Some remarks on Navajo geometry and piagetian genetic theory

Abstract

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.