ALCOCK, L., OWEN, A. and ALLINSON, R., 2015. Diagram construction and performance in advanced mathematics. Presented at: 39th Conference of the International Group for the Psychology of Mathematics Education (PME39), Mathematics Education: Climbing Mountains, Building Bridges, 13th-18th July 2015, Hobart, Australia.
We report a study in which 100 students at the beginning of an undergraduate real
analysis course were asked to construct diagrams to represent four general
mathematical statements about functions. We present four theoretical criteria for
analysing such diagrams and illustrate the range of student-produced diagrams; we
then present an analysis showing that performance in the diagram-construction task
was significantly related to subsequent performance in the course.