If Creativity Return Computing: Exploring the Impact of Computing on Students’ Mathematical Creativity in Linear Algebra

The desire for computing in mathematics and statistics education is not a novel concept, as many have rallied support for educational reform to match the needs of a changing world [3, 4, 5, 6]. Nonetheless, these calls typically center the need for preparing students for future careers or the co-construction of both knowledge bases. These calls are important, but what if computing could offer more? Specifically, coding being a rich pedagogical tool that also equipped students with crucial skills and knowledge to thrive. This desire is reified through the calls for increased creativity within mathematics, as many students view the subject as a dead subject that relies on memorizing procedures to answer meaningless questions [2]. Coding is a novel environment where persistence is the norm (i.e. debugging) and students many times are able to pursue their own lines of thinking and solution methods. To explore the potential relationship between computation and mathematical creativity, two research questions were asked. RQ1: How do students engage in mathematical creativity, if at all, when engaging in mathematical computing? RQ2: Does the nature of student’s conceptualization of mathematics change when exposed to computational mathematics, and if so, how? Both questions are centered around using computation and coding, not only as a tool for solving problems, but also a novel environment for students to encounter new mathematics. Therefore, a total of six Jupyter Notebooks were developed using an Understanding by Design Framework [7] to introduce students to linear algebra. Eight participants were recruited from an introduction to computational modeling class, with the sole prerequisite of Calculus I. Participants were placed into groups, which met 2 hours/week, across 6 weeks, with the goal of one notebook per session. Semi-structured entrance and exit interviews were conducted to explore student experiences and conceptions surrounding mathematics, creativity, and computing. Participants also took pre/post surveys which focused on self-efficacy, problem solving approaches, and conceptions of mathematics and computing. Observations and interviews were coded along 5 dimensions of mathematical creativity: originality, flexibility, visualization, elaboration, and risk [1]. The manifestation of each dimension was tracked over time, and dimensional profiles were developed, highlighting which coding and pedagogical features created the opportunity for creativity. Finally, profiles of students were created for before and after the experience to examine views of computation and mathematics. Throughout the study every participant demonstrated numerous examples of mathematical creativity, such as the exploration and visualization of the relationship between the determinant, linear independence, and the volume of a parallelepiped. Further, all students experienced either no change, or a positive shift in mathematical self-efficacy and view of mathematics specifically related to mathematical creative experiences. Multiple students emphasized the ability to pursue their own line of thinking and expressing multiple solution paths, which countered some of the initial conceptualization of a sole answer that is only accessible through one method as dictated by an instructor. This study highlights the vast potential that computation has for mathematics education and potential pedagogical and computational strategies to bring about creativity within coding as well.