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When skill meets struggle: Mapping students’ physmatic difficulties to physmatic skills in physics lessons

Hadas Levi1,2,*, Yaron Lehavi3,4, and Avraham Merzel1

  • *Contact author: hnlevi@gmail.com
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Phys. Rev. Phys. Educ. Res. 22, 010113 – Published 3 February, 2026

DOI: https://doi.org/10.1103/s3wr-sbqb

Abstract

The interplay of mathematics within physics—termed here as physmatics—presents unique cognitive challenges for students, requiring coordination between mathematical reasoning and physical sensemaking. While previous studies have documented common physmatic difficulties, capturing these challenges as they emerge in classroom instruction is rare. This study analyzed 273 teacher–student interactions from 23 video-recorded physics lessons taught across a diverse range of classrooms, aiming to identify and categorize physmatic difficulties as they naturally arose during instruction. Twenty-four codes of difficulties were identified through content analysis and grouped into five overarching clusters: (i) questions about model components, (ii) questions about the model, (iii) difficulties applying mathematics in a physical context, (iv) interrepresentational fluency, and (v) unit-related difficulties. A key finding of this study was the identification of systematic associations between the modeling skills teachers aimed to develop (i.e., mathematization, manipulation, interpretation, and validation) and the corresponding student difficulties. These findings underscore the centrality of modeling as a pedagogical framework for physics instruction and suggest that teachers who are aware of the links between skills and difficulties may be better prepared to anticipate student struggles, respond to them in real time, and even leverage them as part of their instructional practice.

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Outline

Information

Phys. Rev. Phys. Educ. Res. 22, 010113– Published 3 February, 2026
  • Received 3 October 2025
  • Accepted 14 January 2026
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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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