Assessing mathematical sensemaking in physics through calculation-concept crossover

Professional problem-solving practice in physics and engineering relies on mathematical sense making—reasoning that leverages coherence between formal mathematics and conceptual understanding. A key question for physics education is how well current instructional approaches develop students’ mathema...

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Autores principales:	Eric Kuo, Michael M. Hull, Andrew Elby, Ayush Gupta
Formato:	article
Lenguaje:	EN
Publicado:	American Physical Society 2020
Materias:	Special aspects of education LC8-6691 Physics QC1-999
Acceso en línea:	https://doaj.org/article/2e40c70ed24343d5814266e3cd19ec6f
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spelling	oai:doaj.org-article:2e40c70ed24343d5814266e3cd19ec6f2021-12-02T11:18:16ZAssessing mathematical sensemaking in physics through calculation-concept crossover10.1103/PhysRevPhysEducRes.16.0201092469-9896https://doaj.org/article/2e40c70ed24343d5814266e3cd19ec6f2020-07-01T00:00:00Zhttp://doi.org/10.1103/PhysRevPhysEducRes.16.020109http://doi.org/10.1103/PhysRevPhysEducRes.16.020109https://doaj.org/toc/2469-9896Professional problem-solving practice in physics and engineering relies on mathematical sense making—reasoning that leverages coherence between formal mathematics and conceptual understanding. A key question for physics education is how well current instructional approaches develop students’ mathematical sense making. We introduce an assessment paradigm that operationalizes a typically unmeasured dimension of mathematical sense making: use of calculations on qualitative problems and use of conceptual arguments on quantitative problems. Three assessment items embodying this calculation-concept crossover assessment paradigm illustrate how mathematical sense making can positively benefit students’ problem solving, leading to more efficient, insightful, and accurate solutions. These three assessment items were used to evaluate the efficacy of an instructional approach focused on developing students’ mathematical sense making skills. In a quasi-experimental study, three parallel lecture sections of first-semester, introductory physics were compared: two mathematical sense making sections, one with an experienced instructor and one with a novice instructor, and a traditionally taught section, as a control group. Compared to the control group, mathematical sense making groups used calculation-concept crossover approaches more often and gave more correct answers on the crossover assessment items, but they did not give more correct answers to associated standard problems. In addition, although students’ postcourse epistemological views on problem-solving coherence were associated with their crossover use, they did not fully account for the differences in crossover approach use between the mathematical sense making and control groups. These results demonstrate a new assessment paradigm for detecting a typically unmeasured dimension of mathematical sense making and provide evidence that a targeted instructional approach can enhance engagement with mathematical sense making in introductory physics.Eric KuoMichael M. HullAndrew ElbyAyush GuptaAmerican Physical SocietyarticleSpecial aspects of educationLC8-6691PhysicsQC1-999ENPhysical Review Physics Education Research, Vol 16, Iss 2, p 020109 (2020)
institution	DOAJ
collection	DOAJ
language	EN
topic	Special aspects of education LC8-6691 Physics QC1-999
spellingShingle	Special aspects of education LC8-6691 Physics QC1-999 Eric Kuo Michael M. Hull Andrew Elby Ayush Gupta Assessing mathematical sensemaking in physics through calculation-concept crossover
description	Professional problem-solving practice in physics and engineering relies on mathematical sense making—reasoning that leverages coherence between formal mathematics and conceptual understanding. A key question for physics education is how well current instructional approaches develop students’ mathematical sense making. We introduce an assessment paradigm that operationalizes a typically unmeasured dimension of mathematical sense making: use of calculations on qualitative problems and use of conceptual arguments on quantitative problems. Three assessment items embodying this calculation-concept crossover assessment paradigm illustrate how mathematical sense making can positively benefit students’ problem solving, leading to more efficient, insightful, and accurate solutions. These three assessment items were used to evaluate the efficacy of an instructional approach focused on developing students’ mathematical sense making skills. In a quasi-experimental study, three parallel lecture sections of first-semester, introductory physics were compared: two mathematical sense making sections, one with an experienced instructor and one with a novice instructor, and a traditionally taught section, as a control group. Compared to the control group, mathematical sense making groups used calculation-concept crossover approaches more often and gave more correct answers on the crossover assessment items, but they did not give more correct answers to associated standard problems. In addition, although students’ postcourse epistemological views on problem-solving coherence were associated with their crossover use, they did not fully account for the differences in crossover approach use between the mathematical sense making and control groups. These results demonstrate a new assessment paradigm for detecting a typically unmeasured dimension of mathematical sense making and provide evidence that a targeted instructional approach can enhance engagement with mathematical sense making in introductory physics.
format	article
author	Eric Kuo Michael M. Hull Andrew Elby Ayush Gupta
author_facet	Eric Kuo Michael M. Hull Andrew Elby Ayush Gupta
author_sort	Eric Kuo
title	Assessing mathematical sensemaking in physics through calculation-concept crossover
title_short	Assessing mathematical sensemaking in physics through calculation-concept crossover
title_full	Assessing mathematical sensemaking in physics through calculation-concept crossover
title_fullStr	Assessing mathematical sensemaking in physics through calculation-concept crossover
title_full_unstemmed	Assessing mathematical sensemaking in physics through calculation-concept crossover
title_sort	assessing mathematical sensemaking in physics through calculation-concept crossover
publisher	American Physical Society
publishDate	2020
url	https://doaj.org/article/2e40c70ed24343d5814266e3cd19ec6f
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Assessing mathematical sensemaking in physics through calculation-concept crossover

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