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    Mathematical sense-making in quantum mechanics: An initial peek

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    PhysRevPhysEducRes.13.020141.pdf (179.1Kb)
    No. of downloads: 94

    Date
    2017-12-28
    Author
    Dreyfus, Benjamin W.
    Elby, Andrew
    Gupta, Ayush
    Sohr, Erin Ronayne
    Citation
    Physical Review Physics Education Research 13, 020141 (2017) DOI: 10.1103/PhysRevPhysEducRes.13.020141
    DRUM DOI
    https://doi.org/10.13016/M28S4JS3Z
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    Abstract
    Mathematical sense-making—looking for coherence between the structure of the mathematical formalism and causal or functional relations in the world—is a core component of physics expertise. Some physics education research studies have explored what mathematical sense-making looks like at the introductory physics level, while some historians and “science studies” have explored how expert physicists engage in it. What is largely missing, with a few exceptions, is theoretical and empirical work at the intermediate level—upper division physics students—especially when they are learning difficult new mathematical formalism. In this paper, we present analysis of a segment of video-recorded discussion between two students grappling with a quantum mechanics question to illustrate what mathematical sensemaking can look like in quantum mechanics. We claim that mathematical sense-making is possible and productive for learning and problem solving in quantum mechanics. Mathematical sense-making in quantum mechanics is continuous in many ways with mathematical sense-making in introductory physics. However, in the context of quantum mechanics, the connections between formalism, intuitive conceptual schema, and the physical world become more compound (nested) and indirect. We illustrate these similarities and differences in part by proposing a new symbolic form, eigenvector eigenvalue, which is composed of multiple primitive symbolic forms.
    Notes
    Partial funding for Open Access provided by the UMD Libraries' Open Access Publishing Fund.
    URI
    http://hdl.handle.net/1903/20695
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    DRUM is brought to you by the University of Maryland Libraries
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