Proceedings of the Annual Meeting of the Cognitive Science Society

Deep understanding of mathematical equivalence is criticalfor later mathematical understandings. However, researchstudies and national test results have repeatedly demonstratedthat many students fail to develop adequate understanding ofequivalence. Recent work from McNeil and colleaguesproposes that this failure is partly due to the format oftraditional instruction and practice with highly similarproblems. Specifically, the change-resistance account(McNeil & Alibali, 2005) proposes that students struggle withequivalence because they have developed overgeneralized“rules” that affect how they process and approach mathproblems, (e.g., the operators are always on the left side, theequal sign means to “do something” or “give the answer”)and fail to see equations having two separate sides that arebeing related to one another. Extensive practice withproblems in a similar format (e.g., those that present allarithmetic operations on the left side of the equal sign)encourages students to develop ineffective mental models ofproblem types. We replicate and extend prior work that bringscognitive science research to the classroom. Our findingsindicate that applying research-based design principles toarithmetic practice improves student understanding ofmathematical equivalence enough to support transfer to novelproblem types.