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Connecting the learning of advanced mathematics with the teaching of secondary mathematics: Inverse functions, domain restrictions, and the arcsine function
Weber, Keith MejÃa-Ramosa, Juan Pablo Fukawa-Connelly, Timothy Wasserman, Nicholas
Weber, Keith
MejÃa-Ramosa, Juan Pablo
Fukawa-Connelly, Timothy
Wasserman, Nicholas
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Pre-print
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2019-12-26
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Teaching and Learning
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https://doi.org/10.1016/j.jmathb.2019.100752
Abstract
Prospective secondary mathematics teachers are typically required to take advanced university mathematics courses. However, many prospective teachers see little value in completing these courses. In this paper, we present the instantiation of an innovative model that we have previously developed on how to teach advanced mathematics to prospective teachers in a way that informs their future pedagogy. We illustrate this model with a particular module in real analysis in which theorems about continuity, injectivity, and monotonicity are used to inform teachers’ instruction on inverse trigonometric functions and solving trigonometric equations. We report data from a design research study illustrating how our activities helped prospective teachers develop a more productive understanding of inverse functions. We then present pre-test/post-test data illustrating that the prospective teachers were better able to respond to pedagogical situations around these concepts that they might encounter.
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Weber, K., MejÃa-Ramos, J.P., Fukawa-Connelly, T., & Wasserman, N. (2020). Connecting the learning of advanced mathematics with the teaching of secondary mathematics: Inverse functions, domain restrictions, and the arcsine function. The Journal of Mathematical Behavior, 57, 100752. https://doi.org/10.1016/j.jmathb.2019.100752
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Elsevier
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Journal of Mathematical Behavior, Vol. 57, March 2020
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