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Choreo-graphing periodic functions: aesthetically driven covariational reasoning
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DOI：10.1007/s10649-026-10521-5.png)
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Abstract
En 中文
This paper investigates how 11th-grade students’ covariational reasoning with periodic functions emerges when they choreograph function-driven animations to music in a dual digital environment. Building on new materialist perspectives, we reconceptualise covariational reasoning as an aesthetic-material practice distributed across assemblages of students, tools, graphs and sounds. We introduce the construct of aesthetically driven covariational reasoning to describe how emergent qualities of fit and misfit between motion and music participate in organising relations between the varying quantities. The study is part of a design-based research project with students working in pairs to create their function-driven “dancing animations” for given song excerpts. They initially used GeoGebra calculator to plot the periodic functions (simple trigonometric function families of sine and cosine and trigonometric polynomials) by adjusting coefficient values in order to plan the choreography and then they used the MaLT2 digital environment for simulating the animation through a dynamic square. Screen-audio recordings and researcher notes were analysed as aesthetic events, focusing on multimodal instances where reasoning shifted. The analysis identifies four recurrent aesthetic functions—composition, attunement, modulation and provisional individuation—through which reasoning unfolds. Across a series of events, we show how these functions give rise to mathematical meanings about periodic covariation, including amplitude-dependent and amplitude-independent period, relations between vertical span, monotonicity and perceived speed, and emergent derivative-like meanings of local rate of change in trigonometric polynomials. We argue that attending to aesthetic-material dynamics offers a complementary lens on covariational reasoning and suggests design approaches that treat students’ aesthetic responses as productive resources.
Keywords:
Aesthetics
Covariational reasoning
New materialism
Periodic functions
Educational technology
Music
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