I subscribe to Federico Ardila-Mantilla's axioms. Those are:

1. Mathematical potential is equally present in different groups, irrespective of geographic, demographic, and economic boundaries.

2. Everyone can have joyful, meaningful, and empowering mathematical experiences.

3. Mathematics is a powerful, malleable tool that can be shaped and used differently by various communities to serve their needs.

4. Every student deserves to be treated with dignity and respect.

• Fall 2026 Teaching Assignment: MAT 112 - Cotemporary Topics in Mathematics. Here is a link to the course notes.

• I was honored to win the 2025-2026 Graduate Teaching Assistant Teaching Award by the Graduate Studies Committee of the Department of Mathematics and Statistics.

• Past Teaching Assignments at UNCG: MAT 112 - Contemporary Topics in Mathematics, MAT 115 - College Algebra, MAT 118 - Algebra with Business Applications, MAT 296 - Calculus B

• Past Teaching Assignments at NAU: MAT 108 – College Algebra, MAT 121 – Calculus for Business, MAT 125 – Precalculus, MAT 136 – Calculus 1, MAT 137 - Calculus 2, MAT 238 Calculus 3

• Past Teaching Assignments at UVM: MATH 1012 - College Algebra

Teaching Statement

Mathematics is difficult. It asks students to learn a strange language, move beyond computation, and make claims that require connection, justification, and generalization. That difficulty is not a defect in the discipline; it is the reason mathematics is worth learning. My responsibility as a teacher is to create a classroom in which students can meet content with curiosity rather than fear. I want students to leave my courses with stronger mathematical habits – reading carefully, asking useful questions, testing conjectures, and communicating a line of reasoning – as well as the confidence that they belong in a community of people who do those things together.

That work begins with relationships. I believe educators must recognize the inequities students bring with them into a classroom. Students’ experiences of safety, dignity, health, disability, and belonging are not distributed evenly, and I do not believe that equity consists merely of accommodating a student after a barrier has been announced or appeared. It means designing a course with a medley of students in mind from the beginning and remaining willing to revise structures when those structures fail to serve any individual. I learn about students’ interests and lives beyond the classroom; small conversations help make it clear that they are more than a name on a roster. I am lively and conversational in the classroom, but I do not mistake rapport for inclusion. A welcoming room also needs structures that make participation possible for students who arrive with different mathematical experiences, preparation, and demands on their time. I state learning goals and expectations plainly, make materials accessible before students need them, and build reasonable flexibility into deadlines and assessment formats when circumstances warrant it. The aim is to make the path to meeting high standards visible and navigable.

For many years, my syllabi have included a brief statement, Rights of the Learner, borrowed from a former professor. These rights have always resonated with me: the right to be confused; to make a mistake and revise one’s thinking; to speak, listen, and be heard; and to enjoy doing mathematics. These ideals guide how I respond when a student offers an incomplete idea, how I structure discussion, and how I design opportunities to try, revise, and try again. I also establish shared expectations for classroom etiquette: Individual differences are respected and recognized as a source of strength; students are encouraged to ask questions, listen carefully to one another, and collaborate; and every member of the class is responsible for protecting the community we are trying to build. Students need not arrive confident in mathematics (or confident at all), but they should be able to trust that confusion and error will be treated as ordinary aspects of learning rather than evidence of wrongness or that they, as students, do not belong.

My courses are built around exercise, practice, and experience. I use active-learning methods because students learn mathematics by doing mathematics – through the tip of their pencil – not by watching someone else. In a typical class, students might have time to attempt a problem individually, then compare approaches with a partner or small group, and finally help assemble and critique a solution as a class. In others, I might conduct a more standard lecture, albeit one where my quirky examples and anecdotes invite buy-in. We argue about the qualities that make a dog cute while comparing and contrasting my parents’ dogs to learn about why well-defined-ness is an important quality for members of a set. We talk about Sasquatch when learning about witnesses. We might take a detour about Minecraft (subgroups of Cartesian products) or bathroom tile (groups), sidebars that help to make meaning and memory. We use low-stakes problems, short written reflections, and frequent informal checks for understanding to see what students are making of the material and to adjust my teaching before a high-stakes examination does the diagnosing. Clear grading expectations, accessible course materials, and timely, constructive feedback are likewise part of this work: Students should know what they are learning, why they are learning it, and how they can improve.

I use inquiry-based learning when possible. Rather than presenting every theorem as a finished artifact, I ask students to notice patterns, make conjectures, test examples, and decide what would count as a proof. In an introductory proof course, for instance, students might compare several proposed arguments – not all correct – and identify the definitions, assumptions, and logical moves on which each depends. In calculus or quantitative-reasoning courses, I pair conceptual questions with calculations so that students must explain what a result means as well as obtain it. Such work makes thinking visible. It develops independence, but it also establishes collaboration as a serious mathematical practice: Students learn to listen closely, revise their own ideas, and give one another useful feedback. The same habits matter beyond mathematics. Careful attention, reasoned disagreement, and a willingness to change one’s mind in light of evidence are skills I want students to internalize.

Context is another way I invite students into the discipline. Mathematics has a history – tragic and funny and deeply human – and practitioners, uses, and stories. It is not a collection of procedures delivered from nowhere. I draw on the history of mathematics, real applications, and the origins of mathematical language as often as I can. I also make efforts to include stories that are usually omitted. For example, when familiar mathematical ideas have roots outside the standard European canon, we explore that history, like that Pascal’s triangle appeared centuries earlier in Chinese mathematics. A theorem or definition becomes more approachable when students can see what question brought it into being. This is especially important for students who have been taught to regard mathematics as a fixed set of answers belonging to someone else. I want students to encounter mathematics as an unfinished human endeavor – one that rewards precision and imagination along with patience and creativity.

I have taught postsecondary-level content since 2015 and, apart from two years teaching in a magnet high school, my work has been in university classrooms. My teaching has been strengthened by observation, feedback, and reflection. In faculty observations, my observers noted that I invited and used student suggestions, incorporated humor and memorable analogies, and connected concepts to decisions students might make outside of mathematics and the classroom. The observers also found the class engaged and my explanations organized and clear; I used feedback to improve the structure and visual clarity of my board work. Student feedback similarly emphasizes clear grading expectations, patient responses to questions, useful examples, and a classroom energy that makes demanding material approachable. I was honored to receive the University of North Carolina at Greensboro’s 2025–2026 Graduate Teaching Assistant Teaching Award. I value these recognitions not as endpoints, but as evidence that careful preparation, attentiveness to students, and evolution of one’s own practice matter.

My teaching interests include the full lower-division curriculum, precalculus, calculus, quantitative reasoning, and linear algebra, along with an eagerness to instruct – or create – curricula around proof writing, abstract algebra, number theory, complex analysis, cryptography, and the history of mathematics. I am particularly drawn to courses that help students cross the threshold from computation to proof. I would also welcome the intimate challenges and rewards of focused reading courses, independent studies, and an undergraduate mathematics seminar. These settings give students time to follow a mathematical question beyond the catalog, read with care, and practice presenting ideas to others. I have experience mentoring an undergraduate through an exploration of p-adic numbers; giving talks about how our attempts to solve Fermat’s Last Theorem encourage students to learn about more structures and to take upper-division mathematics courses; and, presenting at a mathematics education conference on how famous mathematicians were often wrong, and how those mistakes can teach students determination and resilience.

I learned to teach from people whose care for students was both ordinary and profound. I witnessed Ms. Schmidt’s dedication as she met with me before and after school every day of seventh grade. I felt what it means to belong and be cared for when Dr. Sonderegger skipped an important meeting to listen and advise me on an urgent matter. I saw the preparation and attention to detail Jeff brought to every lecture, and Dana’s commitment to inclusion and adaptability continues to shape my practice. I have seen how Dan empowers and inspires his students. I come from a family of educators, by blood and by bond, and their example has made teaching feel less like a career choice than a calling. I want to carry forward the attention many mentors have given me: to prepare carefully, to notice the person in front of me, and to make room for anyone struggling to find a foothold.

I see teaching as shared work. I ask students to bring their experiences, questions, and effort into the room; in return, I bring exhaustive preparation, boundless energy, and a serious commitment to their learning. I also see the classroom as one part of a larger intellectual community. I value conversations with colleagues about teaching and participation in seminars, colloquia, bootcamps, and workshops. My goal is to make a mathematics classroom where rigor and belonging strengthen one another: A place where every student is expected to think hard, feel supported, and recognize their capacity to make contributions valued by everyone in our community.