Teaching
I am very enthusiastic about teaching, and was a full-time teacher before starting graduate school. I value active learning and work to make my classroom into a supportive environment for all students. Also, I am interested in using technology in math; there are several examples of the exercises and demonstrations I've created below.
University of New Hampshire
Courses taught
Analysis and Applications of Functions (MATH 418): TA, Fall 16.
Calculus I (MATH 425):
Instructor, Spring 19;
TA, Spring 21, Fall 17, Spring 17;
Learning Assistant, Fall 20.
Honors Calculus I (MATH 425H): Facilitator, Fall 19.
Calculus II (MATH 426): TA, Fall 18, Spring 18.
Honors Calculus II (MATH 426H): Facilitator, Spring 20.
Awarded Graduate Teaching Award in Spring 2018, which is awarded annually to four graduate students across the entire university.
Facilitated Mathematics TA Orientation in Fall 2018 and Fall 2020.
Phillips Exeter Academy
Before starting at UNH, I taught mathematics for three years at Phillips Exeter Academy, a boarding school. I usually taught four courses per trimester covering topics in Pre-Algebra, Algebra I and II, Geometry, Calculus I and II, and Multivariable Calculus.
Mathematics classes at Exeter are student-driven. There are no lectures or textbooks, only problem sets written by the faculty. Every day, students present their homework solutions to each other and instructors facilitate discussions as students ask questions and make conjectures. I bring this active learning approach into every class I teach.
I also taught a course on the Exeter materials at the Anja S. Greer Conference on Mathematics and Technology to high school teachers from around the country.
Technology in the Classroom
I believe that using technology to create dynamic models and exercises greatly helps student understanding in the mathematics classroom. Even the simplest models can be very illuminating just because they are interactive. Here are several examples of the activities I have created:
I've used Desmos:
to introduce Riemann sums
to understand how a polar function creates a graph (see video below)
to investigate the relationship between secant and tangent lines
to see how the terms of a Maclaurin series estimate a function
to demonstrate the relationship between the derivatives of a function and of its inverse
to help students visualize a classic harmonic motion problem
to ask students to decide how a parameter would make a piecewise function "connect smoothly"
to introduce normal lines and the basic idea of curvature
to discover how parameters change a graph of a hyperbola
to investigate the difference between a unit tangent vector and a velocity vector
to understand the deleted comb (a classic point-set topology counterexample)
to prove that the real plane with minus a point is path connected
I've used Geogebra:
to explore matrix transformations
to practice reflections in the plane
to construct a parabola
to visualize volume problems where a cross section is described (additional examples: 1, 2)
to demonstrate velocity vectors for a three-dimensional parametric path
to construct the osculating plane
to discover the definition of dihedral angle
to visualize a problem about cutting a cylinder at an angle and unrolling it
to understand stereographic projection
Here is a video I made to explain how to create a graph on Desmos that traces polar curves.