By D. G. Boyle (Auth.)
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Additional resources for A Students' Guide to Piaget
The successive positions attained by revolving a wheel are said to constitute an algebraic group, which has very important properties. Although we must defer discussion of these properties. till later, we can see already how an adult's solution of the problem of the order of the beads is related to the notions of inverse and of identity element. This does not mean that an adult must understand the algebra of groups before he can solve this problem, but it does mean that an adult's thinking can be described in terms of algebraic groups, whereas the thinking of children cannot.
This point, which it is easy to overlook, emphasizes once more the active nature of intellectual development, and shows us why it is impossible to teach such concepts to children before they are ready for them, j At the beginning of this stage children are not ready for these concepts, but they nevertheless solve elementary problems. Suppose three differently coloured beads are to be strung on a wire which is fitted with an opaque sleeve into which the beads can be slid out of sight, as in Fig.
Nevertheless, the child does have some general ideas, and Piaget calls these preconcepts. As an example of a preconcept, Piaget tells us how his young daughter saw a slug when she was on a walk with her father. A little further on she saw another slug and said "There's the slug again". When her father asked her if it were the same slug she replied that it was, but when he took her back a few yards to show her the first slug again, she continued to maintain that it was the same slug. " and she replied "Yes".