ABSTRACT
Geometry is one of the oldest formalized mathematical domains. Having evolved in what came to be the earliest mathematical communities from mundane, pre-geometric experiences in a world of immediately comprehensible three-dimensional objects, it has been “handed down” and developed through the continual reproduction of its shared structures in incarnate geometrical activity. It is therefore not surprising that the Principles and Standards for School Mathematics (NCTM, 2000) identify geometry as one of the content standards for grades K–12. As well, in the more recent Curriculum Focal Points for Mathematics in PreKindergarten through Grade 8 (NCTM, 2007), emphasis is placed on K–4 students’ abilities to: identify geometrical ideas in their world; describe, model, draw, compare, and classify shapes according to their properties; investigate and analyze the composition and decomposition of two-dimensional and three-dimensional figures; and relate geometric ideas to measurement ideas. The question we may ask is how geometry as objective science comes to be reproduced in and through the actions of new generations?
