Improving calculus explanations through peer review

This paper describes Peer-Assisted Reflection (PAR), a peer-review activity designed to help students explain mathematics. PAR was implemented in a single experimental section during two consecutive semesters (phases) of introductory college calculus. During the second semester (Phase II), students were explicitly taught how to provide better feedback to each other. As a result, the amount and quality of feedback provided by Phase II students was significantly improved from Phase I. During both phases, students who used PAR had significantly better explanations than a comparison group that did not include PAR, indicating that student explanations can be improved with relatively little intervention. To capture these improvements, I introduce a new analytic scheme that defines explanation as a cluster concept along four dimensions. This context-neutral scheme operationalizes explanations in a way that growth can be captured longitudinally.