The long way from mathematics to mathematics education: how educational research may change one’s vision of mathematics and of its learning and teaching

Abstract

Mathematicians and mathematics educators are united by their deep care for mathematics. This said, they are sometimes like parents who have differing ideas about what is good for the child. To improve communication between these two communities, I am telling the story of my own transformation from mathematics to mathematics education. In this account, I explain why I was compelled to revise my vision of mathematics and how I eventually arrived at the “commognitive” conceptualization, according to which mathematics is an activity of telling stories that produce their own objects. This change of vision brought many insights about learning mathematics and about factors that may slow students’ progress. I illustrate some of the gains that come with commognitive conceptualization by showing how this approach allowed my colleagues and me to come to grips with some learning-related phenomena that have long been puzzling mathematicians and educators.