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Bridging the Gap Between Set Theory and Logic: Leveraging Computing as a Mediating Tool for Learning


Undergraduate mathematics education research focused on Introduction to Proofs courses has gained traction as more students are experiencing challenges in their proof-based courses. While studies have analyzed the teaching and learning of proofs, there is a growing need for research in students’ understanding of mathematical logic and set theory because of the foundational nature of these topics in more advanced mathematics courses. In this dissertation, I present a teaching experiment that explores how computing/programming can be leveraged to facilitate and strengthen the connection between set theory and logic. Programming is a focus of this work due to the growing need for undergraduate Science, Technology, Engineering and Mathematics majors to be prepared for their future careers, which will likely entail the utilization of computing in some form. The purpose of this study is to take a step in the direction of where undergraduate education is headed and better understand how the use of computing can potentially fit into the mathematics curriculum.

There are three main dimensions of this study. The first is a look at how programming can influence students’ in-the-moment ways of reasoning about mathematical set theory and logic. The second takes a step back to consider the students’ advancing mathematical activity and growth over the course of a multi-session long teaching experiment. The third is a focus on the students’ affective experiences, as non-cognitive factors such as confidence, interest and self-efficacy are analyzed to characterize the shifting nature of the students’ mathematical identities. The results of this study indicate that the students in my study were able to leverage computing as an accessible onramp to the fundamental ideas related to set theory and logic. Moreover, my findings show that computing can have a positive effect on one’s sense of confidence and interest in relation to mathematics and programming.

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