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

最近的报告显示，加拿大学生的数学成绩在下降；在24个国家中，加拿大人在计算能力测试中的得分明显低于平均水平。理解与数学发展相关的心理和生物学方面有助于创造改进的教学方法。孩子们在数学上的成功部分是由于大脑的成熟。他们在接受数学训练的同时，前额叶皮层——大脑中与认知和工作记忆（WM）相关的区域——也在显著发育。WM容量是由不同项目的数量索引的，一个人可以在脑海中协调。WM和数学成绩随着年龄的增长而提高。我们的定量评估可以以真正的分级定量方式评估WM能力的增长。利用功能性磁共振成像（fMRI）对数学认知的早期研究主要集中在顶叶皮层引发的活动；然而，最近的功能磁共振成像工作强调心算是一个多区域的事情。提出的工作将澄清前额叶皮层对这一核心活动的具体贡献及其与WM的直接关系。当前的建议。有三个目标：(a)使用一系列功能磁共振成像数据的荟萃分析，建立参考数学问题解决的神经影像学发现的知识现状。(b)在有机过程/任务分析的基础上，使用一种新的范式，即数量匹配任务（NMT），对整个开发过程中的数字WM能力进行量化。NMT将根据我们的颜色匹配任务（CMT）进行验证，CMT是一种已建立的视觉空间WM测量。(c)在成年人的功能磁共振成像研究中，通过使用这些任务来检查脑活动作为wm需求数值增加的函数。我们假设meta分析将显示多步数学问题会调动内侧前额叶区域，而额下回控制简单问题。我们预计学龄儿童的数字WM能力会增长，这样7-8岁、9-10岁、11-12岁、13-14岁和15-16岁的学生平均WM能力分别为3、4、5、6和7个单位。我们预计大脑活动会随着任务相关区域（如前额叶中部皮质）的WM需求而线性增加，这与我们之前在CMT中的发现相同。我们还预计NMT和CMT在大脑后部区域（即顶叶皮层）有重要差异。方法。荟萃分析：使用关键词（如“功能磁共振成像和数学认知”）检索文献。产生的文章将使用连续的纳入标准进行汇总。数据将使用基于坐标的元分析技术进行分析，称为激活似然估计。发展研究：7-16岁的儿童将接受验证的视觉空间CMT （WM-容量测量）以及新的NMT WM测量。数据将通过方差分析、相关方法和发育测序进行分析。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功能磁共振成像分析协议和线性回归进行预处理和分析。预期的知识产出。研究结果将促进对wm需求、处理复杂性及其在数学推理中的神经功能表达的认识。荟萃分析将产生在心算过程中前额叶皮层活动的立体定向脑图谱。行为和神经影像学研究结果将为数字WM活动的大脑表达提供关键证据，特别是在前额皮质发育中。这项工作的结果可用于设计训练干预措施，以帮助诱导数学缺陷儿童的准备。研究结果将为普通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.