Yvonne Kao, Carnegie Mellon University
John Anderson, Carnegie Mellon University
Abstract: In this research, we combine verbal protocols, eye-tracking, and neuroimaging data to better understand the cognitive processes underlying geometry problem-solving. Our ultimate goal is to design instructional interventions that will improve students' ability to do proofs in Geometry. Although this skill has generally been neglected in the literature and is increasingly being de-emphasized in American math curriculums, it is an area that requires more, rather than less, emphasis because it is an area in which United States students typically perform poorly in international comparisons and it is a fundamental part of mathematics literacy. We trained 15 adult participants to proficiency at a geometry proof task and then scanned them as they performed the task in an fMRI machine. Then we interpreted the results within the framework of ACT-R, a cognitive architecture that maps activity in certain brain regions to specific cognitive processes. We were then able to use these data, as well as data from verbal protocol and eye-tracking studies, to construct a simple cognitive model of the geometry proof task. The predictions of the model provided good fits to the behavioral and neuroimaging data. Our next step will be to compare this model of proficient problem-solvers with a model of novice problem-solvers in order to determine what cognitive processes an instructional intervention should target.