Case study of a college mathematics instructor: Patterns of classroom discourse

In the United States, undergraduates-regardless of their field of study-generally must complete a mathematics course to meet breadth-of-study requirements. This report is aimed at providing a research foundation for practical efforts to improve teaching and learning in such college mathematics service courses (e. g., college algebra, liberal arts mathematics, business calculus). The case participant, Professor Kale, was a PhD mathematician with 12 years of college teaching experience, 6 years as a graduate student and 6 years after the doctorate. He and students in both of his classes agreed to the daily video recording of their meetings for an entire semester. Through constant-comparative analysis of videos and extensive interviews with Professor Kale, as well as brief interviews with his students and other members of the department, we derived a description of discursive patterns in Kale's classes. We conclude with possible implications for future work in college mathematics service course research and teaching.