ROLE: Tracking the Course of Mathematical Problem Solving

Carnegie Mellon University, Pittsburgh PA

Investigators

Abstract

The goal of this project is to improve our ability to track how students solve mathematical problems. This research will use eye tracking to make real-time inferences about what the student is thinking and fMRI imaging to make inferences about different styles of problem solving. This research is done in the context of both the ACT-R theory of human cognition, which allows us to produce computational models of cognition, and a series of cognitive tutors for mathematics education, which are based on the ACT-R theory. The ACT-R theory is a theory of how the cognitive system adaptively uses procedural and declarative knowledge to achieve its goals. The research will focus on the algebra tutor that is currently in use in high schools and is being adapted for use in middle schools. The research will be concerned with the effect of different mathematical representations on problem solving and with different strategies for mathematical problem solving. There will be three lines of research. One, involving eye movements, will document the instructional opportunities associated with eye movements in the context of the cognitive tutors. It will particularly focus on the eye movements associated with competent use of graphical, tabular, and symbolic representations of functions. The second line of research, involving fMRI brain imaging, will study brain activation markers of the course of mathematical problem solving. It will particularly focus on distinguishing between students who use an informal, verbal form of reasoning with students who use a symbolic, visual form of reasoning. This line will also look at how we can merge information from imaging and eye scanning to make both methodologies more effective. The third line of research will study how one can use the information from fMRI scanning and eye tracking to produce more effective instruction. The three lines of research will converge on a culminating study that attempts to improve the effectiveness of the middle school tutor. It will first use fMRI imaging to identify the learning strategies of individual students and then collect real-time eye movement to guide instruction as students are learning. This will demonstrate how we can use some of the new emerging sensing technology to improve mathematics education.