written by Joshua S. Von Korff, Andrew Elby, Dehui Hu, and N. Sanjay Rebello

During a sequence of interventions including a tutorial and a teaching interview, a student ("Bryce") showed evidence of understanding all the steps of Riemann-sum style reasoning about why displacement corresponds to the area under a velocity vs. time graph, which in turn corresponds to the integral of velocity over time. However, he does not view this reasoning as productive for explaining to someone why displacement corresponds to that area under the velocity vs. time curve. We argue that his view stems not primarily from conceptual or mathematical difficulties but from his epistemological stance toward learning integration. Although Bryce tries to mesh physical/conceptual reasoning and other pieces of mathematical formalism (such as simple equations), he views integration as something to be accepted and used. He therefore frames the Riemann sum reasoning as unneeded logical stepping stones rather than as a deeper explanation linking mathematical formalism to intuitive physical ideas.

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Published February 1, 2014
Last Modified January 31, 2014

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