14 - Examining Interaction Patterns in College-Level Mathematics Classes: A Case Study

Summary

While discussing the pedagogical challenges of teaching an undergraduate discrete math course, one of our colleagues recently lamented that

Students are ill-prepared for this course…but this ill-preparation is a curious issue. I think it has more to do with the way they learned mathematics than with the content of the previous courses.

In this chapter, we propose a response to his comment. In particular, the goal of our discussion is to illustrate that the ways in which teachers and students interact can profoundly affect the attitudes students form as well as the content they learn.

Why Study Interaction Patterns?

This view of the importance of interaction styles is consistent with a conclusion reached by Stigler and Hiebert (2004) regarding their recent international study of teaching patterns across the world:

A focus on teaching must avoid the temptation to consider only the superficial aspects of teaching: the organization, tools, curriculum, content, and textbooks. The cultural activity of teaching – the ways in which the teacher and students interact about the subject – can be more powerful than the curriculum materials that teachers use. … We must find a way to change not just individual teachers, but the culture of teaching itself. (p. 16)

In short, not just what we teach, but how we teach and communicate with students – what we call interaction patterns – appears to have great influence on student learning. In this chapter, we describe several interaction patterns that educational researchers have identified.