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This paper presents 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.
Physical Review Physics Education Research: Volume 16, Issue 2, Pages 020121
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![]() <a href="https://www.per-central.org/items/detail.cfm?ID=15672">Gifford, Julian D., and Noah Finkelstein. "Categorical framework for mathematical sense making in physics." Phys. Rev. Phys. Educ. Res. 16, no. 2, (September 22, 2020): 020121.</a>
![]() J. Gifford and N. Finkelstein, , Phys. Rev. Phys. Educ. Res. 16 (2), 020121 (2020), WWW Document, (https://doi.org/10.1103/PhysRevPhysEducRes.16.020121).
![]() J. Gifford and N. Finkelstein, Categorical framework for mathematical sense making in physics, Phys. Rev. Phys. Educ. Res. 16 (2), 020121 (2020), <https://doi.org/10.1103/PhysRevPhysEducRes.16.020121>.
![]() Gifford, J., & Finkelstein, N. (2020, September 22). Categorical framework for mathematical sense making in physics. Phys. Rev. Phys. Educ. Res., 16(2), 020121. Retrieved March 24, 2025, from https://doi.org/10.1103/PhysRevPhysEducRes.16.020121
![]() Gifford, Julian D., and Noah Finkelstein. "Categorical framework for mathematical sense making in physics." Phys. Rev. Phys. Educ. Res. 16, no. 2, (September 22, 2020): 020121, https://doi.org/10.1103/PhysRevPhysEducRes.16.020121 (accessed 24 March 2025).
![]() Gifford, Julian D., and Noah Finkelstein. "Categorical framework for mathematical sense making in physics." Phys. Rev. Phys. Educ. Res. 16.2 (2020): 020121. 24 Mar. 2025 <https://doi.org/10.1103/PhysRevPhysEducRes.16.020121>.
![]() @article{
Author = "Julian D. Gifford and Noah Finkelstein",
Title = {Categorical framework for mathematical sense making in physics},
Journal = {Phys. Rev. Phys. Educ. Res.},
Volume = {16},
Number = {2},
Pages = {020121},
Month = {September},
Year = {2020}
}
![]() %A Julian D. Gifford %A Noah Finkelstein %T Categorical framework for mathematical sense making in physics %J Phys. Rev. Phys. Educ. Res. %V 16 %N 2 %D September 22, 2020 %P 020121 %U https://doi.org/10.1103/PhysRevPhysEducRes.16.020121 %O text/html ![]() %0 Journal Article %A Gifford, Julian D. %A Finkelstein, Noah %D September 22, 2020 %T Categorical framework for mathematical sense making in physics %J Phys. Rev. Phys. Educ. Res. %V 16 %N 2 %P 020121 %8 September 22, 2020 %U https://doi.org/10.1103/PhysRevPhysEducRes.16.020121 Disclaimer: ComPADRE offers citation styles as a guide only. We cannot offer interpretations about citations as this is an automated procedure. Please refer to the style manuals in the Citation Source Information area for clarifications.
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