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Physical Review Physics Education Research
written by Eric Kuo, Michael M. Hull, Andrew Elby, and Ayush Gupta
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.
Physical Review Physics Education Research: Volume 16, Issue 2, Pages 020109
Subjects Levels Resource Types
Education - Basic Research
- Cognition
= Cognition Development
- Problem Solving
= Processes
General Physics
- Physics Education Research
- Scientific Reasoning
- Graduate/Professional
- Lower Undergraduate
- Reference Material
= Research study
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Free access
License:
This material is released under a Creative Commons Attribution 4.0 license.
Rights Holder:
American Physical Society
DOI:
10.1103/PhysRevPhysEducRes.16.020109
NSF Number:
EEC-0835880
Keywords:
concept mapping, sense making
Record Creator:
Metadata instance created May 12, 2021 by Bruce Mason
Record Updated:
January 25, 2022 by Lyle Barbato
Last Update
when Cataloged:
July 30, 2020
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Record Link
AIP Format
E. Kuo, M. Hull, A. Elby, and A. Gupta, , Phys. Rev. Phys. Educ. Res. 16 (2), 020109 (2020), WWW Document, (https://doi.org/10.1103/PhysRevPhysEducRes.16.020109).
AJP/PRST-PER
E. Kuo, M. Hull, A. Elby, and A. Gupta, Assessing mathematical sensemaking in physics through calculation-concept crossover, Phys. Rev. Phys. Educ. Res. 16 (2), 020109 (2020), <https://doi.org/10.1103/PhysRevPhysEducRes.16.020109>.
APA Format
Kuo, E., Hull, M., Elby, A., & Gupta, A. (2020, July 30). Assessing mathematical sensemaking in physics through calculation-concept crossover. Phys. Rev. Phys. Educ. Res., 16(2), 020109. Retrieved April 18, 2024, from https://doi.org/10.1103/PhysRevPhysEducRes.16.020109
Chicago Format
Kuo, E, M. Hull, A. Elby, and A. Gupta. "Assessing mathematical sensemaking in physics through calculation-concept crossover." Phys. Rev. Phys. Educ. Res. 16, no. 2, (July 30, 2020): 020109, https://doi.org/10.1103/PhysRevPhysEducRes.16.020109 (accessed 18 April 2024).
MLA Format
Kuo, Eric, Michael Hull, Andrew Elby, and Ayush Gupta. "Assessing mathematical sensemaking in physics through calculation-concept crossover." Phys. Rev. Phys. Educ. Res. 16.2 (2020): 020109. 18 Apr. 2024 <https://doi.org/10.1103/PhysRevPhysEducRes.16.020109>.
BibTeX Export Format
@article{ Author = "Eric Kuo and Michael Hull and Andrew Elby and Ayush Gupta", Title = {Assessing mathematical sensemaking in physics through calculation-concept crossover}, Journal = {Phys. Rev. Phys. Educ. Res.}, Volume = {16}, Number = {2}, Pages = {020109}, Month = {July}, Year = {2020} }
Refer Export Format

%A Eric Kuo %A Michael Hull %A Andrew Elby %A Ayush Gupta %T Assessing mathematical sensemaking in physics through calculation-concept crossover %J Phys. Rev. Phys. Educ. Res. %V 16 %N 2 %D July 30, 2020 %P 020109 %U https://doi.org/10.1103/PhysRevPhysEducRes.16.020109 %O application/pdf

EndNote Export Format

%0 Journal Article %A Kuo, Eric %A Hull, Michael %A Elby, Andrew %A Gupta, Ayush %D July 30, 2020 %T Assessing mathematical sensemaking in physics through calculation-concept crossover %J Phys. Rev. Phys. Educ. Res. %V 16 %N 2 %P 020109 %8 July 30, 2020 %U https://doi.org/10.1103/PhysRevPhysEducRes.16.020109


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