Keynote Speaker

Lara Alcock is a Professor in the Department of Mathematics Education at Loughborough University in the UK. She has 30 years’ experience of teaching undergraduate mathematics. She conducts research on how students think about mathematics, on differences between student and expert thinking, and on educational interventions. Her research focuses on the challenges students encounter as they make the transition to proof, including the reading skills they need in order to understand mathematical texts.

Abstract: This talk will present a sequence of empirical research studies on expert and novice mathematical reading. In a first study, experts and undergraduates studied purported mathematical proofs while their eye-movements were tracked. We found that experts focused more on the words (rather than the algebra) and shifted their attention in a manner consistent with searching for implicit warrants. In a second, experimental study, undergraduates received self-explanation training or a control activity before reading a mathematical proof and taking a comprehension test. We found that those who had received the training exhibited more expert-like mathematical reading and higher performance in a comprehension test. In a third study, also experimental, undergraduates studied self-explanation training or a control activity in a regular lecture, then read a proof and completed a comprehension test; they also completed a delayed post-test three weeks later. We found that the self-explanation training was effective also in this context. I will discuss implications for teaching effective reading of mathematical text.