Promoting Children's Relational Understanding of Equivalence

Deep understanding of mathematical equivalence is critical for later mathematical understandings. However, research studies and national test results have repeatedly demonstrated that many students fail to develop adequate understanding of equivalence. Recent work from McNeil and colleagues proposes that this failure is partly due to the format of traditional instruction and practice with highly similar problems. Specifically, the change-resistance account (McNeil & Alibali, 2005) proposes that students struggle with equivalence because they have developed overgeneralized “rules” that affect how they process and approach math problems, (e.g., the operators are always on the left side, the equal sign means to “do something” or “give the answer”) and fail to see equations having two separate sides that are being related to one another. Extensive practice with problems in a similar format (e.g., those that present all arithmetic operations on the left side of the equal sign) encourages students to develop ineffective mental models of problem types. We replicate and extend prior work that brings cognitive science research to the classroom. Our findings indicate that applying research-based design principles to arithmetic practice improves student understanding of mathematical equivalence enough to support transfer to novel problem types.