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

Autor/inn/en	Kuo, Eric; Hull, Michael M.; Gupta, Ayush; Elby, Andrew
Titel	How students blend conceptual and formal mathematical reasoning in solving physics problems.
Quelle	In: Science education, 97 (2013) 1, S. 32-57Infoseite zur Zeitschrift PDF als Volltext Link als defekt meldenVerfügbarkeit
Sprache	englisch
Dokumenttyp	online; gedruckt; Zeitschriftenaufsatz
ISSN	0036-8326; 1098-237X
DOI	10.1002/sce.21043
Schlagwörter	Fallstudie; Interview; Problemlösen; Formelsprache; Mathematische Kompetenz; Mathematisches Denken; Naturwissenschaftlicher Unterricht; Naturwissenschaftliches Denken; Physikunterricht
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.
Erfasst von	Arbeitsgruppe Didaktik der Physik, Universität Kassel
Update	2014/3