• Accepted Paper

Chunking of physics formulas: An exploratory study using handwriting recording

Josefine Neuhaus, Pascal Klein, and Andreas Müller

Phys. Rev. Phys. Educ. Res. - Accepted 22 September, 2026

DOI: https://doi.org/10.1103/m6bl-7rnq

Abstract

Formulae are one of the key representations in physics. They serve to model complex physics phenomena using a symbolic mathematical language. Even though it is part of the daily life of physicists to apply formulae in problem solving processes or to discuss phenomena by explaining formulae, little is known about the underlying cognitive processes taking place when we perceive, read or write, formulae. In this paper, this topic is approached through the lens of chunk-based information processing. In a laboratory setting, participants of varying levels of expertise performed a recall task. They were presented with formulae of varying complexity, both in conventional and unconventional representation formats, which they sequentially read, wrote and evaluated in terms of their familiarity. The writing process was tracked digitally, and both recall results and writing dynamics were analyzed.In this recall task, observed patterns are consistent with expertise-dependent chunking in the context of physics formulae. This finding emerges from examining the writing data from different perspectives. Namely, we find that experts are able to reproduce more elements of a formula than the capacity of short-term memory would suggest, with high correlation (ρ = 0.8) between task-specific familiarity and recall results. The relationship between recall rate and expertise was moderated by formula length, as differences in performance across expertise groups were most pronounced for longer formulae, with experts outperforming both lay people and first-year students particularly in this regard. Furthermore, analyses of writing dynamics indicated an increasing relative number of short pauses (tpause<0.54) with task-specific familiarity, as evidenced by a moderate correlation (ρ=0.54) between these metrics. Since within-chunk pauses are assumed to be shorter than between-chunk pauses, this suggests the emergence of larger chunks as expertise develops. Finally, analyses of reordered formulae permit preliminary cautious statements to be made about the nature of these chunks and suggests the potential importance of templates in the perception of formulae.

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