Here is my curriculum vitae.

The CV above has more details on research projects I have been on, this page mostly serves to give links to materials or videos of my research. Here is my dissertation, titled Culture and Context: How Frames of Teaching and of Learning Mathematics Form and Change for Graduate Student Instructors.

In short, my research log has mostly centered in undegraduate mathematics education research through working on several NSF-funded projects with the Center for Science, Mathematics and Computer Science Education at University of Nebraska-Lincoln. I am currently building towards a varied portfolio of research.

Research Journey

I have come a long way in my journey to figure out what it is I want to do as a researcher. At first, I wanted to do partial differential equations research that modeled and animated solid-fluid interaction (initially inspired by the works by Professor Joseph M. Teran).

Then, I found out that I didn't actually want to stand at the pioneering edge of PDE research, instead I found a more personal research problem: why do teachers teach the way that they do? Mostly to understand how cultures of exclusion have perpetuated in mathematics classrooms for so long. This became the focus on my dissertation, using and developing a framework for understanding mathematics instructors' frames of teaching and of students' learning. In short, I found what things instructors think about when they think about their teaching or their students' learning of mathematics.

But now, after co-leading an applied mathematics research project through a summer Research Experience for Undergraduates with another graduate student Michael Pieper, I was reminded of my interest in applied mathematics research. Not to stand at the pioneer's fronteir of PDEs, but this time, to help mentor and advise students who do want to go onto treading new ground in applied mathematics.

Now I'm moving towards a mixture of mathematics education (improving undergraduate experiences and outcomes), applied mathematics (computational PDEs), and data science (machine learning and data visualization).

Math Education Research Papers

  1. Cristobal, J. B. (2025). From “Struggle” to “Acceptance”: Andy’s Narrative of First-Time Teaching and Her Frames. In S. Cook, B. P. Katz & K. Melhuish (Eds.), Proceedings of the 27th Annual Conference on Research in Undergraduate Mathematics Education, Alexandria, VA (pp. 149-156). PDF.
  2. Cristobal, J. B. (2025). Aspects of Culture and Context which Shape Frames of Teaching and Learning. In S. Cook, B. P. Katz & K. Melhuish (Eds.), Proceedings of the 27th Annual Conference on Research in Undergraduate Mathematics Education, Alexandria, VA (pp. 157-164). PDF.
  3. Funk, R., Pai, L., & Cristobal, J. B. (2024). “Persistence in a S-STEM grant: Understanding the Intersectional Experiences of Women Pursuing STEM.” Conference Paper for the 2024 American Society for Engineering Education Annual Conference & Exposition.
  4. Funk, R., Pai, L., Rader, B., Cristobal, J. B., & Lewis, J. (2024). “"Someone has invested in me to do this": Supporting Low-Income Students to Persist in STEM through a NSF S-STEM grant.” Poster Paper for the 2024 American Society for Engineering Education Annual Conference & Exposition.
  5. Cristobal, J. B. (2024). Complicating the Relationship of Frames and Responses in Teacher Noticing. In Cook S., Katz, B., Moore-Russo, D. (Eds.), Proceedings of the 26th Annual Conference on Research in Undergraduate Mathematics Education, Omaha, Nebraska (pp. 268-276). PDF.

I am part of the multi-institution research team of Achieving Critical Transformations in Undergraduate Programs of Mathematics (ACT UP Math). I was involved with the propogation efforts to disseminate the things we learned over the course of three years of data collection and the analysis which happened concurrently and afterwards. I bring these lessons to critically examine my own instruction as a Mathematics professor.

Math Education Research Talks

  • This YouTube playlist contains all recordings of talks I have given, so far just in the Mathematics Education space.
  • My dissertation defense:

Applied Projects

  • MATLAB Implimentations of Topics from Math 151AB Applied Numerical Methods UCLA
  • Image Compression via a K-Nearest Neighbors Algorithm (Final project for Math 833 Nonlinear Optimization)
  • 1-Dimensional Signal Denoising (Mentor role for the First Year First Generation REU at UNL Mathematics)
  • Implementing 2D Fluid Simulation: Navier-Stokes Spectral Method (Personal Project)