Réunion d'hiver 2000 de la SMC

Mathematical Education / Enseignement des mathématiques (Sponsored by the Department of Mathematics, UBC / Parrainée par le Département de mathématiques, UCB)
(George Bluman and Klaus Hoechsmann, Organizers)

ED BARBEAU, University of Toronto, Toronto, Ontario  M5S 3G3
Teaching mathematics-a matter of acculturation

When we travel, it helps to have knowledge of the country we visit. But if we want the experience to touch us, simple knowledge is not enough; we need some feeling for the culture, which speaks to the coherence of the experience. So it is with the Country of mathematics. Liping Ma's book tells me that Chinese teachers, with their Profound Understanding of Fundamental Mathematics, have been able to enter into this culture in a way that their American counterparts have not. What are the hallmarks of this mathematical culture?

LIPING MA, Stanford
To be announced

KANWAL NEEL, Steveston Secondary School, Richmond, British Columbia  V7E 2E3
Numeracy initiatives in British Columbia

Almost everyone knows what math is but what is numeracy? Defined by the British Columbia Association of Mathematics Teachers (BCAMT) as ``the combination of mathematical knowledge, problem solving and communication skills required by all persons to function successfully within our technological world.'' Numeracy is part of literacy. A student's level of numeracy is a significant component of their level of literacy.

CYNTHIA NICOL, Faculty of Education, University of British Columbia, British Columbia
Mathematics by inquiry: a certificate programme for mathematics teachers

The National Council of Teachers of Mathematics (NCTM) has issued a set of principles and standards for K-12 mathematics based on the premise that students develop mathematical competence by being actively and frequently engaged in processes such as problem solving, exploring, conjecturing, and reasoning. Similarly the MAA's Committee on the Mathematical Preparation of Teachers recommended that future teachers be given ``opportunities in their collegiate courses to do mathematics: explore, analyze, construct models, collect and represent data, present arguments, solve problems.'' Mathematics teachers are therefore being asked to teach in ways that are most likely different from the ways they once learned mathematics as students. In order for teachers to engage in the kind of mathematical pedagogy envisioned by organizations like NCTM and MAA, teachers need opportunities to practice the ``doing'' of mathematics and to see the familiar middle school and high school curriculum as a place for mathematical inquiry.
A response to this issue is the development of the UBC Certificate Programme for Mathematics Teachers (first offered in January 1999). The certificate programme is designed for practicing teachers who seek professional development in their own understanding of mathematics and the opportunity to learn mathematics by inquiry.
This presentation will highlight the nature and purpose of the UBC Certificate Programme for Mathematics Teachers and the content and structure of the courses (MATH 336 and MATH 337). The presentation will also raise issues and challenges of offering such a program ( e.g. attracting and maintaining enrollment, strategies and purposes of course evaluation, and connections of mathematics coursework to mathematics teaching practice).

SERGEI NOVOCELSKII, Department of Mathematics, University of British Columbia, Vancouver, British Columbia  V6T 1Z2
Math anxiety in prospective teachers

For the past 3 years, I have taught a course for prospective elementary school teachers. I find it extremely difficult to meet the criteria of the Mathematics Department and at the same time help these students overcome their obstacles to learning. The anxiety of some of them is severe enough to lead to emotional outbursts in and out of class. In an effort to create a positive and enjoyable learning environment, I have developed a variety of strategies which center on interactivity and group projects. I try to make the transition from simple example to abstract theory smooth and almost imperceptible. The results are overwhelmingly good: for many, mathematics became considerably less obscure, and for some, the discovery of their own abilities was a wonderful ``awakening'', as they wrote in their evaluations. However, it is a strenuous uphill struggle, and I wonder what can be done to make it less so.

CHRISTIAN SIEBENEICHER, Universität Bielefeld, D-33501  Bielefeld, Germany
Euler's ``Art of Reckoning''

The Art of Reckoning has always been part of human culture, but to my knowledge there have been only two eminent mathematicians who wrote a book on the subject: Leonardo of Pisa in 1202 and Leonhard Euler in 1738 (for schools in St. Petersburg). While Fibonacci assumes some prior familiarity with it, Euler develops it from its beginning in a timelessly clear fashion. In his preface he expresses his conviction that learning is without value as long as it does not lead to understanding. I think that even today his book can serve as a guide for anyone who wishes to teach arithmetic to children. In my talk I will pay particular attention to the kind of problems used in Liping Ma's survey.

RAVI VAKIL, Department of Mathematics, MIT, Cambridge, Massachusetts  02139, USA
A mathematician talks to high school students

We mathematicians often come into contact with young students who are keen and willing to be inspired, and yet as a profession we do a poor job communicating our excitement with them (despite finding our own work incredibly compelling, and despite having once been young ourselves). I'll describe many of the programmes set up for high school students, both here and in other countries, and relate some of the good ideas that people have tried. As in any mathematical talk, I will also mention some of the open problems in the area: What precisely should we be telling students seeking enrichment? Should we be giving them depth or breadth? Inspiration or knowledge? Specific tools or fuzzy ``big pictures''? Are competitions good? Are puzzles bad?
(The presenter has worked extensively with high school students for many years, through the Olympiad programme and various math camps, and in high schools, both in Canada and the U.S.)
Sponsored by the CMS Student Committee.