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  • Open Access

Categorical framework for mathematical sense making in physics

Julian D. Gifford* and Noah D. Finkelstein

  • Department of Physics, University of Colorado Boulder, Box 390, Boulder, Colorado 80309, USA

  • *Julian.Gifford@colorado.edu
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Phys. Rev. Phys. Educ. Res. 16, 020121 – Published 22 September, 2020

DOI: https://doi.org/10.1103/PhysRevPhysEducRes.16.020121

Abstract

We present a framework designed to help categorize various sense making moves, allowing for greater specificity in describing and understanding student reasoning and also in the development of curriculum to support this reasoning. The framework disaggregates between the mechanisms of student reasoning (the cognitive tool that they are employing) and what they are reasoning about (the object). Noting that either the tool or object could be mathematical or physical, the framework includes four basic sense making modes: Use of a mathematical tool to understand a mathematical object, use of a mathematical tool to understand a physical object, use of a physical tool to understand a mathematical object, and use of a physical tool to understand a physical object. We identify three fundamental processes by which these modes may be combined (translation, chaining, and coordination) and present a visual representation that captures both the individual reasoning modes and the processes by which they are combined. The utility of the framework as a tool for describing student reasoning is demonstrated through the analysis of two extended reasoning episodes. Finally, implications of this framework for curricular design are discussed.

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Phys. Rev. Phys. Educ. Res. 16, 020121– Published 22 September, 2020
  • Received 12 March 2020
  • Accepted 25 August 2020
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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