ABSTRACT
In their introduction of the conceptual framework for this action group, the organizers point out a common misconception regarding mathematics: that mathematical objects somehow exist independently of human experience. Of course, without being a mathematician, one can be aware of the existence of a body of knowledge accumulated by mankind over the years, a body of knowledge that can be found in books, in journals, and in the exchanges of the many different communities of mathematicians. In this sense, mathematics does exist independently of one’s personal experience. But this view does not lead anywhere when pedagogical concerns are at stake, when questions of learning and discovery are involved. And yet, much too often, mathematics is taught in a formal way, with little regard for the cognitive processes involved in the construction or reconstruction of mathematical knowledge by the individual learner. Quite frequently, mathematics is introduced as if mathematical objects had come about suddenly, their existence occurring in some kind of spontaneous creation seemingly unrelated to the learner’s environment.
