Most mathematicians state mathematics is a field of beauty, creativity, and innovation, yet what is echoed by students is not how mathematics allows students to explore, but rather the ways in which it constrains and does not necessitate creativity. In comparison, many students associate coding with freedom, and the ability to create and express themselves. Therefore, a natural question that arises is what if computation, enacted through coding, could offer mathematics education more than just an application or skill? What if computation was a pedagogical design tool for mathematical creativity? This dissertation used cultural-historical activity theory as a theoretical perspective alongside case study methodology to answer the guiding research question: How can computation enacted through coding provide opportunities for students to develop and express their mathematical creativity specifically in the context of learning linear algebra? This study followed students recruited from an introduction to computational modeling course as they engaged with a sequence of eight Jupyter computational notebooks that introduce linear algebra. Each computational notebook was designed using an understanding by design framework with multiple ways to elicit student understanding and engagement with mathematical creativity. Further, use-modify-create cycles were incorporated to scaffold student learning and foster opportunities for mathematical creativity. These notebooks were deployed during an iterative pilot study, after which they were modified for the full study. Students engaged in weekly two-hour observations to complete the modules with their small group, followed by weekly experiential reflections. Students also participated in pre/post surveys and interviews. The data analysis included iterative coding methods using operationalized dimensions of creativity: fluency, originality, flexibility, visualization, elaboration, and risk, as well as framework linking student experiences in mathematics and computation to their relationship with the discipline. Five central claims resulted from this study. The first claim was that computation, enacted in a creative environment, enabled opportunities for experimentation within mathematics through prediction and reflection cycles. Second, computation, enacted through coding, aided in the facilitation of connecting multiple representations. Third, computation provided new opportunities for students to expand their views of the nature of mathematics. Fourth, computation provided a novel environment that challenged previous negative mathematical experiences and allowed for shifts in students’ mathematical self-image. Finally, computation enacted through coding provided the opportunity for students to develop new mathematical habits and strategies. These claims highlighted the potential power that computation has to foster opportunities for mathematical creativity, specifically through computational prediction and reflection cycles, visualization capabilities, and computational practices that align with mathematical creativity. This study serves as a proof of existence case for computation, enacted through coding in a creative environment, enabling mathematical creativity. Additionally, this study provides an alternate pathway for the integration of computation and mathematics. Rather than bringing computation into a mathematics classroom, this study introduces mathematics in a computation setting. This shift provides new potential integration pathways and is especially important for the computational education and computer science education communities. It also counters a deficit view of students, and leverages their assets, namely computation, as way of learning linear algebra. This work serves to contribute to the growing work exploring the integration of computation within post-secondary mathematics while simultaneously advocating for researchers and educators to think beyond computing as a tool, but also as a potential pedagogical approach to transform the undergraduate mathematics experience.
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