Some remarks on Navajo geometry and piagetian genetic theory

Abstract

Spanish

Some of the basic findings of Piaget's study on spatial knowledge in Genevan children are contrasted to Navajo spatial knowledge: there is no unique spatial «primitive» in Navajo knowledge and each and every notion is constituted in a different way than its Genevan correlate. The total system of Navajo knowledge shows a structure of interrelated and codetermining notions which differs markedly from the unilinear logical-deductive structure in the Piagetian model. In the second half of the paper the investigation turns to education and schooling. Here a position is taken against the (Piaget-based) rationalistic education policy one finds in the New Math-movement. Instead, some of the principles of Freudenthal are explored in a non-western setting: children should reinvent geometry on their own, in the terms of their culture. To that end, a curriculum for geometry teaching in a Navajo bicultural school is presented, focusing on the schooling in geometric concepts within the Navajo language and with full respect for the Navajo spatial representations in pre-school children.

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