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    Connecting the learning of advanced mathematics with the teaching of secondary mathematics: Inverse functions, domain restrictions, and the arcsine function

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    Genre
    Pre-print
    Date
    2019-12-26
    Author
    Weber, Keith
    Mejía-Ramosa, Juan Pablo
    Fukawa-Connelly, Timothy
    Wasserman, Nicholas
    Department
    Teaching and Learning
    Subject
    Inverse function
    Inverse trigonometric function
    Real analysis
    Teacher education
    Permanent link to this record
    http://hdl.handle.net/20.500.12613/6292
    
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    DOI
    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.
    Citation
    Weber, K., Mejía-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
    Citation to related work
    Elsevier
    Has part
    Journal of Mathematical Behavior, Vol. 57, March 2020
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    For Americans with Disabilities Act (ADA) accommodation, including help with reading this content, please contact scholarshare@temple.edu
    ae974a485f413a2113503eed53cd6c53
    http://dx.doi.org/10.34944/dspace/6274
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