ABSTRACT

A forceful impetus for changing my teaching has been reflecting on my own experiences in learning undergraduate mathematics and doing mathematical research.1 When I first started teaching, I adopted those practices I had observed as a student: I lectured. I believed that teaching at the post-secondary level involved the transmission of knowledge from me, the expert, to the students, the novices. I saw my job as exposing the students to the content of the course. The students’ job was to master this material by listening attentively as I explained ideas, by watching carefully as I showed them how to solve problems, and by practising solving problems on their own at home. I administered tests in order to measure achievement and to rank students in relation to their peers. Each lecture had a natural pattern: I introduced a topic, covered the blackboard with formulas and mathematical language, and worked a couple of illustrative examples. I asked a few questions. I even elicited a few answers-usually from the same three or four (male) students. Finally I assigned homework. I was considered a successful teacher. My course evaluations proved it. Students praised me for my enthusiasm, my organization, the clarity of my exposition, my knowledge of the material and my accessibility The most critical comment was a request to slow down a little. Yet, when the final examination came, many students failed or wrote such incomprehensible answers that I wondered if we had all been involved in the same course. How could they do so badly, I wondered, when I had explained the material so well? How could they not buy the goods I had sold them so persuasively? Of course this troubled me, but it was easy enough to dismiss: ‘Students come to university so ill-prepared. If only we had better students, just think what we could do!’ A familiar refrain?