Collegiate mathematics teaching: An unexamined practice

Though written accounts of collegiate mathematics teaching exist (e.g., mathematicians’ reflections and analyses of learning and teaching in innovative courses), research on collegiate teachers’ actual classroom teaching practice is virtually non-existent. We advance this claim based on a thorough review of peer-reviewed journals where scholarship on collegiate mathematics teaching is published. To frame this review, we distinguish between instructional activities and teaching practice and present six categories of published scholarship that consider collegiate teaching but are not descriptive empirical research on teaching practice. Empirical studies can reveal important differences among teachers’ thinking and actions, promote discussions of practice, and support learning about teaching. To support such research, we developed a preliminary framework of cognitively oriented dimensions of teaching practice based on our review of empirical research on pre-college and college teaching.