I have experience in a variety of settings, including content and methods courses for prospective secondary mathematics teachers, courses with high school students in formal and informal settings, proof-based courses, first-year undergraduate courses, and professional development for practicing teachers.
When I teach, I think about:
- Who has power? How do I confer and distribute power? How do students confer and distribute power? What does it mean for power to be equitably distributed?
- What language is used? How does language provide access or put up barriers? What is the language of disagreement? What is the language of resolving disagreement? What is the language of consensus?
- What ways of doing mathematics are valued? How do I recognize and articulate mathematical practice? How do students recognize and articulate mathematical practice? How do these values shape the outcomes of the class, especially from a lens of equity?
- How can we — students and teachers — nurture the community around us?
My journey in teaching has been enormously shaped by the Elementary Mathematics Laboratory, the Algebra Project, and the Canada/USA Mathcamp. I wrote about this the (once active) AMS Blog for Teaching and Learning.
Throughout the academic year 2009-2010, I visited the Ypsilanti cohort of the Algebra Project and participated in the weekend planning sessions for the class.
From 2020-2024, I am part of a multi-institutional collaborative project that examines the role of collaborative problem solving in the development of student ideas around the concept of function. I have been involved with the teacher professional development, including (with Cheryl Eames) the development of a teacher-facing learning progression.
University of Nebraska-Lincoln
Algebra for Secondary Teaching
A course emphasizing connections between algebraic concepts. Compares and contrasts correspondence and covariational reasoning. Special emphasis on conceptual understanding of relations and functions, trigonometric functions. Exploring why different characterizations of conic sections (e.g., slices of cones, “stretched” circles, foci-directrix-eccentricity, Ax2+By2+Cxy+Dx+Ey+F=0) indeed characterize the same class of objects.
Understanding the mathematical foundations of sequences, series, functions, derivatives, and integration. Connecting visual heuristics with formal argument. Communicating deductive reasoning and developing stronger relationships between “public” and “private” mathematical spaces (in the sense of Raman, 2002).
One of the hardest parts of this course is learning new structures for proofs. I have written about how I try to make these structures more transparent in the Education column of the October 2021 AWM newsletter.
Euclidean geometry from a transformation perspective, with particular attention to proof, proving, and reasoning within this perspective. Highlights group theoretic properties of transformations. Applies transformation perspective to topics in secondary geometry and algebra curricula. Short excursions into taxicab and spherical geometries. The course has been shaped by conversations with Sherry West, current mathematics department chair of Lincoln Southeast of Lincoln Public Schools, and Josh Males, math specialist for Lincoln Public Schools.
When teaching this course, I seek to develop mathematical community around exploration. I wrote about some ways that I do this in the Education Column of the October 2022 AWM Newsletter, where I introduce a conceptualization of “mathematical claim” for the purpose of teaching.
Discrete Mathematics for Secondary Teaching
The overarching goal of this course is to do mathematics that will help teachers experience mathematical practice. Mathematical contexts to experience practice include graph theory and group theory. The emphasis in graph theory is on Eulerian paths/circuits, colorability, and genus of graphs and surfaces. The emphasis in group theory will be on permutation groups, dihedral groups, and polyhedral groups.
Mathematics courses coordinated
Precalculus (University of Michigan)
Organized and led weekly meetings for instructors, with focus on student think- ing and pedagogy for teaching concepts such as inverse functions and transformations of functions. Designed common exams and coordinated common grading. ∼600 student enrollment, 24 sections.
During my time as coordinator, I worked with a number of international graduate students (typically 15+ out of ~24 instructors) who were adjusting not only to their first experiences teaching, but also their first experiences in the US. During course meetings, I dedicated time to discussing their impressions of culture and language, as well as to their impressions of teaching.
Mathematics education courses taught
Mathematics Education: Geometry (Michigan State University PRIME).
Consultant and co-teacher for graduate level course for mathematics education doctoral students in the Program for Mathematics Education (PRIME), with lead instructor Gail Burrill. Focused on the influence of historical events on geometry curricula and standards; analysis of contemporary documents guiding geometry curricular construction; and comparison of different perspectives on geometry (e.g., transformation approach vs. Elements approach).
Methods for Secondary School Mathematics Teaching (University of Michigan School of Education)
Course for prospective teachers focusing on pedagogy for lower secondary and upper middle school mathematics; concurrent enrollment with field placement and practicum. Worked with field instructors Annick Rougee and Rachel Snider in designing the course. I taught this class in 2012. A the time, I focused on teaching practices addressing the dimension of ”richness of mathematics” in Mathematical Quality of Instruction, an observation protocol whose scores are linked to mathematical knowledge for teaching (Hill et al., 2008) and student outcomes (Kane & Staiger, 2012). If I were teaching this course now, I would emphasize connections between equity, teaching practices, and mathematical ways of knowing.
Mathematical Knowledge for Teaching Teachers
In 2010 and 2011, I assisted in summer workshops led by Hyman Bass on Mathematical Knowledge for Teaching Teachers, a professional development seminar for practicing PK-12 teachers attending the Elementary Mathematics Laboratory.
From 2000-2011, I worked at the Canada/USA Mathcamp. It’s a wonderful place where graduate students and faculty teach high school students about mathematics that has been personally inspiring. I am currently the Vice President of the Board of the Mathematics Foundation of America, which administers the camp.
I have taught the Banach Tarski paradox, Dehn invariants, the Scissors Congruence Problem, Disrete Fourier Transforms, and various pieces of hyperbolic geometry and geometric group theory (such as a class on SL(2,Z).)
At Mathcamp 2010, Ilya Grigoriev and I organized a viewing of Not Knot interspersed with a Q & A about the math. The film is visually beautiful, but can be frustrating to watch without a friend with whom to delve into the mathematics. We aimed to make the ideas more accessible through conversation during and after the film.
At Mathcamp 2008 and 2011, I served as Academic Coordinator.