Understanding Changes In Time: The Development Of Diachronic Thinking In 7-12 Year Old Children

Understanding Changes in Time

Understanding Changes in Time The development of diachronic thinking in 7- to 12-year-old children

Jacques Montangero With the collaboration of Jean-Pierre Cattin, Sylvain Dionnet, Alexandra Jaussi, Danielle Maurice-Naville, Stefano Monzani, Silvia Parrat-Dayan, Francisco Pons, Pierre Scheidegger and Anastasia Tryphon

Translated by Tim Pownall

UK Taylor & Francis Ltd, 1 Gunpowder Square, London EC4A 3DE USA Taylor & Francis Inc., 1900 Frost Road, Suite 101, Bristol, PA 19007 © Jacques Montangero, 1996 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without permission in writing from the Publisher. First published 1996 This edition published in the Taylor & Francis e-Library, 2005. “To purchase your own copy of this or any of Taylor & Francis or Routledge’s collection of thousands of eBooks please go to www.eBookstore.tandf.co.uk.” Library Catalogue Record for this book is available from the British Library ISBN 0-203-45057-4 Master e-book ISBN

ISBN 0-203-45811-7 (Adobe eReader Format) ISBN 0 7484 0470 8 (Print Edition) ISBN 0 7484 0471 6 (Pbk) Library of Congress Cataloging-in Publication Data are available on request

Contents

Acknowledgments Chapter 1

vii

Diachronic Thinking: Known Facts and Unanswered Questions

1

Time as a knowledge perspective

1

The diachronic approach and scientific discovery

2

A hypothesis concerning the role of the diachronic approach in everyday thought

5

The foundations of diachronic thinking in young children

6

Unanswered questions concerning the nature and development 10 of the diachronic approach Chapter 2

Chapter 3

The Development of the Diachronic Approach in Children aged 7–8 to 11–12: Method and Population

13

Theoretical and methodological framework

13

Questions asked and tasks set

15

Variations in the contents and context of knowledge

17

The population studied

18

The Evolution of Conceptions of Biological Transformations (the Growth and Decay of Trees)

19

Draw me a growing tree: from change of size to morphological 19 transformation The past and future of a diseased tree: from external discontinuous changes to progressive internally generated transformations

28

The reforestation of the Amazon: representations of cyclical changes in the distant future

40

v

General conclusions to Chapter 3: biological knowledge and the 51 diachronic approach Chapter 4

Chapter 5

The Diachronic Approach and Physical Transformations

55

A story of thawing ice: an introduction to duration in causal explanation

55

The birth of the stars: children’s representations of the origin and expansion of the universe

65

General conclusions to Chapter 4

75

Children as Budding Developmental Psychologists

77

The artist depicts his own progress: children’s conceptions of the development of the ability to draw a human figure

78

The drawings of Tarzan and wild children: the role attributed to 89 maturation and learning in the development of drawing The bigger you get, the better you speak: children’s conceptions 95 of the development of the ability to describe a picture Do we grow more intelligent?: conceptions of intelligence and 111 its development General conclusions to Chapter 5: the intuitive psychology of 125 children concerning cognitive development Chapter 6

The Representation of Changes Associated with Human Activity Which are not Necessarily Predictable

129

The rich will always be ahead of the poor: the comprehension 129 of a sequence of four cartoons Do the rich stay rich and the poor stay poor?: conceptions of wealth and poverty and the possibility of change

140

The traffic jam: measures to improve the traffic flow

148

General conclusions to Chapter 6: diachronic thinking, domains 158 of knowledge and cognitive interaction Chapter 7

General Conclusions. The Diachronic Approach and Diachronic Thinking: Their Nature, Development and Importance for Knowledge

160

The diachronic approach and diachronic thinking

161

The development of diachronic thinking in children aged between 7–8 and 11–12

173

vi

Why study the diachronic approach?

181

References

183

Index

188

Acknowledgments

The 12 experiments reported in this book have been carried out by the collaborators whose names are mentioned on the title page and five experiments have been designed by some of these persons. I am very much indebted to all these researchers for their rich experimental work and for the friendly atmosphere of our collaboration. Many thanks too to the assistants and students in psychology at the University of Geneva who helped us in this experimental work: Brana Gonthier-Pesic, Hélène Duric, Laurence Poget, Nadège Poschung, Sandrine Vuillemier, Miguel Samaniego and Francis Staehli. I also would like to thank the children who were interviewed and their teachers and heads of schools. As far as the preparation of the manuscript is concerned, I was greatly helped by Francisco Pons and Stefano Monzani, to whom I am very grateful. Finally I wish to say how much I appreciated the support of Leïla and of my two children Serge and Agnès during the writing of this book. The experiments reported in the book were carried out thanks to grants of the Fonds national suisse de la recherche scientifique (grants nos 11–26493.89 and 11–37705.93) and of the Fonds Jean Piaget pour recherches psychologiques et épistémologiques.

Chapter 1 Diachronic Thinking: Known Facts and Unanswered Questions

Time as a Knowledge Perspective Every object of knowledge is situated in time: the idea that occurs to me; the flower or building that meets my gaze; the telling experience I recall to mind. All these things are situated at a precise point in time, are characterized by a certain duration and are ordered within a sequence of events. The study of cognitive psychology cannot therefore afford to ignore the question of the fourth dimension. Indeed, a whole series of studies which I shall describe later has been devoted to investigating the way children conceptualize temporal notions, reason about time or measure events using temporal units. However, these studies are not the subject of this book. What I am interested in here is time as a mode or perspective of knowledge, not as the content of knowledge. In the conclusions to this book I shall define how this term ‘knowledge perspective’ should be understood. For the moment, I shall limit myself to stating that such a perspective is either the dimension within which a reality is framed or the ‘category’ through which it is analyzed in order to be better understood. Thus when confronted with a situation, we may decide to analyze the spatial relations obtaining within it: the relative position of the elements, the overall configuration etc. This is a mode of apprehending the situation which, though not necessarily inescapable, may assist in its comprehension. Similarly, temporality may be employed as a way of apprehending reality. It is not just a dimension of the universe which demands to be structured intellectually as a content of knowledge. Leaving aside the problem of the gradual acquisition of temporal concepts and reasoning, the chapters that follow will be devoted to the study of how children use their temporal knowledge, once acquired, to improve their understanding of things. This placing of the object of knowledge within a temporal perspective is found in science and is known as the diachronic approach or, alternatively, diachronic perspective. This consists of viewing the object within a temporal dimension instead of simply considering it as it presents itself here and now. Such an approach also forms part of everyday thinking. The dual aim of this

2 UNDERSTANDING CHANGES IN TIME

book is to focus attention on the importance of this approach and to attempt to gain a better understanding of it by observing its development in children. The Diachronic Approach and Scientific Discovery There are a number of disciplines which have traditionally focused on the unfolding of events in time. History (in its classic form) is probably the oldest of these disciplines. But does this mean that it is founded on a genuinely diachronic approach? I believe not. I consider the diachronic approach to be a perspective which is not content to describe things in time but instead attempts to understand their development and find in the temporal dimension the explanation for a current state of affairs. More precisely, the diachronic approach views a present situation as one moment within an evolutive process. In this way, we can explain such a situation, at least in part, by reference to what has occurred in previous stages or in the light of its predicted future development. In this interpretation, history is only truly diachronic in conception when it attempts to explain a given event or state of affairs by elucidating the stages which preceded it and the evolutive process which these stages reveal. As historic events are swayed to a significant extent by elements of chance, they can of necessity only be partly explained in terms of developmental processes. Of the relatively long-established disciplines, etymology and historical grammar adopt a truly diachronic approach when they attempt to come to a better understanding of the current state of certain aspects of language by returning to the earliest state that can be reconstructed. At this point I should like to emphasize the crucial contribution of this type of approach in the field of scientific creativity. While modern science dawned when Galileo had the idea of adding time to movement in the description of physical reality, many astonishing discoveries in the history of scientific development have resulted from the application of a diachronic approach to what previously appeared to be an intractable problem or field of knowledge. The most striking example which, because it has inspired so many other disciplines, is also possibly the most fruitful is that of biology in the nineteenth century. The traditional non-evolutionary conception was unable to account for the diversity of living species. At this point Lamarck, inspired by the transformist perspective of Buffon, proposed a theory which no longer held species to be immutable. Viewing the problem as a temporal one, Lamarck suggested that complex species are descended from simpler pre-existing forms. In his Natural History of the Invertebrates, which was published in 1815, he attempted to explain the biological organization of animals and the development of species in terms of a limited number of evolutionary laws. While these laws (development of organs by appetence or in response to a need, inheritance of acquired characteristics) were subsequently to be fundamentally re-examined, the actual idea of the evolution of species together with the concept of evolutionary laws was to become firmly established in biology.

DIACHRONIC THINKING: KNOWN FACTS AND UNANSWERED QUESTIONS 3

It was Darwin who next applied this diachronic approach to the problem of species. It is well known that his theory, advanced in his work The Origin of Species, which was published in 1859, explains the transformation of species in terms of a process of natural selection, itself the result of the struggle for survival. Darwin’s work was to have enormous repercussions and his theory sparked off a number of bitter controversies. It was nevertheless to become the cornerstone of most current thinking on the subject. The evolutionary viewpoint seemed both so new and so rich—and it corresponded so well to the ideology of progress that prevailed at the period— that theorists immediately proposed applying it to the human sciences. It was Spencer, the prophet of progress and eulogist of individualism, who from his very earliest works (Principles of Psychology, 1855) proved to be the prime advocate of the idea. This author considered that the evolutionary viewpoint could be applied to everything: to organisms, of course, but also to the stars and to human phenomena. Spencer’s idea was followed in different fields. In psychology, it is at the root of developmental psychology and genetic epistemology, a field pioneered by J.M.Baldwin (1894). Within this dual discipline, knowledge is studied from a diachronic perspective. Researchers attempt to gain an understanding of it by tracing the evolution of science and observing children’s intellectual development. As we know, this extremely rich approach, which attempts to bring together biology, psychology and epistemology, was developed with considerable success by Piaget. Underlying the theoretical models and the innumerable experimental discoveries contained in the 50 or so books published by this author (see Inhelder, Montangero and Steenken, 1989; Montangero and Maurice-Naville, 1994), we again find a diachronic method. This consists of explaining knowledge in terms of its genesis, that is to say in terms of its origins and the formative processes that give rise to it. An element of knowledge, for example a causal explanation or a logical argument, is not explained simply by its underlying structure but also by the mechanisms which formed it. Moreover, however it is explained, cognitive behaviour is always much better understood when we see how it comes into being and how it develops through childhood. To a large extent, the present-day psychology of cognitive development is a descendant of this application of the diachronic approach to knowledge. Nevertheless, some current research into questions of development is in no way based on this type of approach. In cases, for example, where researchers strive to demonstrate that a 4-month-old infant or a 6-year-old child possesses a particular competence without attempting to explain how this ability came to exist or how it will develop in the future, they are simply making an observation about child psychology, not proposing a truly ‘genetic’ explanation. Nowadays an increasing number of studies published in scientific journals nominally devoted to cognitive ‘development’ fall into this non-genetic category. Freud’s theory of psychoanalysis, which as we know led to such a profound transformation in our understanding of human behaviour, is a further result of the

4 UNDERSTANDING CHANGES IN TIME

application of a diachronic approach to psychology. In this theory, adult neurotic behaviour is explained by certain vicissitudes which disturbed the affective development of the individual. However, in attaching particular importance to one period during this development while neglecting the role of other stages, Freud fails to exploit the full potential of the diachronic approach. It is not just in biology and the human sciences that new discoveries have been made as a result of this integration of scientific explanations into a temporal perspective. Physicists have also found this approach to be extremely fruitful. The three examples which I shall present below demonstrate that in this discipline a diachronic approach need not necessarily be limited to the model of gradual progress which underlies the traditional idea of evolution. The study of changes occurring in time underlies the scientific understanding of thermodynamics, thanks in particular to the work of Carnot (Reflections on the Motive Power of Fire, originally published 1824) and Clausius (The Mechanical Theory of Heat, originally published 1850). These publications ushered in the dawn of a completely new discipline which goes beyond the simple mechanics of heat. The idea of entropy to which this work gave rise can be considered as a law of evolution which does not progress from the simple to the complex but instead from order to disorder or from heterogeneous structure to homogeneous distribution. The concept of entropy has since been transposed to other fields, including communications. In the twentieth century, the adoption of a diachronic perspective has led to important discoveries in other areas of physics. During the 1950s and 1960s two new theories, whose full implications may still remain to be discovered, made their appearance in the fields of physical chemistry and astrophysics. The first of these is the theory of dissipative structures which, according to its originators (see Prigogine and Stengers, 1984), owed its birth to the consideration of time within physico-chemical phenomena. Dissipative structures arise as a consequence of the amplification of random fluctuations within unstable systems. The second of these theories is the big bang theory, together with the variants to which it has given rise. Instead of thinking of the universe as unchanging, today’s researchers view it within a diachronic perspective as an expanding system whose origin has to be explained. The stars, too, are no longer conceived of as unmoving, ageless bodies. Instead they form, develop and wane. They, too, have finally become a part of time. To conclude, we should also note that a number of current developments in molecular biology are due to the interest which has been attracted by the execution of the genetic programme over time. We can see that the considera tion of the temporal dimension of phenomena has not ceased to be a source of inspiration to science.

DIACHRONIC THINKING: KNOWN FACTS AND UNANSWERED QUESTIONS 5

A Hypothesis Concerning the Role of the Diachronic Approach in Everyday Thought If the approach we are considering here has proved to be so fruitful in the field of scientific research, then what role might it play in the thought of the adult nonscientist or the child? My hypothesis is that at these ‘lower’ (or ‘natural’) levels of thought, the adoption of a diachronic approach again greatly enhances the subject’s understanding of reality. In a metaphorical sense, this enhancement operates in both width and depth. First, in width, because the fact that we consider both the past and future stages of a current situation enlarges the scope of the data on which our thought can bear. Second, in depth, because our explanation of the situation benefits from the addition to the factors present here and now of developmental and transformational processes which are not directly observable. Let us look at some simple, concrete examples. Imagine that a child is interested in the flowers of a fruit tree, the behaviour of a dog or the garden wall. The first step in the comprehension of these experiential data is clearly synchronic in nature. It is necessary to observe closely, compare the elements involved and attach a meaning to them. However, the understanding of these three things will be considerably enriched if the child starts to consider them from a diachronic viewpoint. The flower only assumes its true significance in the light of the knowledge that it will turn into a fruit. The behaviour of the dog will be explained more satisfactorily if it is known that the animal is old or, in contrast, very young. The composition of the wall will only be truly understood once its mode of manufacture has been ascertained. The consequence of our hypothesis is that a diachronic mode of thinking, because it is able to enrich our knowledge of phenomena, can help us uncover more or better solutions to the problems which confront us. Let us imagine that the problem takes the form of a disagreement between two people or a difficulty encountered while producing a computer drawing. Everything leads me to believe that the solutions will be more varied and more relevant if they are proposed by a subject who has gone beyond the here and now to reconstruct the origin of the problem and the steps which have resulted in the current state of affairs. The consideration of the possible or probable future changes is a further important aid in any search for a solution. It remains to be determined whether the adoption of a diachronic approach is always of assistance. It could be hypothesized that such an approach is particularly fruitful for the understanding of certain types of phenomena whereas in other cases its contribution may be somewhat less evident.

6 UNDERSTANDING CHANGES IN TIME

The Foundations of Diachronic Thinking in Young Children The chapters which follow will study the development of diachronic thinking in children of 8 to 12 years. It is clear that this mode of thought does not appear ex nihilo in this age bracket: it emerges gradually from the very beginnings of intellectual development. It is this gradual development of the knowledge that underlies diachronic thinking that I shall focus on briefly in this section. This summary will be based on observational data and well-known research results. Infants stop living exclusively in the present as soon as they show themselves capable of anticipations and reconstructions. We can therefore identify the beginnings of diachronic thinking in babies who stop crying when they hear the door to their room open or who are overcome with joy when they see their bottle being prepared. However, it is with the emergence of evocation memory, during the second year of life, that the development of diachronic thinking truly gets under way. For example, a child aged 24 months is taken to his parents’ holiday home which he last visited four months earlier. On arriving in the living room, he makes his way to the window, looks at the meadow beyond and shouts, ‘copter!’. This child is considering a current state (the meadow) and simultaneously evoking a salient memory concerning this meadow: four months ago he saw a helicopter land on it. This behaviour illustrates the beginnings of a diachronic approach which has been made possible by the child’s new evocative capabilities. While evocation memory is a necessary condition for diachronic thinking, it is clearly not a sufficient one. It is also essential that subjects, when confronted by a particular situation, take an interest in its past or future states. Such curiosity can be observed in children aged between 3 and 5 in the form of questions concerning the origins of beings and things. The phenomena of birth and growth stimulate the curiosity of young children who then sometimes apply these concepts to inanimate objects. Thus Piaget (1972a) reports that one of his daughters who was looking at a mountain wondered whether this had originally been a stone which someone had planted in the ground. In order to think diachronically, it is necessary to represent changes along the time arrow. This notion of temporal unidirectionality appears at an early age in children. It is not, however, understood as a characteristic which is attributed to time. It instead relates to an awareness of the irreversibility of certain phenomena. A pilot experiment which I conducted several years ago demonstrated that children aged 4 and 5 attribute a fixed sequential order to photographs presented to them in pairs. For example, they believe that a photograph of an empty glass necessarily follows that of a full one, or that a picture of three birds on a riverbank necessarily precedes one of ten birds on this same riverbank. In my opinion, such a powerful early concept of irreversibility is based on a number of forms of knowledge and knowledge contents which introduce unidirectional links between successive states.

DIACHRONIC THINKING: KNOWN FACTS AND UNANSWERED QUESTIONS 7

First of all, we should note that the planning of any action implies a fixed sequential order. Small children know perfectly well that they must perform certain actions of a procedural nature (the means) before being able to indulge in the activities associated with the desired objective. Second, the concept of causal links which appears at an early age, as a number of studies have shown (for example Bullock, 1985; White, 1988), lies at the origin of a form of irreversibility. In the reality that children experience, certain causes are invariably followed by an effect and these effects never precede their cause. Third, the work of Nelson (1986) has shown that 3-year-old children already have a knowledge of elementary scripts. We know that scripts are generalized event representations with sequences of actions such as those involved in going to a restaurant or boarding an aeroplane. For example, small children know the sequence of actions that follows their getting up in the morning. They are washed before being dressed. Then they eat before leaving for the kindergarten. Similarly, they know the sequence of actions performed by their mothers when they bake a cake: first of all mother prepares the dough, then she mixes in the fruit before putting the cake in the oven. Another important source of the idea of irreversibility is knowledge of biological growth (Gelman, 1993). At approximately the age of 3 years, children expect living beings to change over time in accordance with a number of predictable laws. They expect size to increase regularly with age. At age 6, children also expect the complexity of organisms to increase with growth. Furthermore, children’s very early experiences and interests teach them that the passage of time may bring decay. Toys wear out and break, flowers wither and the leaves of trees turn yellow and fall. The idea of death as the inescapable end of any life process clearly plays an important role in the propensity of human thought to project itself into the future or take refuge in the past. However, for the young child this idea is difficult to understand in a diachronic sense. Children do not exactly consider death to be the termination of a process; rather they see it as one precisely delineated event. In a review of the literature on the subject, Carey (1985) pointed out that children younger than 5 years do not think of death as the final stage of a life cycle. As of 6 years, they view death as an inescapable event without, however, understanding it as the result of a biological process. At this point, let us mention a cultural practice, story-telling, which also facilitates the learning and assimilation of unidirectional links between successive events. We know that small children, from about the age of 4, like to have stories told to them. They do not fail to complain if the story-teller does not respect the narrative order or omits an event. This ability to recognize the fixed order of a known narrative structure appears several years earlier than the ability to produce a complete, coherent story or to reconstruct the chronology of a new story. Discussing this question in a review of a number of authors, Fayol (1985) pointed out that while 4- and 5-year-old children are able to verbalize sequences of events, stories only take on an episodic structure for most children from the age of 8 onwards and the distinction between a narrative with canonical

8 UNDERSTANDING CHANGES IN TIME

structure and an incomplete story or a simple script does not become operative until the age of 9–10 years. Together with the idea of the irreversibility of change, another concept, more logical in nature, forms the indispensable ‘prerequisite’ for any diachronic approach. This is the idea of the constancy of identity through changes in time. If children do not recognize this conservation of identity then processes of transformation or evolution can have no meaning for them: they will witness nothing but a series of unconnected states. For example, a small child commenting on the first picture of a cartoon strip cries out ‘There’s Tintin!’ before looking at the second picture and shouting ‘Another Tintin!’. According to research conducted by Piaget and colleagues (Piaget, Sinclair and Bang, 1968), identity constancy appears only gradually. In one experiment, children were asked to draw the stages of growth of what appeared to them to be seaweed. In fact, the material was potassium ferrocyanide which acquires a treelike structure after a period of only a few minutes. The subjects were then asked to draw the stages of their own growth, from the infant to the adult state. Finally, they produced drawings illustrating the growth of the experimenter. When questioned, the 4-year-old children affirmed that identity was conserved throughout the series of drawings when these related to themselves, but not always when they related to the experimenter. These children refused to accept that the first set of drawings they had produced all represented the same seaweed. At the ages of 5 and 6, the children accepted the identity constancy of growing humans but not of the seaweed. It was not until the age of 7 that the majority of the children considered that the identity of the seaweed remained constant. Thus the idea of identity appears to be a fragile one in young children. Guardo and Bohan (1971, cited in Carey, 1985) found that only a very small percentage of 6-year-old children were prepared to state that they had always been the same girl or the same boy. Moreover, research conducted by DeVries (1969) and Keil (1989) shows that for 4- and 5-year-old children the idea of the identity of an animal is associated with its external appearance. It is not until the age of 9 that identity is considered to be dependent on birth and the internal organs. The knowledge which young children possess in connection with changes over time, knowledge which appears with the beginnings of representative activity and develops subsequently, can only exist if the precondition for a minimum structuring of temporal notions is satisfied. To reason in time implies the ability to understand time, at least in an elementary way. Despite the limited nature of the abilities of young children in this field and despite the difficulties they encounter in comparing durations and sequences in complex situations, they nevertheless possess an elementary form of knowledge concerning these temporal notions. Levin (1977, 1992) has shown that young children are capable of making correct temporal judgements, for example when required to judge the relative duration of the period of operation of two lamps. If the lamps are switched on one after the other and then turned off at the same time, these

DIACHRONIC THINKING: KNOWN FACTS AND UNANSWERED QUESTIONS 9

young subjects know that one of them was lit for longer than the other. I have also defined certain early temporal ‘preliminary concepts’ (Montangero, 1977, 1985). ‘Before’, ‘after’ and ‘long’ are used appropriately when they relate to contents which are neither spatial nor kinematic, such as a period of waiting. Moreover, I have demonstrated the ability of 4- to 5-year-olds to link temporal orders, durations, speeds and distances of travel correctly, provided that their reasoning operates on only two terms at a time. For example ‘finish after’ implies ‘take longer than’ and ‘run faster’ implies ‘arrive before’ etc. It can be seen that at the age of 5, children already possess much of the knowledge that underlies diachronic thinking. They are interested in both the past and the future and are able to reconstruct or anticipate sequences of events, thanks in particular to their knowledge of the unidirectional links (deterministic, teleonomic, conventional, biological) between events. It is this knowledge set that enables them to re-establish the correct order of a series of pictures representing the progress of a simple event. They can, for example, establish the correct order of a set of pictures presented out of sequence, imagine the event that follows the last picture of a short ordered sequence or, albeit with greater difficulty, identify the event that precedes the first picture shown to them (Bonnens, 1990; French, 1989). Further important progress is made at around the age of 8. Thus two early pieces of research conducted by Piaget and his colleagues demonstrated that at this age the difficulties encountered by younger children in the understanding of narrative sequences begin to fade. This research involved tests originally published in 1911 by a Polish psychologist (Dawid) and subsequently standardized by Piaget’s colleagues. In the first test (Margairaz and Piaget, 1925), children were asked to deduce intermediate events from a presentation of the initial and final situations. For example: (1) a child holding a stick moves towards a dog; (2) the child is crying and his trousers are torn. The intermediate events were only deduced by a majority of subjects (75 per cent) at age 8 to 10 or even older depending on the story presented. Another of Dawid’s tests (Krafft and Piaget, 1925) consisted of presenting out of sequence four or five pictures telling a narrative story. It was only at age 7 that the children were able to reconstruct the chronological sequence of the simplest of the stories presented. Piaget’s qualitative analysis of the deficiencies which are overcome at this age emphasizes two factors which, in my opinion, explain the nature of diachronic thinking. First of all, this mode of thought consists of the ability to swim against the tide of impressions and ideas instead of following the irreversible current of consciousness. Second, and most importantly, the reconstruction of a narrative sequence presupposes the ability to perform a synthesis of a series of images. The progress which appears at about age 8 can also be observed in connection with temporal concepts and temporal reasoning. At this age, duration and temporal order are well differentiated, even in complex situations. For example, children accept that two moving objects which come to a halt at the same time may nevertheless have been in motion for differing lengths of time (if one of the

10 UNDERSTANDING CHANGES IN TIME

objects started moving before the other). They can also articulate more complex correspondences between time-related variables, a development which considerably improves temporal reasoning (Montangero, 1985; Piaget, 1969b). For example, when comparing the period of movement of two jumping dolls, one 8-year-old child said: ‘They moved for the same time [duration] because they left and arrived together [order], and the red doll made more jumps but her jumps were shorter than the blue doll’s jumps [work done in terms of discontinuous activity]. She moved more slowly towards the finish [speed] and that’s why she didn’t get as far [work done in terms of distance traveled].’ Furthermore, children start to acquire the conventional units of time such as days of the week, months etc. (Friedman, 1982). At the level of causal explanation, better adapted theories take the place of earlier explanations in terms of the powers with which objects are endowed or ‘egocentric’ explanations which view inanimate objects as living beings or physical phenomena as dependent on human activity (Piaget, 1972a, 1972b). A number of recent studies also reveal the advances made in the explanation of a variety of phenomena. For example, Inagaki and Hatano (1993) have found that when presented with a selection of explanations of biological phenomena, the majority of 8-year-old children choose those which appear most relevant to an adult (as against 20 per cent at age 6). Finally, Piaget and Inhelder (1971) observed significant progress in mental images (studied via the drawings produced or selected by the child) at age 8 to 9. Movements and transformations are correctly anticipated and reproduced at this stage of development (for example, the displacement of a square or the flattening of a wire cord forming a bow). Unanswered Questions Concerning the Nature and Development of the Diachronic Approach We have just seen that when children reach 8 to 9 years of age, they seem to possess all the capabilities required for the correct representation of changes over time. Does this mean that they are then capable of adopting a genuinely diachronic approach in which they associate a present state with the states which have preceded it or which will follow it, in which they can correctly imagine the transformations worked over time and in which they explain the present situation in part by reference to its past or future development? The vast body of literature devoted to the field of cognitive development provides us with no answer to this question. We know of no study to predate our own work in this field which has directly investigated the development of diachronic thinking in children. The first of the unanswered questions which we shall address in this current work is therefore: can children—at least when they have achieved an acceptable degree of skill in temporal reasoning, elementary logic, the causal explanation of a simple phenomenon and the usage

DIACHRONIC THINKING: KNOWN FACTS AND UNANSWERED QUESTIONS 11

of the conventional units of time—consider things from a fully diachronic perspective? In answering this question, it is not possible to start from a precise definition of ‘a fully diachronic perspective’ and then determine whether the components of this perspective can be identified in 8- or 9-year-old children. This is because no such precise definition exists. In consequence, we have remained faithful to the established tradition of genetic epistemology and conducted a series of experiments with a dual objective. On the one hand, they are designed to reveal the fundamental components of the diachronic approach by means of an analysis of the difficulties encountered by children and the abilities which they gradually deploy in order to perfect their skills in this field, or more accurately, mode of knowledge. Given this orientation, the study of the behaviour of children of neighbouring age-groups does not necessarily form part of the discipline of child psychology. Instead it serves, within the perspective of cognitive psychology, to reveal the fundamental elements of knowledge. In consequence, these experiments have an exploratory character. They were not designed, at least initially, to test a hypothesis. On the other hand, this research is designed to reveal whether the mode of knowledge that interests us here develops and, if so, what form this development takes. First of all, this enables us to provide an answer to a general question of developmental psychology: is it possible to define degrees or levels of diachronic thinking? If the answer to this question is affirmative, then we shall take account of the most highly developed characteristics of the diachronic approach that we can identify in our subjects in our definition of the fundamental elements of this approach. Moreover, when viewed in terms of child psychology, the data relating to the diachronic approach will enable us to predict the type of ability that can be expected of 8- to 12-year-old subjects. These results may also be significant for the psychology of education. A number of things which are taught at school (in the sciences as well, perhaps, as in history or even computer science) presuppose the understanding or the adoption of a diachronic approach. How are we to understand children’s ability to assimilate such material if we know almost nothing about their intellectual development in this field? One important theoretical question concerning diachronic thinking remains totally unanswered: this is the question of whether it genuinely exists as a mode of thought distinct from the subject’s other competences. My basic hypothesis is that this is indeed a specific mode of thought, a way of apprehending reality. It might be argued that what I have termed diachronic thinking or a diachronic approach is simply the manifestation of a different competence. More specifically, might this diachronic approach simply be one aspect of temporal reasoning, or one of the characteristics of the causal explanation of evolutive phenomena or else a result of the ability to perform syntheses? To summarize, we can identify the following five questions concerning the mode of knowledge which we are discussing here:

12 UNDERSTANDING CHANGES IN TIME

1. What are the essential components of the diachronic approach that lead to the enhancement of knowledge? 2. Is it possible to define various levels of diachronic thinking? 3. Do children aged 8 and 9 already possess a developed diachronic perspective? 4. If such a perspective does develop between the ages of 8–9 and 11–12, what does this development consist of? 5. Is diachronic thinking a specific mode or does it form part of other aspects of knowledge, such as temporal reasoning, causal explanation or synthetic ability? In the conclusion to this work, I shall also ask why and how this development, which is revealed by the experimental results, progresses. To conclude this section, I should like to underline the epistemological problem that underlies this research and could already be glimpsed in the opening pages of this chapter. At the level of the epistemology of science, I am struck by the difficulty nowadays of identifying disciplines which explicitly claim allegiance to the diachronic approach. Nevertheless, this approach continues to make an important contribution to the advancement of science. However, I believe that it is above all at the level of everyday thinking that the richness and benefits of the diachronic approach have been all too frequently ignored. ‘Thinking in time’ and ‘explaining in time’ add a new dimension to our knowledge of beings and things. This is a complex mode of thought which is most certainly not immediately available in all its potential. It is therefore important to gain some insights into the stages of development of this competence.

Chapter 2 The Development of the Diachronic Approach in Children aged 7–8 to 11–12: Method and Population

Theoretical and Methodological Framework In my opinion, if we are to define a field or perspective of knowledge it is essential to focus on those aspects of reality that are meaningful for the subject. This formulation is not the expression of a naive realism: clearly it is the subjects who select particular aspects of reality and attribute meaning to them. These activities of abstraction and the attribution of meaning take place within a framework of interaction with real data which, of course, have a role to play in cognitive processes. Since we are interested in the aspects of reality which are meaningful for the subject, we shall clearly not be concentrating on the ‘hardware’ of human thought, that is to say the neurons and their functioning. Neither will this be a quantitative study measuring, for example, subjects’ attentional capacities (Halford, 1993; Pascual-Leone, 1987, etc.) as an indicator of the volume of information that can be processed simultaneously while ignoring the nature of this information. Similarly, we shall avoid an analysis in terms of general operations which can be applied to a variety of contents (as in certain passages by Piaget who, however, also analyzed the meanings attributed to the situations presented). In order to define the level of meaning that we intend to investigate here, let us summarize briefly the levels of knowledge which may constitute an object of study for psychologists interested in representations and their development. The most general level appears to relate to the scope of cognitive work (working memory or ‘processing resources’) which increases with development and leads to new possibilities for the acquisition of knowledge. Next comes the dataprocessing level which may be investigated either in terms of the most general mental operations or in a more specific manner. This is followed by the level of meaning, that is to say of concepts each of which is defined by a set of predicates and a network of relations which link these predicates and associate concepts with other concepts. Somewhat closer to the effective course of everyday thinking and cognitive adaptation are the levels of representational strategies (for example the use of prepositional or figurative processing) and problem-solving strategies which also comprise a monitoring function.

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Our study of the level of meaning will be situated within the Piagetian or, more precisely, post-Piagetian research tradition. In many recent publications, the Piagetian perspective has been defined as the search for certain stages of development at which a particular form of reasoning is generalized to cover all contents (for example, Bennett, 1993; Sonuga-Barke and Webley, 1993). This interpretation does not correspond to Piaget’s theory whose principal aim was not the description of general stages but the search for organizational forms and functional processes which explain the nature of reasoning and its transformations during development (see Montangero and Maurice-Naville, 1994). Although inspired by Piaget, my own viewpoint differs from his in a number of questions. My own approach coincides with the Piagetian framework as it concerns the level of behaviour studied, a number of fundamental theoretical questions, and method. Knowledge is studied at the level of individual representations. Its study aims at the discovery of the shared forms and processes which underlie the construction of knowledge irrespective of the particularities of individual subjects. The theoretical perspective employed here is constructivist in nature and is based on the phenomenon of assimilation. What is of interest is neither the pool of innate processes nor a study orientated towards the effects of the environment, but rather the elaboration of forms of knowledge which account for the cognitive interaction between the subject and reality. I am convinced that it is only through their changing frameworks of knowledge that subjects ever know reality. As for the method, this consists of semi-directed interviews and an analysis of the results which is essentially qualitative in nature, moving from a comparison of responses obtained from children of a similar level to a comparison of the responses characteristic of contiguous age-groups. When response classes can be defined on the basis of a qualitative analysis, we then turn to the quantitative data relating to the frequency of these classes in each age-group. The proportion of subjects in a certain class is then expressed as a percentage which does not claim to be a precise indication of the proportion likely to be encountered in similar populations. These are indicative data which reveal whether a particular response type will be found in a majority or a minority of subjects in a given age-group and which make it possible to identify a potentially age-related development. What distinguishes this approach from the Piagetian perspective is, first, the absence of any precise description of structure or any analysis in logical terms and, second, the diminished importance attributed to the idea of stages. What is more, rather than studying the most general operations of thought, I am interested here in those aspects of reality which are of significance to the subject and the way in which they are coordinated. To this end, I have elaborated an analysis of temporal reasoning at the ‘infraoperational’ level (Montangero, 1985). In the current work, I shall not attempt to develop this definition of the systems and subsystems of meaning to the same extent since what we are concerned with here is the investigation of a new and rather more general field,

THE DEVELOPMENT OF THE DIACHRONIC APPROACH 15

namely a perspective of knowledge. My aim is to identify certain ‘schemes’ relating to temporality and change which are sufficiently general to be applied to a variety of contents. The development of this knowledge will be described in terms of the differentiation and coordination of the meanings involved. At the methodological level, my approach is characterized by a systematic comparison of children’s responses to questions on a single theme (namely changes over time) but relating to different contents. Moreover, a within-subject comparison of answers to different questions is sometimes performed. Even today, a Piagetian theoretical framework and methodology can provide a vital substrate for the study of knowledge. For example, Anna Emilia Berti has shown that in research aimed at determining children’s knowledge of economic topics, the study of subjects’ representations independently of their cultural representations and their actual behaviour can make an important contribution which a strictly socio-developmental perspective is incapable of yielding (see her commentary in Sonuga-Barke and Webley, 1993). Whatever the advantages of a post-Piagetian perspective, it cannot claim to solve all the problems associated with diachronic thinking and its development. If we take account of all the levels of knowledge we identified above it would be naive to expect the study of one of these levels (for our present purposes, the level of meaning) to free us from the necessity of studying the remaining levels. Similarly, the cognitive study of individual representations should, sooner or later, be complemented by the study of the other dimensions. Thus we are convinced that the work presented here will have to be complemented by studies undertaken by researchers working from different perspectives and, in particular, approaching the question from the standpoint of psychosocial and differential research and the study of the psychology of personality. Questions Asked and Tasks Set A dozen experiments were conducted in an attempt to find answers to the questions posed in the preceding chapter. While the experimental method changes slightly from one experiment to the next, a number of shared principles and aims were common to the entirety of this research. The main objective was to obtain data concerning the way children represent changes over time when dealing with evolutive phenomena. The term ‘evolutive phenomena’ is here used in its extended sense and applies to phenomena of growth and development, processes of decay, transformations of matter and changes due exclusively to human activity. In order to achieve this goal, it was important to make sure that the children’s spontaneous representations were not influenced by the premature presentation of depictions of the transformations which they were to be asked to complete or seriate. Therefore in the majority of these experiments, the subjects were presented with a situation which constituted an isolated state within a transformational process. The children were then asked to imagine and describe (either by means

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of a drawing or verbally) the past stages of the presented situation or its future evolution. The depictions or verbalizations provided by the children then served as the starting point for a Piagetian-type interview. In such an interview, which is conducted individually, the same main questions are put to each child. However, it may also contain additional questions designed to induce the subjects to explain their responses. A first set of questions was posed in each experiment and was designed to extract from the children a verbalization of the changes which they had attempted to portray in their drawings or descriptions. For example this set of questions included ‘what changes in the tree when it grows?’, ‘what has changed in the tree between your first and second drawings?’, ‘and between the later drawings?’. Of interest also were the causes which the children cited for the imagined changes. The related questions were not asked with the aim of studying children’s causal explanations as an end in themselves. Instead, we wished to gain an understanding of their conception of change and see whether their explanations contained any reference to past events or future transformations. Finally, the subjects were asked a set of questions relating to the temporal parameters of the changes which they had portrayed or described. In particular, these questions were intended to reveal: • at what point they considered the transformations they had depicted to start and stop (for example, at what age does the ability to speak arise and when does it stop developing); • whether the changes take place at regular intervals or just at particular stages or times; • the time elapsed between the different depictions of successive states. This set of questions was posed in the majority of the experiments. A number of other tasks and techniques were introduced depending on the specific aim of the research. For example, in three experiments, pictures depicting successive stages of change were presented out of sequence during the interview. The subject’s task was to place these pictures in chronological order. The aim of this task was to study how children use cues to reconstruct the stages of a process of change. It involves a process of recognition, very different from the evocation of the transformations imagined by the child. This type of task usually enables us to determine the cues that are considered relevant in the reconstruction of development over time. Two of these experiments were designed essentially to study whether the application of a diachronic approach enhances the explanation and solution of a problem. To this end, the children were first asked to find an immediate answer to the problem with which they were confronted. They were then asked a series of questions which encouraged them to consider the situation from a diachronic viewpoint. In effect, these questions required them to reconstruct the past stages

THE DEVELOPMENT OF THE DIACHRONIC APPROACH 17

or predict the future stages of the presented phenomenon. Subsequently, the original question was posed again in order to determine whether the solutions that the children now put forward were different from or richer than their original solutions. Each child was interviewed individually. The interviews, which were conducted in a room devoted to this purpose and which lasted for approximately half an hour, were recorded and subsequently transcribed word for word. Variations in the Contents and Context of Knowledge The experiments which we have conducted into the development of the diachronic approach are more diverse than is suggested by the above description of their shared elements. First, a variety of methods were used to interest the children in the phenomenon or type of change that was being studied. Moreover, the fields of knowledge were systematically varied. This last point represents a fundamental principle of our research since we are interested in a generalizable form of knowledge rather than specific items of knowledge. We consequently varied the field of knowledge involved in order to determine whether certain common characteristics could be identified in the behaviours observed in the different experiments. Three of these fields related to the world of biology. They concerned trees and were associated with progressive evolutive processes (growth and ageing) and a potentially reversible process, namely decay through disease. The methods and results of these experiments will be presented in Chapter 3. Two more experiments were drawn from the physical domain. The first of these related to the transformation of matter, in this case the thawing of ice. The changes in the second case were not observable and concerned the origin and expansion of the universe. This research will be presented in Chapter 4. Another field of knowledge, which is dealt with in Chapter 5, concerns intuitive psychology.The study of this domain is conducted in order to comprehend the foundations of developmental psychology in the child. Although a number of current studies investigate children’s psychological knowledge in the form of the ‘theories of mind’ (Butterworth, Harris, Leslie, and Wellman, 1991; Perner, 1991) no developmental psychologist has so far shown an interest in the origins of this discipline as they are manifested in the child. This subject is naturally of interest to us since it is precisely the diachronic mode of thought that attempts to understand things in the course of development. It was therefore selfevident that we should question children about their conception of the development of cognitive abilities. The result was the performance of four experiments, described in Chapter 5, which related to the way children conceive of the development of drawing ability, verbal skills and intelligence. In the biological and physical fields, transformations are mainly due to natural processes. In contrast, psychological development is subject to both natural laws and human influence. We also conducted two experiments relating to changes in

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domains which are exclusively influenced by human activity. One of these experiments made use of the evolution of economic status (poverty or wealth), whereas the other considered the problems of motorized transport. These two experiments are considered in Chapter 6. The Population Studied Different children were questioned in each of the experiments. We conducted individual interviews with a total of about 700 children undergoing normal schooling in the state schools of a Swiss city (Geneva). While the population we studied contained representatives of a number of nationalities, the majority (approximately 70 per cent) were Swiss. Most of the children came from middleclass families although a small number were drawn from higher or lower levels of the socio-professional hierarchy. In nine of the experiments, the age-groups studied were contiguous (one agegroup per school year). This distribution of subjects made it possible to trace all the principal stages in the development of knowledge, an advantage which is not always available when more widely spaced age-groups are investigated. It is necessary to provide an explanation for the choice of the principal age range treated in our research which extends from 7–8 years to 11–12 years. As stated in the first chapter, our aim was not the study of the knowledge of time but rather the study of the use of time in knowledge. We therefore wish to avoid being in a position in which we would be unable to differentiate between those aspects of the responses obtained which result from a lack of temporal knowledge and those which are due to an insufficiently developed diachronic approach. For this reason, the youngest age-group studied, which usually consists of children aged 8 to 9, had already reached a level of cognitive development at which they possess the well-differentiated intellectual tools necessary for reasoning in time (Montangero, 1985; Piaget, 1969b). By selecting children of 8 years or more as the youngest to be interviewed in the majority of our experiments we have exposed ourselves to the risk of a ceiling effect. It might perhaps be expected that children who, in a number of fields, have attained the level of concrete operations would be able to produce an accurate representation of changes over time and would exhibit only a very limited development in their diachronic approach up to the age of 11. Our research has shown us that this is far from being the case. As we shall see, the age range studied is of considerable interest for the analysis of the development of diachronic thinking.

Chapter 3 The Evolution of Conceptions of Biological Transformations (the Growth and Decay of Trees)

Draw me a Growing Tree: from Change of Size to Morphological Transformation

Objectives and Problems Of the changes that occur in time, there is one that is particularly relevant to children, namely the phenomenon of growth. While children are, of course, most interested in human growth they are far from indifferent to the question of plant growth. Having learned, as early as kindergarten, that a seed will turn into a shoot or, at least in the case of children who have some experience of nature, that a flower grows, blossoms and then withers or that the grass gets longer, young children know perfectly well that the concept of growth can be applied to plant life. We have decided to study children’s representations of the growth of a tree not simply because this concept is familiar to them but also because it is a process which is not difficult to represent graphically. In the first of the experiments to be presented here it permitted us to reduce verbal elements to a minimum. The aim of this research was to see whether the conception of the growth of a tree changes over the age range under consideration. Clearly, there is a development in the drawing technique: between the ages of 7–8 and 11–12 delineation becomes more precise, shapes become more realistic and an increased number of details can be drawn. In contrast, at the level of children’s conceptions of growth, it may well be that no major transformation is observed between these ages since the external manifestations of this phenomenon are relatively simple to grasp. As far as animal growth is concerned, Gelman (1993) has shown that from the age of 3 onwards, children know that size increases with growth and that at 6 they also expect to observe an increase in the complexity of form. It might therefore be supposed that children of 7–8 years of age are already familiar with

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the characteristics of tree growth. If this is so then any progress observed between the ages of 7 and 12 should therefore be quantitative in nature and be reflected in more pictures or a greater amount of detail portrayed. However, I concur with the results obtained by Carey which point to a clear evolution of biological concepts up to the age of 10 (see Carey, 1985) and reject this hypothesis. Instead, I postulate that the child’s conception of growth may indeed change between the ages of 7 and 12. What prompts me to advance this hypothesis is the great complexity of diachronic thinking together with the fact that cognitive abilities undergo considerable progress during this period. The second aim of this research was to study the relationship between temporal knowledge and diachronic thinking. There can be no doubt that we are dealing here with two distinct forms of knowledge. For example, to establish a correspondence between the date or age of the states of a transformation and the total duration of the evolutive phenomenon is a simple question of temporal reasoning. In contrast, the ability to associate a present state with a past state or possess a particular conception of transformations which occur over time does not form part of this reasoning. Instead, it is an attribute of diachronic thinking. The two types of knowledge are combined at the point where the subject needs to establish the precise duration of an evolutive phenomenon. In such a case, the subject must not only be able to conceptualize this evolution (diachronic thinking) but also be in a position to measure it using temporal units (temporal reasoning). Given that in certain cases it is possible, and indeed necessary, to fuse diachronic thinking and temporal reasoning, it seems to me to be important to observe the relations which may obtain between these two types of competence. Tasks and Population An initial experiment, designed and conducted by Dionnet, made it possible to enumerate the behaviours which are of interest in connection with the question of tree growth. This experiment has been reproduced by Pons and Scheidegger with the twin aim of verifying and quantifying certain results and of studying the correlation between this behaviour and responses concerning another evolutive phenomenon. The procedure of the first experiment was as follows. Drawings of the stages of growth of a tree By way of an introduction, the subject was first shown an accelerated video depicting flowers opening. The children were then asked to draw ‘how a flower opens’ and to produce as many drawings as necessary to make it quite clear how flowers open. The experimenter then asked whether ‘it’s the same when trees grow’. Since the response to this question was negative in every case, the children were asked to produce ‘drawings that show just how a tree grows’.

THE EVOLUTION OF CONCEPTIONS OF BIOLOGICAL TRANSFORMATIONS 21

This task therefore required the subjects to imagine a growth process which children aged between 7 and 12 have never seen unfold for any one tree. At most, they might be able to reconstruct the development of a tree on the basis of observations of various stages of growth each of which concerns a different example (trees or shrubs of differing sizes). In this experiment the children’s knowledge was presented in the form of drawings and they were not called upon to verbalize their conceptions. Since Luquet’s work in 1913, we have known that children’s drawings do not simply represent what they see but also what they know. Thus the drawings produced in this experiment reflected not only the observable characteristics of trees and pictures of trees but also what the subjects knew, or thought they knew, about the growth of trees. Questions concerning the temporal parameters The second set of questions posed to the subjects of this experiment related to the temporal parameters associated with tree growth. On the one hand, the children were asked to estimate the total period of growth which they had depicted (‘how much time has passed between what is shown in the first picture and the last picture?’). On the other, they were asked to state the age of the tree that was depicted in each drawing in the series. The aim of this set of questions was to study the relation between children’s conceptions of evolutive phenomena and their temporal knowledge and reasoning. Such temporal knowledge may be further divided into two aspects: first, there is the empirical aspect, that is to say data acquired concerning the duration of tree growth and, second, there is the aspect of deduction or coherence which can be observed in the relationship between the total duration of the phenomenon and the age attributed to each of the depicted trees. The nature of growth The third point studied in this experiment related to the spatial characteristics of growth. In order to determine whether children think of growth as a cumulative or distributed phenomenon, the experimenter drew a cross half-way up the trunk of the first tree drawn by the child. The subject was then asked to indicate the position of this cross in the subsequent drawings which represented more advanced stages of growth. If children considered growth to be cumulative, the cross would not remain half-way up the trunk since this would be thought to continue growing above (or below) the point marked by the cross. In contrast, if growth was considered to be distributed, the cross would be expected to remain half-way up the trunk. In reality, it appears that tree growth is cumulative. However, our aim was not to test whether children were budding botanists but to determine whether or not they were able (based on the model of human and animal growth) to think in

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terms of distributed development which affects the entirety of the segment under consideration. Population It comprised 80 children aged between 7 and 11 (16 per age-group). Second experiment This experiment followed the procedure of the first experiment with the following modifications. The subjects were not shown the film of the flower opening but were instead immediately asked to draw a tree. They were then told: ‘Draw me as many pictures as you need to show me what happened before and then after your drawing.’ Moreover the third part of the procedure (nature of growth) was suppressed. In this experimental variant, the subjects were also asked about the causes of growth. The population comprised 60 subjects. In order to verify the results obtained in the first experiment a group of children of a mean age of 9 years was compared with a group of mean age 12 years (15 children per group). Furthermore, to see whether the developmental trends which were observed became more fully established after the age of 12, a group of adolescents (15 subjects) and a group of adults (15 subjects) were also interviewed. For reasons beyond our control, these last two groups had to be interviewed collectively using a paper-and-pencil questionnaire. Thus any comparison with 9- and 12-year-old groups is purely indicative. The age ranges and mean ages are as follows: 9 years (from 8:6 to 9:5, M=8:10), 12 years (from 11:6 to 12:5, M= 11:10), 14–15 years (from 14:1 to 14: 11, M=14:8) and adults (from 24 to 32 years, M=24:3). Results Depiction of changes As might have been expected, all the subjects tested depicted growth-related changes in the appearance of the tree. The mean number of drawings representing different stages in the growth of a tree has no discriminant validity (the mean number of drawings varied between five and six depending on age). Of far greater interest were the changes depicted by the children in their drawings. The number of changes depicted grew very significantly with age: in the second experiment (involving age groups of 9, 12, 15 and 24 years), the mean number of changes varied between 0.9 and 3 depending on age and an analysis of variance (one-way) yields highly significant results (F=13.97, p< 0. 001).

THE EVOLUTION OF CONCEPTIONS OF BIOLOGICAL TRANSFORMATIONS 23

The changes depicted concerned the size and thickness of the tree, the number of branches and leaves, the presence of a crown (simply added as a circle) or the transformation of the shape of the tree. Moreover, some of the drawings did not depict a standing tree but rather a seed, a shrub, a felled tree etc. In the drawings of the 12-year-olds it was frequently possible to observe the depiction of people tending the tree. An analysis of the nature of the depicted changes shows that constancy or variation in the shape of the tree was the clearest indication of development in the conception of growth. We grouped the drawings into four categories (see figure 3.1 a, b, c, d): (1) constant shape (absence of morphological change; the dimensions simply increased progressively); (2) minor changes in shape (either the shape of the tree itself remained constant, as in (1), but was preceded by a different shape—for example, that of a seed—to depict the tree’s origin, or the shapes of the tree remained very similar and were differentiated only by the addition of a circle to depict the crown or by additional branches which did not modify the general aspect of the tree); (3) different and identical shapes (at least three different shapes while many successive drawings possessed an identical shape as in (1)); (4) shapes all different (one shape per drawing). In the first experiment, most of the youngest subjects (62 per cent of 7-yearolds) depicted type 1 growth which consisted exclusively of an increase in the size of the tree. The shape remained identical in all the drawings while growth was indicated by the inflation of this shape (see figure 3.1 a). At the age of 8, half of the children still produced this type of drawing. In contrast, 75–80 per cent of the 10- and 11-year-old subjects depicted clear morphological changes during growth (see figure 3.1 d). If the four types of drawing are combined to produce two general categories: (I) identical or closely related shapes (types 1 and 2); (II) varied shapes (types 3 and 4), then we find that a majority of subjects can be placed in category II from the age of 10 onwards. In the second experiment, in which the youngest subjects were 9 years old, there were almost no type 1 drawings (one drawing only at age 9 and age 12). Table 3.1 presents the distribution of the subjects in the four age-groups over the two categories which we have formed from the four types of drawing. It can be seen that two-thirds of the 9-year-old children are placed in category I, whereas the majority of the 12-year-old subjects (12 out of 15, or 80 per cent) produced category II drawings. Six of these subjects produced type 4 drawings (one shape per drawing), while none of the 9-year-olds produced this type of response. These results, which are in agreement with the experimental data which we shall present in the following chapters, draw our attention to the importance of the representation of qualitative changes (different shapes or structures) from a certain level of development onwards. This can be contrasted with the more quantitative conception of change that is observed in children aged 7 to 9. When we turn to children’s global conception of growth, we are able to identify two general types. On the one hand, there was gradual, linear evolution progressing from a beginning to an end and, on the other, we observed a cyclical

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Figure3.1: Tree growth Examples of series of drawings: (a) constant shape, (b) minor changes in shape, (c) different and identical shapes, (d) shapes all different

THE EVOLUTION OF CONCEPTIONS OF BIOLOGICAL TRANSFORMATIONS 25

Table 3.1: Categories of drawings. Percentage of subjects per age-group (N=15 subjects per group) and category

conception of development. In this latter conception, the old tree produces seeds which form the starting point for growth identical to that depicted in the first set of drawings. It is linear evolution that we found depicted most frequently in subjects up to the age of 15. The spontaneous representation of cyclical growth was very rare in 9-year-olds (13 per cent of subjects) and increased notably with age (40 per cent at age 12, 46 per cent in adolescents and 66 per cent in adults). Temporal parameters A study of the temporal parameters which children attributed to the stages of tree growth revealed a change in their conception of the total duration of the phenomenon. The majority of 9-year-old subjects (87 per cent) believed that this duration was less than 10 years. Amongst the 12-year-olds, however, the estimated duration was considerably longer: 11 children out of 15 (73 per cent) thought that the process extended over a number of decades, generally taking about 100 years. The most striking characteristic of these estimates concerned the age attributed to each of the trees in the series of drawings. The first experiment revealed that most 7-year-old children believed that there was a fixed interval between the various stages of growth (for example, the trees in successive drawings were considered to be 1 year old, 2 years old, 3 years old etc.). In the second experiment it can be seen that two-thirds of the 9-year-old subjects still believed that there was a fixed interval between the stages of growth. This type of evaluation had disappeared completely in the 12-year-old group. A study of the relationship between the ages attributed to the trees and the total period of growth revealed that there was still no correspondence between these two types of evaluation at the age of 9. Most of the children (87 per cent) estimated ages which did not correspond to the duration of growth. For example one subject stated that ‘it took ten years’ from the first to last drawings of the sequence. However, he also thought that the tree in the first drawing was 2 years old whereas that in the final drawing was 4 years old. Another child stated that seven years had passed between the first and last drawings and that each of the trees depicted on the nine drawings had gained one year, the first being two years

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Table 3.2: Correspondence between temporal estimates. Percentage of subjects per agegroup (N=15 subjects per group) whose estimation of the age of drawn trees corresponds or not with the total duration of growth

old and the final one 10 years old. Three of the 15 adult subjects also made similar mistakes. As Table 3.2 shows, only a minority of 12-year-olds failed to establish a correspondence between age and total duration. Correspondence increased with age, the greatest progress being made between the ages of 9 and 12. Drawing the cross When we turn to the cumulative or distributed nature of growth, we find that the first of these conceptions predominated in all the age-groups studied in the first experiment. However, from the age of 9 onwards, a minority of subjects thought that the cross would remain half-way up the trunk. This belief may derive from a distributed conception of growth (the subject believed that each part of the segment grows). However, this behaviour may also be indicative of the primacy of the idea of the middle and imply no kinematic representation of changes in time. Summary and Conclusion It is clear that this initial research does not enable us to draw any general conclusions concerning the development of the diachronic approach. However, it does demonstrate that children’s conception of a simple evolutive phenomenon, such as the growth of a tree, changes between the ages of 7–8 and 11–12. A new way of conceptualizing this phenomenon makes its appearance at age 10 and becomes established one year later. What evolves with the age of the subjects is the variety and nature of the changes they depict. Young children, primarily at age 7 but also sometimes up to the age of 9, imagine that a single aspect—or a very restricted number of aspects —changes with time. In contrast, children aged 11 or 12 imagine that a whole set of transformations take place in the course of time. The criterion of development

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which I propose observing in order to trace this evolution relates to the morphological changes involved in tree growth. It seems to me that what is important for development is not the variety and complexity of the depicted shapes but the tendency, when asked to represent the growth of a tree, to depict a different shape in each drawing. By the end of this evolution, children depict growth as a series of distinct steps. In other words, they represent the stages of this evolutive phenomenon. Younger children depict particular moments in the modification of one or two dimensions. These initial results enable us to formulate a hypothesis which we will have to test in other domains: the development of diachronic thinking is characterized by the ability to imagine qualitative changes in time which complement the essentially quantitative changes depicted by children aged 7 to 9. When we turn to the temporal parameters which children attribute to the stages of growth of a tree, we observe that the total estimated duration of the evolutive phenomenon increases with the age of the subjects. There is nothing surprising in this. Since the 12-year-old children have lived longer than the younger subjects, they have learned to think in terms of longer periods and are more likely to have discovered that trees live for a long time. However, in my opinion, this does not explain the very substantial difference in the estimates obtained from the 9- and 12-year-old groups. The 9-year-old subjects imagine a period of growth on the scale of their own lifetimes (less than 10 years). However, by the age of 12, children are quite capable of imagining a growth process which extends over a temporal scale which bears no relation to their own lives (100 years). This is clearly more than a simple quantitative increase. This research has shown us that the majority of 7-year-old children (and, indeed, one-third of 9-year-olds) tend to imagine that there is a fixed interval between the stages representing an evolutive process. For the moment we shall simply note the presence of this inflexibility in the attribution of dates and the duration of the stages of the growth process. We must wait to see whether this type of behaviour is observed in connection with other evolutive phenomena before attempting to analyze it and evaluate the implications. Another noteworthy result obtained among the 9-year-olds and younger subjects is the lack of correspondence between the ages attributed to the tree at each stage of growth and the overall estimated duration of the growth process. It might be thought that at the age of 9 mental arithmetic is not sufficiently automated to permit the spontaneous monitoring of the correspondence between the different values estimated by the child. However, is this really an adequate explanation when the values to be compared are as low and as divergent as in the two examples cited above? Whatever the answer, it is clear that children at the start of the concrete operational stage (between 7 and 9) do not apply the instruments of knowledge which they are able to manipulate (calculation in the arithmetical field, the association of sequences and durations in the field of temporal reasoning) to their spontaneous representations of evolutive phenomena. Children do not make the effort to establish a correspondence

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between their temporal evaluations and, from the conceptual viewpoint, they do not necessarily relate the idea of age to that of duration of existence. To conclude, let us return to a result which relates to the general conception of growth. This is the tendency which children display to conceive of growth as a linear phenomenon with a beginning and an end, whereas it can also be thought of as a cyclical process. Drawings of the stages in the life of a tree which progress from a seed to the mature state simply isolate a sequence within this cycle: on reaching maturity, the tree produces seeds which are the starting point in the life of a new tree. It is clear that 9-year-old children are familiar with the idea of plant reproductive cycles. They should therefore be capable of recognizing the representation of a cycle and of producing such a representation on request. Here we see the gulf which can divide recognitive knowledge, or knowledge which can be activated on request, from spontaneously evoked knowledge. This type of spontaneous evocation occurs more frequently in the 12year-old subjects (40 per cent compared with 13 per cent among the 9-yearolds). However, it is only in the adult group that it can be observed in a majority of subjects. It would appear that humans must think of themselves as physically and socially capable of having children before they think of life as a cyclical process. The Past and Future of a Diseased Tree: from External Discontinuous Changes to Progressive Internally Generated Transformations Objectives and Problems Not all changes in time take the form of a process of progress or growth. In the biological as in other fields, change may follow the path of decay. Similarly, some changes in time are, unlike growth, not irreversible. In order to study children’s representations of these negative and reversible changes, Maurice-Naville designed an experiment concerning spruce disease (Maurice-Naville and Montangero, 1992). The subject of forest disease made a deep impact on public consciousness during the 1980s, particularly in certain European countries such as Germany and Switzerland. Throughout history, the forest has been an object of respect, as much for its value to man as for its symbolic connotations. A mythical place providing shelter for fairies and elves, Sleeping Beauty’s castle and a hideaway for the outlawed hero, the forest is also a source of valuable raw materials coveted by craftsmen and industrialists alike. While aesthetes admire its beauty, the forest is for many people the embodiment of the dynamism and integrity of nature. And this is not to mention its role in maintaining the climatic balance of the planet. It is easy to understand the shock felt by ecologists on learning from

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expert observers that the health of our forests is in decline, probably as a result of air pollution. A number of studies have investigated children’s representations of human disease. While certain authors have revealed a qualitative change in the evolution of such explanations during the course of children’s cognitive development (for example Bibace and Walsh, 1981; Del Barrio Martinez, 1990), Eiser, Eiser, Lang and Mattack (1990) cast doubt on the existence of such a qualitative difference and assert that young children already possess a good understanding of disease. According to these authors, the explanations provided by young children are not very different from those produced by adults. In our study, we were concerned with any age-related changes in children’s conceptions of spruce disease. What interests us here is not the study of the explanation of biological phenomena per se. Instead, the object of our investigation was the correlation between the explanation of the disease and the degree of development of diachronic thinking in the child. If the hypothesis proposed in the first chapter is correct, then the explanation of an evolutive phenomenon should improve as diachronic thinking develops. We therefore expected that between the ages of 8 and 11, the development of children’s explanations of spruce disease would mirror that of the diachronic aspects of the representations of this disease. The primary objective of this experiment was thus to study certain aspects of the diachronic approach which could not be observed in the preceding research, as well as to confirm or deny the general validity of the results obtained during the course of this research. In attempting to identify the development of diachronic thinking, the study of children’s conceptions of spruce disease allows us to investigate two fundamental questions. The first concerns the nature of the links between successive stages of an evolutive process. Are these links as strong and necessary in the representations of the younger subjects as they are in those of their older colleagues? This problem of the connections introduced between the stages of an evolutive phenomenon is of crucial importance for our understanding of the diachronic approach. Indeed, this approach can be defined as the ability to establish links between a current situation and the stages which precede or follow it. The second question concerns the relationship between past and future changes. Do children consider such changes to be similar or dissimilar in nature? As far as temporal measurements and temporal logic are concerned, there is no reason to distinguish between the intervals or sequences which occurred in the past and those which may occur in the future. However, Fraisse (1963) and Harner (1982) have emphasized the asymmetry between past and future which exists in both the temporal estimation and the language of young children. Moreover, it is essential that the past, present and future modes are distinguished in a conceptualization of time which involves diachronic thinking. Is this a purely semantic distinction, a type of label which can be attributed to each successive state, or does it affect the way the data are processed (in other words,

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the way these states are linked)? This question is as yet unanswered and necessitates a comparison of the representations of past and future changes. This new experiment also examines two points relating to the verification of the results obtained in our study of the representations of tree growth. First, it is necessary to determine whether the representations of changes develop as clearly and at similar ages between 8 and 11 when these concern a process of decay. Second, we wanted to investigate whether the tendency of young subjects to imagine fixed intervals between successive states is also observed in connection with the stages of a disease. Questions and Population Drawings of past and future states After a familiarization phase (verbal exchange about the forest and about healthy and diseased trees), the subject was shown a photograph of a diseased spruce tree and asked: ‘Does this tree look all right or is there something wrong with it? Do you think it has always looked like that?’ The child was then asked to draw the tree as it was before and to draw as many pictures as necessary to make clear what had happened to the tree. When the drawings of past states were completed, the experimenter pointed to the photo of the diseased tree (which was at the end of the series of drawings) and asked whether the tree would always look like that. If the answer was negative, the experimenter said: ‘Now draw what is going to happen to the tree.’ ‘And then?’ ‘And then?’ Children’s comments The child had to answer the following question: ‘Can you explain to me what is the meaning of your drawings?’ Since the method of interview was semidirected, other questions could be asked, so that the children could specify what they meant. Seriation Five photos showing successive states of the tree disease (from the initial healthy state to the state of dead tree) were shown in random order. The children were asked to put them in the right order. They were then requested to explain why and how they had proceeded to seriate the pictures and to say what was represented on each photo and what changed from one picture to the following one.

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Questions about temporal parameters ‘How much time has passed between the first photo and the last one?’ ‘Is there the same amount of time between each photo, or does it vary?’ Reversibility ‘Is it possible to tell the story in the other direction, to tell what happened starting from the last picture?’ ‘Can we reverse the order of the photos?’ Explanation of the disease If this explanation was not given spontaneously, the child was asked about the causes of the disease and the possibility of contamination. Population The population comprised 52 children divided into four age-groups of 13 subjects each: 8 years (8:1 to 8:10, M=8:5), 9 years (9:0 to 9:11, M=9:6), 10 years (10:1 to 10:10, M=10:6) and 11 years (11:1 to 11:10, M=11:6). Results We will first deal with the conceptions of the transformations due to the disease, which can be divided into three categories of answers. Then we will consider the results concerning the answers to the questions about temporal parameters. Lastly the explanations of the disease (answers to the questions about its causes) will be presented. Conceptions of transformations We have considered the different answers given by each child concerning the number, the form and the continuity of the transformations due to the disease. The set of answers can be classified into three categories each of which corresponds to a distinct level of development. Level I is characterized by the representation of discontinuous states. In level II answers, changes are gradual and external and in level III subjects depict changes that are also gradual but with a continuity introduced between states thanks to the reference to an internal process. Table 3.3 shows the proportion of subjects of each level by age-group. At the age of 8 years, the majority of subjects fell within level I, at 9 they were divided almost equally between levels I and II and at the age of 10 between levels II and III. The majority of 11-year-olds gave sets of answers of level III.

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Table 3.3: Pine tree disease. Percentage of subjects per age-group (N = 13 subjects per group) and per level of representation of changes due to disease

In level I responses, there were few drawings depicting the evolution of the disease and there was no link between them. Each child produced two to three drawings, with a maximum of one drawing showing what was going to happen in the future. In these drawings and in comments made about them changes appeared to be sudden. When the future was represented, it obeyed a different law of evolution than the past. In some subjects (5 out of 17) the drawings revealed a confusion between the progression of the disease and the passage of the seasons. Here are a few examples which illustrate this category of answers. Child aged 8:9 (see figure 3.2 a). This subject produced one drawing only. ‘First some leaves. Here [showing the photo of the diseased tree] they have nearly all fallen off.’ The child was asked whether the tree would always remain like this. She answered affirmatively. Child aged 8:3 (figure 3.2 b). The subject produced one drawing for the past and one for the future. ‘Here [past] there were more leaves than now, the tree was younger. There [future] the wind is going to blow its leaves off.’ Child aged 8:6 (see figure 3.2 c). The subject drew one picture for the past and one for the future. ‘Here [past] it was small. Here [photo] it does not have any leaves because it is autumn…it is sick, because it is losing its leaves. Here [future] it looks nice because it is summer.’ This is a clear example of lack of differentiation between multiple processes of change over time. The child represented both the growth (increase of height) and the change of seasons although he was requested to depict the evolution of the disease. As far as the sedation of the five photos was concerned, it was correctly executed by the majority of subjects, from this age onwards. These children had no difficulty in reconstructing a series of states which follow one another chronologically. What they lacked was the spontaneous representation of a differentiated evolutive process constituted by gradual changes. When asked questions about the reversibility, most of these children accepted the idea that the story can be told from right to left as well as from left to right. This was however a case of pseudo-reversibility, since the process of change was thought to be different in each direction. For example, in one direction ageing was mentioned: ‘This one is young. Now it is older. Still older.’ In the other direction, the same subject referred to a regenerating process due to the change

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Figure 3.2: Examples of drawings of level I representing the stages of disease of a tree Source. Reproduced from Maurice-Naville, D. and Montangero, J. (1992) The development of diachronic thinking: 8–12-year-old children’s understanding of the evolution of forest disease, British Journal of Developmental Pyschology, 10, 365–83, with kind permission of The British Psychological Society, London, UK.

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of season: ‘There [drawing of a dead tree] there is something wrong. Here it is better because it is summer. Here it is in good health.’ At level II, characterized by external gradual transformations, more drawings were produced (mean of five drawings per child) and they depicted a more progressive change (the gradual falling off of leaves), with intermediate states between the states drawn by level I children. Verbal descriptions often comprised expressions indicating the progressive aspect of changes: ‘It is beginning to, there are some more, it becomes more and more.’ At this level, children ceased to mix growth and disease in their representations of successive states. Half of the children of this level anticipated only one future outcome whereas the other half mentioned successively two possibilities. For example, they drew a progressive decay until the death of the tree. Then they said they could draw another series of pictures for the future and they depicted a regeneration of the tree resulting from some form of human intervention. Here are examples of the different subcategories. Child aged 9:6 (figure 3.3 a): ‘At the beginning [first drawing], there were a few more leaves and each time [following drawings and photo] it lost a few more.’ For the drawing of the future state: ‘These branches are beginning to go yellow and the bark will become dry.’ Child aged 10:9 (figure 3.3 b): ‘[First drawing] There were lots of branches at the top and lower down as well. [Second drawing] I will put fewer branches and the lower part will start to go bare. [Photo] It is a diseased tree. [Drawing 3] It is going to get worse, it is beginning to lose its needles higher up as well, the roots are starting to be damaged by insects. [Drawing 4] It is going to die. Then the subject proposes another outcome [Drawing 5]. We could try and make it better, maybe cut the trunk. [Drawing 6] It is beginning to grow again.’ As far as the question about reversibility was concerned, only a minority of subjects at this level accepted that the story could be told from right to left and imagined that some human intervention would put an end to the disease. At level III the transformations were conceived as continuous and due to an internal process. The states of the disease drawn became more numerous (mean of 11 per child). Sometimes the internal process was only vaguely alluded to: the disease or dryness spreads into the tree. Here is an example (child aged 11:2, figure 3.4): ‘[1] It is healthy. [2] Then it becomes a popular place for tourists. People come and throw things, for example banana skins. There are gaps in the vegetation. [3] There are more and more gaps in the forest. It is polluted; more and more people pass by. [4 (Photo and next drawing)]. They are more and more diseased. [5] Here it is completely bare, it is beginning to go dry and die. [6] There it is rotten.’ More often children of this level explicitly referred to what was supposed to take place within the tree. For example, one subject said: ‘The water gets polluted and then it gets into the roots, it rises with the sap, it’s spread everywhere, the tree cannot get proper nourishment any more, it is weakened, it has less and less resistance.’

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Figure 3.3: Examples of drawings of level II representing the stages of disease of a tree Source: Reproduced from Maurice-Naville, D. and Montangero, J. (1992) The development of diachronic thinking: 8–12-year-old children’s understanding of the evolution of forest disease, British Journal of Developmental Pyschology, 10, 365–83, with kind permission of The British Psychological Society, London, UK.

As far as the future was concerned, several possibilities were mentioned by each subject. One child said, for example: ‘It depends whether the tree is strong enough to resist and it also depends on the season and on the type of soil.’ Another asserted: ‘Either it will become worse and worse and it will die or it is strong enough to resist and it will get healthy again, or else it will stay like this [with some branches without needles] for the rest of its life.’ Since they were able to imagine several possible outcomes, the children of this level accepted the idea that the evolution can also be described from right to left (reversibility of transformations). Temporal parameters Let us now consider the answers concerning the time that elapses between the successive states depicted. At level I, half the children thought that the interval between each picture was constant. As of level II, subjects imagined that the evolution had an irregular rhythm. Practically all of them thought that the interval between the final stages of the disease would be shorter than the duration between the initial states: they imagined an acceleration of the process of decay. Some level III subjects thought that different rhythms were possible, as a function of the age of the tree, of the climate, etc.

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Figure 3.4: Examples of drawings of level III representing the stages of disease of a tree Source. Reproduced from Maurice-Naville, D. and Montangero, J. (1992) The development of diachronic thinking: 8–12-year-old children’s understanding of the evolution of forest disease, British Journal of Developmental Pyschology, 10, 365–83, with kind permission of The British Psychological Society, London, UK.

Explanations The diverse explanations given to account for the spruce tree disease can be divided into two categories which correspond to two developmental levels. In the first category, the cause of the disease is punctual and most often due to a human intervention. For example: ‘One day people passed by and threw rubbish near the tree. It gave it the disease.’ At this level, explanations referred to one cause only and tended to confuse the disease with other processes of transformation such as ageing or the course of seasons. When asked: ‘Are the disease and the course of the seasons one and the same thing or are they different?’ they often answered: ‘It is more or less the same thing, because they lose their needles in winter and also when they are diseased.’ In the second category (and second level) of explanation, the disease was presented as an internal biological process which developed gradually. There were no more confusions between the disease and other evolutive processes. An important characteristic of the explanations of this level was their multicausal nature. Each subject mentioned several causes from the following factors: pollution due to car fumes, climatic conditions, nature of the soil and biological factors such as the age or the degree of resistance of the tree. There is some intersection between our definitions of the levels of development of diachrony, on the one hand, and of explanations on the other. Both level III of diachronic thinking and level II of explanation comprise a

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Table 3.4: Comparison of levels of diachronic thinking and explanation in 10- and 11year-old children (N=26)

gradual and internal conception of the disease. However, the main criterion for allocating the subjects to one or other of the levels of explanation was the multicausal aspect of their answers. This criterion is a priori unrelated to changes over time. We have checked whether there was a high level of correlation between levels of diachrony and explanation. The analysis was conducted using the answers of 10- and 11-year-old subjects, who had received comparable information at school concerning biological phenomena. Table 3.4 reveals a perfect correlation between the levels of diachrony and of explanation. Out of 26 subjects aged 10 and 11, only 10 were still at an intermediate level of diachronic thinking (level II). These 10 subjects were precisely those who did not give multicausal explanations and who were consequently at level I of explanation. The remaining 16 subjects were at the upper level both for diachrony and explanation. Summary and Conclusion This experiment shows that the way a sequence of reversible changes leading to decay is represented develops in parallel to the representation of growth, that is, of a sequence of irreversible changes taking the form of an increase or progress. In both cases, 11-year-old children’s graphical or verbal descriptions contrast with those of 8- and 9-year-old subjects and a transition between these two levels is observed at the age of 10. We have identified three levels in the representations of changes due to the disease. At the first level, changes are discontinuous, at the second they are gradual and external and at the third level gradual changes are explained by an internal process. What differentiates these levels is, first, the varied nature of the representation of the stages in the process (and therefore the number of drawings produced), second the link introduced between the steps and third the internal or external nature of the changes envisaged by the child. The temporal parameters of the phenomenon, its possible reversibility and the causes mentioned also vary as a function of the children’s developmental level. The majority of 8-year-olds and half of the 9-year-olds were at level I. Level II could be observed in the other

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half of the 9-year-olds and in 54 per cent of the children aged 10. The remaining 10-year-olds and the majority of 11-year-olds were situated at level III. In the following summary of the results, we shall recall the characteristics of the extreme levels (I and III) for each aspect that we have considered. As far as the richness of the representation of changes and the links between steps are concerned, the drawings and verbal comments of level I children revealed a striking absence of continuity in the changes. The children imagined a limited number of changes and conceived of sudden transformations at the beginning of the process (a punctual cause provoking the disease) or later on (for example, all the needles were supposed to fall off at once). There was no continuity between past and future and the latter, when represented, was reduced to one state only. At level III, there was first significant increase in the number of steps depicted. Furthermore, the links between steps were much more evident: changes were gradual and some internal process was thought to connect the successive states. A given state could be explained by what had happened before, since the state of the tree was viewed as the result of the spread of microbes or ‘pollution’ that had appeared during the preceding state. The disease was thus seen as a single process, well differentiated from other evolutive phenomena, in contrast with what occurred at level I. Indeed younger children did not differentiate clearly between growth, disease and changes due to the seasons. In the evolution they depicted, these different forms of change could be readily substituted for one another. I do not want to assert that 8-year-olds are incapable of distinguishing between the concepts of seasonal changes and of disease. However, when these children imagine an evolution over time, they tend to confuse these concepts. The fact that level I children managed to seriate five pictures representing successive stages of the disease correctly reveals the important difference between a recognition task dealing with cues that indicate an evolution and an evocation task which consists of reconstructing the evolutive process. The status of the future changes considerably between levels I and III. Younger subjects envisaged one change in the future, whose nature was different from that of the past changes. Toward the age of 11 years, children depicted a future evolution which was in continuity with the past changes and they imagined a variety of outcomes. Thus it is only at this level that the future acquires its true status of a set of possible events. As far as the temporal intervals thought to occur between the stages of the disease were concerned, this experiment replicates the findings of the preceding experiment about tree growth. Some of the 8- and 9-year-olds (almost a third of them) imagined fixed temporal intervals between each picture. This suggests that young children have difficulties in dissociating the representation of the passing of time from the representation of the stages of a process. This point deserves to be studied further and will be investigated more thoroughly in a subsequent experiment bearing on physical transformations.

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As far as the nature of changes was concerned, younger subjects depicted quantitative modifications (changes of height or of number of leaves) whereas 11-year-olds mentioned more qualitative transformations like the weakening of the tree, its dryness or rotting and the spreading of the disease inside the tree. This developmental tendency is similar to what we observed concerning tree growth. An experiment should not only confirm hypotheses but also suggest new ones. In this respect, the present research allowed us to observe a new developmental trend: the tendency of older children to refer not only to external changes, as younger children do, but also to allude to an internal process, that is, to what is going on inside the tree. This observation mirrors results obtained by other authors. An advanced form of understanding of biological processes stresses the internal structures rather than the external appearances (Gelman, 1989). Carey (1985) asserts that toward the age of 9 years, children have constructed a model of biological functioning in which substances like air and blood are supposed to pass through the body and be used by it. The 9-year-olds in our experiment very seldom mentioned the idea of internal propagation when they described changes due to the disease. This might stem from a décalage (internalization would be conceived of later on where plants are concerned). It is more likely that children of 9 years of age know that things happen inside trees, but do not resort to this idea when they explain changes over time. From this experiment on the spruce tree disease it can be concluded that children initially think in terms of external transformations and that the consideration of internal phenomena corresponds to a more developed form of diachronic thinking. We shall have to see whether this modification of the nature of the conceived changes can be observed in other experiments or whether it is restricted to the topic of the spruce tree disease. The current experiment raises two further questions: first an apparent contradiction with the results obtained concerning the growth of the tree, second the issue of the distinction between the development of diachronic thinking and the improvement of domain-specific knowledge. I have characterized the development of diachronic thinking as applied to the growth of a tree by the passage from a snapshot representation, where a single aspect is modified (enlargement of the tree) to the representation of qualitatively different stages. Therefore, the discontinuity in the drawings of the growth of the tree was greater in the 11-year-old children than in the 9-year-olds. In contrast, as far as the tree disease is concerned, I consider that the continuity between successive states is a criterion of an advanced diachronic approach. The contradiction disappears if it is admitted that the discontinuity in the older children’s drawings depicting stages of growth is only apparent. The fact that they depicted different stages in the growth does not mean that these children were unaware of the existence of a connection between these stages. Further results described in the following chapters will confirm the increasing importance with age of the continuous character of evolutive phenomena.

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I will also show in the following pages that the development of diachronic thinking cannot be confused with the improvement of specific knowledge about the phenomena considered by the child. Concerning forest disease, one may think that the reference to internal phenomena (like the propagation of microbes or pollution by the sap) simply results from the learning of new information in this domain. As for the differences between recognitive and evocative behaviours, it is necessary to differentiate between stored knowledge and spontaneously applied knowledge. Children aged 8 and 9 have certainly heard about the sap and the blood. They do not, however, use these concepts when they explain the tree disease, because they tend to limit themselves to the representation of external changes. This is a hypothesis whose general applicability will have to be confirmed by further experiments. The Reforestation of the Amazon: Representations of Cyclical Changes in the Distant Future Objectives and Problems In the two preceding experiments, the evolutive phenomenon studied concerned one individual example of a species of plant. However, if we ask children to imagine changes in time relating to a group of plants (in this case a forest) we will be able to test a number of hypotheses derived from our earlier observations and study a new set of problems. The first of these problems concerns the independence of biological change from human intervention. Do children, inspired by some remnant of what Piaget (1972a) termed artificialism, imagine that naturally occurring phenomena are the result of human actions? Or, in contrast, do they think that plant growth occurs spontaneously and cyclically? This question goes beyond the simple study of the explanations of biological phenomena and carries us into the domain of diachronic thinking. In fact, the reactions of children to the problem of the spontaneity of biological transformations reveal their tendency to represent changes in time and their linear or cyclical conception of these changes. These are indeed questions which bear on the problem of diachronic thinking. The results of research conducted by Stavy and Wax (1989) suggest that we should observe a development in children’s attitudes to this question between the ages of 7 and 11. Stavy noted that the proportion of children who attribute a reproductive function to plants varies between 50 per cent and 65 per cent between the ages of 7 and 9 and reaches a distinctly higher level at the age of 10 (at least 80 per cent of subjects). The same author also observed that even at 12 years of age, a number of children still did not think of plant growth within the framework of a reproductive cycle. The second problem we wished to study in connection with representations of growth concerns their uniform or non-uniform character. In effect, if the future

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of a forest is not conceived of as a static phenomenon (persistence of the current state), its development can be imagined as unidirectional (continuous growth), bidirectional, that is to say comprising two aspects (growth followed by decay) or cyclical (growth and decay followed by the growth of a new tree) in nature. The bidirectional and cyclical representations reveal a richer, more extensive capacity for diachronic thinking. If we are correct in considering this more highly developed diachronic approach to make its appearance at the age of 10 to 11 years, then these ‘varied’ representations should also be observable in subjects of this age. The current experiment will allow us to verify this hypothesis. Moreover, we hope that the results will provide us with information concerning our hypothesis relating to the introduction of continuity into representations of change from the age of 10 to 11 onwards. I consider this to be a fundamental step in the development of the diachronic approach. However, while such progress can be observed in the behaviour concerning tree disease, the representations of tree growth observed at about the age of 10 seem to suggest that it is discontinuity that predominates. We therefore decided to return to the subject of growth while placing it in a different context. Our primary object of interest in this experiment is the study of the future mode. In consequence, the changes which the children are asked to imagine are considered to take place after the initial situation which has been presented to them. One question which needs to be asked concerns the way in which future time is differentiated. We might well wonder whether young children possess only a vague notion of the future and fail to distinguish between the near and distant future. It was for this reason that the questions which we asked related to an indeterminate future, a long-term future and a very long-term future. Despite the fact that our object of study is not temporal reasoning (because we are concerned with representations in time rather than inferences about time), we once again wish to concentrate on the relations obtaining between temporal reasoning and the diachronic approach. The fact that we are presenting a situation concerning a set of plants allows us to study the coordination of speed, space and time. This coordination forms one of the bases of temporal reasoning. When it bears on the movement of two objects, this coordination is displayed by the majority of 8-year-old children (Montangero, 1985; Piaget, 1969b), despite the fact that the way the problem is posed may cause difficulties for older children (Crépault, 1989; Siegler and Dean Richards, 1979). In the case of the two moving objects, some of the parameters to be correlated (distance travelled and relative start and end positions) are visually denned and can be ‘read’ at any time in the form of two parallel paths representing the distances travelled. However, if we turn our attention to the question of the growth of large trees compared with that of shrubs, the spatial parameters are much less clearly defined and are consequently less easy to compare. We can therefore expect our subjects to encounter a number of difficulties. Does the ability to overcome these problems evolve in parallel with the development of diachronic thinking? That is the final question that this research was intended to study.

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In order to find a solution to this set of problems, Maurice-Naville designed an experiment which asked subjects to comment on the possibility of the regeneration of the Amazon forests as a function of the degree of deforestation sustained (Maurice-Naville, 1993). We have already pointed out in connection with our experiment concerning pine disease that the subject of forest disease worries adults and children alike. It is, moreover, perfectly suited to the study of the various points listed above. Questions and Population Familiarization with the pictures presented After a conversation about the Amazon forests, the child was presented with three photographs of deforested areas in this region: P1. Small area. ‘Men cleared this part of the forest in order to build a hut.’ P2. Larger area. ‘Men have deforested this part of the forest to grow crops.’ P3. Large-scale deforestation. ‘Men cleared this part of the forest to exploit the subsoil, for under the forest, the ground is very rich in iron ore.’ In order to be sure that the degree of deforestation was evaluated correctly, we asked the subjects to classify the photographs in order of increasing deforestation. The children were also asked to establish a correspondence between three pictures showing workers (lumberjacks or bulldozer drivers) in increasing numbers and the three deforested areas. Change or stability in an undetermined future ‘The workers have left the Amazon forest and nobody comes back there. Do you think it will stay like it is in the photo or will it change?’ The same question was then asked about the three different pictures (P1, P2 and P3 separately). Duration of regeneration ‘How long will it take for [P1, P2 and P3] to become a beautiful forest again?’ Relative growing speed About photo P1, which shows savannah, bushes and big trees: ‘Will it grow at the same speed everywhere?’

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Situation during regeneration ‘What will it be like when half the time it needs to become a beautiful forest has passed?’ Distinction between area to be reforested and growth About P2: ‘If instead of clearing this whole area, the men had cleared only half of it, do you think it would take the same amount of time, more time or less time for it to become a nice forest again?’ Change or stability in the long-term future The question was asked about a photograph showing an intact, non-deforested part of the Amazon forests. ‘Imagine that this photo was taken when you were very young. Now imagine that you come back to this spot when you are an old person, at the age of 85. In the meantime, no-one has been into the forest. You take a photo. Will it be the same as this photo or will it have changed?’ Change or stability in the very long-term future Same question as the preceding one, but the interval between the first and second photo is of a thousand years. Population The population comprised 66 subjects divided into five age-groups of 12 to 15 subjects each: 7 years (7:0 to 7:11, M=7:3), 8 years (8:2 to 8:11, M=8:5), 9 years (9:0 to 9:11, M=9:4), 10 years (10:3 to 10:11, M=10:9) and 11 years (11:3 to 12: 6, M=11:6). Results Representation of changes The representation of autonomous changes (that is, without human intervention) in deforested woods develops considerably with age (see table 3.5). In answer to the question: ‘Will it always stay like this?’ more than half the subjects aged 7 and 8 years did not anticipate any change. In our sample of children, there was an important effect of the sex variable: girls anticipated a status quo, whereas boys imagined some slight changes. Moreover, the more deforested the area, the more generalized was the anticipation of a status quo. From 9 onwards, the majority of children thought that the forest would change. However, only a minority of 9-year-olds (42 per cent) believed in the possibility

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Table 3.5: State of the forest in undetermined future. Percentage of subjects per age-group anticipating a change or not

of an autonomous regeneration of the forest. Of the subjects of this age who predicted a change, 37 per cent anticipated a decay (that is, the tree would go rotten). At the ages of 10 and 11, children’s theories on this question had changed. Almost all of them expected the forest to change and only a few subjects (25 per cent or less) predicted decay. However, when confronted by large-scale deforestation, as in photo P3, some of these children anticipated no change (more than half of the subjects at 10, 38 per cent at 11 years). Qualitative aspect of changes How did the children envisage the nature of changes in deforested areas? Their answers to our questions about the state of the area when half the time necessary for regeneration has elapsed gave us some information about this point. The most striking difference between the answers of younger and older subjects lies in the static or dynamic nature of the description. At 7 and 8 years, they described a state: ‘There will be big trees and small trees’ or ‘There will be more trees’ or ‘Big trees will have fallen down, and the others will be half of their normal height.’ In 44 per cent of the subjects at the age of 9 and in the majority of 10- and 11year olds (about 65 per cent), answers alluded to a dynamic process such as growing, evolving, disappearing. These children also often mentioned a difference in the speed of growth. For example, one child said: ‘Small trees will grow a little, but they will remain smaller than the big trees. Big ones will not grow, they are tall enough.’ Speed of growth When they were specifically questioned about the speed of growth, younger children imagined different speeds for big and small trees. This showed that, on request, young children are able to differentiate between the speeds as a function

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of the age of the tree. However, the temporal reasoning underlying young children’s speed judgements was far from correct. These children judged that big trees grew faster than small ones: ‘The big ones grow faster, because they were planted first’ (child aged 7:10). Such answers resulted from a confusion between two meanings of the term faster in French (plus vite), the correct, usual cinematic meaning (faster) and the ordinal meaning (first) that can be found in children’s language. The speed judgement ‘bigger entails faster’ could be observed in all the 7-year olds, 69 per cent of the 8-year olds and still 58 per cent of the children aged 9. From the age of 10 onwards, this type of judgement became extremely rare (8– 13 per cent of the subjects). These older children not only related the speed of growth to the age of the tree, but they judged that young trees would grow faster. Moreover they thought that the speed of growth depended on several factors such as the age of the tree, the quality of the soil and the water available. Changes in the long-term future Let us consider the results relating to the long-term or very long-term future (see table 3.6). As already mentioned, these questions were not asked about deforested areas, but about an intact part of the forest shown in a photograph. Four types of answers could be given: • • • •

status quo (The forest will remain as it is in the photo); indeterminate change (It will not be the same); decay (Trees are going to dry or rot); renewal (New trees will grow).

When the interval is of 85 years, the majority of the 7- and 8-year-olds anticipated an unspecified change. A third of the 7-year-olds, however, thought that nothing would change. At the age of 9, they all imagined some kind of modification and the idea of decay was mentioned by the majority of children (73 per cent of them referred to decay alone or together with the renewal of other trees whereas the anticipation of renewal, alone or together with decay, was found in only 27 per cent of the children of that age). In the 10- and 11-year-olds the idea of decay was still predominant, but the concept of renewal appeared in the answers of half the subjects. When subjects were asked to anticipate the state of the forest after an interval of a thousand years, the proportions of types of answers changed (see table 3.7). At the age of 7, answers of the status quo type were practically nonexistent. Besides, a small minority (around 20 per cent) of young children referred to the ideas of decay and renewal. A third of the 9-year-olds were puzzled by the question and said they did not know the answer. At the ages of 10 and 11, the concept of renewal appeared very frequently and predominated over the idea of decay.

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Table 3.6: State of the forest in 85 years. Percentage of subjects per age-group and type of response

Table 3.7: State of the forest in a thousand years. Percentage of subjects per age-group and type of response

The answers mentioning both the ideas of decay and renewal were very rare before the age of 10 and were given by half the 10- and 11-year-olds for an interval of 85 years. When the delay was of a thousand years, the percentage of subjects giving such answers diminished at the age of 10: the majority thought that the trees in the initial photo would have disappeared and would be replaced by new trees. In contrast, 11-year-olds anticipated both decayed and renewed trees. This probably does not mean that they thought the life expectancy of trees was a thousand years, but rather that they imagined that after such a time some of the trees (different from the trees on the initial photo) would be decaying whereas other trees would be in full health. Regeneration period for half the deforested area The last result that will be described here is related to the evaluation of the relative duration (more or less time) of regeneration when only half the area shown in picture P2 is deforested. Three categories of answers could be observed.

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Table 3.8: Duration of regeneration of half the P2 area. Percentage of subjects per agegroup and type of evaluation

In the first one, the time for regeneration of half the area is longer than the duration necessary for the whole area to be reforested. This is an inverse relation (less area entails more time), which is somewhat surprising. Children’s comments revealed that they imagined that regeneration depended on human intervention. According to these children, people would take care of larger areas first, hence the shorter time needed for their regeneration. In the second category of answer, the regenerating of half the area takes less time than the regeneration of the whole. Lastly, in the third type of response, the regeneration time is equal for half the area and the total area. Such answers show that children differentiate between the extent of the area to be regenerated (horizontal growth) and the growth of trees (vertical growth), which does not depend on the extent of the area. Table 3.8 shows the frequency of answers of the different categories in each age-group. At the age of 7, the most frequent answer (50 per cent of the subjects) was of the first category. A quarter of these children established a relation belonging to the second category (less area=less time). Another quarter judged that durations were equal for half the area and the total area, because in both cases people would take care of the forest. The 8-year-olds’ answers were equally divided between the first category (less area=less time) and the second (half the area=half the time). At the age of 9 the first category of answers disappeared, with a clear majority of answers (82 per cent) falling into the second category (less area=less time). This type of answer still predominated at the age of 10 (60 per cent of answers). The third category of answers (less area but equal time) appeared in an important minority of the 10year-olds (40 per cent) and in the majority of 11-year-olds. Summary and Conclusion Striking changes take place, between the ages of 7 and 11 years, in the anticipation of the regeneration or the decay of a forest. These changes do not

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only reflect a transformation of the children’s biological concepts, in accordance with the findings of Carey (1985). They also express the development of diachronic thinking. The progression of the more or less developed behaviours that constitute this development will be summarized below. After that, I will sum up the main characteristics of each age-group. Concerning the reforestation of deforested areas, the most primitive behaviour consists in imagining that nothing will grow again without human intervention. This residue of artificialism (that is, the tendency to think that natural phenomena have a human origin) shows that no reproductive function is attributed to plants, in accordance with Stavy and Wax’s (1989) findings in children younger than 10. In my opinion, this result does not only stem from a lack of biological knowledge. This type of answer is also (and perhaps mainly) due to the fact that young children have difficulty in imagining cycles of changes in the future. Another type of answer is the anticipation of the decay of the remaining trees, rather than of the growth of new trees. In this case, the future is conceived of as an extension of the past (the forest deteriorates). From a diachronic viewpoint, it reveals that a relation of identity is established between the past and the future. The third type of answer, which is typical of older subjects, consists in anticipating the growth of trees in the deforested area. The direction of the changes anticipated (growth) is opposite to that of the preceding human intervention (deforestation). When children have to imagine the state of an intact part of the forest in the long-term future, the three types of answers described above can be observed, with importance of the idea of growth diminishing. The fact that the first type of answer (absence of change, in this case after an interval of 85 years) is also given by some children shows that the static aspect of younger children’s answers is not necessarily due to a lack of knowledge concerning the growth of trees. In addition to the three types of answers already observed for the reforestation, another answer can be found when children anticipate long-term transformations of the forest: the reference to a renewal. The forest will still be there, but it will be composed of new trees. From the point of view of diachrony, this idea implies the representation of a continuous cycle of transformations. The apparently most advanced form of anticipation consists of imagining both decayed and new trees. In this case, the child simultaneously envisages different kinds of changes. Our experiment reveals that children have differentiated representations when they consider an undetermined, a long-term or a very long-term future. Even though the notion of future is rather poor in young children (as shown in the experiment on tree disease and other studies on this topic), an interval of a thousand years lowers the proportion of subjects who do not anticipate any change. In older children, such a long-term interval entails qualitative changes in the representation of transformations. The proportion of representations of renewal increases considerably.

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In order to understand how children view a step in the future development of a forest, we must take into account their answers to the question about the state of a deforested area after half the time necessary for its regeneration has elapsed. Two types of conceptions succeed one another between the ages of 7–8 years and 10–11 years. Younger children have static representations of more or less differentiated configurations (‘There will be more trees’ or ‘Big trees and small trees’). Older children have a dynamic conception of steps within a growth process (with reference to the fact that ‘trees grow’ or ‘the forest evolves’). This indicates that more developed representations of changes have a greater continuity than the conceptions of younger children. This aspect of continuity is also revealed by the anticipation of a renewal, which can be found in 10- and 11year olds’ answers. The anticipation of a renewal of the forest in 85 or a thousand years implies the representation of a sequence where the trees currently alive first decay, then die, then are replaced by new ones. Thus we find in these results a confirmation of the hypothesis that was put forward in the previous section about tree disease: the steps of a transformation imagined by younger children are discontinuous states, whereas older children introduce a link between these states. As far as temporal reasoning is concerned, young subjects do not correctly coordinate the duration of growth, the speed of growth, the order of succession (big trees have grown before small ones) and height. For this reason, they think that ‘taller’ entails ‘faster’: big trees have been planted first, therefore they grow faster. This also reveals some limitations in diachronic thinking: The past (when big trees have grown more than small trees) and the future are not well dissociated. In contrast, more evolved answers present the future as different from the past and dependent on the present state. The big trees are probably assimilated to grown up people and are expected to keep the same height or to grow a little, whereas small trees are expected to grow faster. These answers are based on an inverse relationship between speed and height. Moreover, explanations are multicausal at this level of development, like the explanations observed in the experiment on forest disease. Children mention several factors of growth and several possibilities. The question about the length of time necessary for half the deforested area to be reforested elicits answers of three different levels. At the first level, children think that more time will be necessary for half the area to be reforested, at the second they think that the duration is proportional to the area involved and, at the third level, they dissociate the surface area vegetation from its vertical growth. As a matter of fact, the duration of growth does not depend on the extent of the area. This judgement results both from a development of the concepts of time and space, which can be well dissociated, and from progress in diachronic thinking. The latter enables children to anticipate distinct evolutions during the same interval of time. Let us now recapitulate the characteristics of the two main levels of answers concerning forest regeneration. At the ages of 7 and 8, more than half the

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children do not anticipate any change in a deforested area in the absence of human intervention. As far as an intact forest is concerned, and after a long-term interval of 85 years, the majority of these children anticipate some changes, but they do not mention decay or renewal. The answers are different when the interval is longer (a thousand years) in a minority of the subjects only. At this level of development, children have a static conception of the steps of reforestation and do not refer to the continuous process of growth. Concerning the speed of growth, 7- and 8-year olds imagine that big trees will grow faster than small ones. Lastly, they anticipate that if the deforested area is smaller, the time for regeneration is either longer or shorter than the period necessary for a larger area to regenerate. On the whole, these children anticipate only limited changes and do not correctly coordinate the speed of growth and the age (or height) of the trees. At the ages of 10 and 11 years, the conceptions of future modifications change completely. Most children think that a deforested area will regenerate. They become able to anticipate varied and cyclical transformations in the long term: The trees grow, then they decay and they are eventually replaced by other trees. Intermediate steps are described in a dynamic way, like different moments in a process of changes. The relationship between the height (and age) of the tree and its speed of growth is reversed (‘taller’ entails ‘less fast’). Lastly the oldest of these children (that is, 11-year-olds) are able to dissociate a development in the vertical plane (growth of the trees) from the extent of the vegetation in the horizontal plane. In 9-year-olds, the proportions of answers falling into the different categories are intermediate between those of younger and older children. From a qualitative viewpoint, these children’s conceptions are characterized by the importance of the idea of decay. Rather surprisingly, this idea also appears when they imagine the future of a deforested area. The same concept of decay is frequently mentioned when they anticipate the state of an intact forest in the long term (85 years) and it is not replaced by the concept of renewal when the interval is a thousand years. What have we learned from this experiment concerning the components and the development of a diachronic approach? First, an evolved form of diachronic thinking can be defined by the ability to anticipate varied and cyclical transformations within evolutive process. Such an ability is involved in the anticipation of the renewal of the trees of a forest. Renewal implies a succession of changes that differ both in nature and direction. Growth and maturity are followed by decay and death and the latter is followed by another process of growth. A second conclusion that results from this experiment is the striking parallelism between the developments of both cinematic reasoning and the diachronic perspective when they bear on a process of growth. The conceptual confusions between time, speed and spatial extent (involved in the judgement: ‘Taller trees will grow faster’) disappear when children’s diachronic thinking

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improves (ability to anticipate a renewal cycle). Simultaneously (in the majority of 11-year-olds), children become able to perform complex spatial-temporal dissociations, as witnessed by the distinction they introduce between horizontal surface and vertical growth. General Conclusions to Chapter 3: Biological Knowledge and the Diachronic Approach An observation of the way in which children aged between 7–8 and 11–12 reconstruct or anticipate the stages of tree growth or decay reveals striking modifications which, depending on the particular object of study, take place in the majority of children at the age of 10 or 11. First, these changes consist of an improvement in the understanding of biological phenomena. Disease is no longer thought of as something that progresses in an abrupt and external manner but instead is seen as a biological process which depends on the circulation of sap, the age of the tree etc. Cleared areas of forest are expected to grow back without human intervention— provided that the level of deforestation is not too high. The future of a forest is viewed as a cycle extending over multiple generations. This enhancement of biological knowledge corresponds to the restructurings which have been reported by Carey (1985) at about age 10. However, it should also be noted that certain advances are not observed until the age of 11–12 (for example, the appearance of a multicausal explanation of disease or the regeneration of the forest) and that there is no reason to believe, as might be concluded from Carey’s work, that the biological conceptions of 10-year-old children are in every respect similar to those of adults. What needs to be emphasized here, following our three experiments concerning the past and future of trees, is the progress observed in the diachronic approach employed by the subjects. For example, the ability to conceive of a series of varied changes in both nature and direction illustrates the functioning of diachronic thinking and not of a particular item of knowledge concerning biological phenomena. Thus 7- or 8-year-old children most certainly know that trees are not eternal. The animistic tendencies exhibited by young children— confirmed by research conducted by Carey (1985) and Ochiai (1989)— undoubtedly lead them to model the life of a tree on that of a person. Despite this, they do not anticipate the decay or renewal of a forest even in the very long term. This failing must be due to an insufficiently developed capacity for diachronic thinking. In contrast, the older children think of a tree from a diachronic perspective, viewing it as something that is born, changes and gives birth to other trees as time progresses. It is possible to provide further examples of difficulties observed, sometimes up to the age of 9, which are due to an inadequate diachronic approach and not to a lack of biological knowledge. The confusion between the passage of the seasons and the progress of a disease which was observed in some of the

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children’s drawings results not from the inability to distinguish between these two concepts but from the difficulty the subjects experience when trying to imagine multiple evolutive phenomena simultaneously. As a result, they simply alternate between the various phenomena. Moreover, the failure of the youngest children to establish any continuity between the past and the future, as was observed in connection with the diseased spruces, again relates to diachronic thinking. The same is true of the static or dynamic vision of the future. Children of 7 or 8 years of age know that trees grow. It is not therefore a lack of biological knowledge that leads them to expect no long-term change in a forest or prompts them to provide a static description of the intermediate stages of forest growth. Let us summarize what the last three experiments have taught us about the diachronic approach between the ages of 7 and 12. Most children of 7, 8 and 9 years of age are perfectly capable of imagining the past stages and a future stage of a biological phenomenon. They reconstruct and seriate the stages of a transformation, provided that these stages are presented as ‘snapshots’ within a homogeneous transformation, that is to say one which concerns a single dimension. These snapshots are considered to be states which possess no real connection with one another. Transformations in time are apprehended as external phenomena. These children are not able to dissociate and consider a variety of evolutive processes simultaneously (ageing and the passing seasons, for example, or decay and growth). The future is the object of relatively unvaried representations. At about the age of 10 or 11, our subjects’ capacities for diachronic thinking are significantly enriched. At this age, children reconstruct or anticipate a much wider variety of changes. They are aware that time brings a range of modifications, many of which are thought of as qualitative transformations. However, while they depict a variety of stages, they are able to introduce an element of continuity between them by thinking in terms of internal processes and by linking the phases of a transgenerational cycle. Their descriptions of stages of growth, which make use of terms such as ‘grow’ and ‘develop’, testify to this continuous, dynamic vision. These children also simultaneously take account of a variety of evolutive processes which progress at different rates (ageing, seasons, disease, the growth of trees or shrubs etc.). At this level, the conception of the future is considerably enriched. On the one hand, the future is viewed as a set of varied possibilities while, on the other, these children are capable of the spontaneous representation of transformational cycles. It is clear that the representation of a cycle is based on the ability to imagine changes of different types and directions which, nevertheless, combine to yield continuity. It is striking that in its main characteristics the diachronic approach develops in the same way for an irreversible phenomenon such as growth and for reversible processes such as decay due to disease. At the same time as witnessing these changes in the diachronic approach, we have also been able to observe modifications in the application of temporal reasoning (measurements of time) to evolutive processes. Some of the 7- to 9-

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year-old children imagine that there is a fixed interval between drawings or photographs representing a change over time. Most of them are unable to establish a correspondence between their estimation of the total duration of the process and the age of the tree at each stage. They find it difficult to dissociate size, age and speed of growth. These difficulties disappear in children aged 10 and more. Their estimates of time are no longer discrepant. Age is therefore considered as indicative of an elapsed duration, a characteristic which is not observed in the younger children. Moreover, the relationship between speed of growth and tree size is inverted. Globally, we can observe important advances at three levels between the ages of 7–8 and 11: in biological knowledge, the diachronic approach and the application of temporal reasoning to evolutive processes. I hypothesize that the improvements in the first two levels (biology and diachronic approach) develop in tandem. A sound understanding of biological processes implies an ability to think of things in time. It is necessary to establish links between origins and stages of development, imagine cycles, think in terms of internal transformations over time. Viewed from this perspective, biological knowledge is dependent on the development of the diachronic approach. At the same time, the acquisition of knowledge about living organisms— and children’s interest in such knowledge—provides the content which is necessary for the expansion of diachronic thinking. Here we are in the presence of a developmental circle: progress in one domain informs development in the other domain which, in turn, has an effect on the first. My hypothesis concerning temporal reasoning is different. We know that 8year-old children establish complex correspondences between speed, time and space when confronted by easily representable events (such as the movement of two objects or the successive activation of two lights). In my opinion, such reasonings are not generalized to biological changes because diachronic thinking is not sufficiently developed to make a clear representation of these changes possible. To conclude, I should emphasize that these results draw attention to the necessary distinction between the ability to store and recognize knowledge which can be activated only by an explicit request and the spontaneous use of this knowledge. This can be clearly observed in connection with the idea of cycles and the recovery of a forest, phenomena which 7- and 8-year-old children are most certainly capable of understanding and recognizing when required to do so. However, these same children do not make use of the content of this knowledge when asked to predict the future of a forest. Despite my arguments to the contrary, some readers may still think that the development of the diachronic approach which has been revealed is rigidly connected to the knowledge contents studied in this chapter. If this approach is indeed a mode of apprehending reality which can be applied to a variety of

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contents, then it should be possible to study it in contexts completely different from the representation of the growth and decay of plants. This is the challenge we shall take up in the following chapter which will concentrate on physical phenomena, that is to say inanimate objects obeying the laws of causality.

Chapter 4 The Diachronic Approach and Physical Transformations

A Story of Thawing Ice: an Introduction to Duration in Causal Explanation Objectives and Problems The comprehension of changes over time is one of the elements involved in causal explanation. In fact, the intimate relationship between causality and time is apparent in the very definition of causality as proposed by Hume. This definition evokes the temporal relations, of succession and contiguity, between cause and effect. A number of studies conducted in the field of developmental psychology have revealed this close association of temporal and causal relations. For certain authors, such as Piaget, the knowledge of time is founded on a knowledge of causal relations. However, the majority of authors emphasize the time-dependent nature of causal relations. Evoking a theory first proposed by the philosopher Brunschvicg, Piaget claimed that the temporal order of events is based on a knowledge of the pragmatic links or causal relations which obtain between these events. In his study of the development of temporal reasoning (Piaget, 1969b), the author explains the progress observed in a task requiring the reconstruction of a temporal order in terms of causal relations. It is worth examining this experiment in some detail because, in my opinion, it mobilizes a number of elements of the diachronic approach. The experiment consists of asking the subjects to watch a coloured liquid flow from an upper container, which is initially full and which we shall term A, to a lower, empty container termed B. The liquid flows from A to B in a number of stages and the subjects are asked to draw the level of the liquid in the two containers at each stage. When the drawings are then presented out of sequence, children aged approximately 6 to 7 are able to reconstruct the chronological order on the basis either of the progressive lowering of the level in container A or its progressive raising in container B. However, when the drawings are cut in two, that is to say when the graphic representations of containers A and B are

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separated, the task is only successfully completed at a more advanced age. The younger subjects appear unable to establish a correspondence between drawings of A and B which portray developments in contrasting directions (as time passes the level drops in A and rises in B). The subjects who at the age of 8 to 9 are generally able to establish a correspondence between the separated drawings and seriate them correctly do so on the basis of the movement of liquid from A to B. Piaget concludes from this that it is the understanding and awareness of the physical phenomenon of liquid movement that enables subjects to reconstruct the order of temporal succession. Thus the understanding of temporal relations is founded on the ability to grasp causal relations. Here we should note two points. First, children possess an idea of temporal order which allows them to distinguish between before and after at the moment the flow of liquid is observed. Second, the task of establishing a correspondence between the two sets of drawings and the task of seriating them demands a developed diachronic approach in view of the necessity of simultaneously taking account of two developments operating in different directions. Research into the reconstruction of a series of pictures representing a succession of events (Bonnens, 1990; Brown and French, 1976; French, 1989) tends to confirm the fact that it is the coordination of causes and effects that permits the reconstruction of the temporal direction of events. The contrary (or reciprocal) hypothesis of the time-dependent nature of the causal link is confirmed by a large number of studies in the field of developmental psychology as well as by research into the perception of causality (Michotte, 1963): the order of succession and temporal contiguity play an important role in the comprehension of the links between cause and effect. This can already be observed in the infant (Leslie, 1984) and the very young child (Bullock, Gelman and Baillargeon, 1982; White, 1988). In these various studies, time generally takes on an ordinal character. Duration, that is to say time perceived in the form of an interval, is most frequently mentioned in opposition to causality: if there is a gap between cause and effect then the absence of contiguity weakens or even eradicates the causal link. However, time intervals are involved in causal phenomena and it is precisely these intervals that are of interest for our study of diachronic thinking. In effect, diachrony is not limited to the introduction of an order of succession between phenomena. It integrates phenomena into duration. How can this duration affect causal explanation? First, the occurrence of a physical phenomenon needs a certain period of time. Moreover, when taken in connection with the two components of a causal relation (cause and effect), duration may have a role to play at the level of the cause, the interval between cause and effect or at the level of the effect. Some causes produce an immediate effect while others take time before an effect is observed. In the latter case there is necessarily an interval between the moment at which the cause appears and the point at which the effect is observed. The effect may also be limited or extended in time.

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My hypothesis is that as long as children possess only a poorly developed diachronic approach they find it difficult to imagine a phenomenon which has an extended cause and which requires an interval before the effect is produced. In effect, this type of representation requires the correct integration of the various aspects of the phenomenon in time and the simultaneous representation of two distinct developments or temporal processes: the development of the cause and that of the effect. In order to study this question, Dionnet invented a task in which children represent causes and effects even though this is not explicitly asked of them. This representation initially takes the form of a brief picture story before being subsequently verbalized (Dionnet, 1993; Dionnet and Montangero, 1991). I pointed out at the start of this chapter that the understanding of a set of pictures which tell a story has been studied by numerous researchers. As far as I know, the production of a picture story has never been systematically studied. The only aspect of the drawings produced by the subjects which was of interest in this experiment was the way in which they conceived of the cause of and stages in a physical change which is well known to children, namely the transformation of ice into water. In these representations of the causal sequence, we shall attempt to discover whether or not the explanation of a stage in the transformation refers to a previous stage. In effect, one key characteristic of the diachronic approach consists of explaining a state at least partially in terms of what preceded it. The subject of thawing ice also allows us to study a question raised by some of the results obtained in the research presented in Chapter 3. It may be recalled that some children aged 9 and younger believe that a fixed time interval separates the drawings or photos which represent the stages of a transformation. I believe that this behaviour is the result of a difficulty in dissociating the representation of the progress of time itself from the representation of the stages of the evolutive process. In other words, young children tend to think that the drawings or photos which depict successive stages also represent the passage of time. That is why, for example, they often believe that if there are four drawings then the change has taken four days (or four months or four years). If this interpretation is correct then the subjects who possess a largely undeveloped diachronic approach will tend to consider that the number of drawings representing the stages of a transformation will vary as a function of the duration of this transformation. In contrast, the children who possess a more developed diachronic approach will think that the number of drawings required to represent a transformation will be the same however long this transformation takes to complete. It was in order to study this point that Dionnet designed a second part to the experiment which we shall discuss below.

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Method and Population Part one: imagining and representing graphically a sequence of events that led to the situation presented The child was presented with a drawing representing a step in a physical transformation, namely ice thawing. The situation presented lent itself naturally to narration because it depicted two story-book characters (Babar and Celeste) in a difficult situation: they were skating on blocks of ice floating on water (see Figure 4.1 a). The causal phenomenon we wanted to study thus appeared as an element of a narration. The subject had to describe the image, then imagine what must have happened and finally draw what had taken place before the situation presented and what would take place afterwards. The child understood that the task consisted of drawing a story about Babar and Celeste skating and that the story had to include the image first presented. With this aim in view, we provided sheets of papers on which just the two characters were drawn (see Figure 4.1 b). When the subjects had finished drawing a ‘story’ or ‘scenario’, they were asked to comment upon the drawings and to indicate what was the cause of the thawing, at what moment the cause started and whether it was present in more than one of the steps depicted in the drawings.

Figure 4.1: Drawings presented to the subjects: (a) first drawing (b) basic drawing to be completed Source: Reproduced from Dionnet, S. and Montangero, J. (1991) Temps de la cause et temps de l’effet dans la représentation du changement chez des enfants de sept à douze ans, Archives de Psychologie, 59(231), 281–300, with kind permission of Archives de Psychologie, Genève, Suisse.

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Part two: representations of the change of the state of matter as a function of the duration of the transformation The task was first to draw the internal transformations of an ice cube during several steps of the melting process. Children were told that the ice container had just been taken out of the freezer. They were asked to draw the relative space occupied by the ice and by the water in the different steps of the transformation and to draw as many pictures as they wanted in order to show how the ice is transformed into water. When the drawings were completed, the subjects were asked whether the same series of drawings could represent what happened when the ice cube is placed in a very hot room and thaws rapidly. A similar question was asked about an ice cube taken out of the freezer and put in a cold room. The experimenter then asked: ‘Why do you think that it is possible (or not possible) to keep the same series of drawings?’ Population The population comprised 60 children aged from 7 to 12 years, divided into three age-groups of 20 children each: 7–8 years (M=8:1), 9–10 years (M=10:0) and 11– 12 years (M=11:11). Results and Discussion Part one: type of scenarios produced The series of drawings produced by the children in order to depict what happened to Babar and Celeste could be allocated to four categories, depending on the lasting or immediate character of the cause and the immediate or deferred occurrence of the effect. In order to illustrate these different categories, we will choose scenarios comprising the same number of drawings (namely four images), although some children produced scenarios containing a different number of drawings. In the first type of scenario (see S1, figure 4.2), the cause was punctual and the effect was immediate. Here is an example of comments made by a child producing such a scenario: • • • •

‘Babar and Celeste are ice-skating.’ ‘All of a sudden a boat runs into the ice and breaks it.’ ‘Babar and Celeste find themselves on little bits of ice.’ ‘They fall in the water.’

In this type of scenario, duration was absent at the three levels of the cause, the cause-effect sequence and the effect. The child imagined a causal chain in

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the form of a succession, without any mention or depiction of a temporal interval. The second type of scenario (see S2, figure 4.2) depicted a lasting and progressive cause accompanied by an immediate effect. The verbal description of such series of drawings took the following forms: • • • •

‘Babar and Celeste are ice-skating.’ ‘The sun comes out and starts to melt the ice.’ ‘The sun gets hotter and hotter and makes the ice melt more.’ ‘The sun gets so hot that it melts all the ice and Babar and Celeste fall in the water.’

In this type of scenario, duration played a role at the levels of both the cause and the effect. In contrast, there was no interval between the cause and the effect. This type of scenario depicted a clear covariation between the two components of the causal relation. It referred to a single transformational process which simultaneously involved the cause and the effect. In the third type of scenario (see S3, figure 4.2), there was a lasting cause and a deferred effect. However, from the moment the effect occurred, it covaried with the cause. Here are the child’s comments: • ‘Babar and Celeste are ice-skating, they are making marks on the ice.’ • ‘They go on skating, they make more and more marks. The ice which is too thin is beginning to crack.’ • ‘The more they skate, the more the ice cracks. Babar and Celeste are left on little bits of ice.’ • ‘They fall in the water.’ In these scenarios, it was possible to observe not only the introduction of duration at the level of the cause (as in S2), but also a dissociation between the time of the cause and the time of the effect. At the beginning of the story (first two pictures) there was no covariation between cause and effect, hence the delay between these two aspects of the phenomenon. However, as soon as the effect occurred (third drawing), it was thought to develop in parallel with the cause. The fourth type of scenario depicted a lasting cause and a deferred effect whose evolution did not covary with the evolution of the cause (see S4, figure 4.2). Children’s comments: • • • •

‘Babar and Celeste are skating in the sunshine.’ ‘Little by little, the sun melts the ice.’ ‘The sun goes on melting the ice and Babar and Celeste are left on bits of ice.’ ‘The ice goes on melting and Babar and Celeste end up in the water.’

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Figure 4.2: Example of sequences of drawings produced by the children, for each type of scenario (S1, S2, S3 and S4) Source: Reproduced from Dionnet, S. and Montangero, J. (1991) Temps de la cause et temps de l’effet dans la représentation du changement chez des enfants de sept à douze ans, Archives de Psychologie, 59(231), 281–300, with kind permission of Archives de Psychologie, Genève, Suisse.

In this type of scenario, any covariation between the cause and the effect had disappeared. The children imagined a constant cause, whose effect was both deferred and cumulative. They conceived of two different progressions over time which overlapped but were totally dissociated. Each component of a causal relation (the cause and the effect) had its own course in time. If we consider the frequency of the scenarios of the four types in each agegroup (see table 4.1), we see that for the phenomenon of thawing ice, the majority of children in all age-groups imagined a lasting cause (scenarios S2, S3 and S4). Moreover, the type of scenario produced depended very significantly on the age of the subject (p=0.000 ± 0.000, 2000 trials). In the 7–8 year age-group the scenario S2, which involves a complete covariation of cause and effect, predominated (50 per cent of subjects) and was followed by the scenario S1 with punctual cause (30 per cent of subjects). In the next age-group (9–10 years), the same two types of scenarios predominated, with an inversion of the position of S1 and S2: punctual causality was slightly more frequent than the covariation of the effect with a lasting cause (40 per cent and 30 per cent). Thus the representation of a causal phenomenon with deferred effect (S3 and S4) was rare from the age of 7 until the age of 10 years. In contrast, the great majority of scenarios produced by the 11–12-year-olds involved such an interval. In 45 per cent of these subjects, cause and effect had completely dissociated progressions

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Table 4.1: Percentage of subjects per age-group (N=20 subjects per group) and type of scenario. S1: punctual cause and immediate effect, S2: lasting cause and immediate effect, S3: lasting cause and deferred effect, S4: constant cause and deferred effect

(scenario S4) whereas in 40 per cent of the subjects the covariation reappeared as soon as the effect occurred (S3). On the whole, the introduction of an interval between the cause and the effect is a good indicator of development. However, in order to describe the evolution with age of the representation of the causal phenomenon studied, special attention must be paid to the covariation between cause and effect. The majority of children aged 10 and under tended to think that cause and effect covaried. At 11 and 12 years they dissociated these two aspects of the causal relation, a complete dissociation being observed in the scenarios of type S4. Part two: steps of the transformation when the length of the process is longer or shorter No developmental tendency could be observed in the way the phenomenon of thawing was drawn. As explained in the introductory part of this section, the point which we wanted to study was whether children thought that the speed of the transformation, and therefore its total duration, had to be taken into account in their drawings. To this end, after having produced a series of drawings depicting the stages of thawing, they were asked if the same drawings could be used to describe what happens when the ice container is taken out of the freezer and put in a very hot room. Two main types of answers were observed, each one being subdivided into two categories. In the first type, the children thought that the way melting was depicted should be different if the phenomenon took less (or more) time. They either did not specify what changed (first subcategory) or specified that the number of drawings had to be changed (second subcategory). Here is an example of an answer of this last category (child aged 9:7): ‘I will take these two drawings’ [the first and the last of the series he had first produced]. [Why?] ‘Because it melts down much faster.’ [And what happens if I put the ice in a cold room?] ‘It will be very long, we will need at least 20 drawings.’ The second type of answer consisted of retaining of the sequence of drawings, whatever the time taken by the thawing process. Children would either

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Table 4.2: Figuration of thawing speed. Percentage of subjects per age-group (N=20 subjects per group) and type of response

Table 4.3: Relationship between thawing speed and type of scenario. Percentage of responses (N=60) per type

only say that the same drawings could be kept (first subcategory) or they would provide an argument, as in the following answer given by a 12-year old: ‘The same drawings can do.’ [Why?] ‘Because it melts faster but the number of steps is the same.’ [Can you explain more precisely?] ‘Because it is a whole process, it is not possible to skip some steps and jump from one stage to another.’ Table 4.2 shows the frequency of the types of answers per age-group. We can see that the first type of answers, involving a change of the drawings as a function of the speed and duration of the defrosting, was given by a majority of subjects in the first two age-groups. The assertion that the same series of drawings will do appeared in the majority of 11- to 12-year-olds. It means that most children of this age were aware that they had drawn the stages of an evolutive process and that the stages were independent from the duration of the process. What is the relationship between this ability to dissociate the stages and the duration of a process and the way in which the causal relation involved in the thawing of ice is conceived? In order to answer this question we compared, for each subject, the type of scenario produced and their response to the question about the relation between the depiction of the physical transformation and that of the time taken by the process. Table 4.3 shows that a majority of subjects dis sociating time and process (retention of the same drawings) could be found only in the group which produced a type S4 scenario. Incidentally, this confirms that S4 scenarios, which depicted a complete dissociation between the progression of

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the cause and of the effect, were more advanced than S3 scenarios, since the latter were accompanied by a majority of type 1 answers (necessity of changing the number of drawings if the speed of thawing changes). Summary and Conclusion This experiment yields interesting results about both causal explanations and diachronic thinking in children. First, our findings show that the causal explanation of certain phenomena has to take into account duration and not only the order of succession. A lot of phenomena that children can directly observe at the macroscopic level are characterized by a lasting cause and a deferred effect. This is true of phenomena involving heat, for example when water or food is warmed up or when it is frozen or defrosted. Wearing effects are of the same type. Thus a battery ceases to produce an effect after a certain time of functioning. Children can experience in their bodies more or less painful consequences that are the deferred effects of a lasting cause: sunburn, colds or stiff muscles. In order to understand these phenomena, it is necessary to acknowledge that duration plays a role: there is a time interval at the level of the cause, and also between the cause and the effect. Our results show that children aged 7 and 8 can already take into consideration the fact that a cause extends over a certain period. However, before the age of 11 years they tend to imagine a covariation between the cause and the effect. The effect progresses simultaneously with the cause. This way of understanding a causal progression is clearly shown in S2 scenarios (figure 4.2). In a first step, there is no sun and the ice remains intact. In the second step the sun shines only a little, almost entirely hidden by clouds and the ice melts a little. Then the sun is hardly hidden and the ice has almost entirely melted. Finally there are no clouds, the sun shines brightly and the ice has completely disappeared. Thus children of this level conceive of a causal relation as a single progression. The correct representation of this type of phenomenon requires that the progression of the effect is dissociated from the progression of the cause. If these correct representations do not usually appear before the age of 11, it is because diachronic thinking has not sufficiently developed. As far as this modality of thinking is concerned, four conclusions can be drawn from our experiment. First, our interpretation of the children’s responses concerning tree growth or disease are confirmed. According to this interpretation, children first have the ability to imagine the steps of a single evolutive process. The ability to take account of several evolutive processes, each with its own rhythm (ageing, disease, season or growth and decay as far as trees are concerned) requires an advanced form of diachronic thinking which usually appears after the age of 10. The existence of this development is confirmed in the case of thawing ice: the representation of independent progressions for the cause and the effect appears only in the 11- to 12-year-old group.

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Second, the fact that children under the age of 9 can imagine a succession of steps does not mean that they consider the phenomenon from a fully diachronic viewpoint, in which each step can be partially explained by the preceding one. Type S2 scenarios reveal that the state of the ice at a particular moment is explained only by the context (the fact that the sun is more or less hidden by the clouds). In more advanced types of scenarios, the state of the ice depends on what happened before: the sun has shone and warmed the air up. It is in these scenarios only that a continuity is established between the successive steps of a transformation. At an earlier stage of development, the transformation is understood as a succession of juxtaposed states. The third conclusion is that the hypothesis I have proposed in the preceding chapters about 7- and 8-year-old children’s representations of steps in an evolutive process is confirmed. According to this hypothesis, the sequence of drawings produced represents both moments in the passing of time and steps of the process. In the present experiment, a majority of children until the age of 10 (80 per cent at 7–8 years and 60 per cent at 9–10 years) thought that it was necessary to change the number of drawings depicting the thawing if this took more (or less) time. This clearly shows that before the age of 11 children do not tend to differentiate between the progression of time and that of the process. The development of diachronic thinking therefore also consists of the acquisition of the ability to represent steps of an evolutive process as necessary stages which are not confused with the progression of time. The last point I would like to emphasize is the existence of a strong correlation between, on the one hand, this ability to represent stages of a transformation without confusing them with the passing of time and, on the other, the level of conception of the causal phenomenon (type of scenario produced). It is only in the group of children producing a type S4 scenario, with perfect dissociation between the development of the cause and of the effect, that a majority of subjects thought that their drawings of the steps of ice thawing could illustrate a slow process of melting as well as a fast one. This result shows that the way this type of causal phenomenon is conceived is closely related to the more or less advanced level of diachronic representations. The Birth of the Stars: Children’s Representations of the Origin and Expansion of the Universe Objectives and Problems Following our study of children’s conceptions of an observable physical phenomenon, it seemed to be of interest to ask them about a phenomenon whose spatial and temporal scale debarred any observation on their part. In the complete absence of any experiential data concerning physical reality do children revert to a primitive explanatory model? In other words, should we expect their

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representations of a non-observable phenomenon to be animistic or magical in character and to develop independently of their explanations of observable phenomena? I believe that if children possess no data whatsoever concerning a state of affairs they employ the conception or theories which they have constructed in connection with analogous phenomena. Thus asking subjects about unknown physical changes provides an opportunity to determine which are the most influential theories held by children and to investigate whether these theories evolve over the period of development in question. Clearly, even if the phenomenon under investigation does not fall within the scope of school tuition it will still be the object of scientific or other theories with which children may well have had contact. Thus the study of physical phenomena which are unknown to the child also enables us to determine when and how children assimilate adult theories concerning such phenomena. The phenomenon chosen for this study was the origin of the universe and the representation of its expansion. While it is impossible for children to observe these physical changes they relate to observable entities, the stars. The theory of the expansion of the universe following an initial explosion or big bang did not gain general acceptance in astrophysics until the late 1960s and general public familiarity with the concept is even more recent. The observational facts that underlie this theory (for example, the receding of galaxies and the increase in the speed of recession with distance) cannot be observed by children or, indeed, by adults other than astrophysicists. Asking children about the origin of the universe enables us to study three questions. First, is it the idea of invariance or that of change that prevails when children are asked to imagine the distant past of an apparently static phenomenon, namely the configuration of the stars? Second, this question allows us to study an aspect of diachronic thinking: the conception of the origin of a phenomenon. When children propose explanations for the origin of a phenomenon which is situated at a great spatio-temporal distance, do they transfer their knowledge of other physical or biological phenomena to this new field or do they repeat commonplace scientific explanations? Finally, this experiment is also designed to enable a study of the ability to abstract and generalize a fairly simple form of change over time based on the schematic graphic representation of the recessive movement of the stars. Taken overall, this research, which was conducted by Monzani, will allow us to determine whether a transformation in children’s representations of change is again observed from the age of 10 onwards in connection with a phenomenon which they are totally unable to observe and which is unlikely to awaken their spontaneous interest. At the same time, the results will provide new evidence for the discussion of the role of cultural data and data perceived in the development of diachronic thinking. Very little research has concentrated on children’s conceptions of astronomic phenomena. Vosniadou (1992) and his co-workers have shown that the

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conceptions held by preschoolers and even by children starting primary school differ significantly from adults’ knowledge of these questions. For example these conceptions, which are based on everyday observations, consist of believing that the earth is flat, situated at the centre of the universe and that it is larger than the sun. These models possess deep roots and when adults provide the correct information concerning these questions, children initially respond by constructing compromise solutions (synthetic models) which integrate the data underlying adult knowledge and the beliefs inherent in their own models. Thus being exposed to precise information is not sufficient to provoke the assimilation of this information. For example, of 54 9-year-old children who were unaware of the correct explanation of the day-night cycle, only two modified their initial model after reading an explanatory text on this subject. This all provides evidence in support of Piaget’s belief that knowledge is assimilated into subjects’ conceptual frameworks and that these frameworks undergo progressive restructuring. Method and Population Spontaneous representation of the origin of the universe This part of the experiment started by familiarizing the subject with the material by means of the following questions: ‘Have you already seen the sky at night? What’s it like?’ ‘Have you noticed that some stars make shapes, constellations, for example the Great Bear?’ ‘Has anyone told you at home or at school or have you seen anything on TV about the universe and what it was like long ago?’ When this phase was concluded, the experimenter posed questions concerning the origin of the universe: ‘Do you think that it has always been like you see it now?’ If the reply is negative: ‘What do you think it was like?’ And irrespective of whether the reply is positive or negative: ‘Do you think it was like that as far back in time as you can go?’ ‘Did the universe have a beginning?’ Graphic representation of the future and origin of a group of stars The subjects were presented with two pictures which were said to portray a segment of the sky as it is seen today and as it was in the days of the earliest humans (see figure 4.3). These two pictures made it possible to deduce the expansionary movement of the universe: in the picture of the present state (picture a) the stars were smaller, less numerous and were further away from one another than in the picture of the earlier state (picture b). The children were asked to describe the differences between the two drawings and questioning continued until they pointed out that the stars were further apart in drawing a than in drawing b.

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• Picture of the future. A mask was placed over drawing 4.3b and the children were asked to draw what they thought the group of stars would look like in a million years. • Picture of origin. The subjects were asked to draw the same group of stars as they were at the beginning of the universe. The method included other elements which I shall not describe here since the results obtained will not be presented in the current work. Population It comprised 60 children aged 7 to 12 years, divided into five age-groups: 7 years (from 7:9 to 8:5, M=7:11), 8 years (8:1 to 9:3, M=8:9), 9 years (9:4 to 10:3, M =9:9), 10 years (10:4 to 11:4, M=10:9) and 11 years (11:3 to 12:2, M=11:8). Results Spontaneous conceptions of the beginning of the universe When questioned about the origin of the universe, the majority of children, with the exception of the 9-year-old group, thought that there had been a beginning. A third of the 8-year-old subjects and half of the 9-year-olds thought that the sky was unchanging and had no definite origin. Only one quarter of the 9-year-old subjects stated that the universe had a beginning and another quarter said that they did not know. The idea that there was no beginning to the universe was only rarely encountered among the 10- to 12-year-old children: only 17 per cent of the 10-year-olds and 8 per cent of the 11- and 12-year-olds thought in this way. Of the 43 subjects who thought that the universe had a beginning, almost half did not refer to a formative process. Most of them did not give any explanation (15 subjects) and the others provided a non-causal description (reference to ‘someone’ or God as the creator of the universe or description of a universe emerging from nothing: ‘First there was nothing, then the stars came’). These responses were not characteristic of any particular age-group. In contrast with these types of answers, we can identify two response types which refer to a formative process: allusions to an initial explosion (corresponding more or less to the adult model) and original explanations in terms of an elementary physical or biological process. The following are two examples of the ‘big bang’ type of explanation: • ‘The planets exploded and others were made’ (12-year-old subject). • ‘A block exploded. The bits joined together and that made the planets’ (11year-old subject).

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Figure 4.3: Drawings of the sky as it is seen today (drawing a) and as it was seen ‘from the same place at the time of the first humans’ (drawing b).

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One subject, aged 10, provided another explanation which corresponds to scientific theories: • ‘Gases formed the stars.’ The following examples are illustrative of the ‘physical process’ type of explanation (children’s original theories): • ‘Things formed the stars’ (9-year-old subject). • ‘One ball gets joined up then another ball and that’s what makes the stars’ (8year-old subject). • ‘Bits get loose from the craters on the moon and make the stars’ (11-year-old subject). We also encountered explanations in terms of an initial collision. These may be distorted assimilations of the big bang theory: • ‘Balls crash into one another and the bits get stuck together’ (10-year-old subject). • ‘Asteroids come from other galaxies. They bump into one another’ (10-year-old subject). Finally, here are two examples of explanations in terms of ‘biological processes’: • ‘After they are born, the stars grow and become planets’ (11-year-old subject). • ‘The earth forms, the sky and the stars form at the same time and get bigger’ (11-year-old subject). Table 4.4 shows the distribution of the principal explanatory categories. It does not present all the results obtained for the 9-year-olds given the very low number of responses affirming that the universe had a beginning. Allusions to an initial explosion, which were probably derived from explanations heard concerning the big bang, did not appear until the age of 10 and were encountered in three children of ages 10 and 11 (about a third of the subjects of this age claiming that the universe had a beginning) and five subjects at age 12 (45 per cent of those who believed that the universe had a beginning). It should be noted that these five subjects were the only ones to provide an explanation of the beginning of the universe. These children provided no explanations whatsoever in terms of physical or biological processes. However, such explanations were also far from frequent in the other groups (two to four subjects per age-group, that is to say 25–40 per cent of the subjects who asserted that the universe had a beginning). Several of the 10-year-old subjects provided a variety of response types involving processes or references to adult models.

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Table 4.4: Explanation of the origin of the universe. Number of subjects per age-group (N = 12 subjects per group) and type of response

Note: *Only three subjects affirm the existence of the beginning. Three others don’t know

A comparison of the number of explanations of the beginning of the universe in terms of an adult or the child’s own model with the number of responses which claimed that the universe had a beginning but failed to explain this origin yields the following results. At age 8, a clear majority of subjects did not explain their response (six against two). At the age of 10, the opposite is true with seven subjects providing an explanation as against three who did not. In the 11- and 12year-old groups, the proportions of responses containing an explanation was about 50 per cent. Thus children in their fourth year of primary schooling indisputably tended to refer to a formative process. This tendency could be seen even more clearly .if we take account of the total number of responses since certain subjects provided more than one response. Representations of the future and origin of the universe If we consider both the comments provided by the children and the pictures they drew to represent the sky as it would be a million years from now and as it was at the beginning of the universe we can group the responses into five categories. The first category is that of linear development which takes account of criteria which evolve in different directions. In the pictures which were shown to the children, change over time was illustrated by two criteria whose value falls as development progresses within a given area and an unchanging configuration: the number of stars and their size. In effect, the picture of the sky today contained fewer stars (because they were further apart), each of which was smaller than the corresponding star in the picture representing the past appearance of the sky. In contrast, there was one criterion whose value increased as the system developed: this was the distance between the stars. If the child’s drawings of the future and origin of the universe took account of this twofold evolution (for example, fewer stars and greater distance between them for the future state) they are classed in the ‘linear evolution’ category. This means that

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the children have abstracted the criteria of time-related change which are contained in our pictures and that they take account of them despite the relative difficulty of making sense of criteria which evolve in opposite directions (both increasing and diminishing). To summarize, the drawings of the future which testified to a linear conception of evolution presented a greater distance between the stars, a smaller number of stars and/or stars of a smaller size. In the case of the origin of the universe the opposite was true: smaller distance between the stars, more stars and/or larger stars. The second category of representations was the covariation of the criteria. The children changed the spacing between the stars in the same direction as changes in number or size of stars. For example, the drawing of the future state included more stars, larger stars with a larger distance between them. Responses illustrating the opposite development were also grouped in this category (smaller spacing, size and number). The third category was that of inverted evolution. The children took account of variations in opposite directions but illustrated either a contracted future (smaller distance but larger size and greater number) or an expanded origin (greater distance, but smaller number and size). In the final two categories, the subjects took account of only one criterion, namely the time-related change in the spacing between the stars. We have distinguished between the categories ‘continuous increase of distance’ and ‘inverted development of distance’. In the first category, the distance increases with time whereas in the second the spacing contracts (reduction of distance). Table 4.5 indicates the percentage of responses obtained for the various categories for each age-group. The responses obtained for the future and past have been totalled. Linear evolution accounted for an average of 44 per cent of response at ages 8 and 9 and rose to 70 per cent or more among the 10-, 11- and 12-year-olds. It can thus be seen that some of the young subjects were able to take account of criteria that evolve in different directions within a framework of expansion and that the majority of children aged 10 and more possessed this ability. Responses in the ‘covariation of criteria’ category were rare and appeared more frequently at age 8 than among the later age-groups. Inverted evolution (contraction with time) was encountered even more rarely and was observed only in the 8- and 9-year-old subjects. When only the spacing between the stars varied, the responses, which were relatively infrequent, depicted a continuous increase of distance (‘expansion’). No subject provided a response of the ‘contraction’ type where the spacing evolves in a direction opposite to that indicated in the presented model. In order to determine the proportion of children who took account of the criterion of the progressive change in the distance between the stars over time we considered only this criterion in all the response categories. At all ages, a majority of subjects produced drawings illustrating an increase in distance with

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Table 4.5: Representation of the evolution of stars, in the future and at their origin. Percentage of responses per age-group and type of representation (N=24 responses per age-group)

time. In the drawings of the future this was observed in 52 per cent of the 8-yearold subjects, 75 per cent of the 9-year-olds, 100 per cent of the 10- and 12-year-olds and 92 per cent of the 11-year-olds. For the second drawing, namely the one concerning the past, identical proportions were found in the 10- and 12-year-old subjects, whereas the percentage was slightly higher in both the 8-year-olds (75 per cent of subjects drawing smaller distances) and the 9-year-olds (92 per cent). Summary and Conclusions First, these result show us that from the ages of 8 to 12, with the exception of the 9-year-olds, children tend to think that physical objects such as stars possess an origin. It should be noted that both the primitive tendency to explain things on the basis of a model of manufactured items or living beings and scientific theories agree on the fact that stars have an origin. Despite this, a third of the 8-year-old children and half of the 9-year-olds thought the sky has always looked as it does now. The generalization of the idea that apparently immutable things have an origin thus appears at the same age as the emergence of an advanced type of diachronic thinking, that is to say, at about the age of 10. Some of the children who believed that the universe had an origin provided no explanation of this origin. This was true of the majority of children at the age of 8 or 9 (75 per cent) and half of the subjects at 11 and 12. Summary explanations were proposed by a quarter of the younger children and by half of the 11- and 12year-olds. It is among the 10-year-olds that we find the greatest proportion of summary explanations of the beginnings of the universe. This result, which may appear surprising at first, may be explained in the following manner: thanks to the development of diachronic thinking, 10-year-old children have little difficulty in representing transformations over time and attempt to explain the succession of states of an evolutive phenomenon. In this respect they do not

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differ from older children. It is possible to hypothesize that, unlike the older children, the 10-year-old children are easily able to assimilate unobservable facts and adult explanations into familiar schemata and theories. At the age of 11 or 12 they are probably more aware of the gap between scientific theories and everyday representations and this results in a slight fall in the number of explanations provided. The children of the oldest group studied in this experiment refused to apply a familiar schema to the question of the origin of the universe: they have either assimilated adult theories or they have decided not to provide an explanation. This provides a compelling argument in support of the idea that there is an internal restructuring of theories of time-related change as a result of the development of diachronic thinking. When we examine the question of the explanation of the beginning of the universe we find that 10-year-old children differ significantly from younger subjects in that they tend to provide an explanation. However, this explanation does not always correspond to what they have learned and may sometimes constitute an original model (such as the idea of stars that grow or balls that crash together and stick or meteorites that fall from the craters on the moon). It is likely that such models represent compromises between simple theories derived from the observation of everyday phenomena (the agglutination of matter, division, growth) and explanations provided by adults in a way that resembles the synthetic models proposed by Vosniadou (1992). In general, preadolescents either invoke models provided by adults or are careful to avoid providing explanations of phenomena which they are unable to observe or comprehend. The progress made by 10-year-old children in the field of representing time-related changes leads them to explain the origins of such changes without differentiating clearly between adult models derived from scientific knowledge and familiar explanatory schemata. Essentially, the second part of this experiment tells us that children find it easy to extract and generalize the spatial and numerical criteria of time-related change. They were presented with two pictures which depict the expansionary movement of the stars by means of three criteria: while the configuration remains unchanged, the distance between the stars increases and, as a consequence, the number of stars present in a given area falls and the size of the stars also diminishes. In their drawings of future and past states, the majority of 10-year-old and older children (more than 70 per cent) reproduce at least two of these criteria which vary in opposite directions. For example, when they draw the sky as they imagine it will be in a million years they increase the distance between the stars from the value indicated in the drawing of the sky as it is at present and they reduce the size and number of the stars or, at the very least, they take account of one of these two criteria. A non-negligeable proportion of 8- and 9-year-old children do likewise: 50 per cent and 38 per cent respectively. It can thus be seen that children of school age are able to abstract developmental criteria from representations of change (and observations of

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change where these are possible) and apply them to the representation of new changes. This ability can be observed even when two or three criteria, whose values change in opposite directions, are involved. It should be noted that the criteria presented here are numerical and spatial in nature. Other developmental criteria might prove to be more difficult to abstract and even more difficult to apply. In contrast, if subjects are asked to consider only one criterion (in our experiment, an increase in the distance between the elements) success is achieved earlier and is more generalized. In all case, success is achieved more frequently in the groups aged 10 and above than in the 8- and 9-year-old groups. Here we find once more, both for the representation of the expansion of the universe and for that of its origin, that behaviour undergoes a change at about the age of 10. Even though the children are asked to perform a task which is based on knowledge which is unfamiliar to them we can still identify a development of diachronic thinking which follows a similar curve (here it occurs slightly earlier) to that obtained for representations of familiar phenomena. General Conclusions to Chapter 4 Although it is not possible here to expound a number of general conclusions concerning the relationship between diachronic thinking and causal explanations since this would require us to develop our investigation of this field somewhat further, we may nevertheless point to certain consequences of the two experiments presented in this chapter. When presented with physical phenomena, such as those of a biological nature, young schoolchildren of 7 to 8 years are able to identify the spatial and numerical criteria of time-related change. They are also able to use these criteria in their depictions of the earlier or later states of an evolutive phenomenon. Another ability, which appears at an even earlier age, relates to the comprehension of the relation between cause and effect which is essentially based on relations of temporal succession. This comprehension requires only a very elementary level of diachronic thinking. To this end it is sufficient to apprehend the order of temporal succession of a very small number of events and the human mind manifests this ability at a very early age. However, we have already seen that the ability to perceive, reconstruct or predict a succession of states does not necessarily imply the adoption of a diachronic approach. It is possible to represent a succession of states to oneself without understanding the links which make them into a single evolutive process. Thus, for example, the pictures drawn by children up to the age of 10 to depict the thawing of a block of ice are snapshots of a change and not the steps of a process since the children believe that it is necessary to change the number of pictures as a function of the time the ice takes to thaw. Moreover, the type S2 scenarios concerning Babar and Céleste tell us that while children of age 7 and 8 are able to imagine the

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successive stages of a causal process, they tend to explain a particular stage in terms of its context rather than by what happened at an earlier stage. Causal explanations develop considerably when, at about the age of 11, children not only introduce links between a number of successive stages but are also able to account for two temporal progressions simultaneously: that relating to the cause and that relating to the effect. It is not until this point that the development of diachronic thinking permits children to understand a whole set of phenomena having persistent causes and delayed effects. The experiment into children’s conceptions of the beginnings of the universe also testifies to a correlation between the progress of diachronic thinking, from 10 years onwards, and the tendency to explain the origin of things, even if they cannot be observed, in terms of familiar schemata of transformation or by starting to integrate adult theories. In my opinion, these transformations are not due to the fact that children of this age have heard adult theories as the majority of the explanations provided by 10-year-old children fail to reproduce adult models. The results presented here can be better explained by the hypothesis of progress in the ability to ‘think of things in time’ which allows children to construct explanations of the origins of things and to start integrating the models supplied by adults. In conclusion, if we are to understand all the components of causal explanation in adults and its development in children, it is important to take account of the aspect of diachronic reasoning. To define causality as the simple succession of cause and effect, as has been done for centuries, is to reduce considerably the complexity of causal reasoning.

Chapter 5 Children as Budding Developmental Psychologists

Genetic psychology, together with its latest offshoot, developmental psychology, has researched the evolution of children’s knowledge in a number of fields. For Piaget, the originator of much of this research, the study of children had a dual objective: namely, to observe the development of knowledge and to investigate certain epistemological problems relating to a number of specific fields (Piaget, 1972c). For example, he wanted to determine whether the idea of speed is more fundamental than that of time, whether an essentially perceptual intuition of geometrical ideas exists or else, what might be the relationship between numbers and logical classes. Even if, in general terms, present-day developmental psychology is no longer concerned with these epistemological considerations, it still helps to demonstrate the basis, in children’s thought, of knowledge elements which also form the object of scientific investigation. We thus possess data concerning the foundations of logic, mathematics, geometry, physics, biology etc. A number of works focusing on what is generally termed the ‘theories of mind’ (for a summary, see Bennett, 1993) demonstrate the existence of early elementary psychological knowledge concerning the beliefs, knowledge, desires and intentions of other people. Despite the scale and diversity of their work, developmental psychologists have apparently never enquired about the foundations of their own discipline in the child. The only exception I know of is the study by Flavell and Wellman (1977) showing that from the age of 5 years on, children know that memory abilities increase with age. If from the beginnings of thought, and even more clearly at school age, there exists an embryonic or elementary logic as well as the ability to attribute ideas and feelings to others, why should there not also exist an elementary developmental psychology? This question arose quite naturally as part of the research into diachronic thinking in which we were involved, since the aim of this research is the study of children’s conceptions of evolutive phenomena. We therefore conducted experiments into the way 7- to 11–12-year-old children think of the development of psychological abilities in the fields of drawing, language and intelligence.

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In asking children how they think that their knowledge or abilities develop with age we are addressing two aspects of cognition. On the one hand, we are dealing with metacognition (Flavell, 1979), that is to say subjects’ ability to reflect on their own knowledge. Thus in the research presented in this chapter we shall see how children are able to describe their own progress, compare it to that of other children or imagine its origin. Second, the task which we presented to our subjects required the application of a diachronic approach. The children were not, or not simply, required to consider their current abilities. They were also asked to consider them as the result of a development and to produce hypotheses concerning the form of this development. Such hypotheses can only be partially based on observed facts (the behaviour of younger children or the memories of the subject). As our results will show, the reconstruction of the age-related evolution of abilities in three different fields is based on schemes or theories which vary with the child’s level of development. The Artist Depicts his own Progress: Children’s Conceptions of the Development of the Ability to Draw a Human Figure Objectives and Problems Children’s drawing and its development has been studied since at least the beginning of the twentieth century (Stora, 1963). The stages in this development have been described from a variety of perspectives. Luquet (1913) as well as Piaget, Inhelder and Szeminska (I960) and Reith (1990) have analyzed this development in terms of the relative importance of perceptual data and intelligence. Goodenough (1926) and then later Harris (1963) in a revised approach, suggested using the drawing of a human figure as a test of intellectual development, while other researchers such as Goodnow (1990) have focused on such behaviour as a manifestation of the socialization of knowledge. What knowledge do children themselves possess concerning the development of the ability to draw a human figure? We know that such drawings are frequently produced (Harris, 1963). As soon as they go to kindergarten, and later school, or even at home with their own families, these budding artists are able to compare their productions with those of other children. It is, moreover, highly probable that they possess global theories of the progress that comes with age in all fields. Many authors (Goodnow, Wilkins and Dawes, 1986; Hart and GoldinMeadow, 1984; Reith, 1990; Trautner, Lohaus, Sahm and Helbing, 1989) have studied children’s ability to judge the relative age of the creators of drawings of human figures. These studies show that young children (from 4 to 6 years depending on the authors) are easily able to determine the relative level of development of drawings presented to them two at a time. Furthermore, an

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experiment conducted by Goodnow et al. (1986) reveals that if children of 6 or 7 are asked to choose which of a series of drawings they prefer, the criterion which is spontaneously employed by these children is the level of development of the drawing. Such studies investigate children’s recognitive knowledge of the evolution of drawings of human figures. It is one thing to compare two drawings and recognize that one is more or less developed than the other. It is quite another thing to possess a representation or theory concerning the age-related development of the ability to draw a human figure. It is precisely this latter question that Tryphon wished to study as a part of our research into the development of the diachronic approach (Tryphon and Montangero, 1992). Before asking her subjects to seriate a set of drawings in the order of age of the artists she therefore decided to ask them to draw pictures of human figures which would illustrate the successive stages of the ability to draw. The main aim of this research was to study the criteria which children spontaneously apply when accounting for the development of the skill in question. Theoretically there may be very many such criteria: aesthetic quality, relative precision of lines, the more or less realistic nature of the production (that is to say its conformity to observed reality), number of details depicted etc. If the diachronic approach is indeed a generalizable mode of knowledge then we should discover, as in the case of the growth and decay of trees, that the quantitative criteria applied by the youngest subjects give way to qualitative criteria in the older children. This is the first hypothesis that can be verified by this experiment. We also wanted to determine whether our earlier results concerning children’s conception of developmental steps as delineated stages are confirmed or invalidated by this experiment. According to these results, from the age of 11 onwards children represent a state within an evolutive process as a stage which is distinct from the passage of time. Another point on which we wished to focus in this experiment relates to children’s conceptions of the causes of development. In view of our hypothesis that diachronic thinking is a mode of knowledge which is not limited to a particular domain or context, we expected the results concerning the development of drawing ability to resemble those which we obtained in connection with tree disease. Explanations in terms of external factors, given by young children, give way to explanations of change which take account of internal processes at about the age of 10–11. It can be seen that in this experiment concerning drawings of a human figure we are again attempting to define the nature of diachronic thinking in children through a study of the way in which they reconstruct or predict the stages of an evolutive process. However, diachronic thinking is not manifested simply at the level of these reconstructions or predictions. It is also—and perhaps primarily—a type of attitude or tendency of thought which consists of the spontaneous comparison of a current situation with its past or future states. This ‘diachronic tendency’ enables us to understand without hesitation a question concerning the

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past development of a present situation. In the experiment concerning drawings of a human figure we were able to study this point by posing the question: ‘Have you always drawn like that?’ If it is not natural for children to integrate a present fact into a lengthy evolutive process then they will find it difficult to understand this question. If, in contrast, their thought is diachronic in nature, they will doubtlessly understand that the question relates to the development of their ability to draw. The final point which we studied in this experiment concerns the relationship between the recognition of the stages involved in the drawing of a human figure and the way in which children conceive of these stages in a drawing. We wanted to see whether the ability to recognize the level of drawing development in a set of drawings which are difficult to place in chronological order evolves in parallel with the ability to represent the development of drawing techniques. To this end, Tryphon selected 12 pictures drawn by children and adolescents and asked her subjects to place them in chronological order. Questions and Population First part: production of drawings Each child was provided with sheets of paper (A5 format), a pencil and an eraser, and was asked: ‘Can you draw a human figure?’ When the drawing was completed, the experimenter asked: ‘Have you always drawn like that?’ If the answer was affirmative, the children were asked whether they used to draw human figures in the same way when they were younger (‘little’). The subjects were then requested to draw a human figure as they used to draw when they were younger. When this second drawing was completed, the experimenter said: ‘I would like you to do as many drawings as necessary to show how your way of drawing has changed over the years, since the age when you started to draw.’ The series of drawings produced usually depicted in a regressive way the transformation of drawing skills: the first drawing produced revealed the current drawing ability of the child and the following drawings depicted preceding levels of this ability, which were more and more elementary. When the series of drawings was completed the child had to say what had changed with the years in his or her way of drawing human figures. The last question dealt with the causes of changes in drawing ability.

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Second part: seriation of drawings The subjects were presented with 12 drawings of human figures produced by children aged from 3 to 12 years. The drawings were presented in a random order and they had to be ordered according to the age of the artist. The 12 drawings illustrated several levels in the development of drawing abilities and some of these levels were represented by more than one drawing. Population This comprised 70 children aged 6 to 12 years: 10 children of 6 years (6:1 to 6: 11, M=6:7) and 12 children of 7 years (7:0 to 7:8, M=7:4), 8 years (8:0 to 8:9, M =8:4), 9 years (9:0 to 9:11, M=9:8), 10 years (10:4 to 10:11, M=10:9) and 11 years (11:0 to 12:0, M=11:6). Results and Discussion Diachronic tendency Let us start with an analysis of the answers to the question: ‘Have you always drawn like that?’ which was asked when the subjects had finished their first drawing of a human figure. Three kinds of responses were observed. • Affirmative. For example: ‘Yes I have always drawn like that.’ Such answers showed that the children had not understood the question properly. They did not take account of the past tense of the verb and the adverb ‘always’, which referred to a distant past, when they were little children. Since they did not tend to think in a diachronic way, the children who gave this type of answer assimilated the question in a distorted way, as if it were: ‘As you are now, do you always draw like that?’ • Negative, near past. Example: ‘No, I can draw different kinds of pictures’ or ‘Sometimes I draw with coloured pencils.’ These answers dealt with what had happened during a limited interval of time, in the near past (or what was likely to happen in the near future), and they took account of possible variations during this period. The children who answered in this way did not understand any more than those who gave affirmative answers that the question referred to their physical and psychological development. • Negative, past. Example: ‘No. When I was little, I used to draw differently.’ Only these answers revealed a developed diachronic tendency, that is the readiness to consider a current state of affairs as a stage in an evolutive process. These answers also resulted from developed metacognitive abilities. On the whole, the children who answered in this way were able to think about their own abilities from a perspective which went beyond the present time and took into account a long past evolution.

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Table 5.1: Responses to the question: ‘Have you always drawn like this?’ Percentage of subjects per age-group (6–7 years: N=22, 8–9 years: N=24, 10–11 years: N=24) and type of response

Table 5.1 shows the frequency of these three types of answers in the subjects who were divided into three age-groups. There was a significant variation of answers with age (c2 (4)=43.48, p<0.01). The ‘negative, past’ answer was rarely observed until the age of 9 years but was given by about half the 10- to 11-yearolds. The majority of younger subjects (aged 6 and 7 years) gave an affirmative answer, whereas 83 per cent of the 8- and 9-year-olds considered variations in the present or near past (‘negative, near past’). Representations of the development of drawing skills The series of drawings produced by the children were divided into two types: drawings with quantitative changes and drawings with qualitative changes. Each type was divided into two categories. The drawings were allocated to a category by three judges who worked independently. When the attribution did not correspond, the judges agreed on a category. • Series with quantitative changes: (a) The size of the drawing was supposed to increase with age (see figure 5.1, series a). This way of depicting the development of drawing abilities revealed a confusion between the size of the artist and the size of the drawn figure. Verbal descriptions of these drawings explicitly mentioned a variation of size as a function of age. For example a child aged 6:11 said: ‘When I was little, I used to draw smaller pictures.’ (b) The number of elements changed with the age of the artist. The overall structure of the drawing remained more or less the same, the number of elements diminished, the younger the artist was thought to be (this can be seen in part of series b—second to fifth drawing—in figure 5.1). Children who produced these series often said that the more one grows, the more things one knows. For these children, cognitive development was measured in a purely quantitative way. • Series with qualitative changes:

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Figure 5.1: Types of series of drawings produced Source: Reproduced from Tryphon, A. and Montangero, J. (1992) The development of diachronic thinking in children: children’s ideas about changes in drawing skills, International Journal of Development, 15(3), 411–24 with kind permission of Lawrence Erlbaum Associates, London, UK.

(a) Development was supposed to start with a schematic drawing (stick figure) and to end with a more or less realistic drawing (see the totality of series b, figure 5.1). (b) Important changes of shape. There was a change of viewpoint: from drawings in side view to front-on drawings. Or else realistic drawings were preceded by tadpole figures. In short, the representation of the changes in drawing abilities was close to what is observed in the actual development of children and was probably based on sound knowledge of drawings produced by younger children. Responses in this category were rare. Table 5.2 shows the frequency of the two main types of representations (quantitative and qualitative changes) in the three age-groups. In conformity with my hypothesis, the development of the conception of the evolution of drawing abilities is characterized by a passage from quantitative conceptions to

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Table 5.2: Types of transformation of drawings. Percentage of subjects per age-group (6– 7 years: N=22, 8–9 years: N=24, 10–11 years: N=24) and type of representation of changes

qualitative ones. In the 6- and 7-year-old group, most series drawn depicted quantitative changes. In the 10- and 11-year-old group, the majority of drawings illustrated qualitative changes. The latter could be found in a third of the children of the intermediate group (8–9 years). Causes of development When asked: ‘Why does the way of drawing change with age?’, children gave the following four types of answers. • Don’t know: subjects said they did not know. • Age: the relative age of the artist, referred to in terms of being little or big, was supposed to explain the level of drawing skill. For example: ‘When you are little, you don’t know how to draw.’ • External factors: progress in drawing abilities was explained by the existence of models provided by other persons. For example: ‘My mother showed me [how to draw better].’ • Internal factors or processes. Subjects mentioned the role of motricity (‘My wrist has become more supple’), of imagination, of awareness or more generally of evolution or practice. Table 5.3 shows the results for each year of age because there were notable differences between the responses of the 9-year-olds and the 10-year-olds and between the 10- and 11-year-olds. On the whole, the table shows that at age 6 and 7, the most frequently mentioned cause of the development of drawing abilities was the age of the artist (in terms of little or big). For these young subjects, the fact of growing up was sufficient to enable children to do things better. There seemed to be no analysis of specific factors. From the age of 8, the majority of answers referred to external or internal factors. References to internal factors predominated slightly in the 8-year-olds (38 per cent of answers). At the age of 9 years external factors predominated and at 10 years there was an equal percentage of answers referring to external and internal factors. The majority of responses in the 11-year-old group mentioned internal factors.

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Table 5.3: Causes of the development of the drawing skills. Percentage of responses, per age-group and category of response

Contrary to my hypothesis, external factors could not be found in the majority of answers of the younger children. However, in conformity with the hypothesis, the reference to internal factors was a feature of the majority of the answers given by the 11-year-old group. Temporal parameters The temporal parameters attributed by the children to the drawings they produced in order to illustrate the development of drawing skills appeared in their answer to a question about the age of the artist, which was asked for each drawing of the series. Responses could be divided into two distinct types of chronology. In the first type, children attributed a precise age to each drawing and imagined there was a fixed interval between them. For example, an 8-yearold child produced four drawings and said that the first one was done at the age of 2 years, the second at 4 years, the third at 6 and the fourth at the age of 8 years. In the second type of response, the children gave a range of age for each drawing and did not necessarily keep a fixed interval between drawings. Thus an 11-year-old, who had also produced four drawings, gave the following ages for each drawing: (1) between 2 and 3 years; (2) 4 years or so ; (3) about 5 years; (4) from 9 years on. These answers revealed a dissociation between the depiction of the stages of an evolution and the representation of passing time, as we had already observed in previous experiments. The mention of an age range rather than a precise age showed that each state of the depicted evolution corresponded to a stage and not to a precise moment in a continuous transformation. Table 5.4 shows that there was a majority of the first type of responses at 6–7 years, whereas the second type increased regularly with age and accounted for the majority of responses (74 per cent) at 10–11 years. It can be seen once more that the young subjects tended to confuse the passing of time and the successive

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Table 5.4: Estimation of the artist’s age. Percentage of subjects per age-group (6–7 years: N=17, 8–9 years: N=22, 10–11 years: N=23) and type of estimate

states of a development and that the 11-year-olds conceived of these states as stages in an evolution. Seriation of drawings In order to judge the results observed for the chronological seriation of 12 drawings, it was necessary to have a standard order with which to compare the children’s answers. To this end, five experts (psychologists studying children’s drawings) were asked to seriate the drawings. There was a high inter-judge reliability (Kendall coefficient r=0.97, χ2 (11)=0.123, p<0.001). The 12 drawings were numbered 1 to 12 in accordance with the order given by the experts. The children’s responses have been analysed in terms of their correlation with the experts’ sequence. The correlation was already reasonable in the 6- to 7-yearolds (Kendall coefficient r over 0.6 for 73 per cent of the subjects). However, in most cases the order chosen by these children did not correspond exactly to the order of the standard response. The correlation increased notably with age. If we consider only the responses whose order either corresponded exactly to the one proposed by the experts or differed on one point (correlation coefficient of 0.9 to 1.0), such responses were found in 18 per cent of the subjects at 6–7 years, 34 per cent at 8–9 years and in 54 per cent of the 10- to 11-year-old children. Summary and Conclusion The hypotheses proposed above in the section devoted to the objectives and problems of this experiment are either totally confirmed or—in one case— partially confirmed. The way that children represent the transformation of drawing skills with age develops between the ages of 7 and 11 years, passing from a quantitative to a qualitative view of this transformation. In the most primitive depictions of the development of drawing abilities, only the size of the drawings of a human figure changes with the age of the artist. I have explained this type of representation in terms of a confusion between the size of the artist and of the drawn person. It should be noted, however, that this result corresponds to a more generalized schema already observed in the experiment on the growth of a tree. The less

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developed tree drawings also depicted the changes over time as an increase in size without any change of shape. Thus when they draw the states of a developmental process—either biological or psychological—some of the 6- to 8year-old children resort to the schema ‘things get bigger with time’ and do not take account of other changes. Another way to depict the development of drawing abilities with age consists in adding elements to each drawing of the series (or in progressively removing elements when a regressive sequence is produced, from present to past). Incidentally, it should be noted that this regressive type of representation of changes over time was easily performed by the subjects, which is not surprising for school-age children. The depiction of the transformation of an ability with age in terms of the number of things done reveals a cumulative conception of cognitive development. Thus when children of this level assert that ‘the more you grow, the more things you know’, this should be understood literally as the expression of a quantitative conception of knowledge acquisition. At around the ages of 10–11 years, the conception of the transformation of drawing skills is completely reorganized. Qualitative changes are taken into consideration by most subjects. The shape and the realistic aspect of drawings of a human figure are thought to change with age. It might be argued that younger children have this kind of knowledge, but lack the graphical skills necessary to depict these changes. I think this assumption can be rejected, because stick figures, which many of the older children draw in order to represent a first-level of drawing abilities, do not require sophisticated graphical skills. The fact that 10- to 11-year-olds choose the stick figure as the least advanced form of drawing also permits me to reject another hypothesis: the idea that the development we observed is simply the result of an improvement in domainspecific knowledge (in this case, information about children’s drawings). Actually, the first types of human figure drawn by children are never stick figures. Consequently 10- to 11-year-old children draw such figures to represent a first stage in drawing abilities because of their general ideas concerning development and not because they know more than younger children about this development. According to these general ideas or schemes, development progresses from simple to complex and, as far as drawings are concerned, from less realistic to more realistic. I think that the use of qualitative criteria to represent changes over time is due to the fact that older children want to depict the stages of an evolutive process rather than snapshots of more or less continuous changes. This stage-like conception of transformations had already been observed in the experiments involving tree growth and thawing ice. Another result, relating to the age attributed to the artist of each drawing, confirms the appearance of the idea of stage after the age of 10 years. Whereas the majority of 6- to 9-year-old children attribute a precise age, most 10- and 11-year-olds establish a correspondence between each drawing and an age range. For example, the child points to

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a drawing and says: ‘I used to draw like this when I was between 2 and 3 years old.’ At the moment when the conceptions of development change (after the age of 10 years), half the children start to find it easier to compare their current level of ability with previous levels. This is revealed by the immediate comprehension of the question: ‘Have you always drawn like that?’. In contrast, most younger children do not understand that the question refers to the development of their drawing abilities. As far as the causes of this development are concerned, the majority of 11year-old children invoke internal factors, such as advances in motricity or cognition. An advanced form of diachronic approach, which permits the subject to represent varied changes over time, is allied to an awareness of the internal processes which provoke changes. An identical conclusion could already be drawn from the experiment on forest disease. However, the hypothesis according to which the stress on internal factors, at about the age of 11 years, is preceded by an emphasis on external factors is not confirmed. When they have to explain the development of skills such as drawing, 6- and 7-year-olds assert that the degree of competence depends on the age of the artist. In other words, they seem to have a maturational stance (without of course imagining neurophysiological transformations). For these children, becoming older (or ‘bigger’) seems to be a sufficient condition for improving one’s skills. From the age of 8 years onwards, the subjects abandon this type of explanation. They account for the development of drawing skills in terms of external factors (such as learning by imitation) as well as internal factors. I will end with a few remarks about the results concerning the chronological ordering of 12 drawings of a human figure as a function of the age of the artist. In the first place, it is not right to assert (as Goodnow et al., 1986 and many other authors do) that 6-year-old children can easily order a series of drawings. When the number of drawings is high and when more than one drawing illustrates one age or level, these children encounter difficulties. In these conditions, the accuracy of the seriation improves with age until 11 years. Progress is particularly important between the ages of 6–7 years and 8–9 years. To sum up, the ability to judge the more or less advanced character of a child’s productions seems to appear very early, and even in complex conditions (12 drawings) 6-and 7-year-old children can correctly order some of the drawings they are presented with. However, in these conditions the recognitive ability of children improves notably after that age. On the whole, the results of this experiment again show that the diachronic approach develops markedly in school-age children. Several indicators reveal this development. First, 6- to 7-year-old children are centred on their current abilities and performances, without establishing a relationship with their previous levels of ability, whereas half the 10- to 11-year-old group immediately understand what is required of them when they are asked to compare their present and past levels of ability. Second, the method of depicting the development of

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drawings skills changes over the age range studied: quantitative criteria give way to qualitative ones. Furthermore, the method of dating the drawings (that is, of attributing an age to the artist) also changes considerably and reveals the appearance of a stage-like conception of development toward the ages of 10–11 years. Finally, the fact that these older children no longer consider that equal intervals separate the images illustrating the steps of the development shows that the representation of an evolutive process is no longer confused with the representation of the passing of time. The Drawings of Tarzan and Wild Children: the Role Attributed to Maturation and Learning in the Development of Drawing Objectives and Problems In their explanations of the development of the ability to draw a human figure, the children aged 6–7 years who were questioned as part of the previous study referred to the age of the artist. For example, they stated that when you are small you do not know how to draw or that a particular picture was better than another one because it was drawn by a 9-year-old rather than by a small child. We consider that these responses reveal a maturational perspective: To grow older is all that is required for one’s abilities to improve. However, with each additional year children’s opportunity to learn increases, both through practice—by drawing pictures—and by imitating models. It is therefore possible that when children explain progress in drawing in terms of age (or the idea of ‘little’ and ‘big’) they are considering not simply growth but also the opportunity for learning. In fact, the two factors of growth and learning are intimately linked in normal development. In order to examine the hypothesis of the maturational perspective (that is to say explanations in terms of growth), Tryphon designed a complementary study in which the children were asked to compare the drawing abilities of individuals who differed in age but not in the experience or tuition they had received with regard to this ability (Tryphon, 1994). This complementary research had the additional aim of advancing the study of children’s capacity to place a series of drawings of human figures in chronological order (that is to say, to seriate them by level of development). In the previous experiment the set of drawings presented to the subjects was complex, both because of the number of drawings and because of the presence of multiple examples of different levels. It might therefore be concluded that the results obtained (notable improvement in the quality of drawing level categorization between the ages of 6–7 and 10–11 years with a major qualitative jump at age 8 to 9) are linked to this complexity.

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In the complementary experiment the categorization task is simpler because there are fewer drawings present (4 instead of 12) and because no two drawings belong to closely related or identical levels. This enables us to discover whether the children of the youngest age group (6–7 years) perform this task with ease as authors such as Goodnow, Wilkins and Dawes (1986) might suggest. Moreover, the arguments given to justify the seriation of the drawings as a function of the level of development of the artist are of interest to us because the results obtained by Reith (1990) suggest that justification in terms of the age of the artist is late to appear. In our opinion, this type of explanation provides a good indicator of a developed capacity for diachronic thinking. We shall develop this point further in our analysis of the results of this experiment. Procedure and Population First part: chronological seriation Subjects were presented with four images (13×8 cm) illustrating four different levels of development in the drawing of a human figure. The order of the drawing which corresponded to the increasing age of the artist was: D1, D2, D3 and D4. The drawings were placed in a row in front of the subject in the order depicted in figure 5.2 (D3, D1, D4, D2). The experimenter said: ‘Here are four drawings of people. Do you think these pictures were drawn by one child or by different children?’ ‘Were they the same age or not?’ ‘Can you put these drawings in the right order?’ This task not only permitted us to study the children’s ability to seriate, it also constituted a necessary preliminary reference for the second part of the

Figure 5.2: The four drawings to be ordered chronologically Source: Reproduced from Tryphon, A. (1994) Quand Tarzan dessine: théories psychologiques intuitives chez les enfants de six à douze ans, Archives de Psychologie, 62 (240), pp 43–58 with kind permission of Archives de Psychologie, Genève, Suisse.

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experiment. The four drawings and the questions asked provided a simple introduction to the topic of the development of drawing skills. Furthermore, each of these drawings constituted a reference level for the questions asked in the second part devoted to the drawing skills of ‘wild’ persons. When the seriation was completed, subjects had to give the reason for their choice: ‘What did you look at in order to place the drawings in that order?’ Finally, the children had to determine the age of the artist for each drawing. Second part: attribution of levels The task required subjects to attribute a level of drawing ability to three imaginary characters who were of different ages but had a complete lack of practice of drawing in common. To this end, the experimenter said: ‘Let us imagine that in the jungle there is a 4-year-old child who is wild, that is, who lives with animals and does not know how to speak, to read, to write, and of course who does not know how to draw. One day, explorers find the child and bring him [her] to Geneva, here to your school. They give the child a sheet of paper and a pencil and they ask him [her] to draw a person. What kind of picture do you think he [she] will draw?’ The same question was then asked about a wild 10-year-old child and about Tarzan (after making sure that the subject knew that Tarzan was an adult). Population This comprised 72 children aged 6 to 12 years (12 children for each year of age) divided into three age-groups of 24 children each: 6–7 years (M=7:0), 8–9 years (M=8:11) and 10–11 years (M=10:11). Results and Discussion As far as the seriation task was concerned, it was successfully performed by all the children from the age of 8 years onwards and by 71 per cent of the 6- and 7year-olds. The errors observed in the latter age-group were of different types. The difficulties encountered did not concern the relative level of the drawings. Even when the series did not correspond to a chronological order, the verbal attribution of an age to each drawing was correct. For example, a child aged 6:9 arranged the drawings in the following order: D4, D2, D3, D1, but attributed a correct level to each drawing, in terms of the school year of the artist. This lack of correspondence between the level attributed to each drawing and the order assigned to the images can be explained by the difference between the strategies used in these two tasks. When they seriated, these children seemed to use a twoby-two comparison strategy. In the example above, the subject chose to illustrate a regressive order and placed D4 followed by D2 (as they were placed in the initial order), then D3 followed by D1. In contrast, the verbal attribution of a

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Table 5.5: Justification of the order given to the drawings. Percentage of responses per age-group (N=12 subjects per group) and per category of arguments

level was performed in a more absolute way, by attributing a school year to each drawing in view of its characteristics. In any case, it is clear that the errors made in ordering the drawings stemmed from difficulties in ordering differences (when more than two or three elements were involved) as analysed by Piaget and Szeminska (1965). These errors did not necessarily result from an inability to recognize the relative levels of the drawings. The arguments given in order to justify the chosen order could be divided into three categories. • Lack of precise criterion. For example, when asked: ‘How do you see that these pictures were drawn by children of different ages?’, some children answered: ‘Because the drawings are not the same’ or ‘Some are nicer than the others’. • Enumeration of elements. The subjects took the details in each drawing into consideration. For example: ‘D1 is less well done, there are two circles; D2 has two circles and four bars. D3 has one circle with hair, eyes, a nose, a mouth, and also clothes and legs.’ • Reference to the level of development of the artist. The subjects referred to the age or school year of the artist. They often thought that the four drawings had been produced by the same child. For example: ‘These pictures were drawn by one child’ [‘How old?’] ‘He has grown up and draws better and better.’ The frequency of the different arguments per group of age can be found in table 5.5. Answers of the first type (absence of precise criteria) were in the majority in the 6- to 7-year-old group and decreased with age to reach a frequency of about 30 per cent at 10–11 years. The quantitative criterion of enumerated elements increased between 6–7 and 8–9 years. The reference to the age of the artist appeared more and more frequently with age but was not more frequent than other responses at 10–11 years. It can be seen that younger children focused on the characteristics of the production proper to each developmental level—analyzed either in vague normative terms (‘nicer’) or in the quantitative terms of the number of elements — whereas older children focused on the level of the ‘producer’ and on the

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phenomenon of development. However, this centration on the diachronic aspect was not observed in the majority of 10- to 11-year-olds. Attribution task There were three categories of responses to the attribution task. • Differentiation as a function of age. Although the three imaginary characters had no practice of or knowledge about drawing, the children thought that they would not draw in the same way. They imagined that the drawings would become more and more complex with the age of the artist. For example, a child aged 7:10 thought that the 4-year-old wild child would draw a picture similar to D2. [‘Why?’] ‘Because he never drew a man.’ [‘What about the wild 10-year-old?’] ‘Like D3.’ [‘Why?’] ‘Because he is bigger, then he does D3.’ [‘And Tarzan?’] ‘D4.’ [‘Why?’] ‘Because Tarzan is bigger.’ • Children-adult dichotomy. In this category of responses, the subjects also thought that drawing skills develop with age, independently of experience. However, they thought the developmental difference would occur only between children on the one hand and adults on the other. For example, a subject aged 10:6 said about the 4-year-old wild child: ‘He will only make lines, because he doesn’t know really how to draw.’ [‘What about the 10-yearold wild child?’] ‘The same. Since he has never drawn, he will make lines.’ [‘And Tarzan?’] ‘It will be difficult for him, too, his drawings won’t be very nice.’ [‘Will he also make lines?’] ‘A little better, I think.’ [‘Why better?’] ‘Because he is bigger; sometimes he uses sticks.’ • No differentiation. The subjects who gave this type of answer thought that the three imaginary characters’ performances would be identical. They imagined either that the three wild persons would be incapable of drawing, or that they would doodle or else make a drawing corresponding to the first drawing of the series (D1). Such answers were sometimes justified by the lack of drawing practice and more often by a lack of knowledge concerning drawing or other domains. Here are the responses of a child aged 10:10. ‘The 4-year-old won’t even know what a pencil is, he won’t know what to do.’ [‘Do you think he could draw?’] ‘He would do anyhow, lines. He doesn’t know what to do, he has never drawn before.’ [‘What about the 10-year-old?’] ‘Like the younger one.’ [‘Why?’] ‘He has never drawn. It could be an adult, someone very old, if he has never drawn, he doesn’t know what it means.’ [‘Precisely, if it were Tarzan?’] ‘It will be the same.’ A number of the 6-year-olds did not give any answer to these questions and the frequency of answers was different in the 10- and 11-year-olds. For these reasons, table 5.6 shows the frequencies for each year of age from 7 years onwards.

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Table 5.6: Attribution of a level of drawing as a function of age. Percentage of subjects per age group (N = 12 subjects per group) and category of response

The answers in the first category (the ability to draw differs as a function of the age of the artist) were the most frequent on the whole and they were given by the majority of subjects from 7 years to 9 years inclusive. The second category of answers (difference between children and adults) appeared in a minority of 8year-olds and slightly more frequently from the age of 9 onwards (33 per cent). The third type of answer, the absence of differentiation, was the least frequent type of response, except at the age of 11, when it was the most frequent answer (50 per cent of the subjects). Summary and Conclusions Given the results of this experiment, it can be said that until the age of 9 years, children tend to have a maturational view of the development of drawing skills. They think that physical growth necessarily accompanies the development of this ability. The majority of these children think that the practice of drawing and the existence of cultural models are not necessary factors in development. In contrast, at the age of 11 years, practice and cultural models begin to become essential factors for the development of drawing skills. Such a result may seem contradictory to the data obtained in two of our previous experiments, namely the fact that internal factors of development were taken into account by older children only. Thus younger subjects seemed to have a rather empiricist view of development, as for them progress was due to the influence of the environment. I would like to advance a hypothesis which can synthesize these two apparently contradictory results. According to this hypothesis, until the age of 9 years two causes are supposed to comprise the development of skills and knowledge: the fact of growing up (pseudo-maturational thesis) and learning, mainly by imitation, which accounts for specific knowledge. Since both learning and physical growth increase with age, the two theses can coexist in the mind of children. When one of the two

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causes is absent, the other one is still thought to be effective, hence the responses which distinguish between drawing modes as a function of the age of wild persons. The changes that take place after the age of 10 years in the way of explaining psychological development will be denned in the general conclusions to this chapter, after we have considered the results of two other experiments. Let us note here that the role of both the practice of drawing and cultural prerequisites— such as language comprehension—is mentioned by the 11-year-old children who think that Tarzan would not draw better than wild children. This experiment also helps us explain the seriation of four drawings with reference to the increasing age of the artist. Although the task is much easier than the seriation performed in the previous experiment, almost 30 per cent of 6- and 7-year-old children fail. This does not prevent them attributing the correct age or school year to the child who is supposed to have drawn the pictures. The errors do not result therefore from an inability to judge the developmental level of the drawings, but from some more general deficiency in the ability to seriate more than two or three elements. Some children, up to the age of 7 years, still use a two-by-two strategy in this task. When dealing with the problem of the ability of children to order drawings by the age of the artist, it is necessary to consider the number of elements to seriate and the presence or absence of multiple examples for a single level. The study of the justifications of the chosen order shows that at the age of 10– 11 years, the mention of the age of the artist and of his or her growth becomes one of three arguments given with approximately equal frequency. This results from the awareness and verbalization of a factor which was already considered to be necessary and sufficient by younger children. The reference to the age of the artist reveals two points. First, from the age of 10 years onwards, the role of the subject in the subject-object dyad is beginning to become important in children’s explicit representations. Second, there is a new tendency, in these children, to adopt a diachronic approach spontaneously. The Bigger you Get, the Better you Speak: Children’s Conceptions of the Development of the Ability to Describe a Picture Objectives and Problems Of the cognitive capabilities which develop with age, one which is easiest for children to note and analyze is the ability to use language. This is, of course, a production, that is to say an ‘output’, and is therefore always easier to apprehend than the internal processes or systems which generate the production. Moreover, language changes considerably between the time of its first appearance towards

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the end of the second year of life and adolescence. Finally, language is a subject studied at school. A number of psycholinguistics texts tell of children’s ability to adapt their own linguistic productions to the level of linguistic development of their interlocutor (see, for example, Brami-Mouling, 1977; Bredart, 1980; Berko-Gleason, 1973; Shatz and Gelman, 1973). Children do not speak in the same way if they are speaking to a friend of the same age, a smaller child or an adult. It remains to be determined whether this adaptive ability is accompanied by an awareness of the characteristics proper to the various levels of linguistic development and ideas concerning this development. This interests us not so much as a question of metalinguistic knowledge but rather as an example of a conception of an evolution over time. Adults possess a variety of general conceptions concerning the form of any evolutive process. For example, it is possible to think of the development of an ability in terms of constant progress or a stage-by-stage progression, as a continuous improvement or an improvement followed by a period of stability or a decline. The study of such forms interests us for a number of reasons. On the one hand, they represent generalizable schemas for diachronic thinking while, on the other, these forms or developmental curves reveal a number of conceptions which underlie the idea of progress. Thus the idea of progression by stages takes the form of a curve incorporating a number of periods of stability. In contrast, the idea that development depends on growth can be thought of as a continuous progression followed by stability once adult age has been reached. One of the aims of our experiment was to reveal which of these forms children employ when they think of linguistic progress and how such forms may change between the ages of 8 and 12. Furthermore, we wanted to discover whether the characteristics of the development of diachronic thinking which we had observed in connection with biological or physical changes and drawing ability would also be manifested in children’s ideas concerning language development. In the light of our general hypothesis which holds that the diachronic approach consists of a set of knowledge elements which are gradually generalized to a variety of contents I am able to propose four specific hypotheses. First, 11-year-old subjects’ representations of the steps involved in linguistic development will take the form of stages rather than snapshots within a continuous development, a conception which is found in younger subjects. Second, in these more developed representations the stages of linguistic improvement will be dissociated from the representation of the time elapsed. Third, the youngest subjects will tend to think of quantitative changes in the development of speech, while 11- to 12-year-old children will think more in terms of qualitative changes. Finally, reference to internal factors to explain linguistic advances will only be generalized in the older subjects. In order to study these various questions, we designed a method comprising two distinct components. In the first part, which could be called the

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recognitive section, the subjects were asked about two verbal productions taken from children of different ages. The second part investigated the way in which the subject conceived of linguistic development. To ask the children about language in general would have been too vague. In consequence, we focused on one verbal ability, the description of a picture which was presented to each subject in the experiment. The picture which Parrat-Dayan, who conducted this experiment, chose to be described, lent itself to both a simple description (enumeration of the elements forming the picture) and to a type of narrative (evocation of the events preceding or following the moment depicted in the picture). This enabled us to study the spontaneous tendency to employ a diachronic approach in the description of the picture (Montangero and Parrat-Dayan, 1992). By this we mean the fact that instead of contenting themselves with the elements present in the picture, certain children evoke past or future actions. As might be expected, our hypothesis is that such a tendency appears at about the age of 11 years. We shall subdivide the description of the results of this experiment into three sections. In the first, we shall analyze the responses relating to two verbal descriptions which were read to the children. In this section we shall see whether children recognize the difference in the linguistic level of the two descriptions from the outset and we shall be able to identify the criteria which are of importance to them in the two verbalizations. The second section will be devoted to the presentation of the results relating to the form and rhythm of linguistic development as it is conceived of by children. The third section takes the form of a study of the correlation between subjects’ spontaneous tendency to employ a diachronic approach in their description of a picture and the tendency, or lack of it, to provide a synthetic description of a series of pictures which are presented to them. Why study the correlation between diachronic and synthetic abilities? It is because one of the conditions for diachronic thinking is the creation of an integrated whole from a series of states. If no diachronic approach to things exists then each situation, each state within an evolutive process is considered without any linkage to the situations and states which precede or follow it. Before subjects can understand and take an interest in an evolutive process they must synthesize the series of states that is presented to them. In his initial research into the development of knowledge in children, Piaget attributed considerable importance to the appearance of synthetic abilities which he contrasted with the tendency to perform juxtapositions (when the parts predominate to the detriment of the whole) which is found in younger children (Piaget, 1969a; Margairaz and Piaget, 1925). Might the development of the diachronic approach which we observe in children aged between 8 and 11 simply be a consequence, or an aspect, of progress in the ability to synthesize? We shall return to this question in the third section of the presentation of our results.

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Procedure and Population Introductory phase The children were presented with a picture to describe. The picture depicted a cartoon character perched on top of an unstable pile consisting of a chair topped by a stool with a large book on it. In the picture, the character is trying to reach a pot of jam in an open cupboard (see figure 5.3). The experimenter said: ‘You are going to tell me everything you can see in

Figure 5.3: Image to be described

this picture, to tell me what is going on. Later on a child will be shown this picture among other ones and the child will have to recognize the picture thanks to your description.’

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Comparison of two descriptions This part was devoted to the comparison of two descriptions of the same picture given by two children of different ages (one was a 3-year-old and the other a 10year-old). The experimenter said she was going to read two descriptions of pictures that had been given by two children named John and Paul. The texts, written on sheets of different coloured paper, were as follows: • John’s description: ‘He is standing, on a chair. He wants that. He has got his hat on and that is on the wall.’ • Paul’s description: ‘It is a duck child who has climbed on a chair and then he opens the cupboard and tries to take the pot of fruit.’ The subjects were asked whether the two descriptions described the same image, whether the two children described it in the same way and, since the answer to this question was always negative, why the two children did not describe in the same way. Subjects then had to say what was different in the two descriptions. Moreover, they were asked to estimate the approximate age of the authors of the descriptions. To this end, they were presented with a row of nine pictures representing stages in the life of a person. The children had to attribute each description to a picture in the row. Finally the experimenter asked whether John (the younger child) could describe the picture like Paul (the elder) and whether Paul could describe like John. Conceptions of change The second part of the experiment consisted of a verbal exchange about how the manner of describing a picture changes with age. The questions were asked with reference to the series of nine drawings mentioned above. These drawings, of 13. 5×13.5 cm each (see figure 5.4), represented the following steps in the life of a boy: (1) baby; (2) toddler; (3) 4-year-old; (4) first or second grader; (5) 10- or 11year-old; (6) about 13-year-old; (7) teenager; (8) about 18-year-old; (9) about 30year-old. The experimenter made sure the subjects understood what was represented on each image and that the nine images showed the same person. Then questions were asked about four topics: • Continuity or discontinuity of development. ‘When in the life of this person (at which picture in the row) do changes occur in the way he describes a picture?’ • Rhythm of development. ‘Is there as much time between the first steps of development (e.g. between pictures 2 and 3 of the series) as between later steps (e.g. between pictures 4 and 5)?’

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Figure 5.4: Series of nine images representing the life cycle of a person (note that the pictures were presented to the subject in a single row)

• End of development. ‘Does the way he describes a picture stop changing at a certain moment, or does it go on changing into old age?’

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• Causes of changes in the manner of description. ‘Why does the way he describes a picture change with age?’ Population This comprised 60 children aged 7 to 12 years, divided into four age-groups of 15 children each: 8 years (7:9 to 8:11, M=8:2), 9 years (9:0 to 9:11, M=9:3), 10 years (10:0 to 10:11, M=10:5) and 11–12 years (11:0 to 12:9, M=11:10). Results: (1) Comparison of the Two Heard Descriptions Although the two descriptions read to the children were very different, all the subjects asserted that they were descriptions of the same picture. These children knew very well that several forms of verbalization may correspond to one single reality. As far as the cause of the difference between the two descriptions was concerned, only in the older group of age did a majority of subjects (67 per cent) spontaneously mention a difference of age between the two children who had produced the descriptions. Younger children, aged 10 years and below, usually thought that the descriptions were different because the two children who had produced them were different, or because their ideas, their imagination, etc. were not the same. We can see that adopting a diachronic approach, in other words, resorting to the idea of change over time, when it comes to explaining differences in language is a late acquisition in cognitive development. This late appearance characterized the spontaneous representation of development and not the possibility of recognizing that each description corresponded to a different age. When they were invited to compare the developmental levels of the two descriptions, by means of the question: ‘Do you think one of these children was older than the other?’, even the younger subjects answered correctly. They not only immediately accepted the idea that the ages of the speakers were different, but they judged that John was younger than Paul. As for the nature of the difference between the descriptions, the children referred to three main criteria. • Lack of identity between the two descriptions. The subjects made a comparison of the elements of the descriptions, mentioning what was different or what was lacking in a description as compared with the other. For example a child aged 7:10 said: ‘Well, at the beginning: “It is a duck child” and John says: “He is standing on a chair” and Paul he says something else. This one [Paul] he says: “He takes a pot of jam”, then the other says: “and that is on the wall”.’ • Quantitative criteria. The subjects considered the number of words, the length of sentences or the amount of information. For example, a child aged 9:1 said: ‘Paul and John don’t describe the picture in the same way, because this

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Table 5.7: Nature of the differences between the two descriptions. Percentage of subjects per age-group (N=15 subjects per group) and per category of response

sentence [pointing to the sheet on which Paul’s description was written] is longer than the other. Paul told everything that happened in the picture, and the other [John] less.’ • Qualitative criteria. These were either semantic or grammatical (usually the fact that sentences were incomplete). In the first case, subjects took into account the informative or communicative function of language and indicated the ambiguities involved in John’s description. Here is an example of reference to a semantic criterion, quoted verbatim from the protocol of a child aged 10:11: ‘Well, he [John] speaks of “that” when he means the jam or the pot of fruit. He [Paul]: “It is a duck child”, then the other says: “he”. This one [Paul], there’s more. He explains what he wants to do, then the other one [John] he just says: “That is there”, but we don’t know what he is talking about.’ As shown in table 5.7, 8-year-old children mainly explained the difference in terms of lack of identity, or else they referred to quantitative differences. At the age of 9, the results were similar, except for the appearance of qualitative criteria in a minority of subjects. From the age of 10 years onwards, there was a striking change: the perceived difference was of qualitative nature. This occurred in 87 per cent of the 10-year-olds, whereas in the 11- to 12-year-old group all the subjects mentioned a qualitative difference. A third of the subjects in this group pointed to a grammatical difference, rather than a semantic one, between the two descriptions. When considering the attribution of the two descriptions to one of the developmental levels illustrated in the series of nine drawings, we first questioned a control group of adults. The vast majority attributed John’s description to stage 3 (when the boy starts kindergarten) and Paul’s description to stage 5 (end of junior school, about 11 years). The children’s answers to this question were judged correct if they corresponded to the adults’ attribution (plus or minus one rank). At the ages of 8 and 9 years, half the children attributed

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the descriptions to the correct ages. From 10 onwards, most subjects attributed the descriptions successfully (74 per cent at 10 years and 87 per cent at 11–12 years). It should be remembered that the subjects had no information about the age of the authors of the descriptions. This result therefore revealed a good ability to evaluate the age of children on the basis of a sample of their verbal production. The question about the possibility for Paul and John producing similar descriptions usually elicited asymmetrical judgements. All the children thought that the younger one (John) could not speak like the elder, because he was too young or had not yet learnt enough. Some children among the younger subjects (40 per cent at the age of 8 years, 13 per cent at 9) thought it would be impossible for Paul, the elder, to speak like John. He could not do it, said these children, because he is big. However, the majority of 8- and 9-years-olds and all the subjects aged 10 and over thought that Paul could describe the image like the younger child. The justifications for these answers often referred to the integrative nature of language development: ‘He can do what he has already done’, said a 10-year-old. Another subject aged 11 said: ‘We can always go lower, because we were little once.’ Results: (2) Conceptions of the Development of Verbal Descriptions Children’s conceptions of the continuous or discontinuous aspect of language development changed with age. The majority of 8-year-olds thought that the way of describing a picture improved at each step of development illustrated in the nine drawings. Half the 9-year-old children made a similar judgement, whereas the other half gave the type of answer that appeared in the majority of older children: progress was not thought to be continuous, it occurred every two or three images. Thus from the age of 10 years, the improvement of language abilities was conceived of as a slow and discontinuous process, which was not confused with the passing of time or with physical growth. As far as the rhythm of development was concerned, the responses observed in younger subjects did not correspond to the responses given in the experiment on tree disease, where these subjects either imagined a fixed time between each step or judged that the later steps would take less time than the initial ones. For language development, the majority of subjects in all age-groups thought that more time elapsed between two initial steps than between two later steps, because more things had to be learnt at the beginning of language development. The answers about the moment when progress in the ability to describe a picture ceased showed a clear developmental trend. Eight-year-old children thought that this ability improved into old age. At 9 years they judged that this ability would cease to develop earlier: either in adulthood (50 per cent of subjects) or at about 14–15 years (50 per cent). The latter judgement was found in the majority of 11-

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to 12-year-olds. On the whole, the older our subjects, the earlier they thought language development would end. Let us now turn to the responses concerning the causes of the development of the ability to describe a picture. Between the ages of 8 and 10, most subjects started by answering that language improved because one grew up. The older children often used the verb to develop. When they were asked further questions about what they meant by growing up, the subjects gave three categories of causes of verbal development. • Physical growth. For example, an 8-year-old child said: ‘As you grow, you learn how to describe things better because your teeth grow; that makes you speak.’ Other children mentioned the fact that the voice, the chest (and even in one case the feet) grow. • Learning. Subjects alluded to the role of imitation and repetition, for example a 7-year-old answered: ‘You say a word a lot of times, and then you learn’ (incidentally, this showed a metacognitive knowledge of the strategies used to memorize). Sometimes the alleged cause was language learning in school and more frequently all the subjects learnt in school: ‘Older children describe things better because they know more things. They have learnt them at school: more words, maths, everything’ (answer of a 10-year-old subject). • Internal causes. The answers classified in this category mentioned the development of the brain or of thinking abilities or of some more specific ability such as memory or perception. For example, a 12-year-old child said: ‘It is obvious that it isn’t enough to have people round you and to hear. You need a more developed brain to learn the meaning of words.’ Two points should be noted about this answer. It combines external factors (the verbal environment of the child) and internal ones (the development of the brain). Moreover, the internal factor is mentioned in order to explain the understanding of words, which is implicitly distinguished from the mere repetition of words. The frequency of the three categories of responses can be found in table 5.8. The table shows that from the ages of 8 years to 10 years, a majority of explanations referred to learning (73 per cent of the subjects at 8 years, 80 per cent at 9 and 93 per cent at 10 years). The most commonly mentioned type of learning was the acquisition of general knowledge at school. Imitation was rarely invoked, and usually by younger subjects. There was a very significant relationship between the age and the category of explanation (chi-square (6)= 37.33, p<0.001). The 11- to 12-year-old children gave different explanations than the younger ones: most of them (67 per cent) mentioned internal causes.

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Table 5.8: Causes of verbal development. Percentage of subjects per age-group (N=15 subjects per group) and category of response

Results: (3) the Diachronic Tendency and Synthetic Ability The descriptions provided by each of the subjects at the start of the experiment enable us to distinguish between three stages of development of the tendency to consider a situation from a diachronic standpoint. • Absence of diachrony. The description is confined to the elements present on the picture or mentions at most one action which is not depicted. Here are three examples: ‘Well, there’s a duck. I don’t know who it is; there’s some jam, there are cupboards, there are drawers, there’s a book, there’s a stool, there’s a chair’ (child aged 7:9). ‘There’s a person who’s on some chairs. He’s in the kitchen and is looking for pots of jam in his cupboard’ (subject aged 12:0). ‘There are some bowls of jam, there are…Wait. There’s a chair on a stool, then the little duck. There’s a book on the stool. The little duck climbs on it. He wants to get the pot of jam’ (child aged 8:2). One element of this final example refers to a past action of which only the result is visible on the picture: ‘The little duck climbs on it’. Despite this, however, this description does not evoke any temporal process. Although not totally adiachronic, this description belongs to the first category. • Low level of diachrony. This category contains the descriptions which, on the one hand, list the stacked objects in the order in which they were stacked and, on the other, evoke an action which is not shown in the picture. When these elements are present, the overall description does, to a certain extent, evoke a process. ‘He’s on a chair, a stool and a book, then he tries to get the pot of jam. Then he’s going to fall because it moves’ (child aged 9:4).

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Table 5.9: Diachronic aspect of the description of the first image presented. Percentage of subjects per age-group (N=15 subjects per group except for the 8-year olds, N=14) and level of diachrony

In all these descriptions, however they are classified, we ignore the use of the adverb then or and then since we know that this does not necessarily possess a temporal significance for young children (Fayol, 1985). • Diachrony. The descriptions in this category evoke a temporal progression of actions, frequently preceded by an initial descriptive sentence which is generally static in nature. These descriptions express the relationship between means and ends. ‘It’s a duck. He takes a pot of jam and then for him to get the pot he brings chairs then a book, then he takes the pot’ (child aged 10:9). In some cases a particularly large number of events are evoked while in others the temporal process is particularly well described. ‘It’s Fifi who’s quite small and can’t reach the pots of jam. So he brings a chair and then it’s still not high enough. So he puts on a stool and it’s still not high enough. He puts on a book and then he can at least reach the cupboard. Well, now the problem is to get the jam without falling down. Well, he tries but he looks a bit worried…’ (child aged 10:7). In defining these levels of diachrony, we have not focused on any particular linguistic marker. The tense of the verbs, in particular, must be considered to be an inadequate indicator. In effect, while almost all the children who use the past tense belong to the group displaying the most highly developed level of diachronic ability, almost half of the children in this group fail to use this tense. It can be seen from table 5.9 that the tendency to employ a diachronic approach in the description of the presented picture increased with age. Most of the descriptions provided by the 8-year-olds revealed the absence of diachrony (50 per cent of subjects) and this type of description diminished with age. In contrast, the proportion of subjects providing a diachronic description increased with age, growing from a minority status at 8 to 9 years (36 per cent to 46 per

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cent) to reach 67 per cent at age 10 and 74 per cent among the 11- to 12-yearolds. In examining the degree of synthesis in the description of the nine ordered pictures (response to the question: ‘What does all that represent?’) we have again allocated the descriptions to three categories. • Absence of synthesis. The descriptions proceed picture by picture with certain pictures sometimes being omitted. ‘It’s a baby [picture 1] and another who’s playing with building bricks [picture 2]. There’s his daddy who’s showing him the school [3]. Here he’s going to school, he’s starting to work [4 and 5]. Afterwards he gets bigger then when he’s big he goes by car [8] and then he becomes a daddy [9]. It’s the same child’ [subject aged 7:9]. When a non-synthetic description is encountered in 11- to 12-year-old children, it generally involves fewer pictures and includes a reference to the process of ‘getting bigger’. • Partial synthesis. The description involves two periods: an evocation of the initial phase followed by a synthetic description of the remaining stages presented in the pictures. ‘That’s when he was a baby and when he got bigger’ (child aged 9:3). • Synthesis. The set of nine pictures is described in a single phrase. In some of the cases an expression such as ‘from…to’ indicates the plurality of the states depicted: ‘It’s the life of a person, from very young to very old’ (child aged 9:3). In other cases the synthesis is more marked: ‘It’s a child growing up’ (subject aged 9:5). Table 5.10 presents the frequency of the descriptions corresponding to these three levels. At 8 years of age, the clear majority of descriptions were nonsynthetic. The frequency of this type of description had fallen greatly by age 9, while the number of partially or totally synthetic descriptions increased. Amongst our subjects, the age of 10 was characterized by a decline in the level of synthesis. The majority of subjects in the 11- to 12-year-old group provided synthetic descriptions. Once we had determined the level of diachronic ability (in the description of the first picture) and the level of synthetic ability (in the description of the set of pictures) for each subject, we were in a position to conclude this last part of the experiment. It will be remembered that we were interested in the correlation between the levels of synthetic and diachronic ability. We have therefore constructed a dual entry table (table 5.11) which shows the number of subjects belonging to the different cells.

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Table 5.10: Levels of synthesis in the description of the nine images. Percentage of subjects per age-group (N=15 subjects per group, except for the 8-year olds, N=14) and level of synthesis

The absence of any correlation was so obvious that there was no point calculating the correlation level. Of the 59 subjects, only 18 simultaneously displayed either a low or a high level of both diachronic and synthetic ability. Sixteen other subjects were situated at opposite levels in the two tasks, displaying a high level of ability for one task and a low level for the other. We must therefore abandon the hypothesis that the tendency to employ a diachronic approach is subordinate to the child’s synthetic abilities. The spontaneous introduction of past and future events as well as of a temporal process into the description of a picture is not related to the tendency to produce a synthetic description of a set of pictures representing an evolutive process. Summary and Conclusions When children are read two verbal descriptions produced at two widely divergent ages (3 years and 10 years), it becomes possible to measure the extent of the gap between the ability to recognize the existence of a time-related Table 5.11: Percentage of subjects of all ages (N=59) per level of diachrony and level of synthesis

development and the spontaneous application of this idea of development in the explanation of a perceived reality.

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Our 8-year-old subjects—and quite probably much younger children—are perfectly able to recognize the relative ages of the authors of the descriptions. This is an ability which has already been observed in connection with the judgement of children’s drawings. What is more, half of our 8- and 9-year-old subjects attributed the authors of the two descriptions an age very close to the real one. However, these judgements were obtained following a suggestion made by the experimenter which consists of the question of whether the authors of the two descriptions are of the same age. In the absence of such a suggestion, 8- and 9year-old children do not think of explaining the differences between the descriptions in terms of the age of the authors. Instead they think that the descriptions are expressed differently because they stem from different children who have different ideas. We observe that the budding psychologist turns more spontaneously to a differential perspective than to a genetic or developmental viewpoint. Now, this latter viewpoint is nothing other than the application of the diachronic approach, that is to say the appeal to transformations over time in order to explain a reality. This diachronic approach is only spontaneously adopted by a majority of children in the 11- to 12-year-old age-group (67 per cent of subjects). This early ability to recognize the developmental level of a verbal production is unaccompanied by the possibility of analyzing what it is that distinguishes these levels. When asked to analyze the differences between the two descriptions they have heard, most 8-year-old children limit themselves to saying that they are not the same. A mere third of them define the differences in quantitative terms. This situation changes abruptly at the age of 10 when 87 per cent of subjects analyze the difference in terms of semantic ambiguity or clarity. At this age, the functional purpose of language (that is to say the objective of communicating information) is foregrounded. Once more, we see (although earlier than for other contents) the appearance in the older subjects of a qualitative criterion for describing an evolutive process. When we investigate the perceived rhythm and curve of the verbal development in question, we find that children from the age of 8 onwards form fairly precise ideas but that these ideas change with age. The youngest children consider development to be continuous (often day by day) and to continue without interruption through to old age. From the age of 10 (and already in half of the 9-year-olds), children think in terms of development by stages which ends either at adulthood (half of the 10-year-old children) or at the onset of adolescence (the majority of 11- to 12-year-old subjects). To summarize, we find that the youngest subjects possess a cumulative conception of linguistic development which is poorly distinguished from the other changes which occur over time. As the subjects grow older, this idea is replaced by a different conception of verbal development which is now seen as a process which develops by stages and completes its evolution independently of other processes of growth.

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When we consider the causes cited for the development of verbal descriptions, we find that the 8- to 10-year-olds refer to external factors: the acquisition of various types of knowledge, often as part of school work. In the group of 11- to 12-year-olds the idea of learning is supplemented, in 67 per cent of subjects, by the idea of internal causes: intellectual development or the growth of the brain. It can thus be seen that children’s theories concerning the explanation of language development are empirical in nature at the age of 8 to 10 years and tend to become constructivist (interaction of internal and external factors) from the age of 11 onwards. The hypotheses proposed in the summary of the objectives and problems of this experiment are thus clearly confirmed by the results. The evolution of conceptions of linguistic development is characterized by a movement towards the dissociation of the steps in the evolutive process from other changes over time, towards a centring on the qualitative aspects of change and on internal causes. Moreover, as in the preceding experiments which involved different contents, the older children thought in terms of an evolution in stages rather than a process of continuous change. It also seems that the integrative character of development is recognized at a very early age: things that are learned by young children remain accessible to older ones. The majority of children in all agegroups believe that a 10-year-old child is able to speak like a smaller one. Nevertheless, 40 per cent of the 8-year-old subjects consider this to be impossible. This type of response confirms the absence of continuity between the different stages in young children’s conceptions of a developmental process. To conclude, let us turn to the results concerning the hypothesis that holds that the development of the diachronic approach is subordinate to the development of the synthetic ability. First of all, let us recall that we have used the term ‘tendency towards diachronic description’ to describe the verbalization of a sequence of events, some of which are not depicted on the picture which is presented to the subjects, rather than the simple description of the visible elements only. Diachronic descriptions reconstruct the series of acts (stacking the chair and stool, climbing onto them, opening the cupboard etc.) which have resulted in the situation presented in the picture (the little duck is in front of the open cupboard). This tendency to describe the presented picture in a diachronic way increases with age and appears in a majority of subjects from the age of 10 onwards. Furthermore, when presented with a set of nine pictures representing the stages in the growth of an individual, the children are able to produce juxtaposed or, in contrast, synthetic descriptions. The synthetic descriptions account for the entire series of pictures in a single formulation (for example ‘it’s a child growing up’). While the frequency of this type of description increases with age, in the same way as diachronic descriptions, a regression is observed among the 10year-old subjects. At this age, synthetic descriptions are encountered less frequently than among the 9-year-old subjects. The majority of the descriptions provided by the 11- to 12-year-olds are synthetic in nature (60 per cent).

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There are thus two reasons for expecting to find an excellent correlation between diachronic and synthetic descriptions. The first reason is theoretical in nature: in order to apply a diachronic approach, the subject must be able to link the past and the future and consider states as moments within an evolutive process. This presupposes the ability to unite past, present and future within a single whole. The second reason is empirical: the two characteristics in question —diachrony and synthesis—become increasingly prevalent as the subjects grow older. An analysis of intrasubject responses reveals no correlation between these two characteristics. Moreover, the diachronic tendency appears slightly earlier than the synthetic tendency (at the age of 10, for example, the majority of descriptions are diachronic whereas only a few are synthetic). The ability to consider a situation from a diachronic standpoint thus appears to develop independently of the synthetic ability. Do we Grow more Intelligent? Conceptions of Intelligence and its Development Objectives and Problems The preceding chapters have shown that, for children, drawing and verbal skills unquestionably develop with age and experience. However, do school-age children have similar conceptions of a much more fundamental and abstract attribute, namely intelligence? The idea of intelligence is valued, at one degree or another, in every section of the population and it gains importance as children progress through the educational system since intelligence and academic success are frequently equated with one another. In contrast with the ability to draw or speak well, intelligence manifests itself in a much more varied and abstract way. In effect, it is not revealed by a concrete production (or ‘output’) such as a drawing or sentence which can be easily compared with other, similar productions. It is therefore not possible to know a priori whether children think of the development of intelligence in a way similar to that of drawing or language. The limited amount of research which deals with children’s conceptions of intelligence barely touches on the problem of its development. A study conducted by Leahy and Hunt (1983) reveals certain factors proposed by 6- to 10-year-old children and by adolescents to explain both intelligence and its development. These two authors assert that the idea of passive learning, which is prevalent in 6-year-old children, gives way at the age of 10 to an emphasis on motivation and the effort to learn. Factors of a social nature (incentives, social interaction) are primarily proposed by 16-year-old subjects. In contrast, Yussen and Kane (1985) claim that even young children believe that the role of family and school is fundamental in the development of intelligence. However, these

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same authors are also of the opinion that children of under 9 years of age seem to conceive of intelligence as something innate, a belief which would seem to exclude the idea of development. If we are to study children’s conceptions of intellectual development, we must first discover what children understand by the expression ‘to be intelligent’. In the experiment conducted by Monzani and Jaussi, we therefore thought it essential to start with an attempt to understand these conceptions of intelligence. The most fundamental question that interests us here is that of knowing whether the conception of intelligence changes over the age range that we are studying or whether children of 8 and 12 years share a number of common beliefs. In effect, what is important for us is to compare the results relating to children’s conceptions of intelligence with those concerning the possible development of children’s conceptions of intellectual development. A number of authors have demonstrated the existence of age-related changes in children’s definitions of intelligence. Leahy and Hunt (1983) have identified three levels which correspond to the three age-groups in their sample, that is to say subjects of 6, 10 and 16 years. Between the ages of 6 and 10, conceptions of intelligence cease to be based on the consideration of specific, observable behaviours and are increasingly founded on psychological factors such as individual traits and the motivation involved. This internalization of the conception of a skill is similar to that which we have observed in the case of drawing and language. For Leahy and Hunt, social skills and characteristics acquire importance at the age of 16, whereas Yussen and Kane (1985) consider these factors to characterize the responses of the 6- to 7-year-olds. Nicholls, Patashnick and Mettetal (1986) also distinguish between three levels. For young children, intellectual abilities are proportional to the subjective difficulties involved in the resolution of a task. At the age of 8 to 9 years, the volume of knowledge possessed and the effort made to learn assume the greatest importance while among the 12- to 13-year-olds there is a clear distinction between verbal and abstract reasoning. These authors consider this to be a reflection of the academic distinction between fluid intelligence (problem resolution) and crystalized intelligence (verbal skills). This differentiation of the forms of intelligence with age is also identified by Yussen and Kane. One observation which is common to all these different studies (Leahy and Hunt, 1983; Nicholls, Patashnick and Mettetal, 1986; Yussen and Kane, 1985) is the tendency of 9- to 10-year-olds to confuse intelligence with the effort invested in studying and academic skills. Not all authors insist on this difference in the conception of intelligence at different age levels. Moreno, del Barrio and Soto (1992) claim that at all age levels the definitions of an intelligent person employ five categories: general intellectual ability, general knowledge, academic success, practical reasoning and social skills. The frequency of responses referring to general abilities and practical reasoning increases with age. At the same time, certain categories

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which are never mentioned simultaneously by the youngest subjects may coexist in older children. For our purposes, what is significant in these various studies is, on the one hand, the importance which children attach to academic skills when defining intelligence and, on the other, the fact that intelligence can be subdivided into a number of abilities. The first of these subdivisions that is of interest to us is the distinction between intelligence as a form of reasoning and its content, which is more closely linked to memory skills. Such a distinction is blurred in certain perspectives of presentday cognitive psychology which appear to reduce almost any cognitive activity to a question of memory. Despite this, intellectual operations involving the manipulation of meanings seem to us to be quite distinct from memory abilities whose main function is to retain the contents of knowledge. This distinction plays a key role in ideas concerning the development of intelligence. In the absence of a distinction between form and content, it becomes possible to believe that intelligence grows continuously with every newly acquired item of knowledge. In defining a theoretical starting point for the study of children’s conceptions of intelligence, it is useful to recall Piaget’s (1952) definition of intelligence in infants. For this author, intelligence at this age consists of finding the means, though still unapplied, of attaining an end. This definition makes it possible to account not just for the practical know-how of infants but also for the later conceptual abilities relating to problem solving. Certain aspects of know-how are, of course, non-intelligent and based on the automation of habits. Do children distinguish between this type of know-how and intelligent activities? This question would appear to be worthy of study. As for problem-solving behaviour, this contains both a deductive and an inventive aspect. We shall attempt to discover whether children consider this latter aspect, that relating to invention or creativity, to be intelligent. To resume, the first part of our experiment aims to discover what children understand by ‘being intelligent’ and thus to provide us with a way of evaluating any progress which may occur in the age-related differentiation of the forms of intelligence. To this end we shall not ask our subjects to define intelligence since a definition may ignore many aspects of what children consider intelligence to be. Instead we shall present our subjects with a set of abilities and ask them to judge the extent to which they imply intelligence. These abilities will illustrate the four forms of intelligence which we have distinguished between: reasoning, memory, inventiveness and know-how. Each of these categories will be illustrated by three types of aptitude: academic prowess, which as we know tends to be overvalued; ludic abilities, whose gratuitous nature opposes them to the academic abilities; and, finally, another set of abilities which we shall term general.

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Part One: Method and Population During this part of the experiment, which was designed to study conceptions of intelligence, the subjects were asked to classify nine skills each represented by a drawing on a board of 7.5×10 cm on a five-point rating-scale ranging from ‘not really intelligent’ to ‘very, very intelligent’. The drawings were presented one by one, defined by the experimenter and then placed by the subject on one of five rows drawn on a sheet of A3 paper. Each of these rows represented one point on the rating-scale. The task was described to the subjects as follows: ‘Do you think that what this child knows how to do is not really intelligent [the experimenter points to the lowest row], a little bit intelligent [second row], intelligent [third row], very intelligent [fourth row] or very, very intelligent [top row]?’ The nine drawings of skills were chosen from the following set of 13 drawings, each of which represents one of the four categories (reasoning, inventiveness, memory, know-how) and one of the three types (general, academic, ludic): • General type. — Proportional reasoning. ‘This child has two piles of counters, one pile with four counters of which two have a cross on the back and one pile of six counters, three of which have a cross on the back. Most children say that they have a better chance of picking a counter with a cross on the back if they take one from the pile which has three crosses. But the child you can see in this picture is the only one who says that isn’t true and that there is just as much chance of picking a cross straight away in both piles. Actually, he’s the one who is right.’ — Practical invention. ‘It’s vital that this child gets to a village lower down in the valley because he has to take some medicine to his grandmother who is ill. The road has been blocked by an avalanche. The child thinks of using the river but there’s no boat. Then he has the idea of building a raft using some inner tubes which he finds at the garage. He is able to go all the way to his grandmother’s house.’ — Memorizing street names (useless). ‘This child has found a map of Paris. He has learnt most of the street names by heart. He has never been to Paris.’ — Memorizing street names (useful). ‘This child has learnt by heart many of the street names of Geneva. He lives in Geneva and wants to be a taxi driver.’ — Know-how: driving a car. ‘This child has been taught how to drive by his father. Because he isn’t old enough yet, he’s only able to drive around the garden of his house.’ • Academic type.

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— Mathematical reasoning. ‘This child is very good at maths. He understands the explanations very quickly and always gets the answers to his schoolwork right.’ — Narrative invention. ‘He always invents wonderful stories when he’s writing stories for school.’ — Memorizing poems. ‘He knows by heart lots of poems which he learnt at school. In this picture he’s reciting one without having to look at the book.’ — Physical know-how: gymnastics. ‘This child is the best in his class at gymnastics. He always gets a good mark for gymnastics.’ • Ludic type. — Reasoning (problem-solving): chess. ‘He’s very good at chess. He always beats everybody.’ — Inventiveness: Lego objects. ‘This child can build beautiful, complicated Lego objects without having to copy any model.’ — Memory: memory game (after making sure that the subject knows the game): ‘he’s got an excellent memory. You can’t beat him at this game.’ — Know-how: computer games. ‘He’s very good at computer games and always beats the computer.’ In each age group, all the subjects classify the general drawings, then half classify four drawings of the academic type while the other half classify four drawings of the ludic type. Population The experiment involved 60 children subdivided into five age-groups, each of which corresponded to a school year (12 subjects per group). Second year: 7:7 to 8:4, M=7:11; third year: 8:6 to 9:2, M=8:11; fourth year: 9:5 to 10:4, M=9:10; fifth year: 10:5 to 11:3, M=10:10; sixth year: 11:6 to 11:11, M=11:7. Part One: Results A score of between 1 and 5 was allocated to each of the skills presented depending on the row in which it had been placed by the subject (1 for ‘not really intelligent’, 2 for ‘a little bit intelligent’, 3 for ‘intelligent’, 4 for ‘very intelligent’ and 5 for ‘very, very intelligent’). In cases where subjects changed the position of a drawing, the allocated score was the average of the scores of the two different positions. The results summary distinguishes between average scores of 4 and more (particularly intelligent), scores of 3 to 4 (averagely intelligent to intelligent) and scores of less than 3 (not intelligent).

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As, in the case of the ludic and academic drawings, there were only six subjects per age group we have aggregated the groups to form two sets: namely the 8- to 9-year-olds on the one hand and the 10- to 11-year-olds on the other. These data are presented in table 5.12 which also presents the results relating to the six 12-year-old subjects by way of comparison. Establishing the mean scores for each of the four categories and for all subjects without distinguishing between skill type (academic, ludic and general) reveals the following order: first place was taken by reasoning with an overall mean of 3.8; this was followed by inventiveness (overall mean: 3.7), memory (overall mean: 3.3) and finally know-how (overall mean: 2.3). In reality, such a mean obscures a number of interesting differences and can be somewhat misleading. For example, general reasoning (proportions) was always considered to be less intelligent than practical inventiveness (raft). The only overall result of note related to know-how, that is to say skills based on sensorimotor coordination, which was always accorded the lowest intelligence rankings. As the scores awarded within the same category or same skill type may vary greatly depending on the particular skill depicted in the drawing, it is worthwhile considering each of these skills in isolation. If we adopt such a viewpoint, the first striking observation is that there were many points of agreement between children of very different ages concerning the evaluation of the degree of intelligence involved in various skills. First of all, from age 8 to 12 the skill considered to require the greatest intelligence was mathematical reasoning (ability to resolve arithmetical or mathematical problems without difficulty). Useful memory (the knowledge by heart of the street names of a city in someone who wishes to become a taxi driver) was highly regarded although there were certain differences depending on age: while judged to be particularly intelligent by the 8- and 9-year-old children, it then fell back to be ranked among the intelligent behaviours, occupying a relatively low position at 10 and 11 years (sixth position out of 13 skills) and a higher position again among the 12-yearolds (third position out of 13 skills). Pure memory skills which confer no social, professional or ludic benefit (learning the street names of an unknown city) were judged to be only slightly intelligent. They were distinguished from reasoning skills in all age-groups. Of the know-how skills, the one to receive the lowest rating was car driving. A number of judgements permit us to distinguish between certain age-groups. The ability to invent and recount stories was held to be particularly intelligent by the 10- and 11-year-olds. The rating of inventiveness using Lego bricks fell from the age of 10 onwards. Part One: Discussion and Summary What is immediately striking about these results concerning the evaluation of the relative intelligence involved in these various cognitive activities is the low level of change observed between the ages of 8 and 12. In other words, despite the

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considerable level of cognitive development that takes place during this period, a number of criteria for the evaluation of an intelligent activity remain unchanged. Over a wide age range, the cognitive activity which is considered to be the most intelligent is the ability to understand and resolve mathematical problems without difficulty. Intelligence is therefore linked to a mental activity (hence the low ranking of know-how) which comprises a reflective and deductive aspect (hence the lower score awarded to inventiveness) and which is abstract in nature. Proportional reasoning (quantification of probabilities) is also the result of a mental activity which deals with numbers. However, it is considered to be substantially less intelligent than mathematical reasoning in general. This is primarily because this task is incomprehensible for children under 10 and easily solved from the age of 11 onwards (‘You don’t have to think much to get it right’ said one subject in this age-group). Here we observe the influence of a criterion which derives from the relative difficulty, as well as the relative interest, of a cognitive activity. The effect of this type of criterion explains why inventiveness in story writing should be so highly valued at the age of 10 and 11. It is not until the age of 10 that children start to write genuine stories (Fayol, 1985). If we return to the question of probabilistic reasoning we should also note that this exercise probably seems gratuitous to the majority of subjects. It would appear that the usefulness of a cognitive activity is a criterion in children’s evaluation of the degree of intelligence it reflects. This can be clearly seen in the difference in the scores awarded to useful, as opposed to gratuitous memory. Equivalent cognitive work (memorizing street names) is judged to be much more intelligent when it can be usefully applied in the future. It would therefore appear that a variety of criteria, some relating to the nature of the cognitive activity and others to its objectives, interact in the evaluation of the intelligence involved in a given skill. To summarize, we can distinguish between: 1. a criterion relating to the mental nature of the cognitive activity; the reflective nature and abstract character of the activity lend greater weight to this criterion; 2. a criterion of relative difficulty which consists of understanding the type of knowledge in question without, however, being able to apply it unproblematically; 3. a criterion of personal or social utility. These three points explain most of the scores obtained for different skills among the 8- to 12-year-olds. A new set of experiments would be necessary to determine whether or not the relative weighting of these criteria changes with age. For example, the criterion of utility (or adaptive value) seems to play a more important role at ages 8 and 9, as is shown by the scores obtained for useful

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Table 5.12: Mean score per skill in each age-group (N=24 subjects per group for the general skills, 12 subjects per group for academic and ludic skills, except for the 12-year olds [asterisk], where there were 6 subjects)

Notes: Proper.: proportional reasoning; Mem.: memory; Inv. Lego: invention, Lego game; Math, reasoning: mathematical reasoning; Nar. inv.: Narrative invention; Comp. game: Computer game.

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memory and the arguments in support of the intelligent nature of gymnastic skills encountered among the 8-year-old subjects (‘if he’s good at gym he could become a sports teacher’). It should be noted that the ability to solve mathematical problems easily satisfies all three criteria whereas the ability to drive a car satisfies none of them. The fact that knowing how to drive equates to matching the know-how of adults is not taken into consideration. Driving is not intelligent because as a skill it is neither mental nor abstract and because as an activity it is not only useless but dangerous (many of the subjects thought a child who drove could cause an accident). The existence of these three criteria means that a variety of skills can be considered to be intelligent (but not ‘particularly intelligent’): not only reasoning but also game strategies, inventiveness, verbal memory etc. Part Two—Method: the Development of Intelligence In order to investigate children’s ideas concerning the development of intelligence, we used the set of nine drawings which were previously employed in the experiment concerning linguistic development. These nine drawings, each of which was presented on a card 13.5 cm square, depicted nine stages in the life of a person, from the infant state to that of an adult with a child of his own. We first made sure that the subjects understood what each state depicted on these drawings represented and were aware of the significance of the set as a whole. We then asked questions which can be grouped under the following headings: • Invariance or change with age. — (Concerning the person illustrated on the drawings): ‘Do you think his intelligence changes when he grows up?’ — ‘Can a person become more intelligent if he wants to?’ • Temporal limits to the development of intelligence. — ‘When did this child [the one depicted on the set of nine drawings] start to become intelligent?’ — ‘Will his intelligence stop growing one day?’ — ‘Will he lose his intelligence one day?’ • Rhythm of development. — ‘Does intelligence increase every day?’ — ‘Are there times when intelligence changes a lot, more than at other times?’

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— ‘Has this child’s intelligence changed more between these two stages [cards 2 and 3: small child playing with building blocks and child going to nursery school] or between these two [cards 6 and 7: child starting secondary school, adolescent of about 16] or has it changed by the same amount?’ • The causes of intellectual development. — ‘Why do you become more intelligent?’ — ‘You know that there are children who don’t go to school, the Amazon Indians for example. Can you become intelligent without going to school?’ Part Two: Results Invariance or change All the children, from age 8 to 12, accepted that it is possible to improve one’s intelligence. However, a number of the 12-year-old subjects distinguished between the form and content of intelligence. For example, one of them told us that ‘intelligence doesn’t grow very much. It’s rather that you know more things.’ A number of the 11- and 12-year-old children used the verbs ‘to develop’ or ‘to grow’. At the same time, in response to the various questions concerning age-related intellectual changes, a small number of subjects (8 per cent at age 8 and 9, 17 per cent at age 10 and 11 and 33 per cent at age 12) referred to the innate nature of intelligence. The 12-year-old subjects who did so drew an explicit distinction between intelligence (form) which was seen to be invariant during growth and knowledge (content) which was considered to increase with age. The temporal limits of development When asked about the start of intellectual development, the younger subjects (60 per cent at age 8 and 9) tended to think that intelligence does not start to change until the start of primary school. At the age of 11 (66 per cent), and even more frequently at 12 (83 per cent), subjects believed that the start of intellectual development is situated at the infant stage (pictures 1 and 2). When considering the question of the end of the development of intelligence, about half of the subjects in all age-groups (42 per cent to 58 per cent) believed that intelligence continues to develop until adult age. An equal number of the 12year-old subjects believed that intellectual development ends before adult age (as against 0 per cent to 17 per cent in the younger age-groups).

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The rhythm of development It was not until the age of 12 that the idea of development by stages occurring only at certain times as a result of learning or other circumstances, which was present in a minority of children aged 8, 9 and 10, was observed in a majority of subjects (67 per cent). The idea of continuous development prevailed before the age of 12, except among the 10-year-olds where the two ideas were encountered with approximately equal frequency. The idea of discontinuity, as measured by the number of moments that are considered to be critical for the development of intelligence, was also observed most frequently in the 12-year- old age-group. Fifty-five per cent of the 12-year-old subjects thought that there are more than two critical moments (stages in life at which intelligence changes a lot) compared with 8 to 25 per cent among the younger subjects. It was only at ages 8 and 9 that the majority of subjects claimed that there is only one critical moment in intellectual development. The younger subjects (75 per cent at ages 8 and 9) considered that intellectual progress was greater between stages at the end of school age than between two stages in infancy. At the age of 12, the opposite response was given more frequently (58 per cent of subjects): progress is greater in the infant than at the end of schooling. The causes of development We identified four types of cause. • External causes relating to the influence of the environment: intelligence develops through the imitation of others or as a result of the effects of school or family. • An undifferentiated internal cause that consists of a reference to the idea of ‘growing up’ (‘You get more intelligent because you grow up’). • Differentiated internal causes consisting of references to brain evolution (‘The brain understands better’ or ‘Because the brain is more developed’). One or two subjects referred to the idea of the realization of an innate potential. For example, one 11-year-old subject claimed that: ‘He was born with intelligence which stayed in a corner of his brain. Later on, he used it.’ • The final type of cause consists of a reference to learning (‘Because he learns’). Table 5.13 indicates the frequency with which these categories of cause were identified by the subjects. It does not differentiate between causes invoked on their own and those cited in conjunction with others. At all ages, learning was the most frequently cited cause. For the youngest subjects, the idea of learning primarily implied the accumulation of knowledge which is mostly academic in nature. (‘You get more intelligent because you learn new things. You learn how

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Table 5.13: Causes of the development of intelligence. Percentage of subjects per agegroup (N=24 subjects per group) and category of explanation

to read and count.’) The 11- to 12-year-old children most frequently referred to the effort or desire to learn. This was an active concept of learning which did not consist solely of academic progress. In fact these subjects believed that infants learn much. Moreover, half of them simultaneously referred to learning and to an external cause. References to the undifferentiated internal cause appeared in 42 per cent of the younger subjects and diminished greatly with age. The differentiated internal causes were found more frequently in the 11- to 12-year-olds (50 per cent of subjects) than in the younger children (12 per cent). If we consider the relationship between internal and external causes, we find that internal causes were cited more frequently than external causes from the age of 11 onwards. The question concerning the possibility that intelligence will develop in children who do not attend school revealed that at all ages the majority of children believe that intelligence may develop in the absence of schooling. From the age of 10 onwards, the subjects stated that this type of intelligence is different from that which is acquired by attending school. Conclusions and Summary of Parts One and Two While judgements relating to the more or less intelligent nature of various cognitive activities vary little between the ages of 8 and 12, the conception of the idea of the development of intelligence certainly undergoes a transformation during this period. It can thus be seen that the study of the diachronic aspect of children’s thought is better suited than a study of ‘static’ judgements to revealing the conceptions which characterize each age-group. These results also argue in favour of the existence of a diachronic approach whose development is distinct from the development of knowledge in a given field.

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As far as children’s conceptions of intelligence are concerned, our results show that children, just as much as adults, harbour implicit theories of intelligence as defined by Neisser (1976) whose ideas were based on Rosch’s concept of the prototype. Children are no more able than adults to define what an intelligent person is in terms of a particular quality. Instead intelligence manifests itself through a variety of relevant characteristics. In view of these results, we believe that three principal criteria are applied by schoolchildren when judging the intelligence associated with various cognitive abilities. The first criterion is subjective difficulty (as revealed in young children by Nicholls et al., 1986): our results suggest that an activity is considered to be intelligent if the subject has an adequate understanding of what it involves but is unable to perform it with any ease. The second criterion is the mental nature of the activity, thereby excluding know-how based on sensorimotor coordination. The importance of this criterion is emphasized by two qualities: the abstract nature of the knowledge content and the thoughtful nature of the behaviour. One is intelligent if one thinks and has good ideas. Deductive operations appear to be considered more important than induction or inventiveness. The third criterion relates not to the complexity of the cognitive activity but to its objective. The intelligence involved in an activity is judged in terms of its adaptive character, that is to say by its personal or social utility. It is possible that the relative importance of these criteria varies with age. However, all three are important at between 8 and 12 years. This explains the results which were common to all the age-groups. First, the high rating awarded to the ability to solve mathematical problems easily. While all children know what this entails, few excel at it (first criterion). It is an abstract, deductive mental activity (second criterion) which is useful at school since it is closely linked to academic success (third criterion). It might be argued that mathematical prowess is highly rated because it is the cultural prototype of intelligent activity (Mugny and Carugati, 1985). We believe that children only appropriate cultural models when these correspond to their own capacity of assimilation and their own theories—which are not always the same as those of adults. The three criteria for the evaluation of intelligence result from an interaction between social importance (and academic importance in particular) and individual metacognitive activity. The second common result consisted of the higher rating given to the memory of street names when this has a future application (that is to say when it will be necessary within the framework of subsequent professional activities). Here we see evidence of the third criterion, quite independently of any difference in the complexity of the activity in question. The low ratings awarded to know-how, such as the ability to drive a car, do gymnastics or play video games, are explained by the fact that none of the criteria is really satisfied. In the case of driving, the third criterion has a negative impact: it is not only useless but also harmful (dangerous). This is why this skill was awarded a particularly low score.

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The criterion of relative difficulty explains the age-related variations in the rating of activities such as writing stories (rated more highly by the 10- and 11year-olds than by the other age-groups). The second part of this experiment, which investigated conceptions of the development of intelligence with age, reveals a difference in the conception of intelligence which was not brought to light by the first part. Whereas at age 8 children possess a largely undifferentiated concept of intelligence/knowledge acquisition, by the time they reach the age of 12 they differentiate between the potential to reason and learn, on the one hand, and the knowledge contents acquired throughout life on the other. There were certain points that were common to all the age-groups we questioned about intellectual development. The first was the idea that intelligence changes over time, increasing even in the absence of academic tuition. At the same time, intelligence is thought to develop as a result of learning activities. However, we have seen that this term may mask a variety of ideas. Apart from these few points, children’s conceptions of intellectual development change considerably over the age range studied. Children of age 8 and 9 primarily think of this development as the accumulation of knowledge of the type which is learned at school. They believe that intellectual progress starts on entry to primary school (this is true in a small majority of cases) and continues until either old age or adulthood. The process is thought to be continuous in nature and to proceed more rapidly during the final years of school than in very young children. Both external (for example, the role of the school) and undifferentiated internal causes are given for intellectual development. Here again we encounter the quasi-maturational conception previously observed in connection with the drawings of wild children: growing up is one cause of the development of psychological aptitudes. From the age of 11 onwards, these ideas undergo considerable change. The development of intelligence is no longer thought to be linked to schooling. Instead it occurs as early as the infant stage. References to the factor of undifferentiated maturation disappear. The growth of intelligence is due to internal causes (in general, the development of the brain) just as much and often more than to external causes. At the age of 12, these changes can be even more clearly observed. The rhythm of intellectual evolution is thought to be much more discontinuous: progress takes place in steps. This is reminiscent of the notion of stages that was observed among the subjects of this age-group in the research presented in Chapter 3. Similarly, the majority of 12-year-old subjects believe that progress is more rapid in small children than in adolescents and half of them think that intellectual development ends with puberty. On this point their ideas coincide with those of Piaget who saw the formal logic exhibited by the adolescent as the final stage of logical development, while also considering that cognitive development continues throughout adult life at a level other than that of logic. Finally, it is at the age of 12 that a third of the subjects explicitly

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distinguish between intellectual capabilities which vary little with age and particular items of knowledge which multiply. Taken as a whole, this experiment confirms the fact that the diachronic approach undergoes important modifications at about the age of 11 to 12. At this age, children tend to abandon their earlier conceptions according to which change is both quantitative and cumulative and explained either by external factors or by an undifferentiated internal factor (the idea of ‘growing up’). In their new conception of change over time, pre-adolescents envisage progress proceeding by qualitative leaps as a result of the interaction of internal and environmental factors. If we analyze this development in terms of the meanings involved, we find once more that it is characterized by the differentiation of initially undifferentiated meanings and by the ability to coordinate a larger number of elements. General Conclusions to Chapter 5: the Intuitive Psychology of Children Concerning Cognitive Development It is clearly no surprise that schoolchildren know that their abilities develop with age and that they possess theories to explain this fact. Children are changing beings who year after year experience changes in their know-how, their status at school and the demands made of them by their families. They may also compare their skills with those of younger or older children. Our experiments show that young schoolchildren of 7 and 8 years of age are so convinced that psychological development proceeds during childhood that they adopt a quasimaturationist perspective, to which we shall return later and which can be summarized in a sentence: The more you grow, the more you know and the better you know how to do things. The experiments which we have conducted in three different fields (drawing skills, the capacity for verbal description, intellectual ability) reveal schoolchildren’s knowledge of these subjects. First, they are able to seriate the productions of children of varying ages by their level of development: drawings of human figures and verbal descriptions. Therefore, at the recognitive level, they possess the knowledge which is necessary in order to identify the more or less developed character of a graphic or verbal production. The errors observed at the age of 6 to 7 in the seriation of four drawings, or at the age of 8 to 9 in a similar task involving a greater number of drawings do not mean that these children are incapable of distinguishing between the levels of development of these productions. If they are questioned verbally, they attribute the correct level to each production. When they are required to explain the development of their own knowledge or know-how, children reveal certain specific items of knowledge which are not generally appropriate until after the age of 10. Here we are speaking of the metacognitive level of the analysis of productions or their evocation (for example, their depiction in a drawing). From the age of 10 onwards, children

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analyze differences in the levels of linguistic productions in terms of their semantic clarity or ambiguity. They therefore consider the communicative function of language before, at the age of 11 or 12 (and at this age only a minority), they start to take account of its syntactic aspects. In the case of drawings, it is the complexity and degree of realism of the production that form the criteria of development. When considering the question of intelligence, children tend to distinguish this, always at approximately the same age, from specific items of knowledge, that is to say that they conceive of it as an ability to understand which is distinct from its contents. The aim of our experiments is not to study this type of progress but rather to identify children’s conceptions of the development of cognitive skills. If we adopt such a perspective, we note that some important changes arise after the age of 10. In our opinion, these changes cannot be explained by the development of knowledge relating to the skill in question (drawing, language or intelligence). Even when children’s understanding of the ability itself changes little (as, for example, in the evaluation of the degree of intelligence associated with an activity) their conceptions of its development still undergo a transformation. Sometimes this modified conception, which appears at about age 11, may be based on a misunderstanding of the facts. For example, 11-year-old subjects represent the progress of the ability to draw a human figure in terms of the transition from a schematic to a realistic drawing. However, in reality the schematic depiction of a human figure is late to appear. Thus these subjects reveal a particular conception of development (the passage from the simple to the complex with qualitative differences between the productions) without possessing detailed information about the facts of this development. Certain ideas concerning development are shared by all the age-groups we questioned. All the children believe that cognitive abilities increase with age, following a development curve which is not necessarily monotonic in nature: the changes may be greater at one end of the curve than the other. When asked about the causes of cognitive development, children refer to learning activities and are generally aware of the educational role of the family and school environment. With these exceptions, the ideas of development which prevail before the age of 10 are clearly differentiated from the theories of development held by children aged 11 to 12. We can summarize the conceptions of development held by 7- to 9-year-old children as follows. First, they consider that change takes the form of a growth, that is to say a quantitative increase in elements (words in the case of language, academic know-how in the case of intelligence and number of details depicted in the case of drawing) which occurs continuously. This cumulative conception appears to be integrative: more highly developed knowledge or abilities contain preceding levels of knowledge or ability. However, in connection with linguistic development we have noted that 40 per cent of the 8-year-old children believe that a 10-year-old is no longer able to speak in the same way as a 3-year-old. This observation suggests the absence of an integrative conception. Moreover, for

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the youngest children, each representation of a moment in time necessarily reflects a new step in the development of the skill in question. If, for example, the life of a person is divided into nine stages, these subjects consider that linguistic or intellectual progress takes place at each of the depicted stages. When presented with a set of drawings, these subjects attribute a fixed age to each drawing level that is shown to them. At the same time, this elementary level of the conceptions of development is characterized by the late age at which development is thought to end. In the case of language, progress is thought to continue through to old age while the development of intelligence is considered to continue either through to old age or until the individual reaches full maturity. Two factors are thought to contribute considerably to the causes of development. The first is the simple fact of growing up. This is what I have termed the quasi-maturationist conception, a poorly differentiated concept which confuses the passing of time, increase in size and the growth of abilities. This is why a ‘wild’ child of 10 years of age is thought to draw better, at his first attempt, than a wild child aged 4. The second factor in development is environmental in nature, namely the role of models furnished by other individuals or by school. The continuity of this progress does not necessarily entail an understanding of the links between the various stages as we can see from the results of the research presented in the preceding chapters. One indication of this fact relates to the conceptions of cognitive development: this is the difficulty of simultaneously considering a present state and its past stages. For example, when 7- to 9-yearold children are asked whether they have always drawn as they do now they do not understand that the question refers to the development of their ability to draw. Or, alternatively, if they are read two descriptions given by children of very different ages, they explain the differences in verbal production in terms of individual differences between the authors. The idea that these differences are due to the different ages of the speakers does not occur to them. Generally speaking, these children do not spontaneously evoke the past or the future when they are asked to describe a state. This can be seen from the low number of diachronic descriptions obtained for the picture presented in the experiment concerning verbal descriptions. The conceptions of cognitive development held by children aged 11 and 12 present a clear contrast with this first type of developmental theory. Here we observe a concept of development by qualitative jumps. Progress is thought to occur in steps which are not found at every one of the stages of life depicted on the drawings. It consists of changes in the complexity and realism of the drawings, in the communicative value of verbal descriptions, in the intellectual potential for understanding rather than in the volume of knowledge amassed. Thus, as in our study of the conception of biological changes in Chapter 3, we again observe the appearance of the notion of stages. This is why these children think that a particular level of production (for example a type of drawing of a human figure) corresponds to an age range rather than to a specific age. They think that

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linguistic or intellectual abilities stop developing earlier than is the case with younger children. It is on reaching adulthood, or even adolescence, that the development of these abilities is thought to end. When asked about the causes of cognitive development, these children no longer evoke the idea of ‘growing up’. What characterizes these more highly developed conceptions is the importance attributed to internal factors such as brain development, motor ability, ideas or imagination. The role of such factors does not exclude environmental influences, especially in connection with the development of drawing and language skills. Children thus move towards an interactionist explanation of the progress of knowledge. The active conception, which places the emphasis on effort and will, simply confirms the presence of this interactionist conception. It is also among the 11- to 12-year-old age-group that we first observe the tendency to consider the past stages of a current state. Some children of this age spontaneously evoke the idea of age-related transformations to explain differences in verbal productions: they therefore adopt a genetic or developmental perspective. This perspective enables them to understand the question relating to their drawing (‘Have you always drawn like this?’) and causes them to evoke past or future events in their description of a picture. This knowledge concerning the development of a variety of abilities shows that at approximately the age of 11, children’s metacognitive activity increases and gains in accuracy, that new explanatory schemes or schemata replace the former ones and that an improvement in children’s capacities of coordination is also observed in the question of the links between the successive stages of a transformation.

Chapter 6 The Representation of Changes Associated with Human Activity Which are not Necessarily Predictable

The changes about which we have hitherto questioned our subjects have been both predictable (for anyone who is familiar with the phenomenon) and natural or, at least, partly natural. They were the result of the execution of a genetic programme (growth of a tree), the interaction of such a programme with environmental factors (illness, development of psychological abilities), or of a physical cause (thawing). We were therefore interested in investigating children’s representations of changes which result from human activity and which are not necessarily predictable. This may well enable us to enlarge our knowledge of the general schemata of change which are employed by children. We are also curious to observe whether some of the major trends noted in the development of the diachronic approach to natural phenomena are also encountered in the representations of changes associated with human activity. The Rich will Always be Ahead of the Poor: the Comprehension of a Sequence of Four Cartoons Generally speaking, humorous stories contain a twist whose comic effect is created by the divergence between what is expected and what actually happens. Studies of the psychology of humour (for example Bariaud, 1983; Goldstein and McGhee, 1972) have identified this violation of expectations as an indispensable and fundamental component of humour. In diachronic terms, this suggests that a funny story consists of indicating a particular type of development over time and then introducing a divergence from the continuation which is anticipated by the reader or listener. Consequently, if the humorous nature of the story is to be understood, the reader or listener must possess a diachronic approach which is sufficiently developed to be able to understand the type of change implied by the story and anticipate its continuation. In order to study this point and also to question children about changes in economic status, Pons and Scheidegger, who carried out this experiment, decided to use a series of cartoons by Sempé (see figure 6.1). The four stages depicted in the drawings represent a variety of types of development: continuous tree growth, increasing building and traffic density, changes in method of transport, modernization of cars or buildings. The most

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Figure 6.1: The series of drawings by Sempé Source: Reproduced from Sempé (1989) Quelques citadins, with kind permission of Sempé & Editions Denoël, Paris, France.

striking of these changes is the progression of methods of transport which are presented in the drawings. The ‘poor’ person gets around on foot, then by bicycle, lightweight motorcycle and finally by car, whereas the rich person changes his cars in each of the first three pictures, always acquiring a larger, more modern vehicle. This series of drawings is of particular interest for our investigation of the diachronic approach not only because of the variety of changes that are depicted but also because of the twist at the end. The final drawing is surprising because the progression of the methods of transport used by the two figures is reversed with reference to the preceding drawings: the rich person is riding a bicycle whereas his poor counterpart is driving a car. The comic content, cynical in nature, is generated by the fact that this inversion reveals an underlying constant: the poor person, even though he finally has his car, will never get ahead of the rich man whose bicycle allows him to thread his way through traffic jams. This set of drawings helps us study three questions. First, the problems of seriating such a varied and complex sequence of changes in chronological order.

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The youngest subjects to take part in this experiment were aged 9 and would therefore experience no difficulty in completing a task requiring the systematic seriation of a set of sticks of slightly different lengths (Piaget and Szeminska, 1965) or of pictures illustrating a simple temporal progression (Bonnens, 1990). The question is how they will approach the problem of establishing the chronological order of pictures representing a set of different developments. The criteria applied by the children when seriating the pictures reveal the relative salience of the cues and the changes presented. Since 9-year-old children experience difficulty when asked to represent a number of developments simultaneously this task should be problematic for them. The second point studied in this experiment is the understanding of the humour generated by the twist at the end of the story, that is to say in the last of the four drawings in the series. Studies of the development of the comprehension of cartoons show both an improvement at age 7 (Shultz, 1972) and substantial progress between the ages of 7 and 11 when the majority of subjects are able to understand a series of 12 drawings (Bariaud, 1983). Understanding of the comic element of the set of drawings selected for this experiment depends on the possession of a highly developed diachronic approach and, to a certain extent, on the habit of comparing the lot of individuals belonging to different social classes. Thus we expected comprehension to be late to appear. For this reason, as well as to enable us to gather data concerning the development of the diachronic approach after the age of 12, the population studied in the experiment consisted not only of children but also adolescents and adults. The final question relates to the assessment of the temporal parameters defining the depicted states. The aim was to determine whether the tendencies observed in connection with biological and physical phenomena would also be encountered in connection with a sequence of ‘non-natural’ events. More precisely, we wanted to discover whether, between the ages of 9 and 12, children abandon the tendency to think in terms of fixed time intervals between depicted states and whether they acquire the ability to establish a coherence between their estimates of the period elapsed between the first and last states and their estimates of the date of each state. Method and Population Seriation Each of the four drawings was reproduced on a board measuring 15×19 cm. First of all, the subjects were shown drawing 3 of the set illustrated in figure 6.1 and were asked to describe it. All four pictures were then presented out of sequence (the sequence was chosen at random for each subject and the correct sequence was excluded). The subjects were told that the pictures represented different stages in the lives of Charles-the-rich and Albert-the-poor and were asked to

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place them in order starting with the oldest stage and ending with the most recent. The subjects were then questioned about the order they had chosen. ‘What did you notice that made you put the pictures like that?’ ‘Why did you put them in that order?’ If the seriation of the four drawings did not correspond to the order intended by the artist, the subject was asked to place the series in chronological order on the basis of the size of the tree. The desired order was then obtained. Comprehension of humour In order to gauge the subjects’ understanding of the humorous content of the drawings, the following question was asked: ‘What did the artist want to say with this series of drawings?’ Temporal parameters In the investigation concerning the subjects’ estimates of the temporal parameters, the questions concerning the total duration and the date of each stage were posed when the drawings had been arranged in the desired order. ‘How much time has passed between the first and the last drawing?’ ‘When did each picture happen?’ Population The population consisted of 60 subjects distributed over four age-groups corresponding to the following levels: third and sixth year of primary school, third year of secondary school (ninth year of compulsory education) and, finally, third year of university (psychology students). These four levels corresponded to the ages of 9 (from 8:6 to 9:5, M=8:10), 12 (from 11:6 to 12:5, M=11:10), 14 (from 14:1 to 14:11, M=14:8) and adult age (from 21:7 to 32, M =24:3). Unfortunately, it was not possible to interview the 14-year-olds and adults individually. Instead each group was asked to complete a questionnaire which was introduced by the experimenter. Results and Discussion Seriation More than half the 9- to 12-year-old subjects seriated the drawings in a way which did not correspond to the intended order (see table 6.1). Although the errors fell into a variety of categories, the most commonly observed failing (committed by half the children who seriated the drawings incorrectly) was to

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Table 6.1: Percentage of subjects per age-group (N=15 subjects per group) who placed the four drawings in the correct order or a different order

arrange the drawings in the order: 1, 2, 4, 3. This seriation may be explained in terms of a centring on the car which fails to distinguish between the vehicle owned by the rich man and that driven by the poor one. In fact, the car which appears in drawing 4 is both smaller and of an older design than the one in drawing 3. While the children correctly seriate the cars in order of age, they are unable to take account of the dual evolution of the rich and poor men’s vehicles. It should be noted that two subjects, both 9-year-olds, failed to establish the correct sequence following the instruction: ‘Look at the tree in the garden.’ With this single exception, there is no clear difference between the behaviour of the 9and 12-year-old subjects. Less than half the children (40 per cent) succeeded in placing the drawings in the correct order, with a major change taking place between the ages of 12 and 14 (Mann-Whitney U=52.5, p<0.01). In effect, at age 14 almost all the subjects produced the required order as in the adult group. We thus note that it is not until age 14 that we observe the generalization of the ability to seriate a set of pictures illustrating more than one evolution and containing both quantitative and qualitative changes as well as an interruption in the continuity of the evolution. When we examine the criteria cited by the subjects to explain their seriations, we observe a clear development in the unicity or plurality of criteria applied (Kruskal-Wallis chi-square=12.8, p<0.01). At age 9, the majority of subjects (60 per cent) applied a single criterion to all the pictures (for example: ‘I looked at the cars’). A third of the subjects in the 12-year-old group still cited a single criterion, whereas the majority of 14-year-old subjects (approximately 90 per cent) referred to multiple criteria (for example: ‘I looked at Charles and Albert’s cars and clothes as well as their houses’). One factor which distinguishes the responses of the 9-year-old subjects from those provided by subjects of the other age-groups is the inconsistency they displayed in the application of their chosen criteria. This difference is highly significant (Kruskal-Wallis chi-square=16.09, p<0.01). One third of the subjects —the ones who referred to multiple criteria—used different criteria for different pictures. In contrast, from the age of 12 onwards the subjects used the same set

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of criteria for each of the four pictures. This may be explained by the tendency of the youngest subjects to seriate the drawings in pairs, a tendency which is replaced by a strategy which takes account of the whole set of pictures in the 12year-olds and older subjects. Let us now examine the elements selected as seriation criteria as revealed by the statements obtained from the subjects (which does not exclude the possibility that other, unmentioned criteria may also have played a role). At all ages, the most salient element (87 to 100 per cent of subjects) was the car, with the twowheeled vehicles being cited much less frequently. The characters themselves were almost totally neglected by the 9-year-olds, whereas they were mentioned in two-thirds of the adult responses. Background elements (houses) were mentioned with much greater frequency by the adults although still only by a minority of them. Comprehension of humour It is clear from the difficulties experienced by the 9- and 12-year-olds in placing the drawings in the order intended by the artist that the humorous content of the sequence will be appreciated by only a minority of the children. Does this mean that those subjects who seriate the drawings correctly at their first attempt grasp the cartoonist’s comic intentions? The verbal descriptions obtained for the set of drawings show that this is most certainly not the case (see table 6.2). We have allocated the verbal descriptions to three categories reflecting different levels of understanding of the humour. Responses indicating a lack of comprehension of the humour of the situation can be divided into two main categories. In the first, the incongruity is incorrectly interpreted with subjects believing that the artist wanted to depict an inversion in the status of the two figures: ‘The poor man has become rich and the rich man has become poor.’ The subjects of the second category mention the socio-economic status of the two figures: ‘It’s the story of a poor man and a rich man’ and sometimes refer to changes over time (‘It’s how two people change’). There is thus no mention of the incongruity (an essential element of any cartoon) of the final drawing in which the poor man is driving a car and the rich man riding a bicycle. We can therefore identify three categories: • Permutation: inversion of rich/poor status. • Dichotomy: the status of both figures is mentioned. • Comprehension: the cartoonist’s intentions are understood: the description mentions the fact that the rich man still has the advantage even though the poor man has finally acquired a car. We were surprised to observe that understanding of the joke is extremely late to appear and is not generalized. Only seven of the 15 adult subjects (47 per cent) and a small minority of the adolescents and 12-year-old children grasped the

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Table 6.2: Comprehension of humour content as revealed by subjects’ statements. Percentage of subjects identifying the joke per age-group (N=15 subjects per group except for the 14 years where N=12)

humour of the situation. This age effect is highly significant (Kruskal-Wallis chisquare=12.7, p<0.01). It should be remembered that here we are examining a spontaneous description of the cartoonist’s intentions in response to the question: ‘What did the artist want to say?’ It is interesting to consider whether a more explicit question would have elicited more responses testifying to comprehension of the humour of the situation. In effect, it is possible that subjects who provide responses which fall into the category ‘dichotomy’ might be trying to summarize the story instead of explaining the joke. We therefore conducted a control experiment using a group of 15 adults similar in composition to the experimental group (15 university psychology students). These subjects were first shown each drawing in the series and were then asked: ‘What did the artist want to say in these drawings?’ When they had provided an answer, the subjects were asked a second question: ‘If you haven’t already mentioned it, say what is funny about these drawings.’ Even when the question was formulated in this way and therefore focused more directly on the comic content of the drawings, the frequency of responses revealing comprehension of the joke was no higher than in the adult group in the full experiment. Returning to the results of this experiment, we observe that the incorrect interpretation of the humour (responses in the ‘permutation’ category) was provided by 20 to 33 per cent of children, fell sharply at the age of 14 and disappeared at adult age. The majority of 9- and 14-year-old subjects and half the 12-year-old and adult subjects mentioned the poor/rich dichotomy. The décalage in the adolescent group between spontaneous success in seriation (14 subjects out of 15) and appreciation of the humour (three subjects only) is striking. The adolescents therefore concentrated on the cognitive demands of the seriation task (identifying the criteria required for establishing chronological order) but did not attempt to understand the joke.

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Temporal parameters When we consider the temporal parameters attributed to the depicted situations, the first striking result we observe confirms our earlier observations concerning tree growth. When estimating the period elapsed between the first and last picture, the youngest subjects (9-year-old group) generally stated a number of years equal to or less than their own age (that is to say nine years or less). This was true of 80 per cent of the subjects of this age-group. In contrast, among the 12year-old subjects the estimates obtained for the elapsed period (which objective indicators reveal to be at least 60 years) were in most cases (60 per cent) considerably longer than the subjects’ own lifetimes (average estimated period of 30 years compared with an average of nine years in the youngest subjects). All the adolescent and adult subjects considered the period which elapses between the first and last events to be substantially greater than their own age (average of slightly more than 50 years in both groups). The majority of 9-year-olds (60 per cent) and 7 per cent of the 12-year-olds used the number 4 (which corresponds to the number of drawings) in their estimate of the elapsed period (for example: 4 years, 4 months). This confusion between the representation of steps within the passage of time and the total elapsed period is certainly related to the confusion between the representation of time and the representation of the stages of a process. The tendency to consider that a fixed or equal interval separates the events depicted in the drawings was observed in 33 per cent to 40 per cent of the children. This tendency persisted in a number of the adolescent and adult subjects (20 per cent and 27 per cent of subjects). We also wanted to discover whether the subjects correlated their estimates of the total duration of the series, that is to say the time that elapses between the first and last pictures, with the approximate dates they attribute to the individual drawings. We were able to identify three types of response. • In the first type the estimates did not correspond. For example, one child aged 8:11 answered the question concerning total duration by saying: ‘In all it takes two years.’ However, when asked to date the individual drawings the same child answered: (1) In the Middle Ages…in 1920. (2) In 1940–41. (3) About 1950–60. (4) About 1970–80. A child aged 11:6 considered the sequence to take a total of 20 years but placed the pictures in different centuries! Some of the errors were less extreme. • The second response type consists of an error resulting from a confusion of the number of units and the number of intervals separating the units. Such responses fail to take account of the fact that a total of N units (whether years, storeys, milestones etc.) are separated by N—1 intervals. The following is an example of this type of response provided by a subject aged 8:8. Total duration: ‘it takes four years in all because it’s year by year.’ Date of individual drawings: 1984, 1985, 1986 and 1987.

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• In the third response type the estimates correspond. For example, a subject aged 12:6 considered that a period of 10 years had elapsed between the first and last pictures and attributed the dates 1960, 1962, 1968 and 1970 to the individual drawings. As table 6.3 shows, uncorrelated estimates were found in the majority of children (9 and 12 years, 67 per cent of subjects), became less frequent at 14 years (40 per cent of subjects) and are rarely encountered among the adults. This age effect is highly significant (Kruskal-Wallis chi-square=15.09, p<0.01). Confusion between the number of intervals and the total number of years was found in a number of subjects of all ages, and especially among the 9-year-olds (33 per cent of subjects compared with 7 to 13 per cent among the older subjects). Approximately half of the adolescents and the majority of adults (73 per cent) provided correlated estimates. Comparison of intrasubject responses In order to assist our understanding of the responses to the various questions and tasks demanded of the subjects, we performed a comparison of intrasubject responses. When we consider the seriation task, we observe that all the children who cited multiple criteria retained them for all the pictures. Despite this, a quarter of the subjects who behaved in this way were unsuccessful in the seriation task. The results relating to the relationship between the attribution of durations (for the entire set of events depicted as well as for each individual event) and the Table 6.3: Correspondence between estimates. Percentage of subjects per age-group (N =15 subjects per group) and type of response

correspondence between the total duration and the dating of the four depicted events are easier to interpret. The majority of subjects whose estimates corresponded (74 per cent) also displayed the most advanced behaviour when asked to attribute durations: the overall duration exceeded their own age, it was not based on the number four and the intervals between the drawings were variable. None of the subjects who produced corresponding estimates belonged to the lowest level for the three factors involved in the attribution of durations

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(duration equal to the age of the subject, reference to four units and presence of fixed intervals). However, 13 of the subjects who occupy the highest level in the attribution task fail to produce correlated estimates. We can thus note that ‘advanced’ attributive behaviour as it is described above is characteristic of a level of development which appears somewhat earlier than the ability to produce correlated estimates. Comprehension of the humorous nature of the sequence of drawings is independent of any particular mode of attributing temporal parameters. The complex diachronic thinking which underlies the appreciation of the joke develops independently of the evolution of the temporal reasoning involved in the metrical evaluation of the duration of events. Finally, this study of intrasubject responses confirms what has previously been observed concerning the relationship between seriation and the understanding of humour. While the subjects who appreciate the humorous content of the drawings produce chronologically correct seriations, success in the seriation task may be accompanied by an inability to grasp this humorous content. This suggests that the ability to place the sequence of drawings in the correct chronological order is a necessary, although not sufficient condition for comprehension of the joke. Summary and Conclusions Presentation of a sequence of humorous drawings allows us to make a number of interesting observations concerning the evolution of the diachronic approach and its relation to temporal reasoning. First of all, it appears that the comprehension of a sequence of events which unfold over time undergoes significant development from the age of 12 onwards. Only the adults (or, at least, half of them) are able to appreciate the cartoonist’s comic intentions. This is because the humour of the situation is based on the ability to comprehend a dual evolution (the development of Charles and Albert’s vehicles) and to recognize that the final stage simultaneously represents a discontinuity as regards the external appearance of the development (increasingly expensive and modern vehicles) and continuity in qualitative terms (the poor man travels more slowly than the rich man). It is, of course, clear that the development of ideas concerning social classes is also involved in the rapid comprehension of this sequence of pictures. Nevertheless, as the results of the following section will demonstrate, 12-year-old children are already able to define the qualitative differences between poverty and wealth and adolescents spontaneously prefer to appeal to such criteria. Is that not sufficient for an understanding of Sempé’s humour? We believe that the fact that an understanding of this humour is late to appear is not simply a function of knowledge concerning social classes but is also, and primarily, due to the diachronic complexity of this four-part story. Such complexity (a dual evolution followed by a stage which simultaneously

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represents discontinuity and continuity) cannot be easily assimilated by 12-yearold children. In the other experiments we have described, this age-group appears capable of diachronic thinking which is apparently as highly developed as that exhibited by adults. In fact, there is still a long way to go before a fully developed diachronic approach is attained. The same is true of the chronological seriation of events. The inability to understand an extremely complex type of evolution, in which discontinuity and continuity are fused, explains the difficulties which persist even at the age of 12 when children are asked to place Sempé’s drawings in chronological order. More surprising, however, is the absence of any correlation in the 14-year-old group between the seriation task (14 subjects out of 15) and the understanding of the joke (absent in 11 subjects). Adolescents possess the intellectual tools necessary to establish the chronological order of the depicted events: they simultaneously take account of various types of change over time. They use these tools to perform the seriation task but do not attempt to seek a solution to the problem of the comic incongruity. When we consider the application of temporal reasoning to the stages of an evolutive process we again encounter certain aspects similar to what was observed in connection with tree growth (see Chapter 3). On the one hand, 9year-old children tend to consider their own age to be the maximum duration applicable to long-term events. They believe that the overall duration of the steps depicted in the drawings is equal to nine years. It can be seen that this type of error does not result from false information concerning the actual duration of the phenomenon. If this were indeed the case then it would be difficult to explain why the same erroneous information (duration of approximately nine years) should apply to phenomena as different as tree growth and the stages in the lives of two individuals. What is more, the children fail to correlate their estimates of total duration and the date of each stage. None of the 9-year-old subjects was able to correlate these data precisely. We may therefore conclude that for these subjects an age or date has the sole function of identifying an instant in the passage of time and that the ‘cardinal’ value of such data is not understood. Ages and dates do not therefore indicate that a particular period has elapsed. A third of the subjects provide slightly incorrect associations of the total duration and the dates of the individual stages due to their failure to establish the correct relations between intervallic and cardinal values. At age 12, a majority of subjects still provide uncorrelated estimates. This result is in sharp contrast with the estimates obtained for the stages of growth of a tree. To conclude, we should note that this study of the relations between intrasubject responses reveals the solidarity of a number of the cognitive characteristics which interest us and the independence of others. We observe a solidarity in the various aspects of the temporal metric (attribution of units of time). Children must first show themselves to be capable of estimating lifetimes independently of their own age and the number of pictures used to depict the

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phenomenon and of thinking in terms of a variable interval between the depicted events if they are subsequently to be able to correlate their estimates of the total duration with their estimates of the dates of the individual events. Comprehension of the humour of the drawings proves to be independent of the behaviour relating to the temporal metric. The correct functioning of the register of diachronic thinking is thus clearly distinguished from the ability to measure durations. In contrast, diachronic thinking incorporates the capacity for temporal seriation. In effect, the subjects of this experiment are able to seriate Sempé’s set of four drawings correctly before being able to appreciate their comic content. Do the Rich stay Rich and the Poor stay Poor?: Conceptions of Wealth and Poverty and the Possibility of Change Children’s knowledge of economic questions (money, banking matters, profits and debts etc.) has been the object of a number of studies, most of them quite recent, which have generally revealed that these notions are somewhat vague and are neither well differentiated nor understood in detail until adolescence (for a summary of these questions, see Berti and Bombi, 1988). In order to study the development of diachronic thinking in this field, we selected two contrasting ideas of a largely non-technical nature, namely wealth and poverty. In contrast with technical concepts such as the interest on deposits or loans (Jahoda, 1984), wealth and poverty are meaningful for children of school age. In fact, from the age of 6 onwards children are able to define the characteristics which distinguish rich people from poor people (Delval, 1994; Leahy, 1981). As Delval has shown, this does not mean that these ideas of wealth and poverty correspond to welldefined categories. Instead, for children between the ages of 6 and 10, it is rather a question of prototypical labels based on salient individual characteristics. What interests us here is to determine whether or not children believe that an individual’s socio-economic status can vary. With very few exceptions, children have never witnessed any radical change in this status. Does this mean that they consider wealth and poverty to be invariant in nature? The responses obtained by Delval (1994) in a study of this question seem to be somewhat contradictory. On the one hand, children between 6 and 10 tend to think that an individual’s socioeconomic status is permanent and irreversible. On the other, when they are asked whether a poor person can become rich or vice versa, the same children consider the transformation to be an easy one which can be accomplished in a very short period of time. The aim of our experiment was to discover whether any of our 9year-old subjects considered that if someone is rich (or poor) then it is forever. What is more, the spectacular acquisition of wealth through the discovery of treasure or the rise of the penniless wretch who becomes a wealthy captain of industry, a film star or a billionaire sporting hero is a popular subject of stories and the object of a certain social ideology or mythology. This poses the question of whether children consider the acquisition of wealth to be more probable than its loss or whether they are more susceptible to the widespread pessimism

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concerning the future of the economy which characterized the period of recession and unemployment during which this experiment was conducted. However, there is a further question which is more closely linked to the diachronic approach in general and is therefore the main focus of our interest in this experiment. This concerns the problem of the form of the evolution which takes place when an individual’s socio-economic status changes. The simplest form is the transition from poverty to wealth or vice versa. A more complex form, which respects the properties of the future, consists of mentioning two possibilities from the outset: one can either keep the same status or one can lose it. Finally, there are longer-term representations which take account of more than one generation. When we considered the future of the forest (see Chapter 3) we found that a cyclical, or transgenerational, conception was late to appear. Does the same apply to the idea of the transmission of an economic status through inheritance? Before studying children’s responses to the question of variations in socioeconomic status we must first determine what meaning the notions of wealth and poverty have for them. A number of studies have revealed that the evolution of conceptions in this field corresponds to the results we obtained in connection with biological or psychological changes (see Chapters 3 and 5). We again witness a transition from the accentuation of easily observable external characteristics to an emphasis on internal qualities or processes. Leahy (1981) distinguishes between ‘peripheral’ responses (allusions to material possessions or appearances) and ‘central’ responses (reference to psychological phenomena such as ideas or personality traits). This author has found that the frequency of references to possessions diminishes between the ages of 6 and 11 while the number of references to appearances increases. However, the point that we wish to emphasize is that the ‘central’ responses increase in frequency during this period and continue to do so between the ages of 11 and 17. In a study of children aged between 8 and 11, Brusdal (1990) found that the younger children define wealth and poverty in terms of material conditions (associated above all with the possession of a house) whereas the older children frequently mention psychological or social consequences. In a study conducted using 6- to 10year- old subjects, Delval (1994) confirmed the younger subjects’ emphasis on the external manifestations of an individual’s socio-economic status. In our research, we wish to analyze the quantitative and qualitative characteristics of the definitions provided by our subjects since this duality, when viewed in the light of the contents dealt with in earlier chapters, has revealed a particular developmental tendency: the transition from a centring on quantitative aspects to an interest in qualitative aspects. We are also interested in the causes attributed to wealth and poverty since these causes determine the variable or constant nature of an individual’s economic status.

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Tasks and Population The population was the same as that participating in the previous experiment into the understanding of humorous drawings. In fact, immediately after viewing Sempé’s drawings and answering the questions concerning them, the subjects were asked questions about wealth and poverty. The first part of the experiment about the cartoons constituted an introduction to the concepts of wealth and poverty. The concepts of wealth and poverty The opening questions related to the definition and explanation of wealth and poverty. • ‘What is a rich person and how can you tell that he is rich?’ • ‘Why is a person rich?’ The same questions are also asked concerning poverty. Evolution of the economic status The question asked concerning the evolution of wealth or poverty is as follows: • ‘If someone is rich [poor] is it forever?’ It should be remembered that, in accordance with the Piagetian method, additional questions may be asked to encourage the subjects to specify exactly what they want to say. Results and Discussion The various responses obtained in connection with the representations of wealth and poverty can be allocated to two major categories corresponding to quantitative and qualitative characteristics respectively. It may be remembered that in other fields children aged 8 to 9 imagined change over time to be quantitative in nature, whereas older subjects also, and sometimes primarily, considered the qualitative aspect of the change. Here we are not asking our subjects to consider a change but rather a particular phenomenon (economic status) which is viewed from a static perspective. We have categorized the following characteristics as quantitative: ‘To have or not to have money (or lots of money)’; ‘To have or not to have lots of things’; quantitative references (‘lots of’, ‘big’) to clothes, cars and housing. Below are two examples of this type of response given by 9-year-old children:

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• ‘Being rich is to have lots of money to buy big cars and big houses.’ • ‘Poor people don’t have money or much to eat. It’s not having a big house.’ The following elements have been categorized as qualitative: references to ‘cars’, ‘clothes’, ‘houses’ etc. when accompanied by epithets such as ‘beautiful’, ‘luxurious’, ‘comfortable’; allusions to behaviour or ways of life: ‘being able to choose what you do’, ‘taking long holidays’, ‘living in good [bad] conditions’. The two examples below belong to the qualitative category and were provided by adolescents: • ‘The rich person has more modern things than other people.’ • ‘You can tell that someone is poor by the people they go around with and the job they do.’ The frequency of responses relating to the criteria of wealth or poverty was not the same in the different age-groups and revealed a distinction between the children (9- and 12-year-olds) and the other groups. In certain areas it also pointed to a difference between the adult group and the other levels. Let us examine wealth first. The use of the quantitative criterion ‘To have lots of money’ to define this concept appeared frequently at ages 9 to 14 (63 per cent to 80 per cent of responses) and fell sharply by adult age (18 per cent of responses). In its place, we observed the criterion ‘To have lots of things’ (47 per cent) which may result from increased attention to the second clause of the last question (‘How can you tell whether someone is rich or poor?’). The qualitative criteria of wealth that were most frequently mentioned by the 9- to 14-year-old subjects concerned the quality of cars and clothes. The adolescent and adult groups differed from the children in the frequency of references to behaviour (26 per cent of responses at age 14 and 41 per cent of adult responses, compared with 13 per cent of responses at age 12 and 0 per cent among the 9-year-olds). Moreover, in contrast with the adolescents, adults mentioned behaviour more frequently than the quality of clothes or cars. As far as poverty is concerned, the frequency of quantitative arguments did not allow us to distinguish clearly between the age-groups, with the response ‘Not to have money’ being cited the most frequently (from 50 to 69 per cent). When we turn to the qualitative criteria we observed the same tendency as for wealth, namely a reference to behaviour from adolescence onwards. An examination of the relationship between the quantitative and qualitative criteria allows us to classify the definitions of wealth and poverty provided by each subject in one of the three categories below: 1. Quantitative dominance: these definitions are composed either exclusively of quantitative elements or of a majority of quantitative elements. 2. Equal number of quantitative and qualitative elements.

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3. Qualitative dominance: exclusive presence of qualitative elements or more qualitative than quantitative elements. Very similar results were obtained for wealth and poverty. At age 9, a majority of subjects provided definitions of the quantitative dominance type (66 per cent). Quantitative and qualitative dominance appeared with almost equal frequency among the 12-year-old subjects while a majority of adolescent subjects provided definitions which fell into the qualitative dominance category (73 per cent). Half of the subjects in the adult group provided definitions of the qualitative dominance type and in a third quantitative and qualitative aspects appeared with almost equal frequency. On the one hand, the responses given to explain the causes of an individual’s socio-economic status invoked what we shall term subjective causes, that is to say causes relating to individual activity. In the case of wealth these may be activities such as saving, working, studying etc. In the case of poverty such activities consist of spending, not working hard, losing money by gambling etc. The classification of responses which involve gambling wins or losses is problematic. We have classified ‘winning money by gambling’ as an external cause of wealth since it occurs without any particular effort on the part of the individual. However, when gambling losses were cited as a cause of poverty there appeared to be an underlying idea of responsibility: the individual throws his/her money away. This is why we have decided to treat this cause as one of the subjective factors, a decision which may be open to question. A further subjective cause which was mentioned only in the adult group consisted of ‘not adapting’. Here are two examples of responses which invoke subjective causes: • ‘To become rich you have to steal and not spend your money’ (subject aged 9: 2). • ‘A person is poor because he doesn’t work hard or because he has lost too much money gambling’ (subject aged 14:8). The other set of causes is external in nature. In the case of wealth these consist of: inheriting wealth, winning money and having a job. In contrast, the external causes of poverty are unemployment, bankruptcy, war, being burgled etc. There follow two examples of responses indicating external causes: • ‘You’re rich because you’ve won the pools or inherited some money’ (subject aged 14:11). • ‘You’re poor because you can’t find work or because there’s a war’ (subject aged 12). If we first examine the results relating to wealth we find that the subjective cause most frequently mentioned by the children was saving (between 38 and 45 per cent of responses), closely followed by ‘working hard’. From 14 years onwards,

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references to saving became less frequent while professional activity (working hard or doing business) took its place as a major cause of wealth (approximately three-quarters of responses). The most common external cause of wealth cited by the 9-year-old subjects was ‘having a job’ (54 per cent of responses), while the idea of inheritance was the cause most frequently mentioned by the adolescent and adult groups (43 per cent and 56 per cent of responses). Winning money by gambling was a cause frequently mentioned by the 12- and 14-year-olds (one-third of responses). When we turn to the question of poverty we note that one particular subjective cause was very frequently mentioned by the children and continued to be cited by half the adolescent subjects: spending. This cause appeared less frequently among the adults and was replaced by a psychosociological consideration: ‘not adapting’. When we turn to the external causes of poverty we find that all the age-groups questioned tended to mention unemployment more frequently than any other cause. References to bankruptcy, while rarely obtained from the children, became increasingly numerous among the 14-year-old and adult groups. The subjects can be classified in three groups to reflect the relative importance of the subjective and external causes: 1. Subjective dominance (exclusively subjective causes or more subjective than external causes). 2. Equal numbers of subjective and external causes. 3. Dominance of external causes. With the exception of the 12-year-old group, the results obtained for wealth and poverty were not identical. In connection with wealth, we find that subjective causes dominate slightly at age 9 (47 per cent of subjects compared with 20 per cent favouring external dominance), while external causes started to dominate at age 12 (47 per cent of subjects compared with 27 per cent favouring subjective dominance) and were predominant in the majority of 14-year-old subjects (60 per cent of subjects compared with 13 per cent). In the adult group we find that the two types of cause were cited with approximately equal frequency (53 per cent of subjects cited equal numbers of subjective and external causes). In contrast, when we examine the explanations of poverty we find that subjective causes no longer dominated at age 9 when, instead, the majority of subjects cited equal numbers of subjective and external causes. External dominance was the most populous of the three categories among the 12-yearolds (47 per cent) and was more clearly so in the adult group (67 per cent). It is only among the adolescents that we found a majority of explanations in which subjective causes dominated (53 per cent). However, this result was due to the frequent mention of gambling losses. When we consider the diachronic vision of wealth and poverty, we find that all the subjects questioned, of whatever age, indicated that such an economic status is not permanent. They responded negatively to the question: ‘If someone

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is rich [or poor], is it forever?’ We can distinguish between two different ways of formulating this change in status. In the first, nothing is said to indicate that there may be two alternatives: maintaining one’s current status or losing it. Responses of this type are limited to a negation (‘No’) in which only one possibility is formulated: ‘Poor people become rich by saving.’ The second type of response contains a reference to these two possibilities, either by means of an allusion or more explicitly. The following two examples illustrate the allusive variant: ‘Not necessarily’ or ‘A rich person may gamble his whole fortune in a betting game and lose everything.’ The following example is illustrative of the explicit way of stating the two possibilities: ‘You can remain poor or become rich.’ Contrary to our expectations, the frequency of explanations in terms of alternatives (either retain or lose one’s status) did not differ significantly between the age-groups. In particular, the results provided in this regard by the 9- and 12year-old children differed only slightly, being provided by 60 and 73 per cent of subjects respectively in the case of wealth and 87 and 93 per cent of subjects in the case of poverty. The most that can be said is that the adults stated the possibility of alternatives more frequently than the children when describing wealth and less frequently when dealing with poverty. Finally, we should note that the concept of wealth passing from one generation to the next (mention of inheritance) did not appear until the age of 12 (60 per cent of subjects compared with 13 per cent at age 9). Summary and Conclusion The ideas of wealth and poverty are relative concepts (except, as Brusdal [1990] has noted, with regard to absolute poverty which is defined as the fact of living below the subsistence level). However, children, together with the majority of adults, fail to differentiate clearly between the absolute and relative aspects of these two concepts. Although wealth and poverty are distinguished relative to a particular norm they are not necessarily defined with reference to this norm. This is certainly the observation that proceeds from our results. When we examine the relative significance of the quantitative and qualitative criteria applied to the two concepts involved in this experiment we find that quantitative criteria (number or size of things owned) dominate in a majority of our 9-year-old subjects. At age 12, the numbers of subjects favouring quantitative criteria and those citing qualitative criteria (in general the quality of clothes or cars) are approximately equal. In the adolescent group we find that qualitative criteria tend to dominate and this dominance persists, though less markedly, in the adult group. In fact, the adults are characterized by their frequent references to what we have termed behaviour. For them, wealth and poverty are manifested in the individual’s freedom to choose or in particular activities rather than in the ownership of particular possessions. These results confirm our expectation of a transition from the quantitative to the qualitative and, in revealing the advent of more psychological considerations, correspond to the

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results obtained by Leahy (1981), Brusdal (1990) and Delval (1994). Thus the age-related development which occurs from 9 onwards can be described both in terms of a transition from the quantitative to the qualitative and as an internalization of the characteristics which are taken into consideration by the subject. As for the question with which we are primarily concerned here, namely that of the static or variable nature of an individual’s socio-economic status, we find few differences between the responses obtained from the various age-groups. All the subjects, including the 9-year-old children, believe that wealth or poverty is not necessarily a permanent status. It is also not possible to observe any clear age-related development in the references to a dual possibility, that of either maintaining or losing one’s current status. However, an examination of the responses concerning the causes of wealth and poverty reveals that the conceptions of change do, in fact, vary with age. The 9-year-old children believe that wealth is the result of individual will or behaviour (saving or working ‘hard’). Causes involving an influence which is external to the individual (for example: having a job) are mentioned less frequently. These subjects do not appear to distinguish between the more or less lucrative nature of various professional activities. However, when considering the question of poverty, the same 9-year-old children attribute greater significance to causes which are independent of the will of the individual, for example unemployment. These causes, which we have termed external, appear with approximately the same frequency as the subjective causes (in particular the fact of spending too much). The 12-year-old subjects emphasize exceptional external influences such as gambling wins and inheritance as causes of wealth and gambling losses or unemployment as a cause of poverty. References to voluntary, individual actions, such as saving or excessive spending, are still present. For the adolescents, exceptional external influences (inheritance, gambling) become increasingly important as causes of wealth and economic activities start to be differentiated: a number of subjects do not consider it sufficient simply to have a job; instead it is necessary ‘to be in business’. As far as poverty is concerned, the emphasis is shifted somewhat more towards individual responsibility, with subjects invoking causes such as gambling losses or excessive spending. When considering the question of wealth, the adults attribute approximately equal importance to subjective causes (doing business, working) and external influences (especially inheriting money). In contrast, when asked to explain poverty they primarily refer to external causes such as bankruptcy or unemployment. The most commonly cited subjective cause is a psychosociological failing: the inability to adapt. It is therefore clear that the conception of the acquisition and transformation of an economic status varies with age. For 9-year-old children this conception is orientated towards individual will and actions, whereas the 12-year-olds are

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aware of causes which are external to the individual and which may relate to the family (inheritance) or social circumstances. Despite the significance of the social dimension in the representations which we are investigating—that is to say observed social facts and culturally specific collective representations—all the results obtained point to the role of individual cognitive development. It is this evolution which, to a large extent, explains the tendency of subjects to consider qualitative factors which are inaccessible to direct observation when assessing wealth and poverty. The Traffic Jam: Measures to Improve the Traffic Flow The final set of experimental results we intend to present before concluding relates to children’s suggested solutions to the problem of improving the traffic flow. The ability to deal with this problem is based on the development of diachronic thinking since in order to find a satisfactory solution it is necessary to imagine both a flow pattern and alternatives to this flow, including temporal arrangements such as staggered starting times for car drivers. As children are never asked to solve traffic problems, questions of this sort may appear to fall outside their scope of interest and knowledge. However, this is a social problem with which every child in a city such as Geneva will have been confronted at one time or other. This problem can also be concretized by presenting the children with a drawing depicting roads, a blocked junction and certain causes of the traffic jam. For both these reasons we expect subjects aged 8 to be capable of proposing solutions for the avoidance of traffic jams. Furthermore, we are able to hypothesize that the solutions proposed by the children of the 10-year-old age-group will be of a higher quality thanks to progress in both spatial reasoning and diachronic thinking, this latter capacity enabling them to represent a flow and its alternatives more accurately. As our earlier research has shown, we can also expect to observe further progress in 12-yearold children. Of the proposed solutions, we shall pay particular attention to effective solutions of a diachronic nature: staggering of the times at which drivers set out from home or leave work, or the alternation of the right to use a car on odd- and even-numbered days. Such solutions imply that subjects are able to leave the here and now of the situation presented in the picture, ask themselves about the origin of the traffic jam and imagine a variety of traffic flows (or series of journeys). On the basis of the results obtained in earlier experiments, we only expect to observe this type of approach in subjects aged 10 and over. However, we are quite unable to say whether at this age such solutions involving staggered departure times, which are based on an analysis of the problem and/ or suggestions made by adults, will be rare or common. A new question which this experiment will allow us to study relates to the synchronism or lack of it in the handling of different types of diachronic problems —in other words, we will be able to gauge the relative difficulty of these

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problems. The capacity for diachronic thinking is constructed gradually. It should therefore be possible to design problems which, though requiring the application of a diachronic approach, are solved at an earlier age than other such problems. In my opinion, children are able to imagine the future progress of an event or reconstruct its beginnings at a relatively early age. In order to verify this point, we presented the subjects of this experiment with a problem requiring them to imagine the short-term consequences of a car stopping at a particular place. While the prevailing traffic conditions lead the driver to stop at this place, anticipation of what will happen later should encourage him/her not to stop there. The decision not to stop at this particular place therefore requires the adoption of a type of diachronic approach (anticipation of future consequences). However, because the subjects of this task are simply asked to anticipate the future of a single event, the complexity of the problem should not be equivalent to that of discovering the solution of staggered departure times which we described in the last paragraph. Our analysis will also go beyond the comparison of diachronic solutions. In effect, the example of the traffic jam enables us to determine whether the discovery of spatial solutions is contemporaneous with the identification of solutions of a temporal nature or whether, in contrast, it excludes the possibility of discovering such solutions. Although I have emphasized that the development of the diachronic approach is independent of that of other capabilities, I of course expect it to evolve in parallel with other fields of knowledge, such as spatial representation. It remains to be seen whether the recently emerged centration on the diachronic aspects of a situation is detrimental or not to the consideration of the spatial aspects. The experiment described here, which was conducted by Cattin, was also designed as a pilot study of the effects of training on the diachronic approach. For this reason, the experiment is structured as a learning study, that is to say it consists of a pre-experimental test, followed by a training period and, finally, a post-experimental test. As we are primarily concerned with the questions posed in the pre-test and repeated in the post-test, the time reserved for training in this experiment was limited to a period of approximately 10 minutes. During this period, the experimental group performs exercises requiring a diachronic approach (anticipation and reconstruction of the position of cars at points in time preceding and following the depicted situation) while the control group is confronted with a spatial exercise which is described below. Given the limited nature of the diachronic exercise, we did not expect to find any striking results in the post-test responses. Method and Population After a brief period of familiarization with the question of city traffic problems, the children were shown a picture (see figure 6.2) depicting a traffic jam at a road junction. In order to ensure that the subjects were aware of the relevant

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elements of the situation which was presented to them, their attention was drawn to and, if necessary, they were informed of the time of day (12.05 shown on a clock in the picture), what is happening at the exit to a bank’s underground car park and the exit of a factory car park, the fact that the cars located at the junction are unable to advance and the position of a removal lorry which is parked on the road. Pre-test and post-test phases The same questions were asked in the pre-test and post-test. Solutions to the traffic jam problem The children were asked to state ‘everything that can be done to stop the traffic jam’. If necessary, further questions were asked to determine exactly what they meant by their solutions and to encourage them to formulate new ones. Stopping at the green light The children were shown a picture of a three-way junction: a main road joined by a secondary road. The traffic light on the main road is green. The picture contains only two lanes of traffic: one lane on the secondary road waiting at the red traffic light controlling the junction and one stopped on the main road just after the junction. If at this point a car were to join this latter lane it would have to stop on the junction and would be in danger of obstructing the traffic entering from the secondary road once the light controlling this lane turned green. The children were asked to describe the picture. They were then given a paper car which was placed on the main road before the junction. They were then asked to point to the place where they thought that the driver of this car, who was described as intelligent, would stop the vehicle. Training phase The children were divided into two groups corresponding to the experimental condition (diachronic tasks) and the control condition (spatial tasks). The subjects in each condition were presented with three tasks and the total duration of the exercise was approximately 10 minutes. Diachronic condition The children were first asked to imagine the origin or cause of the traffic jam by responding to the question: ‘How do you think this came about?’ They were then asked to indicate the position of certain vehicles (the car in the centre of the junction, the lorry, the car attempting to leave the underground car park and the

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Figure 6.2: Traffic jam problem—picture shown to subjects

one at the exit of the factory car park etc.) at various times before and after the depicted situation, for example 30 seconds before, one hour before, one minute after the time shown on the clock (12.05). They were also asked to estimate how long certain vehicles had taken to move from one location to another or how long they had been parked. Finally, the subjects were asked to draw the junction as they imagined it had been one hundred years ago. Spatial condition The subjects in this group were asked to reproduce the roads shown on the picture at a different scale (half size). They were also asked to draw a different junction (in the country for example). Finally, they completed a mental rotation task in which they were asked to indicate the position of the same vehicles as those involved in the temporal task in the diachronic condition on a highly schematic plan of the junction (which was reduced to a cross accompanied by a single building to act as a landmark) which had been rotated through 90°. The population consisted of 72 children divided into three age-groups of 24 subjects, each of which was further divided into two subgroups corresponding to the experimental and control conditions. The two subgroups consisted of an equal proportion of girls and boys (50 per cent) and children from three different social backgrounds. 8-year-old group: from 7:4 to 8:11, M=7:10; 10-year-old group: from 9:5 to 10:8, M=9:10; 12-year-old group: from 11:3 to 12:5, M=12:0.

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Results The number of solutions proposed to the traffic jam situation, both in the pre-test and post-test, increased with age: the 8-year-old children offered 94 solutions, while the 10-year-olds proposed 131 and the 12-year-olds 156 solutions. The relevance of these solutions also improved with age. The relevant solutions, whose feasibility and effectiveness varied, can be divided into the following categories: • anticipatory behaviour (don’t stop in the middle of the junction); • ways of reducing the traffic volume (by increasing car prices, by locating home and place of work in the same district or by encouraging people to travel by other means of transport); • staggering of home or work departure times; • enlarging the road network (creation of new roads or enlargement of existing ones). We shall call this type of solution a quantitative spatial solution; • redesigning the road network (introduction of tunnels, bridges, roundabouts). We shall call this type of solution a qualitative spatial solution; • improvement of traffic control (replacing the traffic lights by traffic control police). Although the usefulness of such measures is questionable we have accepted them as relevant solutions. The irrelevant solutions were either infeasible (the car in the middle of the junction should reverse to make room; everyone should stay at home; cars should be built so that they can fly), ineffective (drivers should obey traffic signs; traffic lights should be green for longer; there should be more stop signs) or, at least, ineffective in any global or collective sense (look out of the window and make sure there are no traffic jams before leaving home). In the 8-year-old group, 15 per cent of the proposed solutions were relevant. Of the solutions advanced by the 10-year-olds, 42 per cent were relevant and the majority of solutions suggested by the 12-year-olds were relevant (59 per cent). The age effect is highly significant. We have calculated the level of significance for both the pre-test responses: F(2.66)=11.42, p< 0.001 and the post-test: F(2. 66)=12.43, p<0.001. A contrastive analysis reveals that all the age-groups differ significantly at a threshold of at least 0.05. If we consider the effect of the short training period to which we exposed our subjects between the pre-test and post-test, we find that the presentation of diachronic tasks resulted in no significant increase in the level of relevant responses or the number of responses mentioning staggered departure times. Similarly, the presentation of spatial tasks (rotation) did not cause any increase in the number of relevant responses or in the number of spatial-type responses. All that could be observed was that at age 12, the number of new solutions proposed was higher in the group which had received the diachronic training than in the group which performed the spatial tasks.

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Table 6.4: Solutions to the traffic jam problem. Percentage of subjects per age-group and type of solution (N=24 subjects per group and several solutions per subject)

Note: See p. 159 for a description of the solutions.

The point which interests us most is the age-related distribution of response types. A qualitative analysis of the type of advocated solution enables us to gain a better understanding of the development of the ability to resolve the problem which we set our subjects and the role played by diachronic thinking and spatial reasoning in finding such solutions. Table 6.4 presents the results in terms of the percentage of subjects in each age-group who proposed a particular type of solution (we should recall that as all the subjects presented more than one solution, the percentages add up to significantly more than 100 per cent). It can be seen that the measure most frequently cited by the 8-year-old subjects (63 per cent) was traffic control. This consists of installing new signs and traffic lights and of obeying existing signs and traffic regulations. We also observe that about half of the 8-year-old subjects referred to what we may term static measures (staying at home or parking one’s car) or to the driver’s behaviour. Such behaviour may be either anticipatory (waiting before starting off or entering the junction) or corrective (less frequent: reversing or advancing somewhat to make room). Solutions consisting of changing traffic conditions such as measures aimed at reducing the number of cars, enlarging or restyling the road network and staggering departure times were only proposed by a minority of subjects (at most a quarter). None of the children suggested a general staggering of travel times whereas a number of them limited themselves to a localized alternation of departures: ‘These cars should go after those other cars, in their turn.’ An analysis shows that the number of subjects proposing temporal measures and those suggesting spatial solutions was approximately equal (less than 50 per cent of subjects). Few children proposed both types of solution. Apart from the fact that traffic control solutions were still proposed by a majority of subjects (71 per cent) and references to drivers’ behaviour were encountered in about half the subjects, as was the case among the 8-year-olds,

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the situation changed at age 10. This category included a third of subjects who considered it necessary to station traffic control police in the place of traffic lights, a measure which was rarely proposed by the younger subjects. There exist a number of types of measure, rarely proposed by the 8-year-olds, which were advanced by approximately half of the subjects in this age-group. This is true of the measures which have an effect on traffic volume (numerical effect). Such measures consist of changing one’s method of transport (by cycling or walking, for example) or, for some subjects, by simply banning cars and, for others, by making cars more expensive and providing meals at the place of work. Quantitative spatial solutions (creating new roads or enlarging existing ones) were found in a similar proportion of subjects as were solutions with numerical effect. A quarter of the 10-year-old subjects proposed a generalized staggering of departure times (‘people shouldn’t all leave work at the same time’), a solution which was not suggested by any of the 8-year-old subjects. Static solutions were very rarely encountered and only two subjects out of 24 proposed qualitative spatial solutions. Overall, temporal solutions did not appear much more frequently than among the 8-year-olds. However, ineffective solutions (waiting) were partly replaced by effective temporal solutions while a greater proportion of subjects referred to spatial solutions (75 per cent as against 50 per cent mentioning temporal solutions). In the 12-year-old group we again found a majority of solutions involving traffic control by means of signs, traffic control police or greater respect for regulations (88 per cent of subjects). A clear majority (71 per cent), a greater proportion than among the 10-year-olds, proposed quantitative spatial solutions. Two more types of measure were invoked by slightly less than half the subjects: a general staggering of departure times (mentioned more frequently than by the 10-year-olds) and qualitative spatial measures (introduction of bridges, tunnels or roundabouts) which were practically unmentioned before this age. As at age 10, spatial solutions were invoked by more subjects than were temporal measures. Let us now turn our attention to the responses to the problem of stopping at the green light. If our subjects failed to anticipate what would happen when the lights change, they replied that the driver should continue beyond the light (because it is green) and stop behind the stationary line of cars slightly further along the same road. In contrast, if the subjects considered the problem from a diachronic viewpoint and anticipated future consequences, they considered that the driver should stop before the junction despite the fact that the traffic light is green. This is because if the driver continued he would prevent the cars in the perpendicular road from entering the junction when their light turns green. We have taken account of each subject’s response in both the pre-test and post-test and allocated the two answers given by each subject to one of three categories: two responses recommending the driver to stop at the green light, one response recommending him to stop at the light and one suggesting he stop behind the line

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Table 6.5: (a) Solutions about stopping at the green traffic light. Percentage of subjects per type of solution and per age (N=24 subjects per group); (b) solutions to the traffic jam problem. Percentage of subjects providing responses involving staggered departures times (e.g. drivers leave at a different time) per age-group (N = 24 subjects per group); (c) solutions to the traffic jam problem. Percentage of relevant solutions per age-group (respectively, 94, 131 and 156 solutions per age-group)

of traffic and, finally, two responses recommending him to stop behind the line of traffic. Table 6.5 specifies the percentage of subjects proposing these three types of response for each age-group and also lists the percentage of responses mentioning a general or local staggering of departure times (diachronic solution to the traffic jam problem) as well as the percentage of relevant solutions provided by each age-group. It can be seen that more than one third of the 8-year-old subjects responded that the driver should stop at the green light in both the pre-test and the post-test, showing themselves capable of a power of anticipation which is absent in many adult motorists. This dual recommendation to stop at the light is generalized to three-quarters of the 10-year-old subjects while the percentage of subjects providing this type of response increases slightly at the age of 12. A comparison of these percentages with the frequency of responses to the traffic jam problem which proposed a staggering of departure times reveals that the traffic light problem was solved at an earlier age. The same observation holds true if we take account of all the relevant responses to the traffic jam problem, such responses only being in the majority, albeit slight, in the 12-year-old subjects. An analysis of intrasubject responses reveals that there is no correlation between the responses to the traffic light problem and solutions involving staggered departure times or responses involving anticipatory behaviour. From this we may deduce that the children treated these two problems, concerning stopping at the traffic light and the avoidance of the traffic jam, as different both in terms of their character and difficulty.

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Summary and Conclusions Viewed from the perspective of the development of the diachronic approach, the principal interest of this experiment resides in the identification of décalages in the resolution of diachronic problems. The results of this experiment also reveal that spatial solutions are more frequently encountered than references to temporal measures in connection with the problem presented to our subjects. Moreover, when we turn to the question of the development of strategies for the resolution of this problem we find that the results point to the existence of both continuities and discontinuities between the ages of 8 and 12. This goes some way to helping us answer the question of the nature of cognitive change (increase in knowledge or partial or total restructuring). To solve the problem of whether or not to stop at the green light, the subject must, to a certain extent, approach the question from a diachronic viewpoint since it is necessary to anticipate the future development of the traffic situation and take account of alternating flows in response to the traffic lights. It should be noted that this problem also requires a decentration on the part of the subjects: rather than simply considering future developments from their own perspective they also need to take account of the viewpoints of other road users. It is at the age of 10 that the majority of subjects (75 per cent) are able to resolve this question, whereas at age 8 this percentage is 38 per cent—a still far from negligible proportion. However, only a minority of the solutions which the 10year-old subjects provide for the traffic jam problem are relevant and only onequarter of these subjects suggest diachronic solutions involving staggered departure times. By the age of 12, progress has been made in both these areas. Nevertheless, only a small majority of solutions are relevant and only 42 per cent of children suggest staggering drivers’ departure times. Why should this latter type of solution result from a more advanced diachronic approach than the solution to the traffic light problem? In my opinion this is in part due to the following two points. First, when presented with the problem of whether or not to stop at the green light, subjects are asked to consider one phenomenon of change (the change in position of the drivers present on the picture). In contrast, in order to find a solution involving the staggering of departure and arrival times, subjects must be able to imagine a number of sets of changes of position (the movements of people who leave work at 11 o’clock, then those who go to eat at midday etc.). Our earlier experiments have shown that the simultaneous consideration of multiple phenomena of change is late to appear. Second, to solve the traffic light problem it is enough to anticipate the continuation of an event which has already commenced. As this anticipation requires both a decentration and the awareness of a phenomenon of alternation, it is not accessible to the majority of younger children. It is, however, within the scope of the 10-year-old subjects. However, when considering the question of the traffic jam, subjects must be able to imagine alternative solutions and they

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must therefore tackle the problem at its origin and imagine a different origin from the one which produced the state of affairs presented in the picture. Not only do these two situations differ in the elements of the diachronic approach which they call on, they are also distinguished by the fact that in one case subjects are required to think about a pictured reality whereas in the other, the problem of the traffic jam, they need to consider the entire set of possible movements and are thus involved in the realm of the hypothetical. When we consider the ratio of temporal to spatial solutions, we find that they occur in approximately equal proportions in the 8-year-old subjects (46 and 42 per cent) and that very few subjects propose both types of solution. As the age of the subjects increases, the frequency of spatial solutions grows more rapidly than that of temporal solutions. In other words, when a spatio-temporal problem is presented in spatial form, spatial solutions are encountered more frequently than temporal solutions in 10- and 12-year-old subjects and are proposed more rapidly by 10-year-old subjects (when solutions involving staggered departure times tend not to be proposed until the post-test). This preference for spatial solutions may be explained either by the hypothesis that progress in spatial reasoning occurs at an earlier age and is more generalized than similar progress in the field of diachronic thinking or, alternatively, by the salience for the subject of the particular elements present in the picture. The spatial alternative (transformation of the road network) relates to what is present and observable whereas the temporal alternative (making drivers travel at different times) relates to something which is not present in the depicted situation. Before describing the development of solutions proposed to the traffic jam problem it would be worthwhile to summarize the results obtained for the different age-groups. At all ages the most commonly encountered solution involves controlling the traffic by means of signs, regulations etc. At age 8, children regard the situational data (number of cars, road network) as invariant and propose either what we might term external regulations, consisting of extra signs or longer green periods at traffic lights, or regulations relating to drivers’ behaviour which may be anticipatory (waiting, leaving room etc.) or corrective (reversing to make room). The only alternatives they propose (54 per cent of subjects) consist of what we have termed static solutions: drivers should stay at home or park their cars. While the 10-year-old children again put forward the types of solution proposed by the younger subjects (external and subjective traffic control), nearly half the subjects of this age suggest three types of alternative which modify the situational data. These consist of measures which have a numerical effect (reducing the number of cars, for example by using other means of transport, by increasing car prices or by destroying a proportion of existing cars), spatial measures (widening existing roads or building new ones) and temporal measures (introducing delays or alternations, effective solutions involving staggered departure times proposed by only a third of subjects). In general, recourse to

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spatial measures of whatever type (including, for example, the building of car parks) is considerably more frequent than in the 8-year-old subjects. At age 12, the new tendencies which first emerged two years earlier are reinforced (increase in the frequency of quantitative spatial measures and general staggering of departure times) but there is no increase in the proportion of subjects proposing solutions which have a numerical effect. There is one new development: the proposal of qualitative spatial solutions (bridges, tunnels, roundabouts), but this is found in only 42 per cent of subjects. To summarize, we observe no linear improvement between the ages of 8 and 12 years but instead, alongside the coexistence of shared strategies, the adoption of a new strategy from the age of 10 onwards (modifying the situational data by proposing numerical or spatial transformations or temporal arrangements) and the appearance of two changes at the age of 12: the introduction of qualitative spatial measures and the disappearance of appeals for self-regulation (drivers’ behaviour). We should note that the qualitative spatial measures are in fact also diachronic in nature. If subjects propose the construction of a bridge or roundabout they must be able to imagine two intersecting traffic flows simultaneously. Our discussion of the effect of diachronic training will be brief. We exposed our subjects to this period of training in order to test the effects of a particular type of task involved in diachronic training: the reconstruction and anticipation of the past or future states of the presented situation. This task, which was in any case very short, had no effect on the number of diachronic solutions proposed in the post-test or on the level of effective solutions suggested by our subjects. We may draw two conclusions from this result. First, the adoption of an advanced diachronic approach depends more on the tendencies and abilities of the subject than on any brief external influence. Second, the training of the diachronic approach requires more tasks than were presented in our experiment. The observation that training results in a larger number of post-test solutions (whether relevant or not) requires further experimental confirmation. General Conclusions to Chapter 6: Diachronic Thinking, Domains of Knowledge and Cognitive Interaction The two experiments involving situations which are dependent on human activity demonstrate that diachronic thinking can also be applied to this type of activity. Children do not consider that such situations remain unchanged with the passing of time. Instead they view them dynamically, reconstruct the preceding stages, anticipate future changes and propose theories to explain the origins and causes of such phenomena. Certain aspects of the development of diachronic thinking which have been revealed in other fields are encountered once more in this type of situation. Thus after the age of 9, at which quantitative factors dominate, the qualitative aspects of states and transformations become increasingly important with age. Similarly,

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advances in diachronic thinking can be observed at the age of 10 (for example, the ability to anticipate changes), while the age of 12 is characterized by a new stage in which children are able to imagine a number of transformations simultaneously and can represent qualitative, non-observable changes. Characteristics specific to reasoning about human activities also appear. For example, when considering activities of a communal nature, young children (aged 8 and 9) generally attribute greater importance than their 12-year-old colleagues to individual intentions and behaviour. An important lesson to be learnt from the two experiments presented in this chapter is that successive stages exist in the ability to solve problems of a diachronic nature. In the populations we have studied it is impossible to assert that an advanced diachronic approach appears definitively at the age of 12. Certain aspects of diachronic thinking are mastered at the age of 10 whereas other, more complex, elements are not fully understood until adulthood. The final point to be revealed by these two experiments is the interaction between diachronic thinking and other fields or forms of reasoning. The application of temporal and numerical reasoning, such as the attribution of a date or an age to the stages of a transformation or the estimation of the length of the intervals separating these stages, is closely linked to the development of diachronic thinking. When confronted by problems which contain a particularly complex diachronic element, such as Sempé’s set of cartoons, subjects continue to make mistakes in their use of temporal reasoning at a later age than usual: 12year-old children provide responses usually associated with 9-year-old subjects faced with the question of tree growth. What is more, the experiment which required subjects to find a solution to the problem of traffic jams shows that spatial and diachronic solutions are initially mutually exclusive until a clear advance in the discovery of spatial solutions permits a collaboration between the two fields from the age of 12 onwards. In my opinion, this results in the identification of qualitative spatial solutions. The necessary interaction between diachronic thinking and other cognitive capabilities can also be observed at the general logical level of decentration and hypothetical and deductive thought. As we have seen, the discovery of satisfactory solutions to the diachronic problem of traffic flow requires subjects to examine the question from a decentred, hypothetical viewpoint.

Chapter 7 General Conclusions. The Diachronic Approach and Diachronic Thinking: Their Nature, Development and Importance for Knowledge

Following our analysis of 12 experiments concerning the development of the diachronic approach in children aged 7–8 to 11–12, we are in a better position to understand what this approach consists of and how diachronic thinking develops throughout childhood. I do not intend to restate the results of these experiments here since readers may, if they wish, consult the ‘summary and conclusions’ section of each experiment reported.1 In these general conclusions I shall start by defining and analyzing the nature of an advanced diachronic approach which permits subjects to gain a deeper

knowledge of beings and objects. This approach will be analyzed as a phenomenon in its own right and I shall not distinguish between its occurrence in adults, at the scientific level or in the realm of common-sense thought, and its manifestation in preadolescents or adolescents. After defining what we may understand by the term ‘knowledge perspective’ (or approach to knowledge) and distinguishing between the diachronic approach and diachronic thinking, I shall

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describe the main characteristics of an advanced diachronic approach and analyze this approach in terms of a process as well as of four ‘schemes’ which form the basis of all diachronic knowledge. In order to clarify the nature of these schemes, the following two paragraphs will be devoted to the knowledge which underlies them and the relation between the diachronic schemes and scripts and schemas. To conclude this section of the conclusions I shall consider the question of the independent existence of a diachronic approach as distinct from other aspects of cognition such as temporal reasoning, causal explanation or synthetic ability. In the second part of these conclusions I shall describe the two main developmental stages that we have revealed in the formation of diachronic thinking between the ages of 8 and 12. Each of these stages will be further defined in terms of the ‘diachronic schemes’ which characterize it. I shall then consider the nature and causes of the striking change that characterizes the development of diachronic thought after about the age of 10. I shall conclude by recalling the importance of the diachronic approach in the acquisition of knowledge and by drawing the reader’s attention to the many problems that remain to be studied in connection with this mode of thinking. The Diachronic Approach and Diachronic Thinking What is a Knowledge Perspective? Alongside the notion of knowledge domain, it is my intention to identify a knowledge perspective. To adopt such a perspective is to place a perceived or evoked situation into a knowledge category such as time, space or number, in order to improve understanding of this situation. If the situation in question is immediately understood in terms of this category because it is essentially composed of elements belonging to the category then we are not able to speak of the adoption of a knowledge perspective. In effect, a subject cannot really do other than consider a set of calculations in terms of number or a question concerning relative duration in terms of time. In neither case do subjects adopt a numerical or temporal perspective: they quite naturally reason in terms of the category in which the problem is formulated. In contrast, if subjects consider a situation or problem in terms of a particular knowledge category although they are not necessarily required to do so, we may conclude that they have adopted a knowledge perspective (numerical, spatial or diachronic). My immediate reaction to the tree in my garden or the water in my bathtub may vary, taking the form of a categorization, a value judgement or some type of habitual behaviour. If I start to count the branches on the tree or estimate the number of litres of water in my bath I am adopting a numerical perspective. If I think that the tree has grown quickly in only a few years and that it will soon block my view or if I start to wonder where my bath water has come

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from and where it will go, then I am adopting a diachronic perspective (or diachronic approach). These are, of course, trivial examples which are of no consequence for the acquisition and enhancement of knowledge. However, the adoption of a numerical, geometrical or diachronic approach has contributed significantly to scientific advancement and I would suggest that the adoption of a knowledge perspective necessarily improves our understanding of a situation. The ability to adopt such a perspective therefore most certainly plays a role, hitherto practically unresearched, in cognition and its development. In order to illustrate in greater depth just what a knowledge perspective is, I shall limit myself to the study of the only perspective about which I currently have any understanding: the diachronic perspective or approach. To a certain extent, all cognitive functioning contains an unconscious reference to the past (because the new is assimilated to the known) as well as an element of vague anticipation (since most activities are goal-orientated). However, provided that our aim is not to evoke the past, predict the future or solve a temporal problem we consider things as they present themselves to us here and now. Indeed, this very often represents an adaptive necessity: it is necessary to comprehend the current data of a situation in order to produce an appropriate behavioural response. If the situation raises a problem or if we quite simply have the time to think about it at leisure, it becomes possible to consider it from a diachronic perspective. Data relating to the current situation are enriched by the representation of past or future stages or by ideas about the way the phenomenon may have evolved etc. This application of a temporal perspective to the situation in question may not be absolutely necessary. It is the result of a spontaneous reaction or of the intention to understand and control the situation better. Depending on the circumstances, this aim may be realized by adopting a different approach, for example by adopting a numerical viewpoint, a spatial analysis or some other perspective. It can be seen that a knowledge perspective is not the same thing as a knowledge domain: it is altogether a wider concept in that it can be applied to numerous different domains. It should also not be confused with any particular logical operation (for example, arithmetic operations, the coordination of duration and speed or the analysis of angles). It may involve the use of these operations as tools but, as I stated at the beginning of this section, it more generally consists of the integration of the situation into a dimension or category of thought. Having provided this definition of knowledge perspectives in general, I should now like to distinguish between the diachronic perspective or approach and diachronic thinking. The former is a mode of apprehension or a method. The latter resides in those aspects of cognition (structures, strategies or concepts) which are brought into play when subjects need to understand or represent transformations over time. At a given level of development, individuals possess a certain form of diachronic thinking. This does not mean that they will necessarily adopt a diachronic perspective when confronted with a problem. In the current

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work, we have primarily investigated the development of diachronic thinking by immediately asking our subjects to imagine transformations which occur over time. At times, it has also been possible to note that some children immediately adopt a diachronic approach even before we have questioned them about the past and future of a current situation. Description of an Advanced Diachronic Approach I shall start by describing the diachronic approach from a general functional viewpoint (the usefulness and consequences of adopting such a perspective), then in terms of cognitive strategies (also at a very general level) before, in the following section, describing it at the more fundamental level of behaviourgenerating entities, that is to say the level of ‘underlying diachronic schemes’. Developmental psychology (which consists of studying cognition from a diachronic viewpoint) teaches us that there is no absolute definition of a mode or form of knowledge. The definition necessarily changes as a function of the degree of development of this knowledge. I should therefore specify that the definition which I intend to give and the analysis I wish to conduct refer to an advanced diachronic approach in which the representation of the past stages and origins of an event make it possible to enrich one’s knowledge of its present and predict its future. The foregoing, a functional view of the consequences of adopting such an approach, constitutes an initial definition of the perspective which interests us here. This diachronic viewpoint consists of considering a present situation not as something unchanging and self-sufficient but as a stage in an evolutive process. The process is formed of a succession of stages which follow one another in accordance with certain laws. Therefore when the biologist Goodwin (1990, p. 58) states ‘thus everything transforms sooner or later and all is flux but it is not chaotic’, it is clear that he is applying a diachronic approach to his view of things. In terms of what might be called general cognitive strategies, the adoption of such an approach involves, in the first place, leaving the present through a specific act of decentration which allows subjects to imagine more than they can perceive in the here and now. Second, it involves imagining certain crucial past stages and predicting the possibilities of future change. Third, the application of a diachronic approach consists of envisaging the various stages as elements in an evolutive process which displays certain characteristics. Indeed, it is this point that makes the reconstruction or anticipation of past or future stages effective. Fourth, the links established between the stages thanks to knowledge of the process of transformation make it possible, in part at least, to explain the present situation in terms of its past stages or future development. The above description barely goes beyond what we knew on commencing this research. However, this research has focused our attention on a number of other necessary aspects of an advanced diachronic approach. Such an approach affords the subject the possibility of imagining varied transformations over time, that is

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to say transformations which involve more than one of the parameters denning the phenomenon in question and which may assume contrasting forms or operate in different directions (for example, growth followed by decay). Furthermore, a variety of transformational processes may be considered simultaneously. The transformations are not purely quantitative but also qualitative in nature and take the form of a succession of stages which do not indicate a precise chronology. What is more, our research has revealed that advanced diachronic thinking is based on the representation of internal processes which constitute the mechanisms or causes of change. The Four Underlying Schemes of Diachronic Thinking Examined from a more analytical standpoint, our work enables me to define the structural and functional entities which are activated when a diachronic approach is adopted. These entities consist of four underlying diachronic schemes which lie at the root of diachronic thinking and which accompany the process of temporal decentration, that is to say the process of distancing oneself from the immediate present. We possess few data relating to this process, which I have termed the ‘diachronic tendency’, since our experiments were not designed to study it in detail. The diachronic schemes themselves are presented in figure 7.1 following the knowledge types which underlie them. The three knowledge types in which these schemes originate will be discussed a little later in an attempt to gain a better understanding of their nature and their status in relation to concepts such as scripts or schemata. Let us start by examining the first type of scheme, the transformation. This scheme defines a principle of change. It may be quantitative and/or qualitative in nature and it may define an increase, a diminution or decay, or a combination of these two ‘directions’. A qualitative transformational scheme may define a change in nature rather than simply an increase or diminution. Let us look at some examples. A quantitative transformational scheme involving an increase or growth postulates that the size or number of elements forming the observed object increase with time. When such a scheme relates to a diminution, the surface shrinks (for example, the surface area of thawing ice) or the tree loses its leaves. Qualitative transformations, on the other hand, relate either to the complexity of objects, to their adaptive value or to their nature. For example, the spatial organization of the shape of a tree or the drawing of a human figure grows more complex with time just as the rhythms of tunes grow in intricacy. Adaptive value relates to the way the effectiveness of beings or things, their health or resilience, their appeal or economic value etc. increases or diminishes with time. Finally, changes in nature may relate to the material itself, its function etc. (for example, the mutation of ice into water or a bud into a flower). For any given phenomenon, an advanced transformational scheme will include both quantitative and qualitative elements. The scheme defines the direction and the

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Figure 7.1: The four underlying diachronic schemes

form of the changes and makes it possible to imagine a past or future stage in a transformation. The second of the underlying diachronic schemes is temporal organization. This scheme defines the temporal links between the stages of an evolutive process. It may also specify the temporal relations between two interacting or, more simply, concomitant evolutive processes. The most basic point defined by the scheme of temporal organization is the sequential order of the stages, for example the fact that the stage in time at which an individual is tall necessarily follows (‘comes after’) the stage at which the same individual is smaller. Temporal organization also regulates the general form of the sequence of stages of a transformation: this may be a linear sequence, an alternation of changes in opposing directions or cyclical development. The scheme of temporal organization may also bear on the rhythm of the changes which may be constant in nature or may accelerate at either the beginning or end of the transformation. Finally, an advanced scheme of temporal organization makes it possible to take account of a number of

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simultaneous transformations each of which progresses at its own particular rhythm. Thus we know that a tree grows more or less continuously during the cyclical passage of the seasons or that the cause for the thawing of ice (the warmth of the environment) remains constant while the effect (the thawing) increases progressively. To conclude, the scheme of temporal organization is closely linked to the transformational scheme (since the latter relates to changes in time) and it defines the sequential nature and the rhythm of evolutive phenomena as well as the relations between multiple simultaneous progressions. The scheme of interstage linkage defines the connections—other than temporal succession—between the successive stages of an evolutive phenomenon. The majority of these connections fall into one of two categories: one representing the relation between a necessary prerequisite and a possible sequel and the other covering the relation between cause and effect. A particular stage may be a prerequisite because of convention or habit. Thus while a canonical narrative starts with an exposition which defines the place and circumstances, a story may equally well start with an action. In other cases, a preceding stage may be a necessary condition for the appearance of a later stage. For example, there can be no growth if there was previously no seed or, in the field of human activity, an aim cannot be achieved in the absence of any preliminary intention or planning. In the causal type of interstage link, a stage or certain conditions prevailing during this stage are the cause of the following stage. For example, the heat radiated by the sun in stage 1 causes the thawing of the ice observed in stage 2 or, alternatively, the drawing lessons attended during the first stage explain, at least in part, the progress in drawing ability which is observed in the following stage. The scheme of interstage links is generally based, at the advanced level on which we are concentrating here, on the representation of inobservable internal processes which bind the stages together. Because of this, the causal explanation of a given stage tends to refer to internal conditions or intrinsic. processes rather than to external factors. Moreover, this scheme does not simply link successive stages, it is also responsible for the linkage of the past, present and future modes. In short, it is this interstage linkage that introduces continuity between stages and makes a diachronic-type explanation possible (explanation of a state in terms of what has preceded it and what will follow it or in terms of the underlying transformational process). The final underlying diachronic scheme which I wish to identify here is the scheme of dynamic synthesis which results from the closeness of the links established by the scheme of interstage links. It consists of forming a whole from the set of successive stages which are thus conceived of as manifestations of a single process of change. Notions such as cognitive development, phylogenetic evolution and other far more usual concepts such as physical growth, human life, the wearing out of an object or the decline of a civilization derive from the application of the scheme of dynamic synthesis to a succession of states.

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In order to illustrate the use of these underlying diachronic schemes in the analysis of the conception of a sequence of states, I shall consider a number of recent theories of cognitive development. First of all, there is the adiachronic viewpoint as expressed by Sugarman (1987), for example. According to this view, it is possible that the only connection obtaining between two successive modes of behaviour is their sequential link (one mode replaces the other). In this case there is no transformational scheme or scheme of interstage linkage and there is most certainly no synthesis. Only the scheme of temporal organization is activated in its most elementary form, that of fixed succession. Similarly, many authors, too numerous to be listed here, have revealed the existence of certain early abilities (relating, for example, to object permanence, ideas of number or causality, extended short-term memory etc.) without specifying how these abilities continue to evolve or detailing their earlier forms. Here, again, most of the schemes of diachronic thinking remain unactivated since there is neither intrinsic transformation (it is always something else that is thought to undergo transformation: the brain, environmental influences, communicative abilities, for example), nor any requirement to introduce the concepts of temporal organization or interstage links. In recent experimental studies, so-called neo-Piagetian authors such as Case (1985), Halford (1993) and Pascual-Leone (1987) have focused primarily on a time-related cognitive transformation involving attentional capacity which governs the number of ‘dimensions’ that subjects consider. Here we observe the application of a scheme of quantitative transformation: the capacity of the processing system—or, more simply, the size of the data store—increases with age. The scheme of temporal organization specifies the order, and indeed the chronology, of the sequence. The fact that it is scarcely possible to apply a scheme of interstage linkage explains why extrinsic explanations (brain maturation) are adduced to account for changes. Things are very different when we turn to theories of conceptual restructuring (Carey, Vosniadou) in which the viewpoint becomes more fully diachronic. The transformational scheme postulates changes of both a quantitative (volume of known information in a field) and qualitative (change in the nature and structure of conceptions) type although the form and complexity of any structural change is not usually specified. Temporal organization is simplified to a large extent by the fact that such theories consider only changes within a given field, which is considered to be unitary. The scheme of interstage links means that a particular stage is a necessary precondition for the appearance of the following stage. The scheme of dynamic synthesis defines the development of a field as a single conceptual reorganization. In my view of cognitive development, as observed in connection with diachronic thinking, the transformational scheme defines both the quantitative (number of parameters of a situation that the child considers, number of states linked within a representation of the evolutive process) and qualitative changes (transition from the consideration of quantitative criteria to that of qualitative

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criteria, appearance of the concept of stage and the scheme of dynamic synthesis, increasingly close coordination of different processes of change etc.). The scheme of temporal organization specifies not only a predictable sequence of behaviours but also the existence of parallel, partly simultaneous progressions. Thus the four types of diachronic scheme do not develop simultaneously and, if we wish to understand the development of diachronic thinking, it is crucially important to take account of the parallel development of empirical knowledge, general logical abilities, temporal reasoning etc. In my conception of development, which corresponds to the views of genetic epistemology, the scheme of interstage linkage establishes a high degree of interdependence between the successive stages of diachronic thinking. The attainment of a certain level of diachronic thinking constitutes both a necessary and favourable precondition for the appearance of the following stage (an explanation follows in the paragraph devoted to the nature and causes of the development of the diachronic approach). Finally, I consider the development of certain cognitive abilities from a synthetic viewpoint, regarding them as a process having certain definable characteristics. Knowledge at the Origin of the Diachronic Schemes The diachronic schemes which I have defined have been formed by abstracting principles of change and relations between states. They originate in at least three different types of knowledge. First of all, I should point out the empirical knowledge concerning states and their transformations. On the one hand, this knowledge is abstracted from the direct observations made by the subject. Thus, concerning language, it may be observed that infants do not speak and that small children have a limited and frequently incorrect grasp of language. Similarly, observation reveals that ice thaws, flowers wither etc. On the other hand, this empirical knowledge derives from cultural representations. For example, as of a certain age children are aware of the traditional way of drawing a fully grown tree which involves the depiction of a trunk and a leafy crown. Equally, they are aware of the stereotypes of wealth and poverty, pollution, illness etc. Diachronic schemes are, in part, abstracted from this type of empirical knowledge. However, these schemes also originate in a different type of knowledge which provides them with an indispensable support. This consists of the subject’s organizational knowledge such as reasoning abilities in the fields of logic, numbers, space and time as well as abilities relating to causal explanations. Such knowledge is called on in the principles of change or linkage such as ‘bigger and bigger’, ‘states a, b, c and d follow one another whereas the cycle A, B, A, B— relating to a different process—repeats’, ‘state 1 is the cause of state 2 for the following reason…’ etc. The content of the diachronic schemes therefore depends on the level of logical development and the level of temporal and spatial structuring attained by the subject as well as on the degree of development of the subject’s capacity for causal explanation.

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Finally, the transformational scheme also calls on axiological knowledge, that is to say all the subject’s value systems. These values make it possible to attribute a direction to changes which may either approach a positive value or progressively diverge from a valued state. Positive values may be biologically based (for example, being in good health) or they may be psychological and social (being happy or intelligent or, more generally, being able to cope with the demands of one’s environment), economic (being rich is generally held to be preferable to being poor), aesthetic etc…. To summarize, let us examine examples of each of these diachronic schemes and investigate the type of knowledge that underlies them. Let us first examine the transformational scheme which specifies that as the age of the artist increases, a child’s drawing of a human figure contains a greater number of elements and depicts shapes and proportions more realistically. This scheme derives from empirical knowledge (observation of children’s drawings, assimilation of the commonly held idea that everything improves as the age of the child increases). It is also based on concepts relating to the domain of organizational knowledge (number, proportions) and it defines a direction which is dependent on the subject’s axiological knowledge (value judgement concerning the degree of correspondence between intentional representations and the model which is to be depicted). As an example of a scheme of temporal organization, let us consider the sequential order attributed to a series of photographs illustrating the stages of growth of a tree, on the one hand, and the understanding of the relations between these stages and the cyclical progression of the seasons on the other. First of all, the scheme of temporal organization is based on the principle of change defined by the transformational scheme: a tree of a larger size and more complex shape ‘comes after’ the same tree when smaller and simpler. This scheme is also based on empirical knowledge such as the observation of the passing of the seasons. As far as organizational knowledge is concerned, this scheme also originates in the capacity for temporal reasoning (relations of temporal succession) and in the general logical abilities which make it possible to coordinate two sets of elements (in this example, the sequence of the seasons and the sequence of stages of growth). The scheme of interstage linkage which accounts for comprehension of the connection between the stages in the development of a disease is partly based on empirical knowledge: cultural data concerning illness and personal observations of disease. However, this scheme is primarily supported by the domain of causal explanation in the wider sense of the term (and therefore by organizational knowledge). It specifies that certain initial conditions caused the disease and that the state of the organism at a certain moment favoured the subsequent spreading of the disease. Finally the scheme of dynamic synthesis which fuses successive states to form a whole—for example, the idea of intellectual development in children or the decline of a great power—is supported both by the scheme of interstage linkage

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and by the general logical abilities which allow subjects to combine a series of elements into a whole rather than view them as individual, contrasting units. Diachronic Schemes, Scripts and Schemata Diachronic thinking establishes the temporal and causal organization of a succession of states. In this it resembles the scripts defined by Schank and Abelson (1977) which have been extensively used in the field of developmental psychology by Nelson (1986) alongside the schemata described by Mandler in 1984. Nelson defines scripts as generalized (or generalizable) representations of events which ‘organize information about the sequence of predictable actions, locations, roles and props that constitute events’ (Hudson, 1993, p. 142). Mandler also defines a schema as a cognitive structure with a spatial and temporal organization in which the connections between individual parts are based on contiguities experienced in time or space. Despite the similarities between scripts and schemata on the one hand, and the diachronic schemes which have been defined and illustrated above, on the other, two fundamental differences can be identified. First, diachronic schemes operate at a more analytical level than scripts and schemata which refer to the entirety of the sequence of events under consideration. Moreover, each scheme may itself be analyzed into its constituent components: the scheme of temporal organization may contain relations defining the sequential order of states as well as relations defining the rhythm of the changes or the correlation of two or more events. The transformational scheme may contain quantitative as well as qualitative rules of change. The analytical character of the schemes does not prevent diachronic thinking from forming a whole, a structure. The coordination of the various components fuses it into a whole: the four schemes are interlinked in an advanced diachronic approach. Furthermore, diachronic thinking yields coherent entities at the representative level in that the states which are represented are part of a whole (the evolutive process). Second, the schemes which underlie diachronic thinking are more abstract, and therefore less closely linked to precise contents and memory processes than scripts and schemata. While a script is of course a generalizable structure, it possesses precise contents rather than principles for structuring or sequencing: in the restaurant script ‘sit down at the table’ is followed by ‘look at the menu’, ‘order your meal’ etc. These different stages form part of the subject’s empirical knowledge and the activation of a script, like that of a schema, appears to activate the subject’s memory and reconstruct a chain of events from the subject’s own experience of event sequences. In contrast, the activation of a diachronic scheme is a constructive procedure which may result in new representations. While the diachronic schemes are based on information concerning the domain in question, they go beyond any specific content to abstract the principles of change or interstage linkage which are applicable to a

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variety of contents. They are less exclusively dependent than scripts on the subject’s empirical knowledge. Sometimes reconstructions or anticipations of sequences of transformations are not based on the schemes of fully fledged diachronic thinking but on structures of the script or schema type. This occurs when the representations of transformations simply juxtapose a succession of distinct states whose sequence has been learned. This is the case, for example, when subjects evoke the successive transformations of caterpillar to chrysalis to butterfly or a sequence of historical or autobiographical events whose evolution is incomprehensible to them. Does Diachronic Thinking have an Independent Existence? All knowledge is linked to other knowledge. If we consider the modules themselves, which were first defined by Fodor (1983) and are considered to be autonomous entities which function automatically, can we imagine that they are totally lacking in any relationship with the central system or other modules? If we look at action procedures or practical knowledge, we find a dialectic relationship with conceptual or representative knowledge (Mounoud, 1993). At the level of the conscious representations which we are studying here, there can be no doubt that there are multiple close connections between domains and registers of knowledge. For example, to bring to mind mental images of the stages of an evolutive phenomenon it is not only necessary to mobilize the processes of visuospatial knowledge (decomposition and reconstruction of images); subjects must also refer to the semantic network involving the concepts in question and make use of what we have termed organizational knowledge. Similarly, all the theories which an individual may develop within a domain and all the strategies for resolving problems occurring in this domain are necessarily based on concepts and relations derived from other domains. And that is not to mention the interaction between individual and social aspects of behaviour and between their cognitive and affective dimensions. When viewed from this perspective, diachronic thinking is naturally dependent on other aspects of knowledge with which it is linked across a network of reciprocal relations. However, in my opinion it is also a distinct mode which forms a whole (which can be expressed in terms of the coordination of the diachronic schemes) and which undergoes a distinct development. There are three arguments opposing this viewpoint. First, one may consider that because it bears on successions, durations and cycles, diachronic thinking is simply an aspect of temporal reasoning or temporal concepts. However, a study of the development of diachronic thinking in children demonstrates that this is not the case. An 8-year-old child is perfectly capable of measuring the relative speed and period of travel of moving objects, distinguishing between intervals and temporal successions and differentiating between these variables and spatial variables. This ability to reason about time is quite different from the capacity to

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reconstruct or anticipate the states of a phenomenon and establish a necessary link between successive stages (see the summary of the limits of diachronic thinking in 8- to 9-year-old children in the second part of this conclusion). Moreover, we have seen that an advanced level of diachronic thinking is a necessary condition for the ability to apply certain types of temporal reasoning to a given content. For example, the coordination of the order of succession, speed of growth and height of trees is only performed correctly by subjects who approach this growth from an advanced diachronic perspective. As far as the ‘diachronic tendency’ is concerned, this propensity for considering things from a temporal perspective is quite distinct from temporal reasoning and is not always spontaneously displayed by children who possess advanced temporal reasoning abilities. The same is true of adult subjects. A physicist specializing in kinematics may well know everything about measuring time but he or she will still frequently consider physical phenomena from a synchronic viewpoint. The second objection to my contention consists of a refusal to distinguish between diachronic thinking and knowledge of a domain. Within this viewpoint, the ability to reconstruct the stages of tree disease and link them through an inobservable internal process would result solely from an improvement in the child’s biological knowledge. This would mean that what I have termed interstage linkage would be nothing other than a process of causal explanation. I can propose three arguments to counter this objection. First, children do not always spontaneously use their knowledge when reconstructing events. For example, 9-year-old children know that human and vegetable life is cyclical and renewed with every succeeding generation. However, none of the children of this age evoked a cycle when describing tree growth or forest regeneration (see Chapter 3). Their insufficiently developed ability for diachronic thinking did not lead them to establish connections between successive generations or between processes operating in different directions, such as decay and renewal. Second, the way in which an evolution is represented may develop even when not based on precise knowledge of the domain. For example, 11-year-old children imagine that drawings of human figures develop qualitatively and not simply quantitatively with age. When depicting this qualitative development they frequently attribute schematic drawings to small children and less simplified, increasingly realistic drawings to older ones. However, in actual fact young children never produce schematic drawings. Third, progress in diachronic thinking often makes it possible for children to understand a domain better and assimilate information provided by adults. For example, biological phenomena cannot be fully understood until the origin is linked to the stages which follow and subjects think in terms of cycles and internal linking processes. The experiment concerning the origin of the universe demonstrates that it is not until the age of 10, an age which represents a threshold in the development of diachronic thinking, that children provide explanations, albeit sometimes fanciful ones, for this phenomenon. The most striking argument in favour of the existence of diachronic thinking as an independent mode is the clear parallelism,

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both at the level of age and cognitive processes, in the development of the conception of evolutions which involve very different knowledge contents. This is the conclusion which can be drawn from the results of the various experiments presented in this book. The final objection that can be levelled at my contention results from establishing an equivalence between diachronic thinking and general logical abilities, for example the ability to synthesize rather than simply juxtapose elements. In effect, to think diachronically is to link the current situation to past and future situations in the knowledge that these situations form part of the same whole: the evolutive process. My initial response to this objection would be to point out that dynamic synthesis is only one of the four major schemes of diachronic thinking. Moreover, in Chapter 3 we studied the intrasubject correlation between the diachronic tendency to evoke past and future when describing a picture and the tendency to provide a synthetic description of a set of nine pictures. No such correlation exists. Synthetic ability and the diachronic tendency are indeed two distinct things. To summarize, all the data I have presented so far show that it is possible to study diachronic thinking and the diachronic approach, to trace their development and assess their progress in a given individual without confusing them with other aspects of cognition. The Development of Diachronic Thinking in Children Aged between 7–8 and 11–12 The argument developed above is based on an analysis of the experimental results conducted in accordance with the traditions of genetic epistemology. The development of an aspect of knowledge in children has been studied with the intention of gaining a better understanding of the nature of this aspect in its fully developed form and in order to resolve some of the problems it raises (for example, is it an aspect in its own right or does it merge with other aspects of the knowledge of time? Is there a relationship between this aspect of cognition and the quality of a subject’s understanding of reality?). In the second part of these general conclusions I shall now adopt the perspective of developmental psychology in order to summarize what the results tell us about the development of diachronic thinking between the ages 7–8 and 11–12. Two very different stages in the formation of this mode of thinking can be identified during the period of development we have observed. Before describing these two stages, I should like to recall that the diachronic aspect of cognition starts with the appearance of thought. Furthermore, its development is far from complete at the age of 12. Our experiment concerning the understanding of a series of cartoons revealed that certain processes involving multiple, complex changes are not understood until after this age.

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Diachronic Thinking in Children Aged 7 to 9: the Representation of ‘Snapshots’ within a Homogeneous Transformation The thinking of the youngest subjects we interviewed (generally aged 7–8 years) is far from being limited to static phenomena. These children are interested in the subject of change. They understand perfectly well that time brings transformations of even apparently stable states, such as an individual’s economic status (which may swing from wealth to poverty, for example) or stellar constellations to which they attribute an original state which is distinct from their present appearance. When asked about their own skills in all domains, they know that these will change with age. Moreover, these children possess theories concerning the causes and chronology of numerous types of change. At the recognitive level, these young children are perfectly capable of distinguishing and ordering, and sometimes even of dating, representations (photographs, drawings or verbal descriptions) of the successive stages in a transformation. They compare the different states with reference to external criteria which are generally spatial in nature, such as the abundance of foliage in the case of tree disease or the number or spacing of elements in the case of a starfilled sky. They are also able to recognize more subtle criteria such as the more or less realistic and controlled character of a drawing on which they base their estimate of the artist’s age. However, when required not to recognize but imagine transformations in time, 7- to 9-year-old children no longer use these more subtle criteria, although they are capable of reconstructing or anticipating a sequence of transformations on the basis of a current situation. They use a diachronic transformational scheme, for example the increase in the number and size of elements as time passes. This results in drawings or verbal descriptions which evoke a gradual change. In children at this level, the scheme of temporal organization is not limited to simply regulating the series of states. It may also define different rhythms of change, for example more rapid language acquisition in small children than in adolescents. While this range of capabilities reveals the existence of diachronic thinking in young school-age children, it is far from fully developed at this age. In effect, the ability to conceive of a series of states illustrating a gradual change does not necessarily testify to the existence of an advanced diachronic approach. This is one of the conclusions that can be drawn from our experiments. If we examine the transformational scheme in children aged 7 to 9 years, we find that it is almost exclusively quantitative, external transformations that are imagined. For example, linguistic progress is measured in terms of the number of words used, drawing development in terms of the number of elements depicted and tree growth in terms of its size or the number of branches. As for the scheme of temporal organization, this regulates the succession of the states forming an event or evolutive phenomenon but it does not coordinate the progression of a

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number of different phenomena. This may lead to confusion, for example between growth, disease and the passage of the seasons, in the representation of tree disease. A further consequence of this shortcoming is the failure to distinguish between the stages of an evolutive process and the representation of the time that passes. If, for example, they view a series of five drawings representing the transformation of a block of ice into water, these children think that it is necessary to add or remove drawings in order to represent a longer or shorter period of thawing. Similarly, when presented with a depiction of the life of an individual, children of this age believe that the evolutive phenomenon in question (linguistic or intellectual ability for example) changes at each moment represented. Approximately one-third of children of this age (and probably more at ages 6 and 7) believe that the stages of an evolutive phenomenon which is presented to them or which they have drawn themselves are separated by a fixed time interval. It is at the level of the scheme of interstage linkage and the scheme of dynamic synthesis that we observe the greatest difference between the representations of young school-age children and those of older children and adults. The idea of causal links clearly exists at this age. However, it does not link together the stages of a transformation when these are numerous. In this regard, the scenarios drawn in order to depict the thawing of a frozen lake are extremely revealing (see Chapter 4). At the level with which we are concerned here, the drawings tend to depict cause and effect simultaneously. A given state is not explained by reference to the preceding state (for example the appearance of the sun some time before the thaw sets in) but by reference to the present context (the sun is half hidden in the drawing where half the ice has melted; it is entirely free from cloud in the drawing in which all the ice has thawed). Apart from this temporal factor, the explanations of a variety of phenomena most frequently refer to external causes. When asked to account for the development of skills in children; subjects of this age propose either external causes (models provided by others) or an undifferentiated internal cause (the fact of growing) and each of these two causes is thought to be sufficient in itself. As few connections are established between the successive states of a phenomenon of change, dynamic synthesis is usually lacking. When presented with a series of photographs or drawings depicting the stages in the life of an individual, 8- to 9-year-old children describe a number of pictures rather than characterizing the set using a noun or verb. At best, they may describe the set using multiple propositions (for example, ‘it’s a baby playing with building blocks, then he grows up’). We may use an analogy to characterize this conception of evolutive phenomena, namely that of a series of photographs taken at regular intervals. In fact at this level, like a series of photographs taken frame by frame, the evocation of transformations in time:

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• constitutes a series of static snapshots (juxtaposition of the different states) rather than a visualization of a process of change which might be compared to a moving film which recreates the movement of the object; • indistinctly represents the successive states and the time that passes rather in the manner of a photograph taken because a minute has passed rather than in order to capture a qualitative change in an evolution; • introduces clear links of succession but no explanatory links between the depicted states (with the exception of occasional links between two successive pictures when there is an immediate relation of cause and effect between them); • records external changes rather than internal processes or modifications; • does not treat each element as a function of the whole (hence the fact that the date attributed to the individual pictures—or the age attributed to what they depict—does not correspond to the total duration attributed to the sequence of pictures). The tendency to adopt a diachronic approach, that is to say the capacity for temporal decentration, is clearly present at this level. Nevertheless, many facts point to its limits. Young school-age children do not always envisage changes in the future. For example, more than half of the 7- and 8-year-old children expected no reforestation of the deforested area in the absence of human intervention. When they describe a picture, these children evoke the past and future less frequently than children aged 11–12 years. What is more, since they are unused to comparing the present to the distant past they do not understand that the question ‘Have you always drawn like that?’ refers to the age-related modification of their drawing skills. Similarly, it does not occur to them that the difference between two verbal descriptions which they hear is due to the difference in the age of the speakers. The Diachronic Approach and Diachronic Thinking in Children Aged 11–12 years The way in which evolutive processes are imagined and the ability to link a present state to past or future states change completely at about the age of 10 to 11. Preadolescents imagine considerably more varied and highly interconnected successions of states and are able to decentre themselves more easily from the present. The transformation scheme which is mobilized in their evocations of evolutive phenomena involves a larger number of variables and defines qualitative rather than simply quantitative changes. For example, each stage in the growth of a tree drawn by a child of this age has a different shape and, when depicting the way drawings of human figures develop with age, these children portray changes in the proportions and realistic nature of the drawings. When considering language, these children think that it changes with age not just in terms of the number of

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words used but also in its communicative function (elimination of ambiguities) or in its syntactic composition. When we turn to temporal organization we find that this arranges changes in different directions as alternations or cycles. This is one of the causes of the variety of represented changes. Thus when asked to predict the long-term transformation of a forest, children aged 11 and 12 anticipate both the decay and renewal of trees. They imagine that the forest will simultaneously contain dying trees and young trees. This last point reveals a new ability which has manifold consequences for the representation of transformations within the scheme of temporal organization: this is the ability to consider multiple evolutive phenomena simultaneously without conflating them. Our experiments provide numerous examples of this new-found ability which, among other things, makes it possible to distinguish between the duration of the cause and that of the effect (Chapter 4) or between the surface covered by an area of growing vegetation and the height of the plants which form it (Chapter 3). This ability also enables subjects to distinguish between the progress of an evolutive phenomenon and the passage of time which accompanies this progress. For example, children at this stage of development consider that a series of pictures depicting the stages in the thawing of a block of ice may represent either a slow or fast thaw. Similarly, when asked to view a series of drawings representing the stages in the life of an individual, they consider that linguistic or intellectual skills do not necessarily advance at each depicted stage. The association of the qualitative changes defined by the transformational scheme and this dissociation of time from the evolutive process leads 11- to 12year-old children to depict the stages of a process rather than snapshots taken within a context of continuous change. Each stage they evoke tends to portray a qualitative leap and a temporal range. For example, for these children a particular way of drawing a human figure corresponds to an age range rather than to a precise moment in the development of the artist’s life. The scheme of interstage linkage establishes close connections between successive states, in particular as a result of the child’s new ability to imagine an internal process which links the states. This means that a particular stage prepares the way for, or even provokes, the following stage: the warmth of the air in the case of thawing ice, the extent of microbial propagation in the case of disease or practice and acquired knowledge in the case of drawing skills are all causes which bring about the following stage in these differing evolutive phenomena. When asked to explain cognitive development, children aged 11 to 12 years tend to adopt a more interactionist or constructivist viewpoint than their younger colleagues. For these subjects, it is a mixture of internal and external causes, in which the subjects’ actions and motivations have a role to play, that stimulate the development of drawing skills, language or intelligence. In contrast, younger school-age children view such developments in quasimaturationist (the fact of growing older necessarily results in cognitive

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advance) or empirical terms (in order to learn, it is enough to observe and imitate). The development of diachronic thinking concludes with the ability for dynamic synthesis. Successive states are considered as moments within an evolutive process (growth, life, thawing, the evolution of knowledge). Even when describing a single future state, children at this level frequently refer to the process of change rather than to the elements of the situation viewed as static entities. As far as the diachronic tendency is concerned, this becomes increasingly common between the ages of 8 and 12. Our subjects started to show themselves able to conceive of reforestation without human intervention at the age of 9. Picture descriptions which introduce past and future elements and which evoke a temporal progression occurred frequently among the 10-year-old subjects (however, this depends on the situation depicted in the picture). At age 11, the majority of our subjects immediately understood that the question ‘Have you always drawn like that?’ refers to the development of their drawing skills as they grow and at the age of 11 and 12 two-thirds of our subjects explained the differences between two verbal descriptions which had been produced by children but were read by the experimenter in terms of the age of the speakers. To summarize, at about the age of 11 or 12, children in our culture possess both the cognitive tools necessary to view things and beings from an advanced diachronic perspective and a tendency to adopt such a perspective. Nature and Causes of the Development of Diachronic Thinking The striking transformations in the way children aged 10 and above think of changes over time does not result from the acquisition of new information but rather from a reorganization or restructuring of their knowledge. What we observe is thus the emergence of a new way of viewing beings and things, as is the case for much of the cognitive progress observed by Piaget and his coworkers as well as for the conceptual restructuring which Carey has revealed in a number of domains. However, it should be emphasized that this transformed diachronic thinking represents no break with the knowledge held by younger children, although it yields completely new conceptions. The conceptual restructuring which we have revealed does not therefore consist of the complete substitution of existing knowledge. The novelty resides in the replacement of changes evoked in the form of snapshots within a transformation by an evocation in which the change appears as a process which introduces a genuine continuity between successive states. This new perspective allows children to enrich their evocations and explanations by the use of concepts such as cycles, evolutions, transmission from one generation to the next etc. to which they previously had only recognitive access. At a more analytical level, in terms of the diachronic schemes, the novelty is found in the appearance of the schemes of interstage linkage and dynamic synthesis. This new

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ability can also be analyzed in terms of a general cognitive progress on which diachronic thinking as well as other modes of knowledge are based, for example an increase in the volume of data that can be processed simultaneously, or the coordination of systems to form multiple systems, the appearance of hypothetical reasoning or the differentiated and coordinated nature of concepts. Despite its novelty, the perspective that appears at about the age of 11 is in continuity with the knowledge of younger children. On the one hand, we have seen that many characteristics of advanced diachronic thinking (such as the awareness of qualitative changes or the consideration of the degree of development of the producers of drawings or descriptions) exist at a recognitive level in young children. On the other, in many of its facets this new form of diachronic thinking represents a reorganization (and principally a coordination) of pre-existing elements. For example, the ability to consider progressions of events simultaneously is simply to process simultaneously what was processed separately at an earlier age. The same is true of the synthesis of the stages of change. In the same way, the deep-seated motivation to understand changes over time can be identified well before the age of 11. It may assume greater importance in the thinking of preadolescents because at this age it can avail itself of more effective cognitive tools to accomplish its designs. When considering the explanation of the clear-cut progress which is observed in the development of the diachronic approach at about the age of 10 or 11, we can merely hypothesize. This is because our experiments were intended to help us understand the components of this approach rather than study its causes. To provide an explanation of the changes observed during development is a complex task which demands that we account for a variety of forms of determination and their interaction (Hopkins and Butterworth, 1990). In line with what I think a diachronic perspective should be, I shall invoke not only causes extrinsic to the phenomenon in question (that is to say the knowledge of change) but also an intrinsic causality in which the elements and processes of which this knowledge is comprised at any given stage partly determine the changes that occur later. When considering extrinsic causality (explanation by factors), we must take account both of the effects of brain maturation and the role of the environment. Nowadays, it is common to emphasize the role of brain maturation in the increase in processing speed and in the volume of information which is processed simultaneously. However, it should be noted that this appeal to maturation cannot explain the décalages observed in the development of diachronic thinking depending on the nature of the changes considered by the child. For its part, the environment provides a number of indispensable elements in the form of demands (children are required to perform increasing numbers of anticipations and reconstructions), specific information about beings and things and adult models of change (which may consist of naïve ideas or of scientific theories concerning biological evolution, learning, the big bang etc.). It may be that the fourth year of primary school constitutes a favourable period for conceptual development since the learning of reading, writing and arithmetic no

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longer absorbs all the child’s efforts and because the techniques which have been learned in mastering these skills may now be used for acquiring knowledge. In all cases, however, the influence of the environment depends on the subject’s ability to assimilate and this explains why a number of theories encountered outside school do not appear in children’s explanations until after a certain age. At the level of intrinsic causality, we must consider two processes which favour the development of diachronic thinking: the presence and the activation of elementary forms of this mode of thinking as well as the numerous interactions with other aspects of knowledge, whether in the form of specific concepts or what we have termed organizational knowledge. Young school-age children extract the principles of change (transformational scheme) from the regular phenomena which they observe. As a result they are able to represent the sequences of states of a gradual transformation. In accordance with the laws of development which bring about the coordination of knowledge elements with age, these principles of change are coordinated and the successive stages merge into a whole. This results in the appearance of a more advanced form of diachronic thinking. As an example of the fruitfulness of interactions between domains I could cite the association of specific information on living beings and diachronic structuration which is necessary for the understanding of biological phenomena. Another example is provided by the relations between temporal reasoning and the diachronic approach. Their mastery of temporal concepts helps children of about 8 to 9 view the situation which confronts them within the temporal dimension. In its turn, however, the development of diachronic thinking is a precondition for the application of correct forms of reasoning to evolutive phenomena. The activation of diachronic thinking and its interaction with other domains play this type of structuring role, because thought tends to become increasingly aligned with reality and to achieve greater coherence. This is the process of optimizing equilibration described by Piaget (1977) which has often been criticized for being too general and impossible to operationalize. It is clearly too general and therefore difficult to test experimentally. However, does this make it any less evident? No one can deny that children’s knowledge tends to change over time. More precisely, is it not true that in every domain many concepts or relations established at a particular level of development are later interlinked within more effective systems? We still need to explain why, in every one of our experiments into diachronic thinking, we observe a qualitative leap at around the age of 10 or 11 years, a leap which has been observed in other aspects of cognition by other researchers. It must be admitted that at the age of 9 or 10, the interaction of the subject’s knowledge systems and the role of a variety of developmental factors combine to create a particularly unstable context in which regulatory mechanisms which favour new reorganizations assume increased importance. We agree that such explanations are still excessively hypothetical and that they require the support of experimental study. Careful analysis of children’s concepts and schemes, of

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the sort I have outlined in connection with diachronic thinking, could provide the necessary basis for this study of the state of fruitful instability in the thought of 9- to 10-year-old children. Why Study the Diachronic Approach? Considering the results of our investigations into the diachronic approach, we have the impression that we have been exploring a little known and still largely uncharted territory. We have revealed the existence of a mode of thought which can be applied to a variety of contents and which makes it possible to understand and describe changes over time. Our research has also revealed the main components of this mode of thought as well as two important stages in its development. However, much work remains to be done in this field. First of all, now that the underlying schemes of diachronic thinking have been defined, it will be necessary to undertake a more detailed study of how they are differentiated and coordinated with age depending on the individual or situation concerned. Second, it would be useful to draw up a list of diachronic problems in order of increasing difficulty. For example, we have seen that the problem of stopping at the green light (second part of Chapter 6) is solved by a majority of 10-year-old subjects whereas the idea of a general staggering of motorized traffic only occurs later. Ideally, we would be able to produce a list of problems which would enable us to study the four underlying schemes as well as the diachronic tendency. This would provide us with ways of evaluating the level of development and particular characteristics of the diachronic mode in a given individual. This would clear the way for the conduct of indispensable differential studies. Not only does the diachronic approach develop with age. It also varies with the individual and the environment. It is easy to see that some people live largely in the here and now whereas the world-view of others is suffused by the wealth of the past and the potential of the future. As far as the environmentally dependent variations are concerned, these should be studied within a perspective of social psychology and intercultural research. Moreover, the diachronic approach expands and contracts as a function of the emotional state and affective balance of the individual. It would be interesting to study the particular characteristics and variants it manifests within the major psychological pathologies. Finally, it would be rewarding to study the manifestations of the diachronic approach and its influence on learning within the framework of children’s academic activity. Why is it necessary to launch a multifaceted programme of research into the diachronic approach? The answer is because this is an aspect of cognition which plays a crucial role in the acquisition and restructuring of knowledge. Many branches of science are based on the comprehension of evolutive phenomena, whether in the field of biology, human behaviour or physical and chemical phenomena. The acquisition of advanced diachronic thinking is an absolute precondition for the assimilation of such material. Moreover, among the

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psychological mechanisms involved in intellectual training, metacognition or the ability to reflect on one’s own cognitive processes is a precious tool. The awareness involved in a metacognitive process, in which subjects reflect on their own time-related development, must include the establishment of relations between present behaviour and past and future actions, even if they are distanced from the present by only a brief interval. Here again, the role of the diachronic approach is clear. Finally, when confronted by a problem, the ability to place it within a temporal perspective may contribute to the discovery of solutions. The potential of these solutions will naturally depend on the degree to which diachronic thinking has developed. We need to think in time if we are to understand the world and adapt to it. This is just as true at the sophisticated level of scientists and decision makers as it is at the level of everyday thought in both adults and children. It is only when subjects’ diachronic thinking has reached a certain level of development that they are able to understand a whole series of phenomena such as boiling, thawing, muscular stiffness, the spread of disease, long-term plant growth and decay and the time-related change in children’s cognitive skills. It is also the application of an advanced diachronic approach that enables subjects to improve their academic results or tell a captivating story. Finally, in order to solve complex problems it is necessary to approach them from a diachronic viewpoint, to identify the origin of the current situation before proposing an alternative to existing practices. In this work I have chosen the diachronic approach both as an object of research and as a method of study. As a field of study, this mode of knowledge possesses all the difficulties, as well as all the fascination, of moving, dynamic phenomena, in other words of life. As a method it is a possible path for the study of cognitive psychology to travel. I hope I have been able to show that this path still remains fruitful.

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Index

Abelson, R.P. 172 artificialism 42, 49 astrophysics 4, 67 attentional capacity 169

external 33, 54, 139, 176–7 internal 38, 40–1, 113, 180 qualitative 24, 40, 83, 103, 128, 148, 169 quantitative 40, 83, 127, 160, 166, 169 rhythm of 37, 104, 121, 168 changes (domains of) biological 20–55 physical 56–77 psychological 78–129 social 141–9 cognitive development 3, 125, 169–70 children’s conceptions of 88, 126–8, 180 conceptual restructuring 53, 75, 157, 169, 180–1 Crépault, J. 43 cycles (anticipation of) 29, 54–5, 175, 179, 181

Baillargeon, R. 57 Baldwin, J.M. 3 Bang, V. 8 Bariaud, F. 130, 132 Bennett, M. 14, 78 Berko-Gleason, J. 97 Berti, A.G. 15, 141 Bibace, R. 30 big bang 4, 67, 71–2, 182 Bohan, J.B. 8 Bombi, A.S. 141 Bonnens, M.T. 9, 57, 132 Brami-Mouling, M. 97 Bredart, S. 97 Brown, A. 57 Brusdal, R. 142, 147–8 Bullock, M. 7, 57 Butterworth, G. 17, 181

Dawes, L. 79, 91 Del Barrio, C. 30, 114 Delval, J. 141, 143, 148 DeVries, R. 8 diachronic approach (or perspective) 165–6 diachronic tendency 82, 106, 112, 166, 174, 180 Dionnet, S. 58 domain specific (knowledge content) 55, 175 drawing skills 79–96 duration See reasoning, temporal

Carey, S. 7, 8, 21, 40, 49, 53, 169, 181 Carugati, F. 124 Case, R. 169 causal explanation 10, 56–7, 65, 77, 168, 174 causes of changes external 85, 105, 122, 146, 180 internal 35, 38, 85, 105, 122, 178 changes (aspects of) continuity & discontinuity 32, 66, 100, 104, 121, 168

economic status 141–9 Eiser, C. 30

188

189

equilibration 183 everyday thinking 5, 12, 184 evolutive phenomena 15

Levin, I. 8 Lohaus, A. 79 Luquet, G.H. 22, 79

Fayol, M. 7, 107, 119 Flavell, J.H. 78–9 Fodor, J.A. 173 forest regeneration 42–52 Fraisse, P. 31 French, L.P. 9, 57 Friedman, W.J. 10 future 42

Mandler, G. 172 Margairaz, E. 9, 98 Mattack, A. 30 Maurice-Naville, D. 3, 29, 43 McGhee, P.E. 130 memory 6, 13, 169 and intelligence (children’s view) 117– 20, 124, 173 mental image 10, 173 metacognition 79, 184 method (context variation) 17 Mettetal, G. 113 Michotte, A. 57 module 173 Moreno, A. 114 Mounoud, P. 173 Mugny, G. 124

Gelman, S. 7, 20, 40, 57, 97 genetic epistemology 3, 170, 175 Goldin-Meadow, S. 79 Goldstein, J.H. 130 Goodenough, F.L. 79 Goodnow, J. 79, 89, 91 Goodwin, B. 165 Guardo, C.J. 8 Halford, G.S. 13, 169 Harner, L. 31 Harris, P.L. 17, 79 Hart, L. 79 Hatano, G. 10 Helbing, N. 79 Hopkins, B. 181 Hudson, J. 172 humour 130–41 Hunt 112, 113 Inagaki, K. 10 Inhelder, B. 3, 10, 79 intelligence 112–26 irreversibility 6, 7, 8 Jahoda, G. 141 Kane, P.T. 113 Keil, F. 8 Krafft, A. 9 Lang, J. 30 Leahy, R.L. 112–13, 141–2, 148 Leslie, A. 17, 57

narrative 7, 9 Neisser, U. 123 Nelson, K. 7, 172 Nicholls, J.G. 113, 124 Ochiai, M. 53 order (chronological) See reasoning, temporal Parrat-Dayan, S. 98 Pascual-Leone, J. 13, 169 Patashnick, M. 113 Perner, J. 18 perspective of knowledge 1, 13–15, 163–4 Piaget, J. 3, 6, 8–10, 13–14, 18, 42–3, 56–7, 68, 78–9, 93, 98, 114, 125, 132, 180, 183 Piagetian method 143 Piagetian perspective 14 poverty 141–9 Prigogine, I. 4 reasoning, temporal development 6–10 duration 26, 48, 54, 137 and causality 57, 60–2, 65

190 INDEX

order of succession 6, 7, 9, 87, 89, 92– 3, 134, 167 and causality 56–7, 77 recognition 29, 41, 55, 81, 110, 176 Reith, E. 79, 91 reversibility 35 Richards 43 Sahm, W.B. 79 Schank, R.C. 172 schema 172 schemes (of diachronic thinking) transformation 166–7, 171, 177, 179 temporal organization 167–8, 171, 177, 179 interstage linkage 168, 171–2, 177, 180 dynamic synthesis 169, 172, 177 scientific discovery 2–5 scripts 7, 172 Shatz, M. 97 Shultz, T.R. 132 Siegler, R.S. 43 Sinclair, H. 8 Sonuga-Barke, E.J.S. 14–15 Soto, P. 114 spatial transformations distance 73, 76 spatial solutions 155–6 stages (children’s conceptions of) 28, 54, 64, 88, 128 stars See universe Stavy, R. 42, 50 Steenken, P. 3 Stengers, I. 4 Stora, R. 79 stories See narrative Sugarman, S. 169 synthesis (synthetic ability) 9, 108, 169, 170 Szeminska, A. 79, 93, 132 thawing ice 56–66 temporal decentration See diachronic tendency time See reasoning, temporal traffic flow 149–60 Trautner, H.M. 79

tree disease 29–41 tree growth 20–9 Tryphon, A. 80–1, 90 universe 67–76 verbal ability 96–112 Vosniadou, S. 68, 75, 169 Walsh, M.E. 30 Wax, N. 42, 50 wealth 141–9 Webley, P. 14–15 Wellman, H.M. 18, 78 White, P.A. 7, 57 Wilkins, P. 79, 91 Yussen, R.S. 113