Students’ Usage of Visual Imagery to Reason about the Divergence, Integral, Direct Comparison, Limit Comparison, Ratio, and Root Convergence Tests

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Abstract/Description:

This study was motivated by practical issues we have encountered as second-semester calculus instructors, where students struggle to make sense of the various series convergence tests, including the divergence, integral, direct comparison, limit comparison, ratio, and root tests. To begin an exploration of how students might reason about these tests, we examined the visual imagery used by students when asked to describe what these tests are and why they provide the conclusions they do. It appeared that each test had certain types of visual imagery associated with it, which were at times productive and at times a hindrance. We describe how the visual imagery used by students seemed to impact their reasoning about the convergence tests.


Location: RUME Conference, San Diego, California
Presenter:

Steven Jones and Mitchell Probst, Brigham Young University