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 naïve!

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.