Investigating Scaffolds for Sense Making in Fraction Addition and Comparison

Eliane WieseCarnegie Mellon University
Kenneth KoedingerCarnegie Mellon University

Abstract

What types of scaffolds support sense making in mathematics? Prior work has shown that grounded representations such as diagrams can support sense making and enhance student performance relative to analogous tasks presented with more abstract, symbolic representations. For grounded representations to support students’ learning of symbolic representations, students’ sense making must be maintained when both grounded and symbolic representations are presented together. This study investigates why students sometimes fail to coordinate these representations, in particular, why performance is high with fraction diagrams alone, but decreases when fraction symbols are included. Results indicate that symbols trigger incorrect transfer from whole-number procedures, and that students lack the qualitative reasoning that the diagrams are intended to tap. Specifically, students do not find it obvious that the sum of two positive symbolic fractions is larger than its two addends. Qualitative inference rules such as this one appear important in mediating the sense making process in the context of tempting misconceptions even when otherwise-supportive grounded representations are available.

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