Sensemaking of physics equations: Rationale, conceptualization, and core strategies
Abstract
In physics instruction, equations are often treated primarily as tools for obtaining numerical results. Yet physicists also use them to describe dependencies, explain why those dependencies hold, predict what happens in new situations, test expressions against physical knowledge, and explore consequences that are not immediately apparent. Although such uses appear throughout the physics education literature, they have not been brought together in a systematic account, and the terminology used to describe them remains inconsistent. Drawing on research in mathematics education on symbol sense and the function concept, we distinguish six epistemic functions of physics equations: calculating, describing, explaining, predicting, evaluating, and exploring. We then characterize six strategies through which these functions can be realized: dimensional analysis, order of magnitude analysis, covariational analysis, special case analysis, limiting case analysis, and formal analogies, illustrating each with examples from introductory physics. To examine how these strategies are viewed within the discipline, we surveyed 31 physicists at one university faculty about five of the strategies. Respondents regarded the strategies as indispensable to physics, judged limiting case analysis to be more difficult for students than dimensional analysis, and reported that their own courses could devote more time to them. By distinguishing what physicists use equations for from the strategies by which they do so, the paper provides a vocabulary for sensemaking of physics equations and specifies what explicit instruction in these strategies involves.
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BibTeX
@misc{hofmann2026sensemaking,
title = {{Sensemaking of physics equations: Rationale, conceptualization, and core strategies}},
author = {Julia Hofmann and Pascal Klein and Andreas Müller and Josefine Neuhaus},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.04458},
eprint = {2610.04458},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.04458},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Sensemaking of physics equations: Rationale, conceptualization, and core strategies
AU - Julia Hofmann
AU - Pascal Klein
AU - Andreas Müller
AU - Josefine Neuhaus
PY - 2026
DA - 2026/10/03
PB - arXiv
DO - 10.48550/arxiv.2610.04458
UR - https://arxiv.org/abs/2610.04458
AB - In physics instruction, equations are often treated primarily as tools for obtaining numerical results. Yet physicists also use them to describe dependencies, explain why those dependencies hold, predict what happens in new situations, test expressions against physical knowledge, and explore consequences that are not immediately apparent. Although such uses appear throughout the physics education literature, they have not been brought together in a systematic account, and the terminology used to describe them remains inconsistent. Drawing on research in mathematics education on symbol sense and the function concept, we distinguish six epistemic functions of physics equations: calculating, describing, explaining, predicting, evaluating, and exploring. We then characterize six strategies through which these functions can be realized: dimensional analysis, order of magnitude analysis, covariational analysis, special case analysis, limiting case analysis, and formal analogies, illustrating each with examples from introductory physics. To examine how these strategies are viewed within the discipline, we surveyed 31 physicists at one university faculty about five of the strategies. Respondents regarded the strategies as indispensable to physics, judged limiting case analysis to be more difficult for students than dimensional analysis, and reported that their own courses could devote more time to them. By distinguishing what physicists use equations for from the strategies by which they do so, the paper provides a vocabulary for sensemaking of physics equations and specifies what explicit instruction in these strategies involves.
ER -