Our research helps identify basic cognitive processes that support the development of mathematics knowledge & examines how to use that information to design effective learning techniques and materials.

Scroll down to check out our 4 Primary Areas of Research.

Primary Areas of Research

We are exploring effective ways to use concrete objects (e.g., blocks, balance scales, counters) as learning tools in mathematics. In particular, we are investigating a method called “concreteness fading” in which you begin with an actual physical object and gradually fade to a more abstract or generic representation. For example, to learn about equality, one might start with a physical balance scale, move to a pictorial worksheet of a balance scale with an equal sign, and end with a traditional, symbolic equation. We are conducting a series of tutoring studies with young children to figure out the best ways to implement concreteness fading and to compare it to other techniques.
Concrete Learning Material

Young children often engage in a variety of patterning tasks – creating, copying, or extending a predictable series of objects of numbers (e.g., circle-circle-square, circle-circle-square). In our research, we explore how patterning skills relate to other types of formal mathematics knowledge. For example, does patterning skill help support children’s ability to perform calculations or to understand key math concepts? We also investigate how the language we use to describe patterns influences children’s performance. For example, when working with young preschool children, should we label patterns using their observable characteristics (e.g., red-blue, red-blue) or in a more conventional, generic way (e.g., A-B, A-B)?
Early Patterning Skills

Imagine a learner encounters a novel math problem. Should feedback be provided right away or should the learner work through the solution on her own? In this line of work, we explore what type of feedback works for whom and under what conditions. A key contribution of this work is to show that, for certain learners, problem solving without feedback can be more effective. We are currently investigating reasons why feedback does not always have the desired, positive effects. In particular, we are focusing on whether the feedback draws attention to a self-evaluation (e.g., I’m not very good at this problem) or to task-specific processing (e.g., what other strategy could work).
Feedback During Problem Solving

ManyClasses is a large-scale collaborative research project investigating the generalizability of educational practices in real classrooms. For decades, researchers from psychology, cognitive science, and education have attempted to identify educational practices that improve student learning. When studied in real classrooms, research on these practices is often limited to a single class or topic, which limits the generalizability of the inferences that can be drawn. To better investigate generalizability, a ManyClasses study examines the same research question in dozens of contexts spanning a range of courses, institutions, topics, and student populations.