Mathematics Majors' Diagram Usage When Writing Proofs in Calculus

We report on a study in which we observed 73 mathematics majors completing 7 proof construction tasks in calculus. We use these data to explore the frequency and effectiveness with which mathematics majors use diagrams when constructing proofs. The key findings from this study are (a) nearly all participants introduced diagrams on multiple tasks, (b) few participants displayed either a strong propensity or a strong reluctance to use diagrams, and (c) little correlation existed between participants' propensity to use diagrams and their mathematical achievement (either on the proof construction tasks or in their advanced mathematics courses). At the end of the report, we discuss implications for pedagogy and future research.