Subjects pressed assigned keys on a response box, for which half of the subjects used their index and middle finger, and the other half responded in the opposite way. This time, however, subjects were asked to evaluate whether both integrand and solution were displayed in the same or different typefaces (Times New Roman vs. For the control condition (font verification task, FVT), the same integration problem was presented along with a candidate answer. Subjects were instructed first to solve each problem mentally and then to verify whether the given solution was correct or not. For the experimental condition (integration verification task, IVT), an integration problem was presented along with a candidate answer on a computer screen. Note that the solution times for each integral were recorded for both training sessions.Īfter the training sessions, we employed a block fMRI design that included an experimental and a control condition. After all integrals were solved correctly, the training session was repeated for a second time. At this time, if needed, subjects could consult a list of “table integrals” demonstrating basic integration rules. If necessary, subjects were provided with a list of integrals for which they gave incorrect solutions and were asked to solve them again on scratch paper. At the end of the first session, one of the authors reviewed subjects’ answers. Subjects were asked to solve the integrals on scratch paper. During the training session, the integrals were presented on a computer screen in a random order across subjects. Therefore, we expected that calculus integral problem solving would most likely engage the same neural networks involved in basic arithmetic problem solving.Ī training session was conducted prior to scanning to insure a similar level of expertise on the task. We assumed that subjects would reduce the task components to basic mathematical skills even though they were solving sophisticated mathematical problems. Before the fMRI experiment, subjects were trained to successfully apply the rules of integral calculus. Subjects were asked to solve each problem mentally and to verify whether the given solution was correct. Using fMRI, we employed a block design to investigate the neural basis of integral calculus problem solving while healthy subjects were presented with calculus integral problems along with a candidate answer on a computer screen. Whereas basic numerical or simple arithmetic problem solving, such as mathematical thinking, calculation experts, complex calculation, and training on calculation problems, have been frequently investigated, comparatively less is known about the cortical areas involved in solving more abstract and sophisticated mathematical equations such as those used in integral calculus. Within the frontal lobe, activation of the dorsolateral prefrontal cortex (DLPFC) has been interpreted as a more supportive and general role in the calculation process by sequential ordering of operations, control over their execution, and inhibiting verbal responses. Finally, the left angular gyrus (AG) is assumed to mediate the retrieval of overlearned arithmetic facts such as the multiplication table. The posterior superior parietal lobe (PSPL) is also activated in tasks requiring number manipulation, but is not specific to the number domain and likely supports attentional orientation to the mental number line. The horizontal intraparietal sulcus (HIPS) is systematically activated in all number tasks and probably hosts a central amodal representation of quantity. Within the parietal lobe, a functional dissociation exists among three parietal regions (see, for a meta-analysis ). Neuroimaging evidence indicates further that performance in simple and complex arithmetic problem solving might be subserved by a fronto-parietal network. Recent evidence from human neuroimaging, primate neurophysiology, and developmental neuropsychology revealed that humans and animals share a system of approximate numerical processing for non-symbolic stimuli. Over the last decade significant progress has been made in uncovering the neural basis of numerical cognition.
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