- 學位論文
以功能性磁振造影探討算術應用題解題之大腦機制
An fMRI investigation of brain mechanisms underlying arithmetic word problem solving
並列摘要
The practice of arithmetic word problems serves to generalize mathematical concepts into real-world settings, but the word problem performances of both children and adults are far from satisfactory. Despite the extensive research on behavioral and cognitive components of arithmetic word problem solving, the underlying neural mechanisms are poorly understood. This current thesis aims to tackle the issue by investigating brain responses towards word problem solving using fMRI. In Study 1, we compared arithmetic word problems and nonarithmetic narrative problems with no numerical manipulation so that we should be allowed to study the specific role of numerical processing embedded within a narrative structure. Results showed that the processing of word problems should be distinct from text comprehension, as the former involved more in the frontal-insular-parietal areas whereas the latter was more strongly engaged in the canonical language system. In Study 2, to investigate how linguistic factors modulate numerical processing during word problem solving, we examined solutions of compare word problems, and each problem includes a relational term comparing the values of two parameters (e.g. dumpling costs 2 dollars more than wonton). Results revealed a consistency by operation interaction in the fronto-insular-parietal network. Specifically, mathematical models requiring subtraction engaged stronger activations than addition during consistent problem solving (in which the relational term was consistent with the required arithmetic operation, e.g., “more than” - addition), whereas the neural activation pattern of the operation effect for inconsistent problems was opposite to that for consistent problems. These findings further indicated that relations between the linguistic and numerical factors were interactive in word problems. In Study 3, we conducted the experiment of Study 2 on children from Grade 3 to Grade 6 to investigate developmental changes in word problem solving. Results suggested greater involvement of the network of inhibitory control in children for inconsistent than consistent problems. Furthermore, the interaction between consistency and operation was observed only in adults but not children, emphasizing that the interaction observed between linguistic and numerical factors could be a learned effect. To sum up, the current thesis examines the underlying brain mechanisms of word problem solving. We demonstrate that word problem solving is more dependent on the cognitive control system than semantic processing, probably due to the need for deriving mathematical problem models from the text. Also, we stress the important roles of interactive effects between different factors in word problems rather than separate components alone, as numerical processing is possibly altered by the problem description. More importantly, we have demonstrated age-group differences in these effects, revealing critical developmental changes in word problem solving. By uncovering brain mechanisms of this school curriculum practice, we potentially provide foundations for deficit remediation and pedagogical improvement.