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

最近的报告显示，加拿大各地学生的数学成绩呈下降趋势；在24个国家中，加拿大人的数学成绩明显低于平均水平。了解与数学发展相关的心理和生物学方面的知识，有助于改进教学方法。孩子们在数学上的成功部分归功于大脑的成熟。他们的大部分数学训练恰逢前额叶皮质显著发展的时期，前额叶皮质是与认知和工作记忆(WM)相关的大脑区域。口碑容量是通过不同物品的数量来衡量的，一个人可以在脑海中协调。工作记忆和数学成绩随着年龄的增长而提高。我们的定量评估能够以真正分级的定量方式评估WM能力的这种增长。早期使用功能磁共振成像(FMRI)对数学认知的研究主要集中在顶叶皮质的活动；然而，最近的fMRI研究强调了心算是一个多区域事件。这项拟议的工作将阐明前额叶皮质对这一核心活动的具体贡献及其与WM的直接关系。 目前的建议。 有三个目标：(A)利用对功能磁共振数据的一系列荟萃分析，参照数学问题解决建立神经成像发现的当前知识状态。(B)根据有组织的进程/任务分析，使用一种新的范式--数字匹配任务--量化整个发展阶段的数字工作管理能力。NMT将根据我们的色彩匹配任务(CMT)进行验证，CMT是一种已建立的视觉空间WM测量方法。(C)通过在成年人的功能磁共振研究中使用这些任务，检查大脑活动作为数字增加的WM需求的函数。 我们假设Meta分析将显示多步骤的数学问题来招募内侧前额叶区域，而额叶下部回控制简单的问题。我们预计学龄儿童的数字工作记忆能力将会增长，7-8岁、9-10岁、11-12岁、13-14岁和15-16岁儿童的平均工作记忆能力分别为3、4、5、6和7个单位。我们预计大脑活动将作为任务相关区域(如中前额叶皮质)WM需求的函数而线性增加，这与我们之前在CMT上的发现相同。我们还预计NMT和CMT在后脑区域(即顶叶皮质)上有重要差异。 方法。 Meta分析：将使用关键词(例如，“fMRI和数学认知”)来搜索文献。所产生的文章将使用连续的纳入标准进行汇总。数据将使用一种基于坐标的元分析技术进行分析，该技术称为激活似然估计。 发育研究：7-16岁的儿童将接受经过验证的视觉空间CMT(WM容量测量)以及新的NMT WM测量。数据将使用方差分析、相关方法和发展排序进行分析。 功能磁共振成像研究：成年人(20-30岁)将在MRI扫描仪中接受CMT和NMT任务。脑图像将使用标准的fMRI分析方案和线性回归进行预处理和分析。 预期的知识结果。 结果将促进对工作记忆需求、处理复杂性及其在数学推理中的神经功能表达的了解。荟萃分析将产生一份关于心算过程中前额叶皮质活动的立体定位脑图谱。行为和神经成像的发现将为大脑表达数字的WM活动提供关键证据，特别是在前额叶皮质的发育过程中。这项工作的结果可以用来设计训练干预措施，帮助数学能力不足的儿童做好准备。研究结果将为正常人群和临床人群的数学教育提供新的相关知识。

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.