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Using Python to Reason About Logic and Set Theory: Three Instrumented Action Schemes

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Abstract

Many areas of mathematics naturally lend themselves to machine-based computing environments, which suggests that computational environments may serve as useful mediating tools for the teaching and learning of mathematical content. While some mathematics classes are leveraging the use of computational tools, the implementation of computer programming to teach and learn mathematics is not widespread. In this study, I highlight the mathematical activity of four undergraduate students who used Python to solve mathematical tasks in the context of set theory and logic. To understand how the students leveraged the computer programming environment, I use the analytical framework known as the instrumental approach, which can be utilized to investigate the confluence of an artifact (often a piece of technology) and the human mind to solve a mathematical problem. Results indicate that the students were able to use Python and its computational capabilities such as For Loops, If Statements, and Functions as artifacts to reason about propositional statements, set intersection, and subsets. Specifically, three instrumented action schemes emerged from their work on three different tasks. These schemes describe the use of Python in creative ways to solve mathematical tasks, which suggests various implications for teaching and research.

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Data Availability

The datasets generated and analyzed during the current study are not publicly available due the fact that they constitute an excerpt of research in progress, but are available from the corresponding author on reasonable request and subject to approval through the California State University, Long Beach Institutional Review Board.

Notes

  1. A 4-year HSI is a bachelor’s-granting (at minimum) institution in which at least 25% of the student population identify as Latinx.

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  1. Department of Mathematics and Statistics, California State University, Long Beach, Long Beach, USA

    Antonio Estevan Martinez IV

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As the sole author, Antonio Martinez conducted all the research, analysis, and writing of this manuscript.

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Correspondence to Antonio Estevan Martinez IV.

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Martinez, A.E. Using Python to Reason About Logic and Set Theory: Three Instrumented Action Schemes. Digit Exp Math Educ 10, 1–28 (2024). https://doi.org/10.1007/s40751-023-00130-9

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