Teaching mathematics graduate students to teach: An international perspective

Abstract

We discuss a new method for the development of university teaching skills: case studies. Case studies are accounts of classroom interactions that pose a set of di-culties or crises to be analyzed. When groups of graduate students and faculty analyze these cases, sometimes from difierent points of view, they are led to think deeply about what makes high-quality mathematics teaching. High-quality teaching of mathematics at the university level is important to every country. Almost all of the best jobs in the global economy require ∞uency in math- ematics, and a great many require advanced technical knowledge. High-quality university math instruction contributes to high student achievement in the quanti- tative disciplines and prepares students for good jobs. Moreover, university faculty in most countries teach the students who will themselves become the next generation of pre-collegiate math teachers. If these teachers are to succeed with their own stu- dents they must have, along with teaching skills, detailed mathematical knowledge, understanding, and skills. So it is important that these teachers-to-be attend well- taught mathematics classes at the university. Thus every nation should be vitally interested in high-quality mathematics teaching at the university level. Such considerations suggest that faculty development as regards teaching might be useful. Though this is certainly true, it is also true that math faculty flnd themselves with a wide range of responsibilities and time constraints and might not be receptive to such development. Instead, it may be more practical to focus on future math faculty. Mathematics graduate students go on to become the next generation of univer- sity faculty. I wish to argue here that it is possible to develop programs for such graduate students that equip them to do an excellent job as future university teach- ers. Moreover, it is possible to do so without unduly impacting their mathematics studies. The implementation of such a program|one whose goal is to prepare its graduates to teach a class independently and excellently upon graduation|can thus be a high-reward, low-cost opportunity. The question of what to do to achieve this goal, then, is the concern here. Cer- tainly, students in such a program should practice giving mathematical explana- tions. One can bring graduate students to the blackboard to explain some problem or concept, and then give them critical feedback. In addition, one should talk about technical aspects of teaching, such as how to plan a course, how to write a syllabus,