Traveling the Second Bridge: Using fMRI to Assess an ACT-R Model of Geometry Proof

We build an ACT-R model of a geometry-proof task based on behavioral, verbal protocol, eye movement, from proficient adult participants and then assess the model using neuroimaging data. Our geometry proof problems differed in terms of the number of steps of inference required to find a proof. Participants’ verbal protocols and eye movements indicated that they first encoded the goal statement, then made a number of inferences, and finally came to a conclusion and made their response. In the imaging study we determined the involvement of a number of brain regions in the various stages of the task. The ACT-R model provided reasonable fits to participant accuracy, latency, and the BOLD response in most of the brain regions. However, there was unexpected activity in the motor region early in the problem solution, unexpected activity in the fusiform late in problem solution, and unexpected anterior prefrontal activity after the problem solution. We conclude that the model underestimates the perceptual-motor involvement in geometry learning just as does much of the educational curriculum.