Developmental involvement of prefrontal cortex and working memory in mathematical problem solving.

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Recent reports show student’s math scores in decline across Canada; and among 24 countries Canadians score significantly below average on numeracy tests. Understanding of psychological and biological aspects related to math development is instrumental to create improved methods for teaching. Children’s success in math is due in part to brain maturation. Much of their math training coincides with a period of significant development in prefrontal cortex –brain areas associated with cognition and working memory (WM). WM capacity is indexed by the number of distinct items, a person can coordinate in mind. WM and mathematical performance improve with age. Our quantitative assessment can appraise in a true graded quantitative fashion, this gain in WM capacity. Early studies of mathematical cognition using functional Magnetic Resonance Imaging (fMRI) primarily focus on activity elicited in parietal cortices; however, recent fMRI work highlights mental arithmetic as a multi-region affair. The proposed work will clarify prefrontal cortex’s specific contribution to this core activity and its direct relation to WM. Current proposal. There are three objectives: (a) Using a series of meta-analyses of fMRI data, establish current state of knowledge in neuroimaging findings with reference to mathematical problem solving. (b) Based on organismic process/task analysis, quantify numeric WM capacity across development, using a novel paradigm, the Number Matching Tasks (NMT). The NMT will be validated against our Colour Matching Tasks (CMT), an established visuo-spatial WM measure. (c) Examine brain activity as a function of numeric increases in WM-demand by using these tasks within an fMRI study with adults. We hypothesize that the meta-analyses will show multi-step math problems to recruit medial prefrontal areas, whereas inferior frontal gyri control simple problems. We anticipate numerical WM capacity in school children to grow such that 7-8, 9-10, 11-12, 13-14 and 15-16 year-olds, have on average a WM capacity of 3, 4, 5, 6 and 7 units, respectively. We expect brain activity to linearly increase as a function of WM demand in task related regions, such as middle prefrontal cortices, replicating our previous findings with CMT. We also expect important differences between NMT and CMT in posterior brain regions (i.e., parietal cortex). Method. Meta-analyses: The literature will be searched using keywords (e.g., “fMRI and mathematical cognition”). Resulting articles will be aggregated using successive inclusion criteria. Data will be analyzed using a coordinate-based meta-analytic technique called Activation Likelihood Estimate. Developmental Study: Children aged 7-16 years will receive the validated visual-spatial CMT (WM-capacity measure) as well as the new NMT WM measure. Data will be analyzed with ANOVA, correlational methods and developmental sequencing. fMRI study: Adults (ages 20-30 years) will receive CMT and NMT tasks in the MRI scanner. Brain images will be preprocessed and analyzed using standard fMRI analytical protocols and linear regression. Expected knowledge outcome. Results will advance knowledge of WM-demand, processing complexity, and their neuro-functional expression in mathematical reasoning. Meta-analyses will yield a stereotaxic brain atlas of prefrontal cortex activity during mental arithmetic. Behavioural and neuroimaging findings will provide critical evidence on brain expression of numeric WM activities, particularly in prefrontal cortex development. Results of this work could be used in designing training interventions to help induce readiness in children deficient in mathematics. Results will provide new relevant knowledge for mathematical education in normal and clinical populations.