Leveraging Computation for Fostering Mathematical Creativity and Learning in Undergraduate Linear Algebra

About This Grant

This project aims to serve the national interest by increasing undergraduate STEM students' mathematical creativity and conceptual understanding through the integration of computation into a linear algebra course. The significance of this work lies in its potential to connect students' existing views of coding as expressive and open-ended with more meaningful experiences in mathematics that foster mathematical creativity and understanding. Positioning computing as a mediator of mathematical thinking and creativity is an emerging area of research, especially within the undergraduate research community. Through the development of a set of open-source computational learning modules, this Level I Engaged Student Learning project seeks to broaden participation in STEM and improve the quality of undergraduate mathematics education by developing opportunities for students to engage in computing practices that foster creative mathematical thinking. The importance of this work is the potential to shift how students relate to mathematics, strengthen problem-solving and perseverance skills needed for success in STEM, and provide accessible resources for instructors interested in intentionally integrating mathematics. The project's goals are to (1) develop and assess the impact of a full-semester linear algebra course based on prior piloted modules that use coding as a pedagogical strategy and (2) investigate how such integration affects student learning, creativity, and perceptions of mathematics. The scope of this work includes designing and implementing Jupyter-based activities that encourage prediction, reflection, and debugging, and studying how these features contribute to student learning. Specifically, which features of the computational tasks and computational environment foster mathematical creativity and promote student understanding. The guiding research questions address how computation influences students' (1) conceptual and procedural understanding, (2) opportunities for creativity, and (3) relationship with mathematics. The project will use an instrumental case study approach employing methods of data collection such as classroom observations, interviews, surveys, and student work artifacts. Findings will inform best practices for designing computational mathematics activities as well as new ways of fostering mathematical creativity, and will be disseminated through peer-reviewed publications, conference presentations, and open educational resources. The NSF IUSE: EDU Program supports research and development projects to improve the effectiveness of STEM education for all students. Through the Engaged Student Learning track, the program supports the creation, exploration, and implementation of promising practices and tools. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.