CAREER: Neural investigations of magnitude processing as a pathway to understanding mathematical thinking

与语言的发展类似，数学的创造和使用是人类独有的能力。然而，尽管我们在使用数学方面取得了成功，但我们对支持这种能力的独特认知和神经过程知之甚少。对数学能力的全面解释不仅对基础科学的进一步发展至关重要，而且还因为这种理解可能会产生更有效的数学教育。越来越多的证据表明，我们的数量感（允许我们在不计数或使用数字符号的情况下判断哪些是多哪些是少）为数学思维提供了基本的基础。对幅度处理的神经基础的研究集中在大脑的一个特定区域，顶叶内沟。然而，简单地将一个大脑区域标记为震级处理的来源并不能解释震级实际上是如何处理的，也不能解释震级处理是如何支持更复杂的数学思维的。该项目旨在研究涉及数量级处理的神经通路的解剖和功能，从而确定支持数学思维这一核心方面的神经机制。此外，通过将这些结果与更复杂的数学能力的个体差异联系起来，本研究试图为成功的数学教育实践背后的因素提供新的见解。总体目标将在一系列脑电图和功能磁共振成像研究中实现，有三个目标。首先，本项目将确定视觉处理路径中非符号大小表征的功能特征，假设存在视觉表征的时间进化，从非常快速和纯粹的感官表征到视觉流中数字大小的较慢的概念表征。其次，本项目将确定数值数量级的神经解剖学基础，并验证大脑使用不同的处理路径来表示不同数值的数量级的假设。第三，使用一种新颖的方法，在个人层面上提供可靠的神经测量，该项目将检验每个人对数量级的神经敏感性预测个人数学技能水平的假设。在理论建设方面，该项目将为理解数学思维的重要基础神经认知基础提供见解。在影响实践方面，本项目可以帮助我们了解非符号量加工与习得的符号数学能力之间的关系，从而为改进数学教育提供机会。此外，该项目本身为培训本科生、高中生和代表性不足的学生提供了教育机会，并为具有不同背景的儿童及其家庭提供了参与科学研究的机会。

Similar to the development of language, the creation and use of mathematics is a uniquely human ability. Nevertheless, despite our success in using mathematics, little is understood of the unique cognitive and neural processes that support this ability. A full explanation of mathematical ability is critical not only for furthering basic science, but also because this understanding may give rise to more effective math education. There is increasing evidence that our sense of magnitude (allowing us to judge which is more and which is less without counting or using numerical symbols) provides a rudimentary foundation for mathematical thinking. Investigations into the neural basis of magnitude processing have focused on a particular region of the brain, the intraparietal sulcus. However, simply labeling a brain region as the source of magnitude processing does not explain how magnitudes are actually processed or how magnitude processing supports more complex mathematical thinking. This project seeks to investigate the anatomy and function of the neural pathways involved in magnitude processing, thereby identifying the neural mechanisms that support this core aspect of mathematical thinking. Furthermore, by relating these results to individual differences in more complex mathematical ability, this research seeks to provide novel insights into the factors that underlie successful math education practices. The overarching goal will be achieved in a series of electroencephalography and functional magnetic resonance imaging studies, with three objectives. First, this project will determine the functional characteristics of non-symbolic magnitude representations in the visual processing pathway with the hypothesis that there exists a temporal evolution of visual representation, from a very rapid and purely sensory representation to a slower conceptual representation of numerical magnitude in the visual stream. Second, this project will identify the neuroanatomical substrates of numerical magnitude, and test the hypothesis that the brain uses different processing pathways to represent magnitudes with different numerical values. Third, using a novel methodological approach that provides a reliable neural measure at the individual level, this project will test the hypothesis that each individual's neural sensitivity to magnitude predicts that individual's math skill level. With regard to theory construction, the project will provide insights into understanding the neurocognitive basis of an important foundation for mathematical thinking. With regard to influencing practice, this project may help us understand the relationship between non-symbolic magnitude processing and learned, symbolic mathematical competence, thereby providing opportunities to improve math education. Furthermore, this project itself offers educational opportunities for training undergraduates, high school students, and underrepresented students as well as for engaging children and their families with diverse background in scientific research.