Cognitive and Neural Correlates of Mathematics Problem Solving Using Diagnostic Modeling and Dynamic Real-Time fMRI

这项研究由凯斯西储大学的一组研究人员领导，其主要目标是进一步了解数学学习的神经和认知基础。重点将放在青少年使用的数学解决问题的策略，以及这些策略如何被采用和改变，因为问题变得更加系统地困难。该项目将研究这些策略与数学相关的认知技能、数学成绩测试分数以及青少年在使用这些策略时所表现出的大脑激活模式之间的关系。问题解决策略之所以引起人们的兴趣，是因为它们与更高水平的数学成就有关，而且它们可以为数学学习中的个体差异提供基础。该项目的长期目标是发现适合个人认知和神经能力的数学学习策略的新方法。该项目还将采用创新的方法来收集数学任务中神经功能的信息，这些信息有可能影响未来对涉及学习和行为的大脑系统的研究。该项目由教育和人力资源理事会核心研究计划资助，该计划支持推进STEM（科学、技术、工程和数学）学习文献的基础研究。参与者将是14-16岁的青少年，他们之前参加了一项关于早产和足月分娩对学校前三年学业进步影响的纵向研究。测试内容包括空间技能、注意力、执行功能（如工作记忆、数字感和数学成绩）的测试；一系列不同难度的心算和分数问题，旨在揭示解决问题策略的个体差异；以及功能性磁共振成像（fMRI）程序来检查这些策略的神经相关性。在对青年成年人进行单独抽样试验之后，将对100名青少年进行认知和成就测试以及对解决问题策略的评估，其中50人将根据其解决问题的策略被挑选出来完成在磁体中解决问题的任务。据推测，具有更先进的解决问题策略（以依赖于检索解决方案为特征）的青少年比使用不那么先进的方法（以更努力的多步骤程序为特征）的青少年表现出更完整的认知概况和更高的数学成就水平。使用更高级策略的青少年也被假设在专门负责有效数学处理的区域（如海马体和后顶叶区）显示出大脑激活的模式，与不那么专门的区域（如前额叶区）相比。随着问题难度的增加，这些参与者的激活模式也会出现不太明显的变化，这表明他们在数学问题解决方面的神经效率更高，对补偿系统的依赖更少。该项目将包括用于认知建模的新颖统计方法，以及在解决数学问题时评估大脑功能的令人兴奋的新方法。本研究将提供认知技能和神经过程与成功解决问题的策略采用相关的见解，重点是神经容量，效率和补偿。

The broad objective of this study, led by a team of researchers at Case Western Reserve University, is to further understanding of the neural and cognitive basis for mathematics learning. The focus will be on mathematics problem-solving strategies used by adolescents, and how these strategies are adopted and changed as problems become systematically more difficult. The project will examine the association of these strategies with mathematics-related cognitive skills, scores on tests of mathematics achievement, and patterns of brain activations displayed by adolescents while engaged in these strategies. Problem-solving strategies are of interest because of their relation to higher-level mathematic achievement and the insights they can offer into the basis of individual differences in mathematics learning. The longer-term objective of the project is to discover new ways to tailor mathematical learning strategies to individual cognitive and neural capacities. The project will also undertake innovative methods of collecting information about neural functioning during math tasks with the potential to influence future studies of the brain systems involved in learning and behavior. The project is funded by the EHR (Education and Human Resources directorate) Core Research program, which supports fundamental research that advances the literature on STEM (Science, Technology, Engineering and Mathematics) learning. Participants will be adolescents, 14-16 years of age, who were previously enrolled in a longitudinal study of the consequences of preterm versus term birth on academic progress across the first 3 years in school. Measures will include tests of spatial skills, attention, executive functions such as working memory, number sense, and mathematics achievement; sets of mental arithmetic and fractions problems of varying difficulty designed to reveal individual differences in problem-solving strategies; and functional magnetic resonance imaging (fMRI) procedures to examine the neural correlates of these strategies. Following piloting with a separate sample of young adults, cognitive and achievement tests and assessments of problem-solving strategies will be administered to 100 adolescents, 50 of whom will be selected on the basis of their problem-solving strategies to complete in-magnet problem-solving tasks. Adolescents with more advanced problem-solving strategies (characterized by reliance on retrieval of solutions) are hypothesized to display more intact cognitive profiles and higher levels of mathematics achievement than those using less advanced approaches (characterized by more effortful multi-step procedures). Adolescents using more advanced strategies are also hypothesized to show patterns of brain activation in regions specialized for efficient mathematics processing, such as the hippocampus and posterior parietal region, as compared to regions that are less specialized such as the prefrontal area. These participants are also expected to display less pronounced changes in activation patterns with increased problem difficulty, suggestive of greater neural efficiency in mathematics problem-solving and less reliance on compensatory systems. The project will include novel statistical methods for cognitive modeling and an exciting new approach to assess brain functioning during math problem solving. This research will provide insight into the cognitive skills and neural processes associated with successful strategy adoption for problem solving, with an emphasis on neural capacity, efficiency, and compensation.