### The Failure of Diagrams on Standardized Testing to Assess Students’ Understanding: What Teachers Need to Know to Use Diagrams Appropriately

#### Abstract

Many standardized tests have begun to broaden their assessment beyond the use of symbolic representations and now include more concrete diagrams. This paper reports on the conceptual resources 5th grade students leveraged when attempting to answer such questions in the domain of fraction operations. Results demonstrate how such questions failed to assess students’ understanding of the diagrams or of fractions, as the vast majority of participants used symbolic procedures or superficial qualities of the diagrams to navigate their answer choice. However, student responses, when pressed to explain their thinking about the diagrams, revealed rich thinking, illustrating how such questions can serve as productive formative assessment tasks.

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