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?

Publications

  1. Hagman, J., Voigt, M., Bolick, M.A., Pai, L., Kress, N., Bennett, A., Tremaine, R., Wonch Hill, P., Quaisley, K., Funk, R., & Smith, W. (Under review). Experiencing tensions of nepantla while working toward critical transformations from within. Conference on Research in Undergraduate Mathematics Education. Omaha, NE.
  2. Bolick, M.A., Pai, L., Voigt, M., Funk, R., & Rader, B. (Under review). Learning to engage students as partners in critically-oriented reform of tertiary mathematics. 15th International Congress on Mathematics Education. Sydney, Australia.
  3. Hagman, J., Voigt, M., Bolick, M.A., Pai, L., Kress, N., Bennett, A., Tremaine, R., Wonch Hill, P., Quaisley, K., Funk, R., & Smith, W. (Under review). Experiencing tensions of nepantla while working toward critical transformations from within. 15th International Congress on Mathematics Education. Sydney, Australia.
  4. Quaisley, K., Funk, R., Pai, L., Ahrens, S., Smith, W.M., & Thomas, A. (Under review). Impacting primary grades STEM teacher leadership identities.

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.

In a collaboration started at GRWC, I worked with Calum MacRury, Tomáš Masařík, and Xavier Pérez-Giménez on studying discrepancy in two models of random hypergraph. The discrepancy of a hypergraph is, in some sense, a measure of how well we can balance a vertex-coloring over the hypergraph's edges.

Publications

  1. MacRury, C., Masařík, T., Pai, L., & Pérez-Giménez, X. (2023). The phase transition for discrepancy in random hypergraphs. SIAM Journal on Discrete Mathematics, 37(3), 1818-1841. arXiv:2102.07342