Southwestern University

We discuss our findings from the use of a strongly communications-focused approach for teaching a liberal arts mathematics course. Our primary objectives are to get students thinking and working through mathematical concepts in non-traditional ways and, in particular, to strive for integrating their creative, right-brained skills with mathematical ideas and conceptualization strategies. A central pedagogical mechanism used throughout the course to accomplish these objectives is to help students learn and discover mathematical concepts through activity exercises, reflective writing and discussion. The course strongly emphasizes exercises and group-work that explicitly require students to formulate mathematical ideas in ordinary words and to communicate them to others.

Several of the key ideas used for developing the content and teaching strategy for this course are adapted from the work of Burger and Starbird. In the present work we focus on issues of implementation and outcomes, and discussing what works and what doesn't.

Communication by students, in the sense of using ordinary words to describe mathematics, occurs at different levels in this course. For convenience, we classify this into the following three categories: (1) in-class activities, (2) written assignments, and (3) group project. The in-class activities typically consist of exercises that require students to work individually or in groups, followed by discussion of outcomes with the class. This includes describing the rationale and connections to the underlying mathematical concept being discussed. In our experience, this strategy does succeed in engaging more students to think through and to understand the concept enough to apply it to the given situation. On the other hand, we also see that it doesn't circumvent the usual problem of getting the "silent students" to speak up.

The written assignments provide one mechanism for getting all students to discuss their ideas and reactions. An unusual element of these assignments is a written portion associated with each problem, which requires students to reflect upon the problem from a technical and a pedagogical viewpoint. Although we allow group work on the problems themselves, each student is required to respond to the written portion individually, since it is meant to communicate their personal reflections.

The group project is intended for students to discover and learn a selected topic in mathematics without teacher guidance, and to develop a presentation that introduces the topic to the rest of the class. Each group generally consists of 2-3 students who collectively research their topic and make their presentation. As with the written assignments, group projects also require each student to write individual statements reflecting upon their side of the learning experience.

To summarize, our strategy for teaching this course relies on a significant communications component wherein students regularly describe mathematical concepts and the experience of learning them in their own words. Our overall experience with this strategy has been extremely favorable, and we feel that it is particularly effective for courses that serve multidisciplinary audiences. Judging from our student responses, this approach does make mathematics more accessible and relevant to their own lives and to their vocational choices. The project and reflective writing components are also an excellent mechanism for incorporating themes of diversity and historically underrepresented mathematicians in a relevant and interesting way.

Edward B. Burger and Michael Starbird. Instructor resources for: The Heart of Mathematics: An invitation to effective thinking, Key College Publishing, 2000.