The Child and his Behavior. A. R. Luria
One of the most powerful tools nurtured by cultural development in the human psyche is abstraction.
It would be wrong to assume that in the psyche of the civilized adult, abstraction is some kind of specific process or special function which combines with others to form our intellectual life. It would be much truer to argue that in the psyche of civilized man it is a necessary component of any thinking, a device nurtured in the process of personal development which is a crucial requirement, and an indispensable tool of his thinking.
Better than any other process, the development of abstraction, that pivotal condition of our thinking, exemplifies the way that a certain type of operation of our neuropsychic apparatus is entirely created, as a product of cultural development, and how, once it has been created, it transforms numerous psychological processes.
The main purpose of this book is to demonstrate the cultural genesis of numerous behavioral processes and the resulting metamorphoses in neuropsychic activity; the study of the processes of abstraction is exceedingly helpful towards that end.
As we have already pointed out (4 and 5 above) the primary, natural forms of perception in the child are distinguished above all by their concreteness. The child approaches each object as an irreproducible concrete specimen. In this sense he echoes the behavior of primitive man: he knows birch, pine, willow and poplar, but cannot name trees in general; if he, like a primitive, is asked to count, he may inquire what precisely he is required to count, as he is able to count only concrete objects; as Stern reports, he knows how many fingers there are on his own hand, but does not know the answer when asked how many fingers there are on someone else’s hand.
In other words, his thinking is thoroughly concrete; in his mind, abstract representation about number, qualities and features is still in the most embryonic forms. Piaget gives the following table, illustrating the development of these processes in the child through a concrete example:
A child of 5 can distinguish his right hand from his left.
A child of 7 can distinguish between right and left in objects.
A child of 8 can distinguish the right from the left hand of someone standing facing him.
A child of 11 can distinguish between right and left in the relationship between three objects in a row.
As we can see, even a concept such as right and left, requiring only a comparatively slight process of abstraction, develops quite slowly in a child. In even mildly complicated cases, the concept does not become fully developed until the age of 8 or even 11 years.
All of this clearly shows that the child finds it difficult to detach himself from the object perceived by him, in all its concreteness, and to identify in it appropriate features that are common to numerous other objects.
The development of the process of abstraction, which occurs only within the process of the child’s growth and cultural development, is closely linked to the beginning of the use of external tools and the elaboration of complex forms of behavior. Abstraction itself may here be viewed as one of the cultural devices grafted onto the child during the process of his development. We can explore the primary emergence of this process through a concrete example, where the mutual relationship between the primitive, integral perception of external objects, and the incipient abstraction crucial to any “cultural” psychological process, becomes particularly obvious.
Here we wish to dwell on our own studies of the development of the counting process in the child, Counting – involving the use of figures and numerical operations – is one of the most typical devices elaborated by culture, which has become firmly incorporated into the psychological inventory of civilized man. The use of figures usually involves the maximum abstraction; therefore, when we talk about ordinary counting processes we are ipso facto talking about cultural functions characterized by maximum abstraction from the concrete forms of objects. This cultural function did not, however, develop instantaneously; in experiments with the child we can examine the whole process quite clearly. We might ask ourselves what takes the place of abstraction in children who have not yet elaborated it?
We gave three or four children sitting at a table some cubes; while playing, a child of 4-5 years was to divide the pile of cubes into equal parts, and distribute them among the players. When the distribution was completed, the child was asked whether each of the players had the same number of cubes; he had to compare the number of cubes distributed and equalize them where the numbers were unequal.[33]
An adult in possession of adequate counting devices would merely count up the cubes and compare the quantities thus obtained. The child still lacks such abstract devices for calculation. Our young test subjects resolved the problem quite differently. In order to compare the separate quantities of cubes they arranged them in a certain shape, and then compared the shapes of the various piles. The children based these comparisons on a variety of shapes. Some of them were rough outlines of familiar objects. Our 5-year olds used the draftsmen or cubes that had been distributed to make a “bed”, “tractor”, or other familiar objects. If each of the participants in the game succeeded in producing such an “object”, they considered the distribution to be correct; sometimes they would make first one “tower” (C), and then others, nearby, levelling them off by touch; or they would lay out their draftsmen in an “arc”, or a “road”, making them all the same size just as concretely, on the basis of their shape.
All of these cases have one thing in common: immediate concrete perception of shape predominates in the child’s operations. As the apparatus of abstraction is not yet adequately developed, the child replaces it with the primitive application of natural processes of perception, in which shape replaces counting as a means of comparison.
The processes we have just described occur in children who have in many cases not yet mastered counting; yet even among children at the first levels of the development of calculation, the immediate perception of form still continues to play an enormous role, often determining the nature of the counting processes themselves.
We asked a child aged 7-8 years, who already knew how to count, to add up some cubes lying in no particular order, and others arranged in a line. As was to be expected, the child performed the second of these operations faster and more correctly: he did not get confused, or count the cubes twice, as often happened when they were laid out at random. Instead, form (a path) precisely determined his count. Then, in order to verify the extent of this influence of form on the counting process, we arranged the cubes so that two distinct systems, sharing common elements, intersected each other. For example, we would give the children a cross made of cubes, or two intersecting squares (Figure 30) and asked them to add up the number of cubes in each figure proposed. If the child’s abstract counting process was adequately developed, we might expect the counting process to take place correctly. That is not at all what we found in the child.
The experiment we propose provided a good opportunity to observe the actual structure of the counting process, its sequence, and structure (the child points a finger at each cube counted). By observing the structure of the process we can identify a number of phases in the cultural development of the child’s psyche.
We have before us a 3-year old. He is still unable to count sequentially, and merely points a finger at the cubes he is counting (we naturally pay no attention to the correctness of the “counting” that accompanies such pointing). In most cases, regularity of shape typically has not yet induced any sequence in the child’s counting; he starts counting from one end of the cross, switches to the other, then returns to the first, pointing at the same elements repeatedly. The process is typified by primary shapelessness.
We found the same to be true of a retarded child – a 13-year-old hydrocephalic, who counted just as chaotically, poking her finger repeatedly at the same cube and returning to cubes already counted.
By the age of 6-7 years, the process assumes substantially different forms, with shape having a decisive influence on counting.
A child of this age already counts the cross by counting up the cubes in a straight line, while adhering to the shape of both squares in the second illustration. Yet it is particularly interesting to note that this influence of shape is so strong here. Abstract calculation, free from the laws of the visual field, is so insignificant that the cubes belonging to both systems (the middle cube in the cross and the two intersecting cubes in the squares) are counted twice or as many times as they fit into the system of shapes. In the first case, the cross is counted as two intersecting linear systems, while in the second we have two intersecting squares. Each time, on reaching the square located at the intersection, our child counts it once again as an element of that particular series. Here again we can see that the cubes are not being counted separately, but as members of a given concrete system.
Our experiments showed that in the easier figure (the cross) mistakes due to the inadequate development of abstraction were made by 62% of preschool children of an average group, and by only 6% of the school children in group 1. However, in the more difficult case (the square within a square) all the preschool children of the average group and 12% of the school children in group 1 produced the same inaccurate count. These experiments show that we can not only confirm inadequate development of abstraction in childhood, but also indicate the timing (and in some cases, the pace) of its onset. [34]
Only later on – from our observations, by the age of 9-10 (though this depends on the child’s intellectual age) – does the “cultural” process develop to the point where it can break free from the influence of the visual field and the laws of concrete perception. Not until then does the child begin to count the elements of a given figure sufficiently correctly, without forgetting to abstract himself from the shape, or counting the same figure twice. One and the same thing, belonging to different systems, continues to be perceived for a long time as two different things; and the echoes of this concrete thinking, caused by concrete situations, remain in the human psyche for a long time to come.
We have also observed this same phenomenon in adults and in some complex real-life situations. In an experiment conducted at the Berlin Psychological Institute, the test subject adult or child was left alone in a room where a number of objects, including a small mirror, were laid out on a table. The test subject, faced with an indefinite wait, began to look through the individual objects. He tested the pendulum and looked at himself in the mirror. As we can see, the mirror, being placed in a certain situation, was used in the normal way. The interesting thing, however, is that when the experimenter suggested using it as a reflector to steer a sunbeam to a particular point on the wall, the mirror lost its previous functions, as not one of the test subjects tried to look at himself in it: they all treated it as an “instrument”, with entirely new functions.
This process, whereby an object, depending on the situation, acquires new characteristics, represents a special type of attitude to the objects of the external world. Drawing on our research on young children, when we found that a cube belonging to two different systems is perceived twice, depending on the “context”, and moving to complex “cultural” forms through the functional use of the objects of an external world that differs in different situations, we come to a relative type of thinking, with clear structural traits. Nonetheless, the elaboration of a stable attitude towards objects, and the creation of the “invariant” that enables us to recognize and assess objects regardless of the ambient situation still require a considerable amount of abstraction.
Let us return, however, to the process of counting in the child and probe from another standpoint the characteristics of the transition from primitive forms of the perception of quantity to complex “cultural” forms.
We asked a child of 7-8 years who knew the meaning of “odd” and “even” to find whether the number of cubes given to him was odd or even. The first time we gave him four cubes arranged in a square (Figure 31), whereupon he promptly replied that they were even. The speed with which he did this seemed suspect, and we noticed that he was not counting the individual cubes with his eyes, but simply looking at the entire figure as a whole. For a control we gave him a second figure (shown in Figure B) consisting of five cubes; again the child instantly told us they were odd. We naturally began to suspect that the child was not counting the cubes in order to determine whether they were odd or even, but merely perceiving the form, in the belief that regular figures were always even, and irregular or “incomplete” ones were odd. To be quite sure, we next gave him a provocative figure (Figure C) in which nine cubes were arranged in a square. Quite as promptly, the child replied that the figure contained an even number of cubes. The converse combination of ten cubes arranged in an irregular shape (Figure D), elicited a confident statement that there was an odd, number of cubes. We then tried to present the experiment even more starkly, by changing the shape in which the cubes were arranged in full view of the child, for example, by changing Figure 10 to Figure E. The child’s immediate answer was that while the first figure contained an even number of cubes, the second was clearly odd.
These curious judgments certainly did not mean that the child had misunderstood our instructions. Several concrete examples given to him orally confirmed that his understanding of odd and even was correct (he always found nine shoes to be odd, and ten to be even). The reason for our result was that the child always perceived the cubes offered to him as a whole concrete shape, and that for him the perception of that shape replaced the process of counting, which he still found difficult and alien.
The process of abstract numerical operations develops in the child quite late. In fact it is only under the influence of school and the cultural environment that the child elaborates for himself this specific cultural device, and that all of the processes just described are noticeably changed.
During the first few years of school we do not find such processes involving the replacement of counting by the primitive perception of shape. The child’s mastery of abstract calculation and the decimal system frees him to a great extent from the absolute dominion of the primary laws of the visual field, which makes the child’s thinking in the early years of his development purely empirical, concrete and dependent on immediate perception.
Thinking, which in early childhood had been a function of the perceptions of shapes, is gradually emancipated and elaborates its own new cultural devices; as it changes, it gradually turns into the kind of thinking we are accustomed to seeing in the civilized adult.