Mathematical actions as procedural resources: An example from the separation of variables
[This paper is part of the Focused Collection on Upper Division Physics Courses.] Students learning to separate variables in order to solve a differential equation have multiple ways of correctly doing so. The procedures involved in separation include division or multiplication after properly groupi...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2015-09-01
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| Series: | Physical Review Special Topics. Physics Education Research |
| Online Access: | http://doi.org/10.1103/PhysRevSTPER.11.020114 |
| _version_ | 1818716668818358272 |
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| author | Michael C. Wittmann Katrina E. Black |
| author_facet | Michael C. Wittmann Katrina E. Black |
| author_sort | Michael C. Wittmann |
| collection | DOAJ |
| description | [This paper is part of the Focused Collection on Upper Division Physics Courses.] Students learning to separate variables in order to solve a differential equation have multiple ways of correctly doing so. The procedures involved in separation include division or multiplication after properly grouping terms in an equation, moving terms (again, at times grouped) from one location on the page to another, or simply carrying out separation as a single act without showing any steps. We describe student use of these procedures in terms of Hammer’s resources, showing that each of the previously listed procedures is its own “piece” of a larger problem solving activity. Our data come from group examinations of students separating variables while solving an air resistance problem in an intermediate mechanics class. Through detailed analysis of four groups of students, we motivate that the mathematical procedures are resources and show the issues that students must resolve in order to successfully separate variables. We use this analysis to suggest ways in which new resources (such as separation) come to be. |
| first_indexed | 2024-12-17T19:22:55Z |
| format | Article |
| id | doaj.art-04d4ef87462e41eeb0d35738b9e99032 |
| institution | Directory Open Access Journal |
| issn | 1554-9178 |
| language | English |
| last_indexed | 2024-12-17T19:22:55Z |
| publishDate | 2015-09-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Special Topics. Physics Education Research |
| spelling | doaj.art-04d4ef87462e41eeb0d35738b9e990322022-12-21T21:35:26ZengAmerican Physical SocietyPhysical Review Special Topics. Physics Education Research1554-91782015-09-0111202011410.1103/PhysRevSTPER.11.020114Mathematical actions as procedural resources: An example from the separation of variablesMichael C. WittmannKatrina E. Black[This paper is part of the Focused Collection on Upper Division Physics Courses.] Students learning to separate variables in order to solve a differential equation have multiple ways of correctly doing so. The procedures involved in separation include division or multiplication after properly grouping terms in an equation, moving terms (again, at times grouped) from one location on the page to another, or simply carrying out separation as a single act without showing any steps. We describe student use of these procedures in terms of Hammer’s resources, showing that each of the previously listed procedures is its own “piece” of a larger problem solving activity. Our data come from group examinations of students separating variables while solving an air resistance problem in an intermediate mechanics class. Through detailed analysis of four groups of students, we motivate that the mathematical procedures are resources and show the issues that students must resolve in order to successfully separate variables. We use this analysis to suggest ways in which new resources (such as separation) come to be.http://doi.org/10.1103/PhysRevSTPER.11.020114 |
| spellingShingle | Michael C. Wittmann Katrina E. Black Mathematical actions as procedural resources: An example from the separation of variables Physical Review Special Topics. Physics Education Research |
| title | Mathematical actions as procedural resources: An example from the separation of variables |
| title_full | Mathematical actions as procedural resources: An example from the separation of variables |
| title_fullStr | Mathematical actions as procedural resources: An example from the separation of variables |
| title_full_unstemmed | Mathematical actions as procedural resources: An example from the separation of variables |
| title_short | Mathematical actions as procedural resources: An example from the separation of variables |
| title_sort | mathematical actions as procedural resources an example from the separation of variables |
| url | http://doi.org/10.1103/PhysRevSTPER.11.020114 |
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