PIAGET—A PRACTICAL CONSIDERATION A consideration of the general theories and work of Jean Piaget, with an account of a short follow up study of his work on the development of the concept of geometry BY G. A. H E L M O RE Diploma in Primary Education University of Leeds Institute of Education Headmaster of Pare Eglos CP, School, Helston, Cornwall 4 P E R G A M ON P R E SS Oxford · London · Edinburgh · New York Toronto · Sydney · Paris · Braunschweig Pergamon Press Ltd., Headington Hill Hall, Oxford 4 & 5 Fitzroy Square, London W.l Pergamon Press (Scotland) Ltd., 2 & 3 Teviot Place, Edinburgh 1 Pergamon Press Inc., Maxwell House, Fairview Park, Elmsford, New York 10523 Pergamon of Canada Ltd., 207 Queen's Quay West, Toronto 1 Pergamon Press (Aust.) Pty. Ltd., 19a Boundary Street, Rushcutters Bay, N.S.W. 2011, Australia Pergamon Press S.A.R.L., 24 rue des Ιcoles, Paris 5" Vieweg & Sohn GmbH, Burgplatz 1, Braunschweig Copyright © 1969 G. A. Helmore First edition 1969 Ali 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 the prior permission of Pergamon Press Ltd. Library of Congress Catalog Card No. 75-94933 Printed in Great Britain by A. Wheaton & Co., Exeter This book is sold subject to the condition that it shall not, by way of trade, be lent, resold, hired out, or otherwise disposed of without the publisher's consent, in any form of binding or cover other than that in which it is published. 08 006892 8 (flexicover) 08 006893 6 (hard cover) INTRODUCTON Tffls short book is a brief statement of the theory of Jean Piaget concerning the general pattern of intellectual development in children which he claims to have found. It also includes an account, and consideration of the results, of a follow-up study conducted among children drawn from two English primary schools in diflfering environments. The book has been deHberately kept short, for teachers and student-teachers do not have time to spare reading unnecessarily wordy expositions; and since they also do not have time to look up continuous cross-references these have been kept to an absolute minimum too. However, for those readers who wish to read further on the subject of Piaget's work. Appendix 2 may prove useful. Appendix 1 has been included for several reasons, most of which are obvious. One that should be emphasized is that any reader of this book can conduct one of Piaget's experiments himself. For every teacher it will be a revelation. I have heard it described by a colleague as "Taking the top oflf the child's head and watching the wheels go round". Try it and see. I should Hke to conclude this short introduction by thanking Dr. K. Lovell, of the University of Leeds Institute of Education, for all his help. It was as a result of his lectures that I first began to understand and appreciate Piaget's work, and I believe he has summed the matter up in his statement in those lectures that "When Piaget's true worth is known he will be owed as much by teachers, as Freud is by psychologists". The protocols used in the conduct of the experiments, and printed in Appendix 1, were drawn up by Dr. Lovell, and I am most grateful for his permis­ sion to reprint them in this book. vii CHAPTER 1 JEAN PIAGET AND fflS APPROACH TO HIS WORK JEAN PIAGET is the son of a Swiss historian. He was bom at Neu- chatel in 1896. At the age of 7 he wrote a Uttle book in pencil entitled Our Birds, and so his first love, zoology, was declared to the world. When he was a 10-year-old boy, Piaget systematically watched and noted the behaviour of an albino sparrow, and his written observations were printed in the local journal of natural history. The curator of the Neuchatel museum, a leading authority on molluscs, then encouraged his natural interest, and directed it to the task of classifying and labelling the specimens of freshwater shells to be found in the nearby lake, and also to investigating the different types of snail and mussel to be found there. The results of this piece of study were printed in a series of articles in the Revue Suisse de Zoologie while he was still at school. In 1918, having graduated in Natural Sciences, Piaget obtained a doctorate with a thesis entitled "Alpine Molluscs". As a result of family upbringing and his education, Jean Piaget now found himself in the centre of a conñict of ideas. His was a strictly religious family, and he reaUzed increasingly that the biologist's view of human nature that he held, as a result of his education, appeared to be opposed to the doctrines held by his rehgion. He sought refuge from the emotional crisis that resulted by writing a philosophical novel which dealt with the problem of the two irreconcilable viewpoints, the hero's solution was, to quote Burt,^*^ "to investigate how human knowledge has evolved, and to do so by applying the methods, not of the philosopher, but of the biologist himself". He seems to have been following his hero's example ever since. 1 2 PIAGET—A PRACTICAL CONSIDERATION Piaget now enrolled in the psychological laboratory at Zurich. There he attended Jung's lectures and amongst others read the works of Herbert Spencer which exercised considerable influence on his later writings. In 1919 he went to Paris where Dr. Simon (Binet's collaborator on the scale of intelligence tests that bear his name) set him the task of standardizing Burt's reasoning tests for Parisian children. He commenced this task without much enthusiasm and soon decided that it was far more important to discover how each child reached his conclusions, especially when those conclusions were wrong, than it was to establish norms. On his return to Switzerland, 2 years later, he was invited to become Director of Studies at the Rousseau Institute of Geneva, which is now part of the University of Geneva, and is known as the Institute of Educational Science. At the age of 26 he accepted the appointment, and has remained there working with research students ever since, studying the mental development of the child. (His present appointment is that of Professor of Psychology at Geneva, and until recently he was also Professor at the Sor­ bonne.) In his work the problem of Piaget has always been the same, and it arises out of Spencer's own doctrine of adaptation. How does the growing child adjust himself to the world in which he lives? How are we to account for the constant recurrence of what, to the rational adult, seem extreme instances of maladjust­ ment? Jean Piaget's search for answers to these questions was begun in the famiUar form of keeping careful records of what young children said and did. He very soon foxmd these methods in­ sufficient and unsatisfactory, however, and he started to develop the ingenious techniques for which he is now world famous. The results of his work have been steadily pubhshed to the world in a flow of books and other publications which has gone on since 1924. Much of his technique of investigation seems to be the very antithesis of normal methods of scientific investigation for he gives his imagination a free hand. He is trying all the time to get inside the mind of the child in order that he may see the world HIS APPROACH TO HIS WORK 3 from the child's own standpoint. A much-quoted example of this was the set of experiments which involved his joining in each child's favourite game on an equal footing with the child, which included such activities as learning how to make a good shot at marbles, how to make a bad shot, and even how to cheat!<»> Piaget's published works are extremely difficult to read, expecially in the theoretical sections. There are several reasons for this and the first, of course, is that he is investigating and writing about an extremely intricate and involved process. Another minor cause is that all of his publications are written in French and it is often extremely difficult to find exact English equivalents for the original French terms used; however, by far the greatest share of the difficulty arises from the fact that, as has already been described, Piaget's own intellectual development and education has been so very comprehensive and complex. The following quotation from Barbel Inhelder, one of Piaget's collaborators, amplifies this point; The conception of mental development as it appears in the works of M. Piaget is somewhat disconcerting, not because of the facts, but because of the terminology. M. Piaget, who is a zoologist by training, an epistem- ologist by vocation and a logician by method, employs a terminology as yet not much used in Psychology. He expresses himself mainly in terms of structures, which by definition are systems of mental operations obeying definite laws of composition, such as, for example, the mathe­ matical laws of group and lattice. According to a number of cybemeti- cists, structures are as much physiological as mental. It seems necessary to keep in mind this triple orientation—biological, epistemological and logico-mathematical—which is continually reflected in Piaget's vocabu­ lary, in order to find one's way easily among the Geneva studies. But once these characteristics are appreciated the data and laws deriving from them become clear and easily verified.^^*^ Despite what appears to be a somewhat over-optimistic claim in the final sentence of this quotation, a careful consideration of the whole quotation does clearly illumine the problem. Piaget's terminology, to those who have not studied his sciences, makes the reading of his books exceptionally difficult, for he so seldom defines the terms he uses, and they often appear to the non-scientist 4 PIAGET—A PRACTICAL CONSIDERATION reader most obscure. However, with familiarity comes com­ prehension, partly from context and partly by a slow growth of understanding (or so I beUeve to be the case), for after the first three or four of Piaget's booTcs, carefully read, the terminology becomes conmionplace, accepted, and even generally understood, but still remains very diflficult to explain to others without using almost equally difficult terms. CHAPTER 2 A SUMMARY OF THE GENERAL THEORIES OF PIAGET— THE PIAGETIAN CONCEPT OF INTELLIGENCE AND ITS DEVELOPMENT PIAGET'S approach is a genetic and biological one. "He attempts to distinguish stages of development in the evolution of thought, and to show how each stage reveals a progressive sequence from simpler to more complex levels of organisation".To do this he has had to develop his own methods which are described later—the Piagetian experiments. These latter require a child to solve a problem, and the basic plan of each experiment is such as to reveal the stages of development toward the full pattern of thought processes involved in the final solution of the problem. Each child's answers, therefore, when recorded, enable the experi­ menter to place him at his stage of development in the evolution of that particular pattern of thought. Chronologically, Piaget was at first a biologist, and so one can understand his selected starting point for all of his theories on the development of intelhgence—it is that higher psychological func­ tions grow out of biological mechanisms. One can also understand that it is logical for him to describe the actions producing this development in biological terms, and so to develop his doctrine of maturation. Piaget<i®> defines intelUgence as "the state of equilibrium to­ wards which tend all successive adaptations of a sensori-motor and cognitive nature, as well as all assimilatory and accommodatory interactions between the organism and the environment". He 5 6 PIAGET—A PRACTICAL CONSIDERATION looks upon the growth of intelligence as the growth of the ability to achieve equilibrium at an increasingly high level of complexity. The meaning of the term "equilibrium" becomes clearer from a consideration of a further statement: "InteUigence is adaptation ... adaptation must be described as an equilibrium between the action of the organism on the environment and vice versa." By "the action of the organism upon the environment", Piaget means assimilation, in so far as this action depends on previous behaviour involving the same or similar objects (or circumstances). "Physiologically" Piaget<i»> states: "the organism absorbs substances and changes them into something compatible with its own substance. Now, psychologically, the same is true except that the modifications with which it is then concerned are no longer of a physico-chemical order but entirely functional, and are determined by movement, perception or the interplay of real or potential actions (conceptual operations, etc.). Mental assimilation is thus the incorporation of objects into patterns of behaviour, these patterns being none other than the whole gamut of actions capable of active repetition. By assimilation, then, it seems that Piaget means the way in which the mind takes its continuing experience of objects, cir­ cumstances, situations, etc., and orders them into schemata of thought for future use. The action of the environment on the organism he terms accommodation. In the physiological sense "the individual never suffers the impact of surrounding stimuli as such, but they simply modify the assimilatory cycle". Piaget^^^^^ states that the equivalent is true in the psychological sense: "the pressure of circumstances always leads, not to a passive submission to them, but to a simple modification of the action affecting them." By accommodation, then, it seems that Piaget means the way in which the mind modifies its schemata in the light of new experi­ ence. In his studies of the progress made by children towards higher levels of equilibrium, there are two key factors emphasized in Piaget's work. The first of these is the extent to which an organism can control shifts of orientation; the second is the ability of the organism to develop operations. An operation is an action that A SUMMARY OF THE GENERAL THEORIES 7 has been internahzed into a thought process. The act of thinking involves the use of groups or systems of such operations. Piaget^^®^ lists five properties of such groups or systems of operations: (i) Composition, Any two units can be combined to produce a new unit. (ii) Reversibility. Two units combined may be separated again. (iii) Associativity, The same results may be obtained by combining units in diflFerent ways. (iv) Identity. Combining an element with its inverse annuls it. (v) (a) Tautology. A classification or relation which is repeated is not changed. (b) Iteration. A number combined with itself gives a new number. Operations and their groupings (i.e. thought processes and their groupings) are the main object of Piaget's developmental ap­ proach to concept formation. From his many experiments per­ formed by children of all ages he claims that there are five main stages in the development of a concept, through which the vast majority of children pass, it being remembered that the bright child will pass through the stages more quickly and the dull child may fail to reach the final stage(s) of maturity. The final statement suggested by Piaget's work, then, is that what we term "thinking", for example the ability to solve theoretical and practical problems—the abiUty to make reasoned judgements, the recognition of relationships, and the associations of ideas, etc. —is, in fact, only the result of a system of thinking that has been slowly built up within the brain. Our ideas of number, space, time, weight, measurement, etc., are not innate, but are built up piecemeal as we hve our early lives, firstly through the sensory and motor activities of our early infancy and then at an accelerated rate through our association with the people around us and our developing ability to understand and use language. These back­ ground schemata so built, then, are the foundations for all our subsequent thinking, will always affect it, and without them, suggests Piaget, "thinking" would be virtually impossible.