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促进基础科学的发展至关重要，而且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，我们的量感（使我们能够在不计数或使用数字符号的情况下判断哪个多，哪个少）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，顶内沟。然而，简单地将大脑区域标记为幅度处理的来源并不能解释幅度实际上是如何处理的，或者幅度处理如何支持更复杂的数学思维。该项目旨在研究参与幅度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，本研究旨在为成功的数学教育实践的基础因素提供新的见解。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，这个项目将确定在视觉加工路径中的非符号性的大小表征的功能特性的假设，存在一个时间的视觉表征的演变，从一个非常快速和纯粹的感官表征的数字大小的视觉流中的一个缓慢的概念表征。其次，本项目将确定数值大小的神经解剖学基础，并测试大脑使用不同的处理路径来表示具有不同数值的大小的假设。第三，使用一种新的方法，提供了一个可靠的神经测量在个人层面上，该项目将测试的假设，每个人的神经敏感性的大小预测个人的数学技能水平。在理论构建方面，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。关于影响实践，这个项目可以帮助我们了解非符号幅度处理和学习，符号数学能力之间的关系，从而提供机会，以改善数学教育。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以及吸引具有不同背景的儿童及其家庭参与科学研究提供了教育机会。

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.