Self-explanation training improves proof comprehension

In this paper we report three experiments demonstrating that a simple booklet containing self explanation training, designed to focus students’ attention on logical relationships within a mathematical proof, can significantly improve their proof comprehension. Experiment 1 demonstrates that students who receive the training generate higher quality explanations and perform better (effect size d = 0.950) on a comprehension test. Experiment 2 demonstrates that self-explanation training increases students’ cognitive engagement and the frequency with which they move their attention around a proof. Experiment 3 demonstrates that a 15- minute in-lecture self-study intervention improves students’ proof comprehension, and that the effect persists over time. Thus we argue that ‘transition to proof’ courses should incorporate self-explanation training.