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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
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![]() <a href="https://www.per-central.org/items/detail.cfm?ID=15684">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.</a>
![]() 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).
![]() 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>.
![]() 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, 2025, from https://doi.org/10.1103/PhysRevPhysEducRes.16.020109
![]() 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 2025).
![]() 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. 2025 <https://doi.org/10.1103/PhysRevPhysEducRes.16.020109>.
![]() @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}
}
![]() %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 ![]() %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 Disclaimer: ComPADRE offers citation styles as a guide only. We cannot offer interpretations about citations as this is an automated procedure. Please refer to the style manuals in the Citation Source Information area for clarifications.
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