Calculus Students' Mindsets are Not So Simplex

Introduction

In Psychological Meaning System Theory, mindsets are attitudes that people hold about themselves (Dweck, 2000). Traditional studies on mindsets are rooted in psychological methodologies, relying on surveys, questionnaires, and psychometric scales. While these tools give researchers initial insight into the mindset phenomenon, due to their nature, they also prime participants to think about specific mindsets in isolation. To study mindsets from a different methodological perspective, Hensley & Gilroy (2025a, 2025b) analyzed the differences in how Calculus I students’ mindsets manifest over a semester depending on students’ first exposure to a Calculus course (high school or university) using data collected from short reflective prompts during an actual Calculus course. Results suggested that students who took Calculus in high school tend to exhibit different mindsets than those taking it in college for the first time.

Topological Preliminaries

In Topology, an intuitive definition of a simplicial complex is a space with a triangulation (Weisstein, n.d.), which is useful for modeling the structure of multi-dimensional combinations of objects. Each simplicial complex contains a variety of sub-dimensional objects; a vertex is zero-dimensional, an edge is one-dimensional, a filled-in triangle is two-dimensional, a solid tetrahedron is three-dimensional, and so on. The purpose of this study is to revisit the coding results from Hensley & Gilroy (2025a, 2025b) and to conduct a novel analysis of the mindsets exhibited by students who were “successful” in Calculus I. We defined “success” as those earning a final grade of “A” (n = 31) or “B” (n = 28). 

Analysis

For each student, we assigned a “mindset simplex.” For each of Units 1, 2, 3, and 4, we constructed a simplicial complex that modeled each student’s combinations of mindset codes. Then, we tabulated the frequency of simplices in each unit whose vertices represented productive mindsets (growth, mastery, strategic, and curious), non-productive mindsets (fixed, helpless, non-strategic, and non-curious), and mixed mindsets (at least one productive and at least one non-productive mindset). We note that the mindset simplices are similar to the Code Co-Occurrence Model produced by software like MAXQDA (Code Co-Occurrence Model, n.d.). Viewing these combinations of mindsets through a topological lens allows for them to be viewed in higher dimensions. We calculated the relative frequency of the types of simplices (productive, non-productive, and mixed): first, on the aggregated data, then disaggregating initial frequency tabulations by gender, final grade earned, and first setting of Calculus, and comparing between groups. 

Findings

We saw the largest differences between students who first saw Calculus in a high school (HC) setting versus a university setting (CC). CC students had higher proportions of strictly productive mindsets than their HC counterparts. This provides further evidence of the conclusions in Hensley & Gilroy (2025a, 2025b) that these two groups of students exhibit different mindset profiles, implying that they experience a typical general Calculus I course very differently. Furthermore, it may be advantageous for instructors to consider these differences when teaching the course.

References

1. Hensley, D. & Gilroy, H. (2025a). “I’VE ALREADY DONE THIS”: How prior exposure affects calculus students’ mindsets during a semester of regular reflections. In S. Cook, B. Katz, & K. Melhuish (Eds.), Proceedings of the 27th Annual Conference on Research in Undergraduate Mathematics Education (pp. 1496-1497). Alexandria, VA. http://sigmaa.maa.org/rume/RUME27 Proceedings.pdf

2. Hensley, D. & Gilroy, H. (2025b). An Extension of Dweck’s Mindset Theory Within Calculus I. In R. M. Zbiek, X. Yao, A. McCloskey, & F. Arbaugh (Eds.), Proceedings of the 47th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 1665-1669). PME-NA. University Park, Pennsylvania. https://doi.org/ 10.51272/pmena.47.2025

3. Code Co-Occurrence Model. (n.d.). MAXQDA. Retrieved November 7, 2025, from https://www.maxqda.com/help-mx22/maxmaps/the-co-occurrence-model

4. Dweck, C. S. (2000). Self-Theories: Their Role in Motivation, Personality, and Development. Essays in Social Psychology. Taylor & Francis.

5. Weisstein, Eric W. (n.d.). “Simplicial Complex.” From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SimplicialComplex.html