Learning and the Development of Cognition (Psychology Revivals)

Barbel Inhelder, Hermine Sinclair, Magali Bovet

• Publisher: Taylor & Francis
• Year: 2014
• Print ISBN: 9781848724501
• eBook ISBN: 9781317673873
• Edition: 1
• Topic: Psychology
• Subtopic: Cognitive Psychology & Cognition
• Index: Psychology

How do children learn and how are new modes of thought developed? These questions have for years been of paramount interest to psychologists and others concerned with the cognitive development of the child.

In this major work, originally published in 1974 and reporting on over ten years' research of the Geneva School, the authors carried the pioneering investigations of Jean Piaget to a new and remarkable level. As Piaget said in his foreword to the book: 'The novelty of the findings, the clarity of the theoretical interpretation, and the sometimes even excessive caution of the conclusions enable the reader to separate clearly the experimental results from the authors' theoretical tenets.'

The authors' learning experiments with children were designed to examine the processes that lead to the acquisition of certain key concepts, such as conservation of matter and length. Detailed study of the progress of each individual subject revealed a number of features characteristic of situations that create conflicts in the child's mind and certain regularities in the way these conflicts are resolved. Such data threw new light on the dynamics of the development of cognitive structures as well as on basic mechanisms of learning at the time.

1
Concepts of Conservation of Continuous Quantities: From Observation to Inference

Introduction

Our first learning experiments dealt with the acquisition of concepts of conservation of physical quantities. The cross-sectional studies had already clarified some of the epistemological and structural aspects of concepts of conservation in general and of conservation of physical quantities in particular. A grasp of these concepts indicates the presence of an underlying system of mental operations that is characterized essentially by two forms of reversibility, inversion or cancellation on the one hand, and compensation of reciprocal relationships on the other. The particular psychological interest of conservation tasks lies in the fact that they elicit judgments and arguments expressing these two forms of reversibility.

From the logical point of view, an operation changes state A into state B, leaving at least one property invariable and allowing for a return from B to A which cancels the original change by means of an inversion. Psychological investigation shows that children support their correct conservation judgments by the following three types of arguments: reversibility by inversion, e.g., “You’ve only got to pour the liquid back into the first glass and you’d see there’s still the same amount to drink”; reversibility by compensation of reciprocal relationships, e.g., “The liquid is higher but the glass is thinner, it amounts to the same thing”; and additive identity, e.g., “We haven’t added or taken anything away.” It is legitimate to hypothesize that concepts of conservation of physical quantity are generated by logical systems of mental operations which, as Piaget has already shown, are isomorphic with the structures of logical “groupings.”

The epistemological interest of the development of conservation concepts is evident. These concepts are neither preformed in the child nor acquired by means of simple observation of real events, but are the product of a process of elaboration which Piaget seeks to explain in terms of equilibration and autoregulation. Conservation concepts are also of special interest to psychologists, because their growth is governed by very regular laws of development. Finally, psychopathological studies of retardation or deviation of normal development highlight the importance of conservation concepts from a different perspective.

Research into the development of concepts of conservation of quantity has been followed with considerable interest by both child psychologists and developmental psychologists and a number of replication studies have been carried out. In the original conservation studies a given quantity of liquid was poured into glasses of different sizes (Piaget and Szeminska, 1941) or a ball of modeling clay was first changed in shape and then broken into several smaller pieces (Piaget and Inhelder, 1941). These studies revealed that the child’s initial understanding of conservation is based on a general undifferentiated concept of invariance which provides the basis for subsequent, more specific quantifications and measurements (e.g., of height and length). This first notion of conservation of continuous (or physical) quantity is developed before any actual physical quantification of mass, volume, or weight is possible. Differentiation between, on the one hand, the underlying synchronic operation structures and, on the other, the continuous and causal action is only partial (Piaget and Garcia, 1971).

Three stages have been found in the development of the concept of conservation of continuous quantities: the first is characterized by a number of answers and arguments indicating an absence of conservation; the second is characterized by responses of an intermediate type; and the third is characterized by the acquisition of conservation.

The common characteristic of the first stage, in which the children do not have the concept of conservation of quantity (either in the case of solids or in that of liquids), is that the children focus either on the action carried out (pouring of the liquid, flattening out of the modeling clay, etc.) or on the resulting appearance of the material. They neglect the fact that the final appearance of the material is determined by the action which brought about the change in shape of the modeling clay or in the level of the liquid. More detailed analyses show that there are several sublevels within this elementary stage. It is only at a certain point in development that the child begins to establish relationships between some of the features of the experimental material, and, initially, these relationships are partial and are restricted to a few features only. For instance, if a child thinks that there is more liquid to drink when it is poured into a thinner glass “because the liquid comes up higher,” he has apparently compared the initial equality of height of the liquid in the two glasses with the subsequent rising (“going beyond”) of one level above the other. A number of studies of spatial representation and concepts of speed and movement in the child have shown that such ordinal comparisons based on “going beyond,” “overtaking,” etc., are fundamental for the elaboration of the elementary systems of space and movement which eventually lead to systems of measurement.

At another substage the child becomes capable of mentally returning to the starting point of the experimental situation and predicting that there will once again “be the same to drink” or “just as much to eat,” although he judges that at present the quantity (of liquid or modeling clay) has increased or diminished as a result of the change in shape. In one of our first publications (Piaget and Inhelder, 1941), this type of judgment was called “empirical reversibility,” i.e., the possibility of an effective return to the initial state, to distinguish it from logical reversibility. The main difference between this reversal and logical reversibility is that in the first instance, although the return action is the inverse of the transforming action, it neither cancels out this transformation nor compensates for it; it is merely a second action which, for the child, is completely independent of the first.

A subsequent series of studies carried out at the Center of Genetic Epistemology on notions of functional dependency and identity showed that this idea of a possible inverse action is subsumed by a system of one-way mappings whose semilogical nature has been shown by Piaget (1970). The child establishes a series of one-way relationships of the type yi = f(x1), where xx is the action of lengthening the clay ball and yx is the decrease in thickness and f = the relationship of dependency of y’ on x’. He then establishes y2 = f(x2), where x2 is the inverse action of “fattening” the sausage into a ball and y2 is the reduction in length. At this level, however, these two covariations, or functions, are still envisaged successively and are not yet coordinated into a single system which will transform the covariations of dimensions into compensations between dimensions.

The semilogical system of one-way dependencies does not yet comprise quantitative invariants, but only an idea of qualitative identity. At this point, the child is unable to distinguish between certain invariant properties of an object and others that change. He will reply, for instance, that “it’s always the same liquid,” “the same clay,” even though he judges that the quantity has increased or diminished. For the child of this level the permanent properties of objects are qualitative in nature and are observed directly, whereas for the child of the operatory level, quantity is conserved; this is possible only if a coherent system of thought operations has been constructed.

The responses of the intermediate type are generally characterized by vacillations between nonconservation and conservation judgments. A child might keep changing his mind in one situation; or he might answer correctly in one situation and wrongly in another equally difficult situation—it is impossible to predict which questions or experimental situations will elicit correct or wrong answers. It is, however, often possible to order the answers of a group of subjects on a post hoc basis.

At the third level, the child maintains conservation of quantity and justifies it by arguments based on logical identity, reversibility by cancellation of the change, and compensation between dimensions, based on an understanding of the reciprocity of the relationships (e.g., every increase in length implies a corresponding decrease in thickness).

There is undoubtedly a continuity from the semilogical and qualitative identities to logical operations and conservation of quantities, but it is also clear that this development is based on a process of integration and complete restructuring. This will become even more evident from the results of the present learning studies. Piaget (1970) notes that logical, quantitative identity is not merely an extension of qualitative identity. This is shown in three ways: (1) quantitative identity results from the product of a direct operation and its inverse; (2) within the framework of a closed, coherent system it is felt as necessary; and, finally, (3) it is only one of the components of this coherent system, and it cannot account for its other components, such as the two forms of reversibility.

Quantitative identity, based on a system of operations, should not be confused with the sort of responses found by Piaget and Taponier (Piaget and Inhelder, 1963, 1966) in situations where the child is asked to show (by pointing, or putting a spot of paint on a glass) where the level of a liquid will be when it is poured into glasses of different shapes, and also to say whether there will be more, less, or the same amount of liquid in the glasses. Some children predict that neither the level nor the quantity will change—here there is clearly no question of “logical” conservation since they do not foresee any transformation at all.

Generally speaking, elementary number conservation is acquired earlier than concepts of conservation of physical, continuous quantities, although the developmental process is similar. In situations where the child is asked to accept the initial equality of a number of beads which have been placed in two identical glasses by means of a process of repeated one-to-one correspondence (see Appendix), and then is asked what happens when the beads are poured into glasses of different sizes, we note not only the same sequence of responses as for the tasks of conservation of liquid or modeling clay, but also the same types of arguments. One notable difference, however, between discontinuous and continuous quantities is that in the former case the children usually say: “There isn’t one bead more (in either of the glasses), we always put one with one.” In terms of the grouping structure, this remark refers to the “identity operation,” since the method of forming equivalent quantities by a process of one-to-one correspondence highlights the action of adding.

In a study (Inhelder and Piaget, 1963) of the child’s understanding of the principle of recurrence, the importance of repeated actions of one-to-one correspondence for the development of concepts of conservation of continuous quantities became very clear. In this study, the child was asked to place two beads simultaneously into two glasses (“a red one with a blue one,” as the children say), and to repeat this action a number of times, first using pairs of identical glasses and then different ones. In the first experimental situations the child could see the result of this repeated action because transparent glasses were used. Then opaque glasses were substituted and the result was no longer visible. The purpose of this study was to have the child predict the outcome of an action that was repeated a great many times (“if we continued to do this all afternoon,” etc.). Another version of the experiment started with unequal quantities. In yet another, a one-to-two correspondence was used, in order to see whether the child conserved both equal and unequal quantities. The results showed that at a relatively early age the child can make inferences from these “recurrences” which lead to the concept of conservation of numerical equality (or inequality), often justified by the following argument: “Once I know it’s the same, I know it forever.” At this stage, however, numerical conservation is still incomplete and cannot immediately be generalized to all situations involving a change in appearance of collections of elements.

The well-known experiments on “spontaneous” and “provoked” correspondence and on the concept of numerical equivalence (Piaget and Szeminska, 1941) provide specific details on the primitive methods whereby the child estimates discontinuous quantities in terms of “numerosity” (i.e., the quality of being numerous) and not yet in terms of the number of elements. At first, the child fails to differentiate between the evaluation of quantity based on numerical criteria and that based on spatial criteria. If children of four to five years are asked to make up a collection of elements which is equal in number to that of the experimenter’s collection, which is presented in a certain way (e.g., “choose as many eggs as there are egg-cups lined up on the table”), there is a tendency for them to construct their collections so that the starting and end points of the rows of objects coincide. However, when they are asked for an evaluation, a different reaction is sometimes noted: they consider the line where the elements are closer together to contain more elements than the longer one in which the elements spread out....

Table of contents

• Cover
• Title
• Copyright
• Original Title
• Original Copyright
• Acknowledgments
• Contents
• Foreword
• Introduction. Cognitive Development and Learning Theory
• 1. Concepts of Conservation of Continuous Quantities: From Observation to Inference
• 2. From One-to-One Correspondence to the Conservation of Physical Quantities
• 3. From Numerical Equality to the Conservation of Matter
• 4. Verbal Training Procedure for Conservation of Continuous Quantities
• 5. Cross-Cultural Study of Conservation Concepts: Continuous Quantities and Length
• 6. From Elementary Number Conservation to the Conservation of Length
• 7. Class Inclusion Training and Its Influence on Conservation
• 8. Conservation Learning and Its Influence on Class Inclusion
• Conclusions
• Appendix
• Bibliography
• Index