It allows us to provide a dynamic alternative interpretation of the van Hiele theory, which shares the same belief as Noss and Hoyles (1996) in the existence of "diverse kinds of mathematics", the same belief as Turkle and Papert (1992) in the existence of "epistemological pluralism" and the same belief as disessa (2000) in the existence of ways of knowing "beyond the stereotypes of knowledge we have culturally institutionalized in school and even in our common sense" (p. 71).