Research

My doctoral degree is in mathematics, and I wrote my dissertation about random hypergraphs. Now, most of my research focuses on STEM education, although I still do a small amount of work in discrete math (and in particular graph theory). Denison students who are interested in working with me on a research project, whether in education or in discrete math, should email me or drop by my office to introduce themselves.

STEM Education

My experiences as a discrete mathematician and a college math instructor have stoked my interest in studying issues related to undergraduate and graduate mathematics education. My current research focuses on undergraduate mathematics education, as well as STEM education more broadly, with an emphasis on understanding how students' various and intersecting identities influence their experiences in mathematics departments and programs.

I believe that critical viewpoints are necessary to understand issues of equity and inclusion within schools and departments. As I develop as an education researcher, I am interested in leveraging such perspectives to investigate the intersection between university mathematics departments, teaching, and equity---how can we support professional mathematicians in seeing themselves as educators bearing responsibility for equity, inclusion, and justice; and, conversely, how can we support professional educators in seeing themselves as mathematicians with the power to make change in math spaces?

Journal Publications

Hagman, J., Voigt, M., Bennett, A., Nicole, F., Bolick, M.A., Pai, L., Kress, N., Quaisley, K., Tremaine, R., Funk, R., Wonch Hill, P. & Smith, W.M. (2024). Experiencing tensions of nepantla with inner-departmental change groups. Frontiers in Education, 9. https://doi.org/10.3389/feduc.2024.1454303
Quaisley, K., Funk, R., Pai, L., Ahrens, S., Smith, W.M., & Thomas, A. (2024). Impacting primary grades STEM teacher leadership identities. School Science and Mathematics 1-13. https://doi.org/10.1111/ssm.18313
Bolick, M.A., Pai, L., Funk, R., & Voigt, M. (Under review). Learning to engage students as partners in critically-oriented reform of tertiary mathematics.
Mei, M., Miller, A., & Pai, L. (Under review). Assessing a first-year calculus placement policy.

Conference Publications

Bolick, M.A., Pai, L., Voigt, M., Funk, R., & Rader, B. (2024). Learning to engage students as partners in critically-oriented reform of tertiary mathematics. 15th International Congress on Mathematics Education. Sydney, Australia.
Hagman, J., Voigt, M., Bolick, M.A., Pai, L., Kress, N., Bennett, A., Tremaine, R., Wonch Hill, P., Quaisley, K., Funk, R., & Smith, W. (2024). Experiencing tensions of nepantla while working toward critical transformations from within. 15th International Congress on Mathematics Education. Sydney, Australia.
Funk, R., Pai, L., & Cristobal, J.B. (2024). (WIP) Persistence in an S-STEM grant: Understanding the intersectional experiences of women in STEM. American Society for Engineering Education. Portland, OR.
Funk, R., Lewis, W.J., Pai, L., Cristobal, J.B., & Rader, B. (2024). “Someone has invested in me to do this”: Supporting low-income students to persist in STEM through an NSF S-STEM grant. American Society for Engineering Education. Portland, OR.
Bolick, M.A., Pai, L., Funk, R., Voigt, M., & Rader, B. (2024). Learning to engage students as partners in critically-oriented reform of tertiary mathematics. Conference of the International Network for Didactic Research in University Mathematics. Barcelona, Spain.
Hagman, J., Voigt, M., Bolick, M.A., Pai, L., Kress, N., Bennett, A., Tremaine, R., Wonch Hill, P., Quaisley, K., Funk, R., & Smith, W. (2024). Experiencing tensions of nepantla while working toward critical transformations from within. Conference on Research in Undergraduate Mathematics Education. Omaha, NE.

Graph Theory

My dissertation is about the threshold for the appearance of perfect matchings in k-uniform, k-partite random hypergraphs. This work is a variation on Shamir's problem, which asks, roughly, how many edges we need to include in a random hypergraph to be (asymptotically almost) sure that it contains a perfect matching.

I have also explored other problems in graph theory and combinatorics at GRWC!