Promoting Children’s Relational Understanding of Equivalence

Abstract

Understanding of mathematical equivalence is critical for later mathematical understandings. Research studies and national test results demonstrate that many students fail to develop equivalence understanding. McNeil and colleagues suggest that this failure is partly due to the format of traditional instruction and practice with highly similar problems. On the change resistance account (McNeil & Alibali, 2005), students struggle with equivalence because they developed overgeneralized “rules” that affect how they process and approach math problems, and fail to see equations having two separate sides that are being related to one another. Practice with problems in a similar format encourages students to develop ineffective mental models of problem types. We replicate and extend prior work bringing cognitive science research to the classroom. Our findings indicate that applying research-based design principles in the form of varied structured practice improved student understanding of the concept of mathematical equivalence, which transfers to novel problem types.


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