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How Students Construct Sophisticated Differential Equations to Model Real-World Contexts

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Abstract

Differential equations (DEs) are a powerful tool for modeling real-world contexts. Most research in this area has examined students’ understanding and reasoning with pre-packaged DEs, with little attention being given to setting up sophisticated DEs to model complicated real-world situations. This study contributes through a collective case study on how individual students constructed DEs for various real-world systems, including a mechanical, a hydraulic, and an electrical system. We examined the students’ readouts (how they “read” a context), their inferential nets (inferences across knowledge resources), and their strategies (what guided their work), according to coordination class theory. Our study contributes the foundation of a knowledge base in students’ DE modeling that further research and teaching work can build on.

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Notes

  1. We use “model” to mean a mathematical object (e.g. equation and graph) that represents some system and from which information about the system can be obtained (see Blum et al., 2007, p.4). In this way, we see a DE in and of itself as a “model” of a system. For example, the physics DE \(x{\prime}{\prime}=-kx\) models a pendulum in simple harmonic motion.

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  1. Brigham Young University, Provo, UT, 84602, USA

    Omar A. Naranjo & Steven R. Jones

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  1. Omar A. Naranjo
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Naranjo, O.A., Jones, S.R. How Students Construct Sophisticated Differential Equations to Model Real-World Contexts. Int J of Sci and Math Educ 22, 945–969 (2024). https://doi.org/10.1007/s10763-023-10411-9

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