Teaching
University of Nebraska-Lincoln
Fall 2015: Math 405: 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.
Spring 2015, Spring 2014: Math 407/807: Algebra for Secondary Teaching
A course emphasizing connections between algebraic concepts. Special emphasis on conic sections and trigonometric functions and understanding why different characterizations (e.g., slices of cones, ``stretched'' circles, foci-directrix-eccentricity, Ax2+By2+Cxy+Dx+Ey+F=0) indeed characterize the same class of objects.
Fall 2014, Fall 2013: Math 408/808: Geometry for Secondary Teaching
Euclidean geometry from a transformation perspective, with
particular attention to proof, proving, and reasoning within
this perspective. Emphasizes group theoretic properties of
transformations, applying transformation perspective to topics
in secondary geometry and algebra curricula. Coordinating course
design with
Sherry West,
current mathematics department chair of Lincoln
Southeast of Lincoln Public Schools.
Canada/USA Mathcamp
Since 2000, I have 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 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.
It was great fun to examine the film with enthusiastic students and a fellow geometer.
Algebra Project
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. Here
are some mathematical and non-mathematical
highlights of the year.
University of Michigan
Fall 2013: Education 413: Secondary Mathematics Methods
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.[course information from 2013]
Winter 2009, 2010, 2011: Math 486:
Mathematics for Secondary Teaching
Mathematics underlying the secondary and middle school curriculum. Related
curricular topics to aspects of group/ring/field theory and real analysis.
[course information from 2011]
Fall 2008, 2009: Math 105: Data, Functions, and Graphs
Mathematics in preparation for calculus.
[current course website]
I have drawn pedagogical inspiration from:
- Loren Larson, who showed me the importance of motivation, and who
compassionately coached me through my very
first mathematical presentation, at the 1996 Canada/USA Mathcamp.
- Misha Kapovich, who impressed upon me the power of well-chosen examples.
- The 2005-2006 and 2006-2007 TAC groups at UC Davis, for giving the space for graduate students passionate about their disciplines and teaching to debate and compare the teaching philosophies prevalent in mathematics, computer science, physics, biology, linguistics, and literature.
- The Elementary Mathematics Laboratory, which gave insight into how children think about fractions,
offers a public teaching experience,
and introduces a broad spectrum of people who care about teaching and mathematics to each other.
| 
