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

Eric Kuo, Michael M. Hull, Ayush Gupta, Andrew Elby

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish (US)
Pages (from-to)32-57
Number of pages26
JournalScience Education
Volume97
Issue number1
DOIs
StatePublished - Jan 1 2013
Externally publishedYes

ASJC Scopus subject areas

  • Education
  • History and Philosophy of Science

Fingerprint Dive into the research topics of 'How students blend conceptual and formal mathematical reasoning in solving physics problems'. Together they form a unique fingerprint.

Cite this