reasoning: development in children

It is commonly claimed that, until the age of 6 or 7, children are very limited in their capacity for deductive reasoning. This claim is made largely on the basis of research carried out within two main traditions: that based on the thinking of Jean Piaget in Geneva, and that based on the thinking of Clark Hull in the United States.

The theories of Piaget and of Hull are in most respects opposed, and their conceptions of the nature of inference are very different. It is all the more striking that their work has led to agreement about young children's lack of competence, and indeed this agreement has seemed to many to be conclusive. More recent research, however, makes it necessary to reopen the debate.

Piaget's claims may best be illustrated by his studies of 'class inclusion'. These have demonstrated that, if young children are shown a group of, say, six flowers, comprising four red ones and two yellow ones, and are then asked whether there are more red flowers or more flowers, they are likely to answer: 'More red ones.' And they will probably justify the answer by pointing out that there are 'only two yellow ones'.

Piaget's explanation is that at this stage a child's mind is lacking in a certain kind of flexibility, a kind crucial for reasoning. Piaget points out that the child who replies 'more red flowers' will normally have no difficulty in recognizing that if you take away the yellow flowers the red ones will be left, and further that if you take away all the flowers none will be left. To reach these conclusions, however, children need only think of the class and the subclasses successively. What they cannot do, according to Piaget, is think of them simultaneously (as they must, of course, if they are to reason as to the relations between them), for when they 'centre' on the whole class they mentally lose the subdivisions, and when they centre on the subdivisions they mentally lose the totality. So the seemingly simple comparison of whole with part is impossible for them. They have no mental structure representing a hierarchy of classes, with some included in others and these again included in still broader groupings, this being of course precisely the kind of structure with which logicians have traditionally been much concerned.

The deficiency in thought that is manifested by young children in the class inclusion task is held by Piaget to be quite general. Until it is overcome children's thinking is said to consist largely of a succession of separate 'moments', poorly coordinated with one another, so that the current one is too dominant. According to this argument, young children are not good at seeing their own momentary 'point of view' as one of a set of possible points of view coordinated into a single coherent system within which reasoning as to relationships can freely take place.

Piaget claims that the process of overcoming this deficiency is one of building 'cognitive structures', for which the original 'building blocks' are overt actions — acts of combining, ordering, etc. carried out on the real world. According to him, such actions, once they have been internalized (so that they can be performed 'in the mind') and organized into systems, are the very stuff of reasoning. It is then interesting to find that, in the other major tradition within which experimental studies of children's reasoning have been carried out — namely, the behaviourist tradition, as exemplified in the thinking of Hull — there appears the same emphasis on actions that are initially overt and subsequently internalized. Beyond this, however, the theories of Hull and Piaget have little in common.

For Hull and his followers, the essence of reasoning lies in putting together two 'behaviour segments' in some novel way, never actually performed before, so as to reach a goal. For instance, one 'behaviour segment' might consist in pressing a button, which act would release a marble from a little slot; a second might consist in putting a marble in a hole, which act would open a little door and allow access to a toy. An act of inference would consist in combining these (separately learned) acts in order to get the toy. Such an inference would obviously have the form: if A leads to B and if B leads to C, then A leads to C.

Work by Kendler and Kendler (1967) has shown that young children who have learned these separate 'behaviour segments' do not readily integrate or combine them. So these investigators, like Piaget, conclude that children under the age of 7 are very limited in their capacity for inference.

There is now reason to think, however, that this conclusion needs to be modified. Simon Hewson has shown that if the apparatus and the procedure used by the Kendlers are changed in certain ways that do not alter the basic structure of the problem, then 5-year-old children can perform as well as did the college students in the original studies.

Hewson replaced the button-pressing mechanism in the first 'segment' by a drawer which the child could open. Also he played a 'swapping game' with the children to help them to understand the functional equivalence of different marbles as means of opening the little door (so that they would realize there had been nothing special or 'magic' about the marble used in their original learning of the second 'segment'). These two modifications produced a jump in the 5-year-old success rates from 30 per cent to 90 per cent.

It seems then that, whatever was the nature of the children's difficulty with the original task, it did not consist in a radical inability to make the inferential link. The conclusion that there is no such radical inability is supported by Peter Bryant (1974). Bryant argues that, in their perception of the world, young children continually make comparisons which depend on reasoning in the form: if A = B and if B = C then A = C. Thus they combine two separate pieces of information to reach an inferred conclusion.

Hewson's demonstration that the difficulty of the Kendlers' task can be greatly altered by inessential modifications has its parallel in studies of class inclusion. These have established that very slight changes in Piaget's class inclusion task can enable many young children to perform it successfully (see, for instance, McGarrigle, Grieve, and Hughes 1978). It now appears that much of the difficulty with this and other similar Piagetian tasks lies in the fact that children are powerfully influenced by context, so that they do not interpret the experimenter's words alone with the strictness and rigour which — by adult standards — a reasoning task demands. It should also be noted that evidence obtained from observation rather than experiment suggests the presence of considerable reasoning skills in children as young as 3 or 4. An example is provided by a comment from a 4-year-old who was listening to the story of Cinderella and looking at a picture of Cinderella marrying the prince. In the picture the prince looked effeminate, and the child thought it was a picture of two women. He called out, 'But how can it be (that they are getting married)? You have to have a man too!'. He appears to have been using two premisses:

1. If there is a wedding there must be a man.
2. There is no man.

And he concludes validly:

So there is no wedding.

The general conclusion which we are now justified in drawing seems to be that young children have a considerable capacity for reasoning deductively about topics related to ongoing activities in which they are spontaneously engaged. What is hard for them is to accept verbal premisses which are 'set' for them by someone else in the absence of a meaningful, supportive context. Young children do not readily constrain their thinking in this way. Cross-cultural studies (for instance, Cole et al. 1971) indicate that the same tends to be true of unsophisticated, illiterate adults.

With increasing age, and especially with the advent of literacy, people tend to become better able to turn their minds deliberately to a reasoning task and respect its constraints. But at all ages this kind of rigorous, disciplined inference is difficult for the human mind (see Henle 1962).

(Published 1987)

— Margaret Donaldson

Bibliography
• Bryant, P. (1974). Perception and Understanding in Young Children.
• Cole, M., Gay, J., Glick, J. A., and Sharp, D. W. (1971). The Cultural Context of Learning and Thinking.
• Henle, M. (1962). 'The relationship between logic and thinking'. Psychological Review, 69.
• Hewson, S. N. P. (1977). 'Inferential problem solving in young children'. Oxford University: unpublished doctoral dissertation.
• Kendler, T. S., and Kendler, H. H. (1967). 'Experimental analysis of inferential behavior in children'. In Lipsitt, L. P., and Spiker, C. C. (eds.), Advances in Child Development and Behavior, vol. iii.
• McGarrigle, J., Grieve, R., and Hughes, M. (1978). 'Interpreting inclusion: a contribution to study of the child's cognitive and linguistic development'. Journal of Experimental Child Psychology, 26.
• Mitchell, P., and Riggs, K. (2000). Children's Reasoning and the Mind.

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