I was fortunate that I returned to school to rediscover my love and passion for mathematics. This was in large part to the excellent faculty at UH Hilo, and in particular, my mentor Dr. Ramon Figueroa-Centeno. It was then that I made the decision to become a mathematician, and in particular, to become a teacher-scholar who helped other students redefine their relationship with mathematics. Unfortunately, math is not the most beloved subject amongst students, and so a lot of care and effort is needed to help them reforge a new positive relationship with the subject. Students frequently are turned off by math because they see themselves as "not a math person", or they don't see the relevance of mathematics to themselves. I now focus on student centered pedagogy, giving them ownership of their own learning. I center the view that everyone can grow to love, appreciate and excel at mathematics.

Authored OER Materials

• TBIL Calculus 2 along with CheckIt Bank
• Team Based Statistics along with CheckIt Bank
• Finite Mathematics: A Tour

My current research focuses on taking ideas from classical homotopy in topology and extending them to graphs via \(\times\)-homotopy. One could just consider the homotopy of graphs as simplicial spaces, but this isn't very interesting! Instead we define homotopy categorically, with looped paths taking the place of the unit interval, and graph homomorphisms taking the place of continuous functions. In our first paper, my collaborator Dr. Laura Scull and I gave a concrete description on how the "continuous" motions of classical homotopy translate to "discrete" motions in graphs. The gif below depicts a homotopy between two functions.

One may suspect that results about classical homotopy would translate readily, but these are really very different settings. For example the product of two connected spaces is always connected, but the product of connected graphs need not be connected! So it isn't obvious that all classical homotopy results have analogues in \(\times\)-homotopy, and it's not clear how these analogues, when they exist, differ. This makes this an interesting line of research! We have several papers developing \(\times\)-homotopy, with more planned and on the way!

I am the founder of the MSU-Billings Math Circle, which as been ongoing for 4 years. We're happily supported by the Mathematical Association of America DMEG grant. We've had close to 100 students attend over the years, even through the pandemic. This program is free, and open to all students grades 4-8, teachers and parents. We play games, explore activities, work on puzzles, and work together to discover new and wonderful mathematics! We recruit MSUB students including pre-service teachers, for which I've recieved the Universities Pippenger Awars.

To expand the reach of Math Circles, I've become involved in the leadership and organization of Math Circles. I serve as the associate editor of the Journal of Math Circles, program coordinator of the MCTS SIGMAA, and was a co-organizer for the 2021 Circle on the Road workshop.