Current Projects
My research broadly focuses on investigating the ways students interact with, interpret, and learn from mathematical "texts," including textbooks, video lectures, and inperson lectures. The goal of this work is to support math instructors in implementing "flipped" classrooms and active learning strategies, which have been shown to improve student learning.
 The Calculus Video Project: The goals of this NSFfunded project are to conduct design research to generate knowledge about how students engage with, make sense of, and learn from videos that address foundational calculus concepts.
 Active Calculus & Edfinity: The Calculus Video Project team is collaborating with the Active Calculus and Edfinity teams to integrate the expertise of each team to develop a modern, dynamic, and free textbook (with embedded videos, Geogebra applets, and Edfinity problems).
 Intellectual NeedProvoking Tasks: Students are most likely to learn a mathematical concept when they feel a need for it—if they encounter tasks for which the concept is essential for understanding the task or for solving a problem. I am investigating ways we can design tasks that provoke intellectual need and how we can evaluate the impact these tasks have on student learning.
 Didactical and Disciplinary Literacy: Textbooks are a readilyavailable resource and are written, in part, to explain mathematical concepts to students. However, we know very little about what happens when students try to read and learn from textbooks. In this project, I am collaborating with colleagues from the Computer Science and Education departments at Ithaca College to describe literacy practices that various readers—both students and nonstudents—bring to the process of reading textbooks and how these practices can facilitate or hinder learning.
Previous Projects

Analyzing Mathematics Lectures: Most math classes still incorporate lecture as a common class format. Students may have difficulty learning from lectures; the goal of this research project is to better understand some potential sources of this difficulty, to identify opportunities for learning in lectures, and to find ways to improve math lectures. To do this, I adapt ideas from various disciplines to describe the various components of lectures, the ways students "participate" in the lecture, and how these aspects interact to influence the ways students make sense of lectures. My work has focused on:

Describing the implied observer of a lecture

Characterizing the gestures used by the lecturer

Identifying student's sensemaking frames

Describing the ways instructors use informal and formal representations to develop concepts


Statistics Education  Sampling Distributions: The concept of sampling distributions is fundamental to understanding statistical inference. Using activities from the CATALYST project at UMN, I am creating and using a theoretical framework that will help us describe the ways students think about these concepts. As part of this project, I have designed software that allows you to simulate the process of repeated sampling to construct sampling distributions. You can download the programs and documentation from the simulator page.

Mental Models for "StudentProfessor Problem": The "studentprofessor problem" is a classic example of students' difficulty translating between symbols and words. It is a useful lens through which to examine students' mental models of comparison word problems and the way various features of the problem situation and its representation mediate their mathematical activity.

Undergraduate Students' Conceptions of the Equals Sign: We often see students use the equals sign in ways that are incorrect, yet efforts to correct these uses typically fail. I have used ideas from semiotics to reconceptualize the way we think about students' use of the equals sign to investigate how these "errors" can be viewed as part of an attempt to imbue mathematical symbols with meaning.

Conceptions of Variables in the Transition from Arithmetic to Algebraic Reasoning: How do students in middle school build on their arithmetic understanding to develop algebraic reasoning, and how can we support this development? I have worked with colleagues from the University of Wisconsin to focus on how students initially develop concepts of variation and an understanding of variables and how this conception develops over time.