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In this paper we examine the application of Tzur’s (2007) fine-grained assessment to the design of an assessment measure of a particular multiplicative scheme so that non-interview, good enough data can be obtained (on a large scale) to infer into elementary students’ reasoning. We outline three design principles that surfaced through our recent effort to devise a sequence of items to assess at which stage—participatory or anticipatory—a child might have constructed the multiplicative double counting (mDC) scheme (Tzur et al., 2013). These principles include the nature and sequencing of prompts, number choice, and authenticity of responses.

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