Cognitive Development

The Child's Acquisition of Diagonality

David R. Olson

• Publisher: Psychology Press
• Year: 2013
• ISBN:
  9781134996247
• Edition: 1
• Topic: Psychologie
• Subtopic: Histoire et théorie en psychologie

When this book was first published, David Olson was examining the developing representation and use of diagonals in the context of much larger questions, questions also explored by Vygotsky, Cassirer, Gombrich, and Bruner. These include such issues as conceptual development, conceptual change, and stage-like transitions in one's knowledge and belief. Some of these problems remain at virtually the same stage of solution to this day. Other problems have indeed been solved or at least come closer to solution, leading the author to think about the precise cognitive representations that allowed for the cognitive growth he examined in such scrupulous detail. The author hopes that both readers and re-readers of this volume will be led to wonder -- as he did while working on the book -- just what there is about a simple diagonal that makes its reproduction so difficult. In so doing, readers will again be reminded of the remarkable resources that children bring to bear on their understanding of the world as well as the blind spots that no simple telling can quite fill in.

1

INTRODUCTION

For centuries men have been looking at the stars. Some appeared to be fixed relative to one another; others appeared to move, sometimes quickly, other times slowly. Besides simply admiring the stars, men have framed hypotheses about their apparent motion. It was long assumed to be a simple perceptual fact that the earth was fixed and at the center of the universe. It was conjectured that stars that formed the well-known stable configurations were farther away than those that appeared to move. Perhaps even those stars moved independently and at high speeds; they just looked fixed because of their great distance from the earth. The theorizing ranged widely from the three-layered dome of Thales to the spheres within spheres of Anaxamander and Aristarchus, and to the geocentric theory of planetary rotation advanced by Ptolemy. We now feel relatively comfortable with the heliocentric system articulated by Copernicus, Galileo, and Kepler, provided that we amend the theory to admit that all motion is relative. We consider all this theorizing to be the gradual discovery of the nature and motion of the planetary bodies, the stars out there that attracted man’s attention.

But such a point of view obscures one of the most interesting things about man’s contemplations. At least to a psychologist, the really noteworthy aspects of man’s theories are not the facts pertaining to the stars, but are rather man’s cognitive activities in the process of creating theories about things, including the stars. As Kepler noted, “The roads by which men arrive at their insight into celestial matters seems to me almost as worthy of wonder as those matters in themselves” (Koestler, 1959, p. 263). In my estimation, this is a fundamental psychological fact that an account of the cognitive processes must explain.

The manner in which children arrive at their insights into the structure of the universe is no less worthy of concern. How children formulate their conceptions of themselves and the world around them, and how they continuously revise these conceptions in light of further experience and the tutoring of adults is one of the concerns of this book. For example, what is the form of the child’s knowledge that permits him to deal with a diagonal pattern, and how was that knowledge acquired or developed?

But it is not at all clear how to describe man’s intellectual contributions to his theories—either the processes involved in the formulation of such theories or those involved in the comprehension of the theories formulated by others. The behaviorist suggestion that the psychological world consists of behavior or responses that are simply selected by their consequences somehow seems inadequate to account for the origin and transmission of knowledge. That a theoretical idea, such as the hypothesis that the earth is in motion, would be simply a low-probability response seems neither to be adequate to the facts nor to excite the imagination of this generation of psychologists. Progressive abandonment of a response model of psychology is more or less obvious in such areas of psychology as perception, psycholinguistics, and intellectual functioning.

If we abandon the older response model of knowledge we are left with the problem of trying to provide a credible alternative. Since our concern is with theoretical ideas, we may expect to receive some help from those whose problem it is to characterize the development of ideas in general; such an account is provided by T. S. Kuhn’s “The Structure of Scientific Revolutions.”

Kuhn has developed a historical account of the formulation, testing, and ultimate rejection of scientific models. A scientific model or theory that is accepted at some point in time he calls a paradigm. A paradigm gains acceptance because it is more successful than its competitors in solving a few problems that the members of the discipline have recognized as acute. Most of the empirical work of normal science is within such a paradigm, an enterprise that “…seems an attempt to force nature into the preformed and relatively inflexible box that the paradigm supplies” (Kuhn, 1962, p. 24). The product of that research is to articulate the paradigm, examine its implications, increase its precision, and reduce its ambiguities. The paradigm involves a set of expectancies that indicates what to look for and what kinds of solutions to expect—and, by implication, what to ignore (for example, such questions as why do like charges repel, what is force, what is a man that he can invent theories about the world). But, often because of the very precision of the paradigm, new and unexpected phenomena occur.

Discovery commences with the awareness of anomaly, i.e., with the recognition that nature has somehow violated the paradigm-induced expectations that govern normal science. It then continues with more or less extended exploration in the area of the anomaly. And it closes only when the paradigm theory has been adjusted so that the anomalous has become the expected (Kuhn, 1962, p. 53).

Kuhn documents the feverish activity and channeled attention that accompanies this detection of an anomaly—Roentgen rarely left his lab-oratory over a period of seven weeks after he accidentally noticed a nearby barium screen light up when he was studying cathode rays; it turned out to be caused by invisible x-rays. The cycle closes with the invention of a new paradigm, which amounts to a scientific revolution, that can handle the anomaly.

Science is replete with theoretical developments that fit this model. The early study of static electricity and its accounts illustrate this (Kuhn, 1962). It was early noticed that a glass rod that was “excited” by rubbing it on silk attracted small bits of paper to itself. The theory that was elaborated to account for this phenomenon postulated “affluvia,” qualities or properties that resided in varying degrees in materials which, in an excited state, reached out and captured small objects. The paradigm worked so well (one could predict the distance the affluvia would reach out on the basis of the degree of rubbing it had received) that it was unnoticed that some bits of paper first approached and then “bounced” away. Finally, when one scientist built a rod capable of holding a large charge, the rebound was so obvious that it could no longer be ignored. The observation presented an anomaly; affluvia could hardly be expected to reach out and attract, change their “minds” and repel. The recalcitrance of the anomaly prepared the way and provided the occasion for invention of the theory of positive and negative charges that defined the new paradigm.

This account from the history of science may provide the alternative paradigm for viewing cognitive development that we have been seeking. The child either begins with a model or constructs a model to deal with the events to which he is exposed. The model or schema is articulated through subsequent encounters; at first, mild anomalies are not noticed. Upon consolidation of the schema, the anomaly stands out in bold relief. The paradigm ruptures and a new schema capable of dealing with the anomaly replaces it. Some start has already been made in showing that this constructive process applies to all knowing or “cognition,” both perceptual and conceptual. Neisser (1967) has recently developed a coherent statement of this cognitive perspective primarily in regard to visual and auditory perception. Piaget (1960), Bruner et al. (1966), Werner (1948), and Sokolov (1969) have been most ambitious in applying this perspective to conceptual or intellectual development.

The study of the evolution and transmission of theoretical knowledge may then provide a paradigm for our viewing the elaboration of the child’s conceptual or intellectual world in terms of such basic processes as theory formation, hypothesis testing, detection of anomalies, and the like. While I have not attempted to work out the implications of this paradigm, it is obvious that it is radically different from the “individual differences” model, or paradigm of human intelligence that has been dominant perhaps since the time of Galton, and certainly since the time of Binet. In that paradigm, the word “intelligence” was preempted to refer exclusively to the differences between people, and not to the accomplishment of skills that are common to the species. Thus, the simple recall of digits could be considered an aspect of intelligence because people differed in their performance, but the acquisition of language, or skills of locomotion, being common to the species, could not be considered intelligent—only variance between people is examined in an individual difference paradigm.

The difference in focus of these paradigms may be indicated by the different questions that they generate. Consider one of the observations on which this book hinges: young children cannot construct a diagonal. The older paradigm would lead one to ask if some children can reach that achievement earlier than others. That variance would then be taken to define “intelligence.” The paradigm offered here would lead one to ask why young children have difficulty with such a problem. What happens in or to a child that subsequently makes it possible for him to succeed on such a task? The concern is not with rank ordering children but with uncovering the mechanisms by which all children become “intelligent.”

In order to study intensely the nature of intellectual development from any perspective, it is essential to restrict the field of study. In this book, I have narrowed the problem by studying only a limited age range, primarily three to six years, and a very limited set of problems, primarily, the diagonal. As to the first of these constraints, several respected psychologists, including Piaget (1960), Bruner (1966), Luria (1961), and White (1965) have presented a wide range of evidence strongly suggesting that some fundamental change occurs in the child’s organization of his experience around the time that the child enters school, a shift we may call the development of conceptual or operational thought. For this reason, the studies in this book examine intensively the intellectual development of children at this age.

The second of these constraints, the choice of the problem, is more difficult and warrants some discussion.

Whenever a psychologist selects a problem to administer to a group of children he makes the assumption that that problem is “representative” of either some target set of problems or of some underlying ability. This is usually described as the problem of validity. An item on an intelligence test is not created because it’s interesting in its own right, but only because it can be shown that this item is representative, that it is a valid estimate of some underlying ability. An experimental psychologist is in a more difficult position. It usually cannot be shown that the task the experimenter is exposing his children to is representative of anything at all. Examples of this could be taken from virtually any branch of psychology, but the situation in regard to concept formation is typical. One group of psychologists (Kendler, 1961) studies how a child comes to make one response to two dissimilar stimuli and takes this problem to be representative of the formation of concepts, while another (Piaget, 1960) studies how a child comes to establish a set of logical relations, including class inclusion, and takes this problem as representative of the formation of a concept. It is clear from Kuhn’s analysis that the experimental findings are due more to the paradigm than to the “structure of the world,” but as each task defines its own paradigm, and since there are an infinite number of tasks, it becomes critical to select for critical study tasks that can be judged or construed as “representative” of the domain of intellectual development. Alternatively, the representativeness of the problem may be indicated by examining the empirical findings in context of the general and basic questions that led to the psychological study in the first place. This informs the present study, because an attempt was made to examine and describe one aspect of development in such a way as to show the nature of cognitive development in general.

The focus of this book, then, is the theoretical and empirical study of the child’s development of a conceptual system relating to the concept of the diagonal during the age range three to six years. A detailed examination will be made of why a young child has difficulty with such a problem, and what occurs during development that removes this difficulty. In the context of these empirical arguments, we shall be examining such theoretical questions as the nature of intellectual skills and conceptual or symbolic knowledge, as well as the role of experience and instruction in their development. The study will conclude with a description of the child’s reconstruction of the diagonal in terms of what at least poses as a general model of perceptual and intellectual development, and accounts for, among other things, man’s increasing ability to apprehend and theorize about the motion of the stars.

While the relevance of our account of intellectual development in terms of the child’s acquisition of the concept of the diagonal must be judged according to a relatively strict criterion of “representativeness,” the selection of the problem was not formally dictated by that criterion. It was selected because it appeared interesting and puzzling, an anomalous observation that failed to fit into (at least my own) prevailing cognitive theory. As part of the pilot work in connection with an experiment on conceptual strategies (Olson, 1966), a series of models or patterns of various geometric shapes were constructed. These patterns were formed by an array of red dots arranged on a gray sheet of paper to form a pattern such as a line, a square, an E, a diagonal, and various other patterns or models. These models were then to be used as a guide to 5- and 6-year-old children who were to press the bulbs on the “bulb-board” that corresponded to the array of dots on the models. The bulb-board, which is shown in Fig. 1–1, shall be described more fully later. The first child that we tried with these materials, Jeff M., a bright 5-year old, looked at the patterns on the model, then went and directly pressed the corresponding bulbs on the bulb-board. He did this with patterns such as a simple top row, or more complex patterns such as the entire outside edges of the bulb-board, or patterns of an E or an H. It then came as a surprise to us that when we showed the child a simple 5-bulb pattern of the diagonal, he looked at the pattern and then pressed bulbs, apparently at random. It was as if he had not looked at the model. We then had the child look back at the model, run his finger over the pattern on the model, and try again. It made no difference; he continued to press almost randomly. What was there about the diagonal that constituted such a problem for the child? Within a week it was clearly established that 7- and 8-year-old children had no difficulty with the diagonal. What happened in the meantime that made the problem so easy for the older children? Our young but persistent child continued in his attempt to copy the diagonal, but with little improvement. When the child did manage to hit one of the diagonal bulbs, thus causing it to light up, he appeared not to notice that it was part of a sequence of the diagonal bulbs, part of a pattern. On one occasion we interrupted the child long enough to press down all five of the correct bulbs simultaneously. The child appeared delighted and quickly began pressing each of five diagonal bulbs in sequence. His success was short lived; as the memory of the bright visual configuration faded, so did his ability to press the diagonal bulbs. After about 15 seconds, he was back to where he had been at the beginning.

Fig. 1–1. Apparatus used in the experiments. (From Bruner, J. S., et al. Studies in cognitive growth. New York: Wiley, 1966.)

About a year or so later the child was able to look at the pattern and copy it much as an adult does with little recollection that such a problem could ever have been difficult. But what has happened in the mind of the child that makes this later success possible? It is that transformation over that year or two interval that has been our primary concern.

The purpose of this study then, is to accumulate and examine some evidence that will permit us to refine our conception of the nature of intelligence of the child and its transformation over the ages of four to seven years. This development, which may be described as the beginnings of operational or conceptual thought, will be examined by reference to the child’s developing ability to copy a diagonal pattern. The study is programatic, if that is not too exalted a term for the gropings reported herein, in that the original hypotheses were somewhat vague, and that each subsequent study was designed to refine the conclusions and to eliminate alternative explanations of the results.

In the process of this study we have given the diagonal problem to almost 1000 children in the contexts to be described presently. The picture one gets of the child and his apprehension of the world resembles that described by Gombrich (1960) of what an artist sees when he looks at the world:

The individual visual information … (is) entered, as it were, upon a pre-existing blank or formulary. And, as often happens with blanks, if they have no provision for certain kinds of information we consider essential, it is just too bad for the information (p. 73).

The more critical kind of question is why does that blank or formulary change to receive certain kinds of new information? More specifically, the primary questions which have been the focus of the studies reported here were the following:

When do children come to construct the diagonal?

Why is the problem difficult?

What do children subsequently know that permits them to construct the diagonal?

How do they come to have that piece or form of knowledge?

What is the relation between perception and a performatory act such as that of constructing the diagonal?

What is the role of experience and instruction in th...