This article investigates the potential of fMRI to test assumptions about different components in models of complex cognitive tasks. If the components of a model can be associated with specific brain regions, one can make predictions for the temporal course of the BOLD response in these regions. An event‐locked procedure is described for dealing with temporal variability and bringing model runs and individual data trials into alignment. Statistical methods for testing the model are described that deal with the scan‐to‐scan correlations (...) in the errors of measurement of the BOLD signal. This approach is illustrated using a “sacrificial” ACT‐R model that involves mapping 6 modules onto 6 brain regions in an experiment from Ravizza, Anderson, and Carter (in press) concerned with equation solving. The model's visual encoding predicted the BOLD response in the fusiform gyrus, its controlled retrieval predicted the BOLD response in the lateral inferior prefrontal cortex, and its subgoal setting predicted the BOLD response in the anterior cingulate cortex. On the other hand, its motor programming failed to predict anticipatory activation in the motor cortex, its representational changes failed to predicted the pattern of activity in the posterior parietal cortex, and its procedural component failed to predict an initial spike in caudate. The results illustrate the power of such data to direct the development of a theory of complex problem solving, both at the level of a specific task model as well as at the level of the cognitive architecture. (shrink)

The persistent educational challenges that fractions pose call for developing novel instructional methods to better prepare students for fraction learning. Here, we examined the effects of a 24-session, Cuisenaire rod intervention on a building block for symbolic fraction knowledge, continuous and discrete non-symbolic proportional reasoning, in children who have yet to receive fraction instruction. Participants were 34 second-graders who attended the intervention (intervention group) and 15 children who did not participate in any sessions (control group). As attendance at the intervention (...) sessions was irregular (median = 15.6 sessions, range = 1–24), we specifically examined the effect of the number of sessions completed on their non-symbolic proportional reasoning. Our results showed that children who attended a larger number of sessions increased their ability to compare non-symbolic continuous proportions. However, contrary to our expectations, they also decreased their ability to compare misleading discretized proportions. In contrast, children in the Control group did not show any change in their performance. These results provide further evidence on the malleability of non-symbolic continuous proportional reasoning and highlight the rigidity of counting knowledge interference on discrete proportional reasoning. (shrink)

We concur with Cohen Kadosh & Walsh (CK&W) that representation of numbers in the parietal cortex is format dependent. In addition, we suggest that all formats do not automatically, and equally, access analog magnitude representation in the intraparietal sulcus (IPS). Understanding how development, learning, and context lead to differential access of analog magnitude representation is a key question for future research.