How students blend conceptual and formal mathematical reasoning in solving physics problems

By Eric Weilin Kuo, M. M. Hull, Ayush Gupta, Andrew Elby. 2011

195 citations recorded by the source corpus.

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.

Subfields: Developmental and Educational Psychology, Education

View Paper: https://www.semanticscholar.org/paper/54adb6a19a08a8af68c52725a3b415dc5ebc0e24

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In Developmental and Educational Psychology

In Education

Citations in the corpus

Synthesis of Discipline-Based Education Research in Physics. (2014, background): “What is the relationship between students’ scores on the Force Concept Inventory and performance in a physics course as measured by grades? What is the relationship between students’ performance on concept tests and measures of their mathematical skills? Several studies have compared scores on conce”
The acquisition of problem solving competence: evidence from 41 countries that math and science education matters (2014, background): “Here, we can also identify overlaps between cognitive processes involved in mathematical problem solving and problem solving in general: Structuring, mathematizing, processing, interpreting, and validating (Baumert et al. 2009; Hiebert et al. 1996; Kuo et al. 2013; Polya 1945).”
Language of Physics, Language of Math: Disciplinary Culture and Dynamic Epistemology (2014, methodology): “(See, for example, Elby 2001, Gupta & Elby 2011, Bing & Redish 2012, and Kuo et al. 2013.)”