COLLEGE OF ARTS AND SCIENCES Department of Mathematics and Statistics
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Mathematics Colloquium: Is it a Function? Generalizing from the Single-to Multivariable Setting


4:10pm EdAdd room 116

Allison Dorko

This talk reports on a longitudinal study regarding what five calculus students generalized as they thought about what it means to be a function in R3. Students answered tabular and graphical classification tasks three times over the span of their differential, integral, and multivariable calculus courses. Findings indicate that students generalized key aspects of how they thought about single-variable functions, such as pattern, equation, univalence, input-output, independence-dependence, and the vertical line test. In this talk, I will focus on some interesting results regarding students’ generalizations of the vertical line test. Specifically, students’ ideas about how to employ the vertical line test in R3 included applying the test to traces, drawing lines parallel to the y axis, and drawing lines parallel to the z axis. These results have implications for how we teach students about single-variable functions and what ways of reasoning allow them to later build on that knowledge, as well as how we teach multivariable functions. Refreshments served at 3:30 p.m. Ed. Add. 116 (same room as talk)