I joined the mathematics department at Ithaca College in 2005. I teach a wide range of undergraduate mathematics courses, including introductory statistics and calculus, courses about the history and philosophy of mathematics, and classes for students who are aspiring teachers. In all of my classes I design activities and projects that have students exploring, discussing, and collaborating.
My research interests are in mathematics education, which is a field that uses tools from psychology, philosophy, history, sociology, and literary criticism (and more!) to investigate how people learn and understand mathematics and statistics. I love working with students on research projects, and have co-authored several papers with students.
My current research spans three areas:
- In one project, I investigate the ways students use and interpret various mathematical texts—textbooks, video lectures, and (live) lectures. As teachers adopt new types of pedagogies—in particular, "flipped" classroom techniques—it is increasingly important to understand how we can help students use these text materials effectively. To investigate this, I draw upon ideas from semiotics, embodied cognition, sense-making theory, reader-oriented theory, and narratology to describe what—and how—students learn from experiencing and interacting with these texts.
- In a second project, I investigate the design and implementation of intellectual need-provoking tasks. These are tasks that present students with an intellectual puzzle that leads them to create a new (for them) mathematical way of thinking. To investigate this, I draw upon ideas from constructivist theory, affective dynamics, and task design theories to create tasks, describe the ways students engage in the tasks, and identify connections between the students' activity and their mathematical learning.
- In a third project, I design and evaluate educational resources for teaching concepts related to introductory calculus. This work started with the Calculus Videos Project (described below) and we hope to expand these resources in the future to include redesigned videos, interactive applets, and intellectual need-provoking tasks.