Autor: Lonergan, Bernard J.F.

Buch: Topics in Education

Titel: Topics in Education

Stichwort: Piaget, Group Theory (Gruppentheorie); a stage in development

Kurzinhalt: Moving up to the group, the child is able to perform a number of the operations, but not the whole system

Textausschnitt: 16/8 Some knowledge of group theory is necessary if one is to understand what Piaget is doing. He is using the idea of the group of operations. When the group or rounded whole is attained, there occurs what Piaget calls a stage in development. Moving up to the group, the child is able to perform a number of the operations, but not the whole system. Consequently, there will be points where he will be blocked, where he will not be able to do things or figure things out. Piaget is able to discern where the group of operations will be lacking. He gives the child things to do and finds that the group has not yet been attained. The child reaches an equilibrium, a capacity to act on a given level, when the group is attained. Development is occurring along a certain line, and the development is attained when the group is attained. From the notion of the group Piaget derives a theoretical structure that defines when development is still occurring and the group has not yet been attained, and again when development is attained. So his theoretical structure gives a precise meaning to stages and to the 'not yet attained' of stages. (199f; Fs) (notabene)

17/8 Piaget thinks up very implausible types of experiments. For example, he will have two large bottles full of water, and he will pour the water from one into a series of smaller bottles. He will then put the empty bottle aside and ask the children, Is there more water in the big bottle or in the series of little ones? Now the children just look; they will not know. It is only at a certain stage, when, instead of comparing the end results, they think of the process and realize that no more water was added and none was spilt, that they will know there is the same amount of water in the series of smaller bottles as in the larger bottle. And only two years later will they be able to apply the same sort of thing to another problem - if we cut something up, does the whole weigh more than the sum of the parts? Again, it is a matter of thinking of and understanding the process, not of comparing the end results. Piaget constructs endless experiments and gives surprising tests to children, but his fundamental inspiration is the idea of the group. And, of course, the notion of the group of operations is used here in a sense that is merely analogous to the use in mathematics. He is not talking about mathematical operations, but about the operations of the child in looking, grabbing, and so on. (200; Fs)