What Does Piaget's Theory Describe?

INTRODUCTION

The title of this article raises a crucial question for educators who seek implications for their practice in Piaget’s theory. He claims that his theory describes a natural process whereby certain concepts develop. The theory is presented as an answer to such questions as: “What conceptions of the world does the child naturally form at the different stages of its development?“1That is, like a description of the natural development of our bodies, given adequate nutrition and exercise, Piaget sees his theory as describing a part of the mind’s natural development, given adequate social, cultural, and physical environments. Also—crucial for the theory’s implications for education—the natural developmental process it describes is seen as determining what children can learn and understand at any stage. If Piaget is right, and his theory does describe this kind of natural developmental process that can tell us what concepts children can and cannot understand at any stage of their development and something of the process by which they come to understand certain concepts, then designers of curricula and teachers have available a potent tool with which to improve education.

If Piaget is wrong about what his theory describes, we have to reconsider whether the many implications that are claimed to follow from his theory to education are in fact legitimate. If—to put it extremely—his theory describes only a part of the normal conceptual development of some middle-class Genevan children, then we would be foolish to make our curricula and teaching methods conform to the theory’s implications—unless we wanted to educate our children to be as like those middle-class Genevans as possible. To put it less extremely, if Piaget’s theory describes not a natural process but a process influenced by cultural environments, it is describing to some degree the results of particular forms of socializing and educating: it is describing the results of forces that it is educators’ proper job to shape—not conform to.

I will present evidence and arguments to support the claim that Piaget’s theory does not describe a natural process of conceptual development and that whatever it does describe is not something that constrains learning, and I will give some reasons to support the judgment “that Piaget’s stage model of cognitive development is in serious trouble.”2

KINDS OF KNOWLEDGE

Piaget distinguishes three kinds of knowledge. The most basic is that which is innate. This largely instinctual knowledge is very limited in human beings. Instinctual knowledge would not take us very far, and needs to be augmented by the second kind of knowledge, that which results from learning. The third kind of knowledge, which results from what Piaget calls development, is the primary focus of his interest. His developmental theory is primarily about this third kind of knowledge. The second kind of knowledge he sometimes calls “figurative” and the third kind, “operative.”

Though Piaget’s later interests drew him to discuss innate knowledge in some detail,3 we may pass over it here as not important to the present argument about what his developmental theory describes. We must, however, consider his distinction between knowledge that results from learning and that which is a product of development. Most simply, we may say that, in Piaget’s view, development is the more profound process and affects the whole of our thinking, whereas learning is the relatively superficial process whereby we may add particular items of information. Learning is different for everybody, and what is learned turns on the contingencies of individual experience. Development, on the other hand, is a natural process whereby the fundamental categories that provide the framework for thinking become increasingly sophisticated by an internal process of self-regulation.

The sharp distinction between learning and development is a crucial one for Piaget, but also a rather difficult one to make clear initially. It is difficult to make clear because the spontaneously developing internal structures are not evident in their own abstract right but are “constantly fused with exterior data,“4 and so can seem to result from learning rather than development. Development is seen in the progressive sophistication of mainly logico-mathematical structures, and these structures are used to organize and make sense of whatever we learn; they are “the natural psychological reality, in terms of which we must understand the development of knowledge.“5 As the body ceases to continue on its natural course of development if not fed, so the natural process of cognitive development will not continue if we cease to learn; the development of operative knowledge requires the continued learning of figurative knowledge. The fact that the body’s development depends on food does not mean that we cannot distinguish between the body and food. Similarly, the fact that cognitive development depends on learning and experience does not mean that we cannot distinguish between this fundamental logico-mathematical knowledge and the more limited kind of knowledge that results from particular situations. Piaget constantly points out that development is affected by social environments and what is learned from individual experience, but, again, this should not lead us to confuse the natural process of development with the social process of learning.

Logico-mathematical/operative/developmental knowledge is not hereditary. Children at birth, according to Piaget, lack knowledge of object constancy, the principle of invariance, class inclusion, transitive inference, and so on, and it takes them a long time to develop such knowledge. Logico-mathematical knowledge is also unlike that which we learn from experience of the external world. While cognitive development requires experience of the external world, what develops as a result of this experience is knowledge of quite a different kind from that which is learned. The difference may be indicated by one of Piaget’s examples. A four- or five-year-old boy sits with a set of stones in a line. He counts them from top to bottom and reaches ten. He then tries counting them from bottom to top and discovers that there are ten that way too. He then puts them in a circle and counts again. Still ten. The child feels that he has made a momentous discovery. What has he discovered? Whatever it is, it is not a property of the pebbles, nor how to count, nor any simple knowledge related to the particulars of the situation. Rather, the child developed important knowledge about the action of ordering things in the world. He discovered, among other things, that the sum of a set of objects is independent of their order. He developed, that is to say, a fundamental category of thought that can be applied generally to other objects in the world.

These logico-mathematical structures do not develop as a result of observing the world passively, according to Piaget, but rather children come to know them as a result of the actions they perform on objects and through perceiving how the objects respond to their actions. (These actions may, during the later stages, be mental.) The crucial point for Piaget is that the structures develop as a result of actions. Learning may result from experience of objects (an experience that has to be mediated always by some structure), but development results from children’s experience of their own actions on objects.

A further feature of the distinction between learning and development is that the former can take place only within a framework that is constituted by the latter. That is, development largely determines learning (“No sort of learning . . . is possible without logico-mathematical frameworks.”6 The qualifier “largely” is there because recently Piagetians have conceded that learning in some conditions can in some small degree stimulate development. More on this later.) According to Piaget, learning initially takes place within a framework of innate knowledge. This framework, however, does not take us very far and is replaced by the logico-mathematical framework as the determiner of learning. Thus, if the fundamental structures of cognition develop according to a particular sequence, that sequence describes and constrains what can be learned at any stage. It is in this relationship between development and learning that educators find the major implications of Piaget’s theory for education.

What Piaget’s theory describes, then, according to Piaget, is the natural sequence of the development of logico-mathematical structures. In so doing, it describes what can be learned at any stage, because “learning is subordinate to the subject’s level of development.“7 Failures to learn, then, are failures of teachers to understand what structures the child has already developed and to make what is to be learned conform to those structures. As Piaget says, “It is not the child that should be blamed . . . but the school, unaware as it is of the use it could make of the child’s spontaneous development, which it should reinforce by adequate methods instead of inhibiting it as it often does.“8

It should also be mentioned that Piaget’s theory is unlike many developmental theories in that it does not claim to describe what people do during various stages of maturation. Rather, its focus is on what they can do. That is, it is a description of competence, not simply performance. It is not articulated in terms of what tasks they perform, but in terms of general abstract structures whose characteristics are inferred from a limited set of particular tasks.

One might ask what evidence there is that the structures in terms of which Piaget’s theory is articulated in fact exist. Connectedly, one might ask what evidence there is that the constraints on children’s learning are consistent with the existence of such structures. The first of these questions challenges Piaget’s account of what his theory describes; the second challenges the main link between the theory and educational practice. These structures are presented as properties of our minds, and as such are obviously not open to any kind of direct observation. Their existence is inferred from the logical structure of particular tasks that children perform. If a child can perform a task whose logical structure is of a kind Piaget calls concrete-operational, then it is inferred that this child has developed concrete operations. If a child systematically fails to perform such tasks, it is inferred that this child has not yet developed the relevant operations.

Where might we look for evidence for or against the existence of the kinds of structures Piaget’s theory describes? We might consider what we would expect to be the case if Piaget’s claim is true and then look around to see whether or not that is the case. We may start this in a fairly simple way. If everyone has a common underlying sequence of cognitive development to go through, we might expect to find certain clear commonalities among everyone’s ability to perform tasks with progressively more complex logical structures. We would expect that the possession of a particular mental structure would enable a person to perform all tasks having a corresponding logical structure and, conversely, that it would be impossible to teach things whose logical structure was in advance of that of mental structures so far developed. We should also try to make sure that the results that emerge from the classic Piagetian tasks—by inference from which the theory is composed—are due to children’s use of their cognitive structures and not due to or infected by some other source, like the peculiarities of the test situation, or children’s growing mastery of language, or whatever. In addition, we need to reflect on the claim that development largely determines learning, to consider what would be the case if this were true, and then to see as far as possible what is the case.

COMMON DEVELOPMENTS

If we all have in common a part of our minds that develops according to a particular sequence, we would expect some clear uniformity to be exposed whenever we could show this level at work underneath the superficial diversity of different experiences and learning. If, as Piaget claims, this is also the most important part of cognition, we would expect it to be fairly easy to expose this level of commonality. This level is composed of what Piaget calls “the development of the operations and the logico-mathematical structures of intelligence."9 And he notes that if his claims about the fundamental nature of these mental characteristics is true, “it would naturally mean a certain constancy or uniformity in development, whatever the social environments in which individuals live.“10

Piaget’s earliest studies were with a homogeneous population, and so it was difficult to establish whether the commonalities he was finding were due to commonalities in the educational and socializing experiences of that population, or in the testing procedures he used, or whether indeed they were due to an underlying developmental process such as Piaget postulated. Thus there was an interest in the results of cross-cultural studies that aimed to discover whether a similar developmental process was evident in quite different populations.

But it is not easy to see what kind of finding from cross-cultural studies would disconfirm Piaget’s theory. One needs to remember that his is not simply a psychological theory; it is, rather, a genetic epistemological theory, which intricately mixes logical constructs and psychological claims. This is important to remember here because those parts of the theory that are logical constructs will guarantee a certain uniformity from empirical results. If, for example, one were to propose a theory that involved the claim that children would learn addition and subtraction before calculus, or would learn some historical facts before developing a sophisticated historical consciousness, one would not be altogether surprised if empirical tests confirmed this part of one’s theory. This confirmation would not be due to the claims’ being obvious psychological truths; rather it would be due to their logical necessity. In the same way, the general sequence of stages as described in Piaget’s theory does not involve psychological claims and is not an empirical matter. Of necessity, formal operations have to succeed concrete operations, for example, because formal operations are defined as operations upon the operations of the previous stage.”11 That is, whatever we conclude about Piaget’s theory, it is a matter of logical necessity that children will learn to perform certain tasks before they will be able to perform tasks that require the earlier tasks and then some additional skill.

So we will expect cross-cultural studies to provide some very general support for the sequence of stages. What is of more interest to our question about the existence of the underlying structures is whether a more detailed uniformity in sequence is evident from such studies. But, again, Piaget accepts that experience, environment, and social interaction will all affect the rate at which people develop these underlying structures, and will affect the extent to which the developments will occur.

Thus, before we conduct cross-cultural studies or look at the data, we are guaranteed a certain general uniformity by logical necessity and we are told to expect certain particular irregularities due to local contingencies. It is not easy to see, then, where we should look for evidence either for or against the existence of Piaget’s operatory structures. The general uniformity does not count as evidence for, and some particular irregularities do not count as evidence against. In addition, the problems inherent in any cross-cultural study—problems of cultural context, of communication, of meaning—are vividly evident in Piagetian cross-cultural studies. How are we to interpret whatever results we do get? If we find, for example, that most Australian aborigine adults fail Piagetian tests of the conservation of continuous quantity,12 “are we to believe that aborigine adults will store water in tall thin cans in order to ‘have more water’; do they think they lose water when they pour it from a bucket into a barrel? “13 That these confusions are not evident in their culture suggests that the classic Piagetian task in such a context is yielding obscure data that possibly has nothing much to do with general intellectual capacity.

And yet this problematic area has attracted an enormous amount of research and we are rich indeed in data. It confirms a very general uniformity, of a kind guaranteed by logical necessity, and a great deal of local diversity.

Apart from the very general developmental sequence that logic guarantees, we might search for evidence concerning the sequence of substages Piaget postulates—such as the sequence in the acquisition of the conservations. While some studies more or less confirm the Piagetian sequence, a number disconfirm it.14 I say “more or less” confirm it, because these studies report averages of test performance, and suggest that some individuals do not conform to the Piagetian sequence even in studies whose generalized trends form the empirical support for the theory. Whatever we make of these results, they hardly support the existence of a universal unfolding sequence of cognitive structures. Reviews of relevant research agree that “the research to date challenges the notion of invariance in the sequence of stage acquisition.“15

CONSISTENT DEVELOPMENT

If we possess certain cognitive structures that in profound ways affect how we make sense of the world and that are basic determinants of the totality of our intellectual life, we would expect that once a particular structure had developed it would be evident in all our intellectual activity.

With the recent proliferation of experiments seeking to test the theory in fundamental ways, rather than elaborate it or replicate its findings, it is becoming clear that the ability to perform a particular task is a poor predictor of a child’s ability to perform other tasks with the same logical structure in different circumstances with different materials. If children have developed the particular logico-mathematical competence to perform a task, it is a problem for the theory to explain why other logically identical tasks are not performable.

There is a set of classic Piagetian experiments that have produced the bulk of evidence for young children’s supposed “egocentrism’‘—their inability to “decenter” like adults. In one of these experiments, for example, children are faced with a three-dimensional model of three different-looking mountains. A doll is then placed to one or another side of the model and the children are asked what the doll can see. Normally children fail to be able to work out what the doll would see from its perspective until about age eight or nine. Children under six normally identify what they themselves can see as what the doll can see. According to Piaget and Inhelder, children “really imagine that the doll’s perspective is the same as their own,“16 despite the fact that they know a view changes as one moves around. Similar findings from a set of similar experiments form the basis for the characterization of the mental structures that preoperational children are supposed to possess.

Margaret Donaldson reports a set of experiments showing that if one is sensitive to children’s language use and the context of human purposes and intentions that are meaningful to them, one can create tasks that have the same logical structure as the classic Piagetian tasks but that can be routinely performed by young children. Donaldson describes, for example, a study by Martin Hughes that uses the same logical form as Piaget’s mountain task but substitutes a policeman doll and a child doll.17 In an apparatus consisting of walls in the form of a cross, the children have to work out at what points the child doll would be hidden from the policeman doll. There are positions in which the child doll would be visible to the subject but not to the policeman doll. Thus children would have to be able to work out what the policeman doll would be able to see from his perspective—the decentering that according to Piaget is impossible for young children because of their egocentrism. In Hughes’s study the vast majority of children had no difficulty successfully performing the task; and, indeed, the ten youngest children in the study, whose average age was only three years nine months, achieved an 88 percent success rate.

Donaldson reports a series of other experiments that challenge the basis on which significant parts of Piaget’s theory rest. The question here is what Piaget’s theory describes. That he has exposed consistent development in the performance of some tasks by some children is clearly true. Donaldson argues forcefully that the egocentric responses Piaget’s tasks record are due, not to the lack of development of some specific structure of the mind, but simply to the fact that the tasks do not make sense to young children for quite different reasons. The classic Piagetian tasks are abstracted from any context of human purposes and intentions that children have learned to make sense of. Once Piaget’s tasks are put into meaningful contexts with meaningful materials, children’s performance becomes much more like that of adults and the characteristics that form the descriptive base for his cognitive structures are no longer evident.

There has been a considerable amount of discussion about what it means to be “in” a Piagetian stage. Connected to this is the problem of how far being in a stage guarantees being able to perform all tasks whose logical characteristics conform with those of the structure that supposedly defines being in a stage. The fact that the structures are descriptions of competences suggests that their operation on different materials might be something learned over time. (This is as close as one comes to finding an explanation of decalages.) This leaves us, again, with some difficulty in working out how to gather clear evidence for or against the existence of these cognitive structures. If some materials and contexts are, for some unknown reason, more resistant to the operation of the structures, then the fact that the structure operates on one task but not on an identical task with different materials can be discounted as evidence against the existence of the cognitive structures. Similarly, as a result of empirical studies, Piaget has incorporated into the theory the observation that as children approach transition points between stages their responses have a much less stable character than when they are more clearly “in” stages. Thus the fact that many children can perform one task but not another despite the fact that the tasks have the same logical structure is seen by Piagetians not as evidence against the existence of structures but rather as evidence that such children are at transition points between stages. In a study concerning the conservation of continuous quantity, thirty-four children between ages five and seven were given tasks that tested whether they could conserve liquids and modeling clay. Fifteen children failed on the tasks and it was concluded that they simply had not yet developed conservation structures. Nineteen children, however, could do one but not the other task, or succeeded in a part of one of the tasks only. These nineteen were thus all classified “intermediate.“18 Similar very large proportions of subjects are consigned casually to intermediate status in most Piagetian experiments, as frequently 50 percent and more of subjects do not display consistent operation of a structure across different materials. In addition, Piagetian theory seems increasingly willing to acknowledge the role of experience in affecting students’ ability to perform particular tasks.19

Thus if we observe, as is the case, that a child’s ability to perform a task with a particular logical structure seems to tell little about whether that child can perform a logically identical task with different materials, Piagetians can claim that these discrepancies can be caused by decalages, by the child’s being “intermediate,” or by some extraneous experiential factor. One can only conclude that if the kinds of structures exist that are the very core of Piaget’s theory they have very weak effects, and have only slight and wavering explanatory force. If such cognitive structures are the most important determinants of what can be learned and understood, their effects should surely not be so elusive in the available data.

If we look at those surveys of empirical data from studies aiming to find evidence of consistent responses corresponding to the use of Piagetian cognitive structures, we find conclusions such as the following: “One would become cautious about assuming ‘conservation’ to be a skill more general than it is content specific”;20 or, “Despite progressive refinement of method aimed at removing from the experimental data all variations due to extraneous factors, the most striking feature of the results of these studies is the degree of inter- and intra-individual variety obtained”;21 or “These data suggest that the assignment to a particular stage seems to depend upon the task used as a criterion, and the implication of structure is that it should not ";22 “In general, logical task structure does not seem to be a good predictor of behavior across situational variations.“23

Piaget’s theory over the decades has amassed a considerable baggage of ad hoc metatheoretical glosses, whose combined contribution is to remove much of the theory from the realm of the testable. If discrepant data can be explained away as a result of decalages, or of intermediate status, or experience, or learning, we are left to wonder what could count as evidence against the theory.

LANGUAGE OR COGNITIVE STRUCTURE

One of the difficulties in convincingly exposing and representing abstract cognitive structures is that their existence is inferred from children’s performance of various tasks and that performance is invariably tied up in complicated ways with language—the language used by the experimenter in giving instructions, the language children use in giving their responses, the degree of understanding and meaning shared by adult experimenter and child subject. A consistent criticism of Piaget’s work has been the casual ease with which he has read through children’s language use to their cognitive structures.24

How do we know when we ask children to perform particular tasks that they understand what we say? If they fail in the task, if they give a wrong answer, how do we know it is not because they have misunderstood due to some linguistic confusion rather than because they have not yet developed the cognitive structure that would enable them to get it right? The problem for the researcher is posed well by Jan Smedslund:

During the prolonged debates about criteria for the presence or absence of certain structures, notably conservation and transitivity. . . I came to recognize a problem which seems to have no satisfactory solution within Piagetian psychology. In order to decide whether a child is behaving logically or not, one must take for granted that he has correctly understood all instructions and terms involved. On the other hand, in order to decide whether or not a child has correctly understood a given term or instruction, one must take for granted that the child is behaving logically with respect to the implications which constitute his understanding. . . . There is a circular relation between logicality and understanding, each one presupposing the other, and this constraint forces the researcher to make a choice of which one to take for granted and which one to study. . . . In so far as Piagetian psychologists focus on logicality as a variable . . . they are making an epistemological error and are out of step with everyday human life as well as with all useful psychological practice. . . . It is a matter of historical record that children who failed on tasks were often simply described as non-logical, and the problem of criteria of understanding has received relatively scant attention in Piagetian literature.25

If Piaget and his followers are not adequately distinguishing among reasons children succeed or fail at certain tasks, it may well be that a cause they are ignoring is responsible for what they attribute to the presence or absence of a particular cognitive structure. The data they use as evidence of the achievement of a particular cognitive structure may be rather a record of children’s normal age of mastery of a linguistic convention that enables them to understand in a different way what the experimenter means.

The Piagetian position on this seems initially straightforward. Piaget asserts strongly that linguistic competence follows on, and is only one among other expressions of, the development of cognitive structures and the operations they make possible. “Linguistic progress is not responsible for logical or operational progress. It is rather the other way around.“26 Children’s language use and comprehension, then, provides only a delayed reflection of underlying cognitive structures. Piaget also asserts that there is considerable murkiness in inferring thought or cognitive structure from language. He notes that language expresses cognitive structures only very vaguely, and points out that his inferences are based not just on language but also on all the child’s various behaviors in the experimental situation.27 He argues that “language is not thought, nor is it the source or sufficient condition for thought.“28

Yet despite the claims that language is determined by cognitive structure and that it can provide only a very hazy reading of present cognitive structures, the experiments whose results provide the bulk of the support for Piaget’s theory rely very heavily on experimenter’s instructions and questions and on children’s verbal responses. Indeed, when some training experiments seemed to challenge aspects of the theory, a major criterion enunciated for judging whether actual structural developments had taken place was “the child’s justification of his answers.“29

So if one looks at the classic Piagetian experiments one seems to see an assumption that language use quite clearly and directly can provide access to thought, or cognitive structures. If such were the case one might test the theory by seeing whether linguistic changes in the context of the experiments, while preserving their logical form, would produce significant increases in children’s successful responses. If one found that they did, this would seem to count as disconfirming evidence against the theory. But Piaget asserted that the path between language and cognitive structures is very murky and complex, so it is not clear what the results of such experiments would show. That is, once again the metatheoretical glosses serve to protect the theory from easy testability.

Even the most general and apparently straightforward Piagetian claim about cognitive structure’s determining language is difficult to test. (This is especially the case when we consider the additional claim that language is partially figurative and partially operative, and that the operative functions seem to be generally ignored by Piagetians.) A recent attempt to test this most general claim, however, concludes that “a perusal of Piagetian literature on language acquisition, in conjunction with the data reported here, provides scant evidence for the contention that language skills are a reflection of more general cognitive operations.“30

When a father phones home and asks his four-year-old son, “What are you doing, Michael?” he should not be surprised to be told, in that tone of voice indicating the usual bewilderment and half-suppressed exasperation at adults’ stupidity, “I’m answering the phone.” If children were psychological researchers such common phenomena would no doubt contribute to a theory about human beings’ increasing inability to decenter with age, leading to a characterization of adulthood as intellectually constrained by egocentrism. Mildly funny as this may seem, there is accumulating evidence to suggest that it is precisely experimenter egocentrism that has produced a restricted understanding of how children think. Let us briefly consider some studies that show sensitivity to children’s contexts of meanings, and see how the results impact on Piagetian claims about cognitive structures.

Donaldson notes three things that influence children’s interpretation of what we say to them: their knowledge of the language; their assessment of what we intend (as indicated by our nonlinguistic behavior); and the manner in which they would represent the physical situation to themselves if we were not there at all.31 Research from a number of sources32 confirms what any sensitive teacher or parent knows: that young children’s responses to verbal commands, requests, and questions is often quite unpredictable. Understanding of particular conventions of language that run counter to the literal meaning of the words (“What are you doing Michael?” “Answering the phone.“) can determine behavior and responses in odd ways. How far a particular convention is understood, partially misunderstood, mixed up by a bizarre association (hare/hair type confusions), is unknowable for any child at any time.

Among the classic Piagetian experiments that support the characterization of young children’s inability to decenter are those that require the children to compare a subclass with a class of objects. For example, if a bunch of flowers is made up of an unequal number of red and white flowers, children are asked, “Are there more red flowers or more flowers?” If there are, say, four red flowers and two white flowers, children under six will normally reply that there are more red flowers. Piaget claimed that preoperational children respond this way because they cannot center both on the whole class and the subclass at the same time in order to make a comparison between them. The cognitive structure that enables this particular task to be performed successfully is assumed not yet to have developed in such children. Is this normal failure indeed due to children’s lack of a particular cognitive structure, or due to the fact that they do not understand what the question is asking them to do? And if the latter, is it the case that this reflects something other than the development of the appropriate structure?

Donaldson, after pointing out that the question about comparing red flowers with flowers is very unconventional and tends to confuse adults until stress is put on the unqualified second “flowers,” describes an experiment devised by James McGarrigle to make the task less confusing. He used four toy cows—three black, one white. He laid them on their sides and told the children that they were sleeping. He then asked two questions whose logical forms are identical. First, he asked the classic Piagetian question, “Are there more black cows or more cows?” Twenty-five percent of the children answered correctly. McGarrigle then asked, “Are there more black cows or more sleeping cows?” Here again the children have to compare a subclass with the class of sleeping cows. Forty-eight percent of the children answered correctly. The addition of an adjective led to a significant improvement.

McGarrigle then experimented with emphasizing the contrast between the subclasses, trying to reduce what seemed like irrelevantly confusing aspects of the tasks.33 While the tasks retained the same logical form, they were gradually disencumbered of linguistic and perceptual confusions. The clearer the tasks were made, the higher the rate of successful responses became, until well over 80 percent of young children showed no difficulty decentering and casually comparing a subclass with a class.

A similar effort to see whether children’s difficulty with certain conservation tasks was due to the artificiality of the classic Piagetian form was conducted by S. A. Rose and M. Blank. The experimenters conclude that their studies support “the notion that the implicit contextual cues which the child first encounters play a large role in determining the response he will employ on this and all subsequent related tasks.“34

What does Piaget’s theory describe? What evidence do the results of experiments such as those reported by Donaldson provide either for or against the existence of the kind of cognitive structures in terms of which the theory is articulated? Theories like Vygotsky’s,35 or that which is sketched by Donaldson,36 seem much more parsimoniously able to account for the array of data we now have about language and cognitive development than Piaget’s. Indeed, Piaget’s theory seems able to accommodate much of the data only with much creaking and straining and with the support of a superstructure of metatheoretical glosses. The claim that language use is determined by the development of cognitive structures is a difficult one to sustain. If we doubt that such cognitive structures exist, there is nothing in the available array of relevant data that asserts their reality. Given the role of language in the experiments that have provided the basic data on which the theory was constructed, the assertion that the development of cognitive structures is responsible for language development is not a conclusion that itself rests on any data but one that is inferred from the truth of theory, which is presupposed.

LEARNING CONSTRAINED BY DEVELOPMENT

One of the most important claims for educators that is made in Piaget’s theory is that learning is constrained by development. Piaget claims that “teaching children concepts that they have not attained in their spontaneous development . . . is completely hopeless”;37 or “the notion of competence has to be introduced as a precondition for any learning to take place.“38 If Piaget is right in his claims about the nature of cognitive structures that develop spontaneously and their relationship to learning, we might expect to find that learning cannot significantly affect the development of structures and that children cannot be induced to learn and understand any concept before the relevant underlying structure has developed. Once imported into education, then, Piaget’s theory serves as a “readiness” model; it describes a sequence of developments that can instruct us about what a child is ready to learn.

Some of the experiments reported earlier in this chapter might be seen as disconfirming evidence against this claim. That is, some of them suggest that very young children can be taught, say, to conserve quantity if only the teacher/experimenter is pedagogically skilled and sensitive. But, as indicated above, much of this learning can be discounted as merely figurative. In Piaget’s view, teaching or training of this kind “produces either very little change in logical thinking or a striking momentary change with no real comprehension.“39 What gives evidence of real comprehension is the child’s recognition that what has been learned from such experiments involves not simple contingent or figurative matters that may well be remembered and used in making responses but rather their recognition that what occurred was a result of logical necessity. This is the major criterion by which we can measure whether operative/developmental knowledge has been acquired. “This logical ‘necessity’ is recognized not only by some inner feeling, which cannot be proved, but by the intellectual behavior of the subject who uses the newly mastered deductive instrument with confidence and discipline.“40

We have available results from a large number of “training studies” designed either to test or to elaborate this claim of Piaget’s theory. But, again, the difficulty of unambiguously exposing abstract cognitive structures that are inferred from performances on particular tasks leaves the results of these studies a subject of continuing dispute between Piagetians and their critics. Some of the earlier North American training studies, some of which tended to take a rather simplistic view of Piaget’s theory and its claims about development and learning, were taken as disconfirming the theory if children could be taught to, say, conserve earlier than the theory predicted. In response to such studies, and to more sophisticated ones that seemed to challenge the theory, Piagetians have attempted to spell out in more detail what kinds of things give evidence of real structural change, rather than of mere figurative learning.

The difficulty in this area is not with any ambiguity in the training-study results. Even before the criteria for “real learning” were articulated there was considerable data from such studies that seemed to meet these criteria and disconfirm Piagetian claims.41 The difficulty in getting clear what is the case in this area is in getting clear exactly what the Piagetian claim is, and what Piagetians will accept as a test of it. The earlier claim seemed clear and unambiguous. It asserted simply that the spontaneously developing cognitive structures determined what could be meaningfully learned. But the results of cross-cultural studies suggested that this simple assertion needed to be elaborated. If spontaneous development relied on interactions with the environment, then perhaps some interactions with some environments might well better stimulate the developmental process than might others. This would account for the considerable differences in the rate and extent of development exposed by cross-cultural studies. The present problem is compounded by the Piagetians’ offering no account of why some interactions with some environments should so powerfully stimulate development, as in Geneva or New York or London, and other interactions with other environments stimulate virtually no development beyond the earliest stages, as in parts of Australia and Africa.

If the nature of the environment and the subjects’ interactions with it can have such a huge impact on development, one might assume that teaching that optimally organizes the environment to encourage cognitive development will be more successful than teaching that does not. Indeed, this is a tenet that guides much Piagetian educational practice, but the nature of its theoretical support remains hazy. Similarly, the ability of some training studies to induce significant learning of operative concepts has been acknowledged, but “operativity is malleable only within certain limits.“42

The Piagetian training studies reported in Learning and the Development of Cognition explored how far and in what circumstances learning could affect development, that is, the degree of malleability in operativity. The results of these studies have been taken as confirming the Piagetian hypothesis: “that under certain conditions an acceleration of cognitive development would be possible, but that this could only occur if the training resembled the kind of situations in which progress takes place outside an experimental set-up.“43 The odd part of this is that while we know very little about how such cognitive development takes place in experimental setups, we know even less about how it occurs outside them; also, the use of “accelerate” presupposes a natural pace. In addition, these studies indicated that progress was dependent on how close subjects already were to acquiring the cognitive skill being trained. This was taken as confirming Piaget’s claim that if subjects

are close to the operational level, that is, if they are able to understand quantitative relations, the comparisons they make during the experiment are enough to lead them to compensation and conservation. But the farther they are from the possibility of operational quantification, the less they are likely to use the learning sequence to arrive at a concept.44

In addition, the studies are taken as confirming the importance, or necessity, of children’s being active discoverers in order that their interactions with the environment stimulate developmental progress. “In terms of successful training procedures, this means that the more active a subject is, the more successful his learning is likely to be.“45 (Unfortunately for the testability of this claim, it is followed by the observation that children “can be mentally active without physical manipulation, just as [they] can be mentally passive while actually manipulating objects. “46) Given the manner in which concepts develop, according to Piaget’s theory, children’s wrong answers, for example, failure to conserve, “should not be regarded as errors which need to be eliminated by suitable training.” Rather they are evidence of “uncoordinated schemes . . . based on a preparatory, ordinal type of reasoning . . . which cannot, and for that matter should not, be eliminated by coercion.“47 “Coercion” here refers to any method that contravenes the “natural” course of events, the “necessary stages of development.“48 This seems to involve the prediction that methods that are coercive—for example, telling children whether their answers are right or wrong—may lead to figurative learning but will not stimulate operative, structural development.

Let us briefly consider a few of the experiments that are commonly cited by Piaget’s critics as disconfirming his claims about development-constraining learning.49 In the following brief review I will draw heavily on Brainerd’s “Learning Research and Piagetian theory.“50

In Chapter 1 of Learning and the Development of Cognition, Inhelder, Sinclair, and Bovet report an experiment concerned with training children to conserve quantity, using an apparatus of containers and water. They found that none of the children who failed the pretests succeeded in acquiring conservation, while sixteen of the nineteen children who were classed as “intermediate level” on the pretests showed improvement in their reasoning in one of the two post-tests and ten even acquired conservation. Thus “the most striking finding was the existence of a close relationship between the child’s initial level of development (pretest) and the types of reasoning he used in the training session.“51 The finding that none of those who failed the pretests learned anything seems to confirm Piaget’s view that “teaching children concepts that they have not attained in their spontaneous development . . . is completely hopeless. “52 In non-Piagetian terms these results suggest that children who know a fair amount about something beforehand manage to talk about it more sensibly and learn more about it than do children who knew nothing about it beforehand. That is, the most striking finding is one that would be predicted by any learning theory.

In a similar experiment, Sheppard recorded quite different results.53 The main differences in Sheppard’s experiment were that his subjects were passive observers rather than active participants and that they were told whether their responses were right or wrong. In addition, all of his subjects failed the pretests for conservation. This combination—nonconservers in a passive condition given verbal feedback in responses (a “tutorial” method)—should, according to the predictions of Piaget’s theory, lead to no progress at all. In fact, between 30 and 40 percent performed perfectly on various of the post-tests and nearly all subjects showed some progress. The learning generalized to four conservation concepts—number, mass, length, weight—in which they were not trained, and the progress proved to be stable across a two-month interval.

The Piagetian experimenters’ failure to achieve any progress with nonconservers was taken as confirming the theory’s claim that developmental level constrains learning. But in an experiment conducted by Gelman, children who failed pretests for conservation of number, length, mass, and liquid quantity later performed perfectly in post-tests in the two areas in which they were trained—number and length.54 Also, they gave correct responses about 60 percent of the time on post-tests in the two untrained areas. Murray conducted an experiment with children who had failed pretests for conservation of number, space, mass, liquid quantity, weight, and discontinuous quantity. About 79 percent of these subjects learned conservation in all six pretested areas, and 81 percent generalized to conserve other areas not trained.55 Emrick trained four-year-olds on number and length conservation. In post-tests for number, length, mass, and liquid quantity conservation more than two weeks after the training sessions, the subjects were successful on 73 percent of the items on the number and length tests. They also generalized to perform successfully on 41 percent of the items in tests for conservation of mass and liquid quantity.56

Now, clearly, getting right answers on tests after such experiments is not what Piaget’s theory is about. Neither are such experiments of any value in furthering knowledge of the underlying processes that the theory is about. Their purpose, however, is not to elaborate the theory but to try to find out ways to test it. We will consider the value of these, and the very many similar experiments that report similar results, below.

First we might briefly consider the main experimental support for Piaget’s belief that teaching conservation concepts to preconservers is completely hopeless. Apart from the Inhelder, Sinclair, and Bovet experiments referred to above, the other experiments commonly cited as supporting the Piagetian position are those conducted by Smedslund and Wohlwill.

Using tutorial methods, Smedslund failed to train nonconservers to conserve weight.57 Hatano has pointed out that Smedslund’s equipment included a pan-balance and his procedures did not include any precaution to ensure that the young children in the experiment understood how it worked.58 In others of his set of experiments similar precautions were not taken to ensure that children understood what was happening-raising the dilemma between comprehension and logicality that Smedslund has so precisely pinpointed since (above, p. 462).59 By eliminating these confusions, and performing experiments demanding the same logical task from the subjects, Gelman succeeded in achieving impressive improvements in number and length conservation, as reported above.60 Hatano and Suga similarly substituted a somewhat different experimental setup that avoided the potential confusions inherent in Smedslund’s. They succeeded in training 60 percent of their subjects to successful number conservation, and there was successful generalization of the ability, and stability over time.61 Similarly, design flaws were identified in Wohlwill’s experiments that might well have been the cause of the subjects’ failure to learn to conserve. 62 Once such flaws were eliminated, similar procedures without the complicated apparatus have succeeded in training significant numbers of preconservers to conserve.63

In addition to these studies, there is now available massive evidence that “developmental concepts” can be taught. These studies would seem to show with overwhelming force that Piagetian claims are simply wrong, and that developmental stage as they characterize it does not constrain what can be understood by children. But of course no Piagetian accepts this. Much dispute has focused on what is commonly called the “criterion problem”: What criteria do experimental training results have to satisfy in order to count as “real learning,” as changes in cognitive structure? Each time Piagetians have spelled out criteria, some training studies have met them. However, this does not prove the inadequacy of Piaget’s theory to Piagetians; it proves only the inadequacy of the statement of criteria, or the simplistic way the (usually North American) experimenter has interpreted the criteria.

The American training studies that attempt to test Piaget’s theory focus on those parts of the theory that seem to yield clear empirical claims. We have already seen that either much of the theory is untestable or it is very difficult to interpret the results of such tests. Piagetians seem to so presuppose the general truth of the theory that they display some irritation at these American training experiments. Piaget saw them simply as part of what he called “the American question” of how fast one can “accelerate” the (natural) developmental process. To Piagetians, that learning is constrained by development seems almost a definitional matter; that is, learning effects are identified by their following the development of a particular cognitive structure. The idea of testing to see whether this is the case seems to strike them as bizarre, and as prima facie evidence that such experimenters cannot understand the theory. The nonpsychologist reading Piagetian and North American studies is struck (or at least this one is) by the lack of engagement of discussion. My view is hardly unbiased by this point, I suppose, but the main hindrance to such engagement seems to lie in the degree to which Piagetians look at the data through the theory rather than using the data to reflect back on the theory.

Piagetian defenses against the accumulating mass of apparent counterevidence remain in place. First, we have the assertion that the American training studies are achieving only figurative knowledge in their subjects. The fact that this knowledge meets all the criteria that Piagetians state for real comprehension means only that the criteria have not been stated, or interpreted, strictly enough. Indeed, what is interpreted by critics as confusions in Piagetian experimental situations are to Piagetians tests of logicality; it is precisely such things that subjects who have developed the relevant operatory structure can work out, and that those subjects who have not, fail to work out. Another defense open to Piagetians is simply to redraw the characterization of the preoperational stage to include more skills than is at present allowed; this would be merely a part of refining the theory in light of new data. Alternatively they may point out that, in their attempts to find some clearly testable part of the theory, North Americans have fixed on the stage concept and interpreted the whole thing far too literally. That is, American critics tend to see the stages altogether too crudely as exemplified in success or failure on particular tests. As Karmiloff-Smith put it:

Stages were initially used by Piaget as a heuristic for seeking far from obvious developmental links across widely differing conceptual domains. From the onset, Piaget’s stage distinctions were not based on success or failure per se, but always pinpointed intermediate, oscillatory levels. . . . The stage concept can only remain a valid heuristic today if the stages described represent more than an analytic tool for the observer and are shown to be psychologically functional for the child. In other words a shift of emphasis is suggested from conservation-attainment to the psychological function of conservation-seeking.64

Thus if a child fails a conservation test, what is more important for assessing developmental level is to analyze responses “in terms of whether they represent powerful heuristics in development or merely shortcomings to be surmounted later.“65 If one presupposes the truth of the theory, then it might provide a reference that would allow one to carry out such analyses. But it leaves even more obscure the problem of how someone might find out whether the theory is articulated in terms of real cognitive structures.

One difficulty in comparing Piagetian research on the theory with that of North American critics is that the former is concerned with elaborating and refining the theory, presupposing its general validity, and the latter are concerned to test its validity. A further difficulty, indicated above, is that Piagetians seem to interpret American training studies less as tests of Piaget’s theory and more as some kind of unnatural scheme aimed, futilely or dangerously, at accelerating the natural process of development. Thus, Karmiloff-Smith concludes the paper cited above: “Well-meaning learning theorists who train small children to ignore perceptual cues, to sidestep misconceptions by reciting verbal rules, and so forth, are doing these children a great disservice. They seem to lose sight of the fact that there is a profound psychological importance in being a nonconserver.“66

It is worth considering this passage briefly. The Piagetian learning experiments referred to above were indeed concerned with how best to help children develop operative knowledge, and they concluded, as predicted by the theory, that active self-discovery methods are best and other methods are useless. American training studies are trying to test the validity of the theory’s predictions; they are not, as Karmiloff-Smith seems to think, exemplifications of preferred pedagogical methods. The nefarious training activities referred to include things like correcting children’s false belief that, say, the quantity of water changes when poured from a fat, wide, container into a long, narrow one. Those who think that one might sensibly point out to young children that the quantity of water does not change are accused of doing children a “great disservice.” There is no evidence to support this wild claim. Nor do those who think it sensible to point out such errors to children “lose sight of the fact that there is a profound psychological importance in being a nonconserver”; rather, they are properly assuming that no such “fact” has ever been established.

CONCLUSION

We have been looking for evidence for or against the existence of Piagetian cognitive structures because nearly all the implications derived from his theory to education require them. Particularly the distinction between the two kinds of knowledge, operative and figurative, between development and learning, suggests that there are two distinct processes that educators have to take careful account of.

Our search for some clear empirical basis for the distinction, and ‘for the distinct existence of the conceptual structures, has not been successful. If we look at Piaget’s writings where the distinction is developed we may find enormous theoretical elaboration of the distinct kinds of knowledge and their sources and their development. When we search this writing for some basis in reality for the distinction we find a simple anecdote such as the one recounted above of the boy discovering that the ordering of stones was independent of their perceptual qualities. We are then told that this kind of logico-mathematical knowledge is not preformed and is not the same as trivial learning of facts. On this simple observation the vast baroque theoretical edifice is then elaborated, and all empirical findings are interpreted in terms of this distinction. It need hardly be said that one might account for differences in kinds of knowledge in many ways. The point here is simply that this massive theoretical structure does not rest on any evident empirical ground, and is built from a simple distinction in kinds of knowledge that remains somewhat arbitrary.

If Flavell’s judgment that Piaget’s theory is in serious trouble is an accurate reflection of the psychological state-of-play (and I have tried to give some reasons for thinking it is), this has obvious implications for those educational practices and programs that base themselves on the theory.67 It implies that programs that make the achievement of concrete or formal operations an objective are engaging in an epistemologically bizarre activity. It implies that teachers who accept Piagetian “conflict” and “discovery” methods as the most effective means of teaching are arbitrarily accepting impoverishing restrictions. It implies that those who build Piagetian curricula, fitting concepts of history or science to Piagetian stages, are similarly arbitrarily accepting impoverishing restrictions. It is perhaps not adequately appreciated that while Piagetian educational rhetoric stresses freedom, expansion, discovery, and so on, in practice Piagetian methods and curricula are most notable for their restrictions. They expose a restricted view of what children can learn (are “ready” for); they propose restrictions in the methods that might fruitfully be used by teachers; they introduce restrictions into the educational aims and objectives proposed for various programs and subject areas. These restrictions might well be justified if based on a theory that is very secure. Based as they are on a very insecure, though prodigious and historically important, theory, they serve mainly to impoverish the practice of education.

It may be objected that I have ignored all the evidence that supports Piaget’s theory and his learning/development distinction, and that I have focused only on data that are discrepant with the theory. We test theories by working out what they predict and finding out whether that is the case, and we seek predictions in areas where falsification is most likely. We do not test theories adequately by constantly replicating the same set of studies or by assuming the general correctness of the theory and seeking to elaborate some detail of it. The crucial test of a theory is less how much of the data it can account for than whether it fails to account for significant data. The phlogiston theory still accounts for most of the available data; its inadequacy is shown by those significant data it fails to account for. Similarly, Piaget’s theory is not disconfirmed by most of the data we have about cognitive development—indeed, it is responsible for unearthing much of them; it’s inadequacies are being exposed by the increasing accumulation of data it cannot account for. I have focused on these accumulating anomalies, from the theory’s point of view, to indicate the validity of Flavell’s judgment and to argue that one of the very weakest and least supported parts of the theory is precisely the point on which the connections with education rely.