A Problem with Current Conceptions of Expert Problem Solving
Year: 2011
Type: preprint
Abstract: Background Current conceptions of expert problem solving depict physical/conceptual reasoning and formal mathematical reasoning as separate steps: a good problem solver first translates a physical understanding into mathematics, then performs mathematical/symbolic manipulations, then interprets the mathematical solution physically. However, other research suggests that blending conceptual and symbolic reasoning during symbolic manipulations can reflect expertise. Purpose (Hypothesis) We explore the hypothesis that blending conceptual and symbolic reasoning (i) indicates problem-solving expertise more than adherence to “expert” problem-solving steps and (ii) is something some undergraduates do spontaneously, suggesting it’s a feasible instructional target. Design/Method Interviewed students were asked to (1) explain a particular equation and (2) solve a problem using that equation. In-depth analysis of two students, Alex and Pat, revealed a pattern of behavior. All 11 interviews were coded to investigate the generalizability of this pattern. Results Alex described and used the equation as a computational tool. By contrast, Pat found a shortcut to solve the problem using a connection he verbalized between the mathematical equation and a physical process. Coding of 11 interviews confirms a correlation between the shortcut solution and a conceptual explanation of the equation. Furthermore, Pat’s blended physical/conceptual and symbolic reasoning is well described by knowledge structures called symbolic forms (Sherin, 2001). Conclusions Undergraduate students can and do blend physical/conceptual and symbolic reasoning to solve mathematics in problem solving. Symbolic Forms provide potential instructional targets for fostering such blended reasoning. This suggests that researchers should reconsider current conceptions of problem-solving expertise that do not include such reasoning. submitted to the Journal of Engineering Education 2
Source: arXiv (Cornell University)
Authors: Eric Kuo, Michael M. Hull, Ayush Gupta, Andrew Elby
Institution: University of Maryland, College Park
Language: English
Subfield: Education
Field: Social Sciences
Domain: Social Sciences
SDG: Quality education
Open Access status: green
OpenAlex ID: W143153547