I'm studying models of students' thinking and connections between various models of students' thinking. In particular, I research how students understand fractions, measure, graphs, and covariation.
At my former job at Colorado State University I co-directed the Calculus Center which provided tutoring for undergraduates. I work with a team of amazing tutor center leaders on a project to identify best-practices for the structure of tutoring centers.
As a secondary high school teacher I spent a lot of time wondering how to support my students in learning meaningful mathematics. Although I knew how important it was that my students learn grade level standards, I felt uneasy teaching a standard when I did not feel the students understood the ideas the standard was based on. I wanted to know more about how to challenge my students intellectually, while also taking into account the mathematical thinking they brought to my classroom. I had a suspicion that if I tried to teach conceptual ideas my students were not yet prepared to understand they would end up memorizing my instruction instead of making sense of it. In graduate school, with the mentorship of Pat Thompson I became much better at building models of student thinking. I began to be able to rigorously explore how students build on prior knowledge to make sense of new ideas.
I'm still interested in building models of students thinking. I also hope to return to the secondary classroom as a researcher with the goal of working with a secondary teacher to providing challenging instruction that takes into account students' thinking.
To stay happy and healthy, I love exploring the world. Some of my more notable expeditions include packrafting in remote Alaskan Wilderness and descending technical slot canyons in the Grand Canyon.