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Multiple Representations of Mathematical Reasoning

by David J. McArthur, Christopher Burdorf, Tor Ormseth, Abby Robyn, Cathy Stasz

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Multiple alternative representations of mathematical reasoning have interesting applications in the context of an intelligent tutor for basic algebra. This Note describes the notion of multiple representations at a general level. It then describes RAND's intelligent algebra tutor and specific tools it contains that support multiple representations: a boxes-and-weights tool and goal commands. These tools provide students with important learning opportunities. The Note concludes with comments about continuing research in this area. It is important to continue implementing different representational systems and testing them in real educational contexts. In addition, theoretical work must be directed toward deriving a general classification scheme for representations.

This report is part of the RAND Corporation Note series. The note was a product of the RAND Corporation from 1979 to 1993 that reported other outputs of sponsored research for general distribution.

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