# Cognitive and metacognitive activity in mathematical problem solving: prefrontal and parietal patterns

Students were taught an algorithm for solving a new class of mathematical problems. Occasionally in the sequence of problems, they encountered exception problems that required that they extend the algorithm. Regular and exception problems were associated with different patterns of brain activation. Some regions showed a Cognitive pattern of being active only until the problem was solved and no difference between regular or exception problems. Other regions showed a Metacognitive pattern of greater activity for exception problems and activity that extended into the post-solution period, particularly when an error was made. The Cognitive regions included some of parietal and prefrontal regions associated with the triple-code theory of (Dehaene, S., Piazza, M., Pinel, P., & Cohen, L. (2003). Three parietal circuits for number processing. *Cognitive Neuropsychology, 20*, 487–506) and associated with algebra equation solving in the ACT-R theory (Anderson, J. R. (2005). Human symbol manipulation within an 911 integrated cognitive architecture. *Cognitive science, 29*, 313–342. Metacognitive regions included the superior prefrontal gyrus, the angular gyrus of the triple-code theory, and frontopolar regions.