Meta-Representation in an Algebra I Classroom

We describe how 1 Algebra I teacher and her 8th-grade students used meta-representational knowledge when generating and evaluating equations to solve word problems. Analyzing data from a sequence of 4 lessons, we found that the teacher and her students used criteria for evaluating equations, in addition to other types of knowledge (e.g., different interpretations of the equal sign) previously reported in the literature. Moreover, the teacher and her students had trouble understanding one another's proposed algebraic models of problem situations due to differences in the criteria that each applied, and this impeded learning. These findings (a) extend an accumulating body of evidence for the role meta-representation plays in mathematics and science learning and (b) add a new dimension to researchers' growing understanding of what teachers must know in order to teach algebra and other complex mathematics and science topics effectively.

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