Saturday, 12 June 2003, 4:00-5:30 pm, Room 2038, Faculty of Education, UWO

Mathematical Thinking & Common Sense: Consonance & Conflict

Uri Leron, Technion -- Israel Institute of Technology

Abstract: I tell the story of some recent advances in cognitive science and evolutionary psychology, and their impact on our understanding of mathematical thinking. My point of entry is a personal story -- my own fascination of many years with the interplay between our intuition, or common sense, and mathematical thinking. As a student, learning mathematics was for me a very personal experience. To understand a piece of new mathematics meant making it intuitive, part of common sense or, at least, a natural extension of common sense. As I climbed the steps of the academic ladder, I carried this view into my teaching. Teaching mathematics, I had believed, meant doing your best to convince the students of the commonsensical nature of what they were learning. At present, with the hindsight of many years of learning about learning, I say to myself: How beautiful, how na´ve!

In recent years I have done some eavesdropping on several neighboring scientific disciplines and listened to their stories about common sense and its relation to mathematical thinking. I'll focus on two such stories. From cognitive science came some answers to the question, How is it that all human beings can at all learn some mathematics? The answers aim to show how mathematical thinking is rooted in more general cognitive mechanism such as imagery, thought experiment, social cognition and metaphor. From evolutionary psychology -- the empirical study of universal human nature and its origins -- came some answers to the dual question, Why do so many find mathematics almost impossibly hard? The surprising answer lies not in any weakness of our cognitive apparatus, but in its peculiar strengths.

In practice, once we realize that mathematical learning can be either supported or hindered by our natural cognitive abilities, we should make an effort to plan our mathematical teaching (contents, methods, tools) as much as possible in consonance with those natural capabilities. The two themes of this symposium -- story-telling and modern interactive technologies -- may well be among the best tools for achieving this consonance.