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Characterizing the mathematical problem-solving strategies of transitioning novice physics students

Eric Burkholder

Lena Blackmon

Carl Wieman

  • Department of Physics, Stanford University, 382 Via Pueblo, Stanford, California 94305, USA

  • Department of Applied Physics, Stanford University, 348 Via Pueblo, Stanford, California 94305, USA

  • Department of Physics and Graduate School of Education, Stanford University, 382 Via Pueblo, Stanford, California 94305, USA

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Phys. Rev. Phys. Educ. Res. 16, 020134 – Published 11 November, 2020

DOI: https://doi.org/10.1103/PhysRevPhysEducRes.16.020134

Abstract

Much work has been done to characterize the reasoning of students as they solve mathematics-intensive problems and characterizing differences in expert and novice problem solving. In this work, we characterize the problem-solving strategies in a classroom setting of “transitioning novices,” students who have completed an introductory physics course and have learned some problem-solving strategies, but are far from expertlike in their reasoning. We find that students mostly use intermediate strategies that reflect an understanding of specific relationships between quantities, such as analyzing the units of an expression, to reason about mathematical expressions. Few students use more sophisticated strategies like checking limits, which require students to run mental simulations to predict how a system will behave as different physical variables are changed. The teaching of more advanced strategies like limit checking will require careful scaffolding of the cognitive complexity, as students generally do not succeed when simply told to check limits. This is supported by the findings of Lin and Singh [Phys. Rev. Phys. Educ. Res. 7, 020104 (2011)] that careful scaffolding is needed to help students solve more complex problems. In this particular group, students were able to successfully analyze the dimensions of an expression and compute component forces and torques to check if their answer made sense. Our results show that there is a need to recognize and teach these intermediary strategies to enable more novice students to check their answers and encourage students to become more expertlike.

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Phys. Rev. Phys. Educ. Res. 16, 020134– Published 11 November, 2020
  • Received 20 August 2020
  • Accepted 19 October 2020
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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