Teaching

Teaching philosophy, experience, awards, and professional development.

I have over twelve years of experience teaching mathematics at the university level, including courses at the University of Michigan, the University of California, Santa Cruz, and the National Autonomous University of Mexico (UNAM).

My teaching emphasizes mathematical reasoning, problem-solving, and communication. I aim to create an inclusive learning environment where students feel comfortable asking questions, exploring different approaches, and developing confidence in their mathematical abilities.

In 2025, I received the B. Alan Taylor Outstanding Postdoctoral Assistant Professor Teaching Award from the University of Michigan.

Teaching Philosophy

My primary goal as a mathematics educator is to help students become independent mathematical thinkers. I seek to develop their confidence in approaching unfamiliar problems, constructing mathematical arguments, and communicating their ideas clearly. This goal guides my course design, classroom teaching, office hours, and mentorship.

I pursue this goal through three complementary strategies: creating a supportive learning environment, designing problems that encourage multiple approaches, and helping students recognize connections between mathematical ideas.

Creating a Supportive Learning Environment

I believe that students learn mathematics more effectively when they feel comfortable asking questions, making mistakes, and discussing their ideas. I emphasize that seeking help is an essential part of learning and that both the classroom and office hours are spaces where students’ questions are welcome.

I also acknowledge my own mistakes and encourage students to make conjectures during class discussions. My goal is to help students recognize that mathematical reasoning develops through exploration, practice, and feedback.

This approach was strongly influenced by my experience as a literacy educator in Mexico. For three years, I participated in the Campaña de Alfabetización Cemac–Logos–C.I.E., teaching adults in Indigenous communities.

The program introduced me to Paulo Freire’s educational philosophy and his culture-circle method, which emphasizes dialogue and the experiences of learners. I learned the importance of creating an environment in which students’ ideas are valued and their experiences become part of the learning process.

Designing Problems to Support Mathematical Understanding

In my courses, I design activities that encourage students to explore different approaches, collaborate with their peers, and explain their mathematical reasoning.

For example, in Math 116: Integral Calculus at the University of Michigan, I used team-based seating and collaborative worksheets to encourage students to solve problems together.

While teaching the ratio test for series convergence, I noticed that some students were unfamiliar with factorial expressions. I therefore designed an activity that broke a complicated factorial quotient into intermediate steps before asking students to determine the radius of convergence.

This experience illustrates an important aspect of my teaching: adapting mathematical problems to students’ different levels of preparation without sacrificing conceptual understanding.

I also emphasize mathematical communication. In Math 440: Laboratory of Geometry, I worked with undergraduate students on mathematical writing, oral presentations, and research posters.

For example, I introduced students to the structure of mathematical definitions and asked each research team to apply these principles to a central definition from its own project.

Connecting Mathematical Ideas

I aim to present mathematics as a cohesive body of knowledge rather than a collection of isolated topics. I design problems that connect ideas from previous courses to more advanced mathematics and applications in other disciplines.

At UNAM, while teaching students from different academic programs, I used linear algebra to introduce the mathematical formulation of the Hardy–Weinberg principle and its connections to genetics and evolution.

At the University of Michigan, in Math 316: Ordinary Differential Equations with Proofs, I emphasized connections between differential equations and linear algebra.

For example, I introduced linear differential operators and guided students to understand the orthogonality of Legendre polynomials through their interpretation as eigenfunctions of self-adjoint Sturm–Liouville operators.

Through these connections, I hope students develop a deeper understanding of mathematics and recognize how ideas learned in one course can become powerful tools in another.

Undergraduate Research and Mathematical Independence

My teaching philosophy also guides my approach to undergraduate research. I seek open problems that students can investigate using mathematics they already know, while introducing them to broader research questions and more advanced mathematical ideas.

Through this process, students develop independence, creativity, and confidence in their mathematical abilities.

For examples of my mentoring activities, see my Undergraduate Research page.

Courses Taught

University of Michigan (2023–2026)

  • Math 433 — Introduction to Differential Geometry (Winter 2026)
  • Math 316 — Ordinary Differential Equations with Proofs (Winter 2024, Spring 2024, Fall 2024, Winter 2025)
  • Math 440 — Geometry Lab (Fall 2024, Winter 2025, Fall 2025, Winter 2026)
  • Math 116 — Integral Calculus (Fall 2023, Fall 2025)

University of California, Santa Cruz (2017–2023)

Graduate Teaching Assistant for:

  • Math 103A — Complex Analysis
  • Math 19B — Integral Calculus
  • Math 19A — Differential Calculus
  • Math 11 — Calculus with Applications
  • Math 3 — Precalculus
  • Math 21 — Linear Algebra
  • Math 24 — Ordinary Differential Equations
  • Math 23A — Vector Calculus with Applications

National Autonomous University of Mexico (UNAM, 2012–2017)

Assistant Lecturer (2016–2017)

  • Differential Calculus (Winter 2017)
  • Integral Calculus (Fall 2016)

Graduate Student Instructor (2014–2016)

  • Abstract Algebra (Fall 2014, Winter 2015)
  • Analytic Geometry (Fall 2015)
  • Differential Calculus (Winter 2016)

Undergraduate Teaching Assistant (2013–2014)

  • Abstract Algebra
  • Multivariable Calculus

Teaching Award

In 2025, I received the B. Alan Taylor Outstanding Postdoctoral Assistant Professor Teaching Award from the Department of Mathematics at the University of Michigan.

This award recognizes excellence in undergraduate mathematics teaching.

View Teaching Award Certificate

Teaching Development and Certifications

I have participated in professional development programs focused on inclusive teaching, educational equity, and creating supportive learning environments.

  • Rackham Professional Development Certificate in Diversity, Equity, and Inclusion — Rackham Graduate School, University of Michigan (2025).

    View Rackham DEI Certificate

  • Preparing for Inclusive Teaching — Center for Innovations in Teaching and Learning, University of California, Santa Cruz (2017, 2018, 2020, 2021).

    View Inclusive Teaching Certificate (2021)