., 45, 5 5 , 78 Gordon, E. W., 32, 33, 78 Gormezano, I., 48, 77 Gough, M. G., 77, 78 Goulet, L. R., 96, 111 Graham, F. K., 192, 193, 194, 202, 211, 212 Grant, A,, 121, 166 Greenfield, P. M., 145. 146, 149, 165 Gregg, L. W., 55, 56, 78 Gruen, G., 62, 75, 78

H Haith, M. M., 181, 192, 197, 202, 211, 212 Hammack, J. T., 7, 10, 28 Heilbrun, A. B., 77, 78 Henry, D. E., 141, 166 Herdan, G., 103, 111 Herrnstein, R. J., 2, 9, 10, 28 Hess, R. D., 32, 78

Hilliard, J., 62, 78 Hiss, R. H., 9, 10, 28 Hoffman, H. S., 196, 211 Holland, J. G., 72, 78 Horn, G. L., 24, 29 Horvath, W. J.. 208, 213 House, B. J., 192, 214 Humphrey, T., 172, 211 Hutt, S. J., 170, 202, 211, 212

1 Ilg, F., 131, 166 Inhelder, B., 132, 164, 166 Ivey, S. I-., 45, 47, 78

J Jackson, J. C., 192, 193, 194, 202, 211 212 Jammer, M., 82, 11 I Jeffrey, W. E., 197, 202, 212 Jenkins, H. M., 25, 28 Jensen, K., 183, 212

K Kantowitz, S. R., 192, 193, 202, 212 Karp, J. M., 32, 7 8 Kass, N., 57, 78 Kaye, H.. 171, 172, 173, 175, 1x1, 182, 183, 184, 191, 212 Kearsley, R. B., 193, 195. 212 Keen, R., 183, 212 Kelleher, R. T., 23, 28 Kemp, F. H., 185, 211 Kennedy, D. B., 8, 9, 13, 29 Kessen, W., 170, 181, 183, 192, 193, 197, 202, 207, 212, 213 Kleinberg, J., 55, 7 8 Koelling, R., 196, 211 Krechevsky, I., 5 5 , 78 Kron, R. E., 185, 186, 212 Kuhn, T. S., 99, 112, 205, 212

Labouvie, G. V., 109, 111 Lachman, R., 205, 214 Lander, D. G., 17, 28 Lane, H., 22. 28 Langer, J., 204, 212 Lashley, K. S., 55, 78 Laurendau, M., 132, 166

Airtlior Index

Lawrence, D. H., 158, 166 Lenard, H. G., 170, 173, 202, 211, 212 Levine, M., 55, 56, 78 Levy, E. I., 119, 166 Lewis, M., 61, 79, 192, 202. 212 Lind, J., 185, 211 Lippman, C . , 172, 212 Lipsitt, L. P., 26, 28, 171, 178. 179, 180, 181, 182, 183, 184, 191, 196, 202, 211, 212, 214 Little, A. H., 196, 212 Long, E. R., 7, 10, 28 Long, L., 120, 166 Lynn, R., 192, 199, 212

M McCandless, B., 32, 79 McCarthy, D., 32, 79 MacLatchy, J . , 121, 123, 126. 130, 165 McLaughlin, G. H., 100, 112 McLaughlin, K., 130, 166 McLellan, J . A , , 119, 166 Malcuit. A,, 194, 213 Marquis, D. P., 181, 182, 183, 213 Mathers, R. A , , 83, 112 May, F.. 7, 10, 28 Meeker, M., 33, 35, 79 Mehler, J . , 119. 132, 166 Meyer. G., 109, 113 Meyers, W. J., 179, 196, 202, 211 Milne, E. A , , 87, 112 Montague, D. 0.. 32, 79 Moore, J . E., 62, 79 Morse, W. H., 4, 10, 14, 17. 23. 28 Mussen, P. H., 96, 112

N Nakamura, H.. 84, I12 Neisser, U., 128, 166 Nesselroade, J. R., 106, I l l Newton, I., 83, 112

217

P Palmore, E. B., 109, 112 Papousek, H., 173, 177, 178, 179. 183. 196, 202, 206, 213 Park, D.. 83, I12 Parmelee, A . H., 172, 208. 213 Passon. A. H., 32, 79 Peiper, A., 175, 198, 213 Pettigren, T. F., 45, 5 5 , 78 Piaget, J., 87, 88, 99, 112, 117, 121, 132, 148, 166, 170, 206, 207, 210, 213 Pinard, A,, 132, 166 Potter, M. C . , 119, 166 Prechtl, H. F. R., 170, 173, 180, 202, 208, 211, 212

R Rachlin, H.. 25, 28 Raph, J., 32, 79 Rapoport. A,, 208, 213 Rashevsky, N., 95, 112 Raven, J . C.. 105, 106, 112 Reese, H. W., 26, 28, 110, 112, 202, 203, 204. 1-10, 213 Reichenbach, H., 83. 112 Reichenbach, M., 83, 112 Reid. R . L., 23, 28 Reiss, A , , 131. 166 Rescorla, R. A., 27, 28, 172, 213 Restle, F., 119, 128, 165 Revusky. S. H., 19, 28 Reynolds, G. S., 5 , 22, 28 Rhodes. A. A., 62, 79 Riegel, K. F.. 91, 95, 99, 103, 104, 106, 109, 110, 112, 113 Riegel, R. M., 106, 109, 112 Riessman, F., 32. 79 Rosenberg, J . , 55. 78 Rothenberg, B., 120, 143, 151, 167 Rotter, J . B., 77, 79 Rubin, A . I., 88. 113 Russell, N . M., 120, 131, 144, 145, 146, 167 Ryder, N., 107, 113

0

5

Olver. R. R.. 145, 146. 149, 165 Ornstein, R . E., 88, 112 Overton, W. Z., 110. 112. 202. 203, 204. 210, 213

Salapatek. P. H., 181, 192, 193, 197, 202. 212, 2 1 3 Sameroff, A. J., 170, 171, 172, 173. 174, 175. 176, 180, 184, 185, 186, 188,

218

Author Index

189, 191, 192, 193, 197, 198, 199, 200, 202, 206, 210, 213, 214 Sarbin, T. R., 83, 113 Schaie, K. W., 106, 107, 109, 113 Scheerer, M., 204, 214 Sedgewick, C. H. W., 103, 111 Segal, E. M., 205, 214 Seligman, M. E. P., 171, 183, 191, 195, 196, 202, 205, 214 Semb, G., 183, 214 Shantz, C. U., 151, 167 Shapiro, M. M., 45, 47, 58, 59, 60, 61, 78, 79 Sher, I. H., 101, 1 1 1 Shipman, U. C., 32, 78 Sidowski, J. B., 62, 79 Siegel, L., 117, 167 Siegel, S., 62, 7 9 Sigel, I., 32, 7 8 Silverman, S. M., 58, 59, 60, 61, 79 Simmelhag, U. L., 23, 29 Simon, H. A., 5 5 , 56, 78 Sinclair, M., 164, 166 Siqueland, E. R., 178, 179, 180, 182, 191, 196, 202, 206, 211, 214 Skinner, B. F., 4, 6, 7, 9, 13, 14, 17, 19, 23, 24, 28, 29 Smedslund, J., 119, 150, 151, 167 Smith, I., 146, 167 Sokolov, 192, 214 Solomon, R. L., 27, 28 Solomons, G., 179, 196, 202, 21 1 Sostek, A. J., 172, 173, 174, 175, 176, 180, 202, 214 Sostek, A. M., 172, 173, 174, 175, 176, 180, 202, 214 Sperry, R. W., 205, 209, 210, 214 Spradlin, J. E., 24, 29 Staddon, J. E. R., 23, 29 Stecher, L. I., 122, 123, 165 Stein, M., 185, 186, 212 Stern, E., 208, 213 Stratton, P., 172, 173, 175, 176, 211 Suchman, R. G., 133, 167 Suppes, P., 56, 7 9

T Torpie, R. J., 101, 1 1 1

Trabasso, T., 133, 142, 167 Tuddenham, R. D., 106, 107, 113

V van den Daele, L. D., 97, 113 von Bernuth, H., 173, 212 von Bertalanffy, L., 170, 204, 208, 210, 214

W Waddington, C. H., 204, 214 Wall, A. M., 61, 79, 149, 167 Wallace, M., 88, 113 Wallach, L., 149, 167 Walson, J. S., 151, 167 Warner, W. L., 33, 35, 79 Wechsler, D., 102, 113 Weinberg, D. H., 150, 166 Weisberg, P., 8 , 9, 13, 29 Welch, L., 120, 166 Wenger, M. A., 181, 182, 214 Werner, H., 171, 206, 214 Whorff, B. L., 84, 113 Wickens, C. A., 171, 214 Wickens, D. D., 171, 214 Wiehe, R., 48, 77 Wilcoxon, F., 51, 7 9 Williams, D. R., 26, 29 Williams, H., 26, 29 Winer, G. A., 151, 167 Wohlwill, J., 148, 165 Wohlwill, J. F., 117, 119, 120, 150, 162, 164, 167 Wolff, P. H., 173, 214 Woody, J. F., 121, 167 Wycoff, L. B., 62, 7 9

Y Yoder, R. M., 5 5 , 78

2 Zeaman, D., 192, 214 Zeiler, M. D., 6, 9, 10, 20, 25, 29 Zigler, E., 62, 75, 78 Zimiles, H., 119, 120, 132, 144, 146, 167 Zipf, G. K . , 103, 113

Subject Index A Adaptation, development models and, 202-203, 209-210 general systems theory and, 207-209 models of infant behavior, 204-207 organismic and mechanistic models, 203-204 Auto-shaping, response-independent reinforcement and, 25-27

B

organismic and mechanistic models, 203-204 qualitative growth models and, applications of, 99-101 general properties of, 97-99 relations with quantitative growth models, 101-103

E Estimators, see under Number concepts Extinction, instructions and training and, 68-72

Babkin reflex, conditioning of, 171-177

G

C Change, see Development Concept formation, see under Learning strategies and socioeconomic status; Number concepts Conditioning, see under Learning Counting, role in number concepts, 128131, 160-162

D Development, 81-1 13, 202-203, 209-210 applications of a quantitative growth model and, 103-107 concept of time and, 95-96 in natural sciences, 83-87 psychological, 87-95 general systems theory and, 207-209 interactions between changes in the individual and society and, 107-109 models of infant behavior and, 204207 of number concepts, see Number concepts

Growth models, see under Development

H Head turning, conditioned, 177-1 8 1

I Individual differences, control of multiple responses and, 21-22 Infant learning, see Learning Instructions, see under Learning strategies and socioeconomic status

L Learning, 169-2 14 development models and, 202-203, 209-210 general systems theory and, 207209 models of infant behavior, 204-207 organismic and mechanistic models, 203-204 infant conditioning in, 171 219

Subject Index

220

of Babkin reflex, 171-177 of head turning, 177-181 of sucking behavior, 181-191 parameters of conditionability in, 191, 201-202 orienting reaction, 192-195 preparedness, 195-201 Learning strategies and socioeconomic status, 3 1-79 concept formation in, 55-57 acquisition and, 34-45 chaotic reinforcement and, 49-52 partial reinforcement of an obvious dimension and, 45-48 pretraining to criterion and, 52-54 pretraining with a fixed number of trials and, 54-55 experimental outline for, 33-34 instructions and training and, 72-74 extinction after, 68-72 reward preferences and, 67-78 amount and probability of, 57-62 with and without signals, 62-67 variables in. 33

M Mediation, control of multiple responses and, 21-22

N Number concepts, 115-167 estimators in, 116-1 19 confidence in, 143-147 experimental investigation of, 131142 historical aspects, 123-128 methodology for, 120-1 23 role of counting in, 128-131 operators in, 116-1 19, 147-148 experimental investigations of, 152162 methodology for, 148-152

0 Operators, see under Number concepts Orienting reaction, conditionability and, 192-195

P Preparedness, conditionability and, 19520 1 Pretraining, to criterion, 52-54 with fixed number of trials, 54-55

R Reinforcement, amount and probability of, 57-62 chaotic, concept formation and, 49-52 partial, concept formation and, 45-48 superstitious behavior and, see Superstitious behavior with and without signals, 62-67 Response(s), control of, see under Superstitious behavior lack of reinforcing, 22-23 new, eliciting, 25-27 previously probable, eliciting, 23-25 temporal patterns of, deliberate and adventitious reinforcement and, 10-13 Response probability, 23-25, 57-62 deliberate and adventitious reinforcement and, 6-10 Reward preferences, see under Learning strategies and socioeconomic status

S Signals, reward preferences and, 62-67 Socioeconomic status, see Learning strategies and socioeconomic status Stimulus control, deliberate and adventitious reinforcement and, 13-18 Sucking behavior, conditioned, 181-191 Superstitious behavior, 1-29 control of multiple responses and, concurrent response-independent and response-dependent reinforcement and, 19-21 mediation and individual differences and, 21-22 reinforcement of lack of response and, 22-23

Subject Index deliberate and adventitious reinforcement and, probability of response and, 6-10 stimulus control and, 13-18 temporal contiguity and, 18 temporal patterns of responding and, 10-13 reinforcement process and, dependencies and contingencies, 4-6 implications of superstitious behavior, 2-3 response-independent reinforcement and, 19-21, 23

221

auto-shaping by, 25-27 elicitation of previously probable responses by, 23-25

T Temporal contiguity, deliberate and adventitious reinforcement and, 18 Time concept, see trnder Development Training, see rrnder Learning strategies and socioeconomic status

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