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Childs Conception Of Geometry

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Jean Piaget (1896-1980) was a Swiss developmental psychologist known for his epistemological studies with children. His theory of cognitive development and epistemological view are known as "genetic epistemology". Bärbel Inhelder (1913-1997) was a Swiss developmental psychologist; she was probably Piaget's most well-known co-worker. Alina Szeminska is another of their co-workers.

The authors state in the Preface, "In our earlier work, Childs Conception Of Space, we studied certain problems of a general nature in regard to the development of spatial concepts in young children, dealing in particular with the elaboration of projective and Euclidean concepts out of the more elementary topological notions. But the problem of spatial intuition as a whole is exceedingly complex, and we were compelled to postpone our discussion of measurement and metrical geometry. These form the subject matter of the present volume."

Here are some representative quotations from the book:

"As often happens in psycho-genetic development, a mental operation is ddceptively simple when it has reached its final equilibrium, but its genesis is very much more complex."
"The study of children's spontaneous behavior in a measuring situation revealed that the notion of a metric unit is evolved only at level IIIB and depends on the previous mastery of qualitative operational transitivity and on the coordination of changes of position at the level of representation, itself a function of a system of references."
"Psychologically, this finding is of the utmost importance. The discovery of geometrical loci ... is the finest example of the direct transition from induction which is empirical and intuitive to operational generalization which is deductive. The end-stage is reasoning by recurrence..."
"Throughout this work we have repeatedly stressed the fact that from the psychological standpoint, the question whether the representation of space is Euclidean or not depends on the construction of coordinate systems."