Categorical framework for mathematical sense making in physics
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 reasoni...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2020-09-01
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| Series: | Physical Review Physics Education Research |
| Online Access: | http://doi.org/10.1103/PhysRevPhysEducRes.16.020121 |
| _version_ | 1818843292187492352 |
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| author | Julian D. Gifford Noah D. Finkelstein |
| author_facet | Julian D. Gifford Noah D. Finkelstein |
| author_sort | Julian D. Gifford |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-19T04:55:33Z |
| format | Article |
| id | doaj.art-f6ec7e5f50f349cfb453b62e60b65540 |
| institution | Directory Open Access Journal |
| issn | 2469-9896 |
| language | English |
| last_indexed | 2024-12-19T04:55:33Z |
| publishDate | 2020-09-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Physics Education Research |
| spelling | doaj.art-f6ec7e5f50f349cfb453b62e60b655402022-12-21T20:35:15ZengAmerican Physical SocietyPhysical Review Physics Education Research2469-98962020-09-0116202012110.1103/PhysRevPhysEducRes.16.020121Categorical framework for mathematical sense making in physicsJulian D. GiffordNoah D. FinkelsteinWe 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.http://doi.org/10.1103/PhysRevPhysEducRes.16.020121 |
| spellingShingle | Julian D. Gifford Noah D. Finkelstein Categorical framework for mathematical sense making in physics Physical Review Physics Education Research |
| title | Categorical framework for mathematical sense making in physics |
| title_full | Categorical framework for mathematical sense making in physics |
| title_fullStr | Categorical framework for mathematical sense making in physics |
| title_full_unstemmed | Categorical framework for mathematical sense making in physics |
| title_short | Categorical framework for mathematical sense making in physics |
| title_sort | categorical framework for mathematical sense making in physics |
| url | http://doi.org/10.1103/PhysRevPhysEducRes.16.020121 |
| work_keys_str_mv | AT juliandgifford categoricalframeworkformathematicalsensemakinginphysics AT noahdfinkelstein categoricalframeworkformathematicalsensemakinginphysics |