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.
