How students blend conceptual and formal mathematical reasoning in solving physics problems
Current conceptions of quantitative problem-solving expertise in physics incorporate conceptual reasoning in two ways: for selecting relevant equations (before manipulating them) and for checking whether a given quantitative solution is reasonable (after manipulating the equations). We make the case...
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Published in | Science education (Salem, Mass.) Vol. 97; no. 1; pp. 32 - 57 |
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Main Authors | , , , |
Format | Journal Article |
Language | English |
Published |
New York
Blackwell Publishing Ltd
2013
Wiley Periodicals Inc |
Subjects | |
Online Access | Get full text |
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Summary: | Current conceptions of quantitative problem-solving expertise in physics incorporate conceptual reasoning in two ways: for selecting relevant equations (before manipulating them) and for checking whether a given quantitative solution is reasonable (after manipulating the equations). We make the case that problem-solving expertise should include opportunistically blending of conceptual and formal mathematical reasoning even while manipulating equations. We present analysis of interviews with two students, Alex and Pat. Interviewed students were asked to explain a particular equation and solve a problem using that equation. Alex used and described the equation as a computational tool. By contrast, Pat found a shortcut to solve the problem. His shortcut blended mathematical operations with conceptual reasoning about physical processes, reflecting a view-expressed earlier in his explanation of the equation-that equations can express an overarching conceptual meaning. Using case studies of Alex and Pat, we argue that this opportunistic blending of conceptual and formal mathematical reasoning (i) is a part of problem-solving expertise, (ii) can be described in terms of cognitive elements called symbolic forms (Sherin, 2001), and (iii) is a feasible instructional target. |
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Bibliography: | istex:AAFF674F9137EDABA34F4BDF8F77C74C6B1D0378 National Science Foundation - No. EEC-0835880 ark:/67375/WNG-7JWGKJXN-Z ArticleID:SCE21043 Contract grant sponsor: National Science Foundation. Contract grant number: EEC‐0835880. The views expressed here are those of the authors and do not necessarily reflect those of the National Science Foundation. |
ISSN: | 1098-237X 0036-8326 1098-237X |
DOI: | 10.1002/sce.21043 |