A fundamental question for learning theory is how people build upon a mature system of knowledge so they can go beyond that system. In an effort to develop a collaborative-from-the-start educational neuroscience, the PIs are addressing this question in the context of mathematics learning. By the age of twelve, children have nearly adult levels of fluency at comparing natural numbers. Child behavioral data and adult fMRI and behavioral data indicate that these comparisons depend on neurological processes that also compare perceptual magnitudes. Around this same age, children are introduced to the integers, which build upon, but go beyond, the natural numbers. The PIs' initial behavioral data indicate that children initially understand negative numbers by applying rules. For example, to determine the larger of a negative and a positive digit, they simply note which one has the negative sign. In contrast, the adult behavioral data exhibit the signature of a perceptual phenomenon known as categorical perception, such that zero has become an important boundary for making comparisons. Using a combination of fMRI, developmental, and instructional data, the PIs are testing whether the long-term combination of rules and the well-known natural numbers evolves into a representation of integers that partakes of perceptual processes. If so, this will provide a model instance of how educational neuroscience can contribute novel theories to education and neuroscience. For example, common wisdom has it that abstract rules arise from perceptual representations, but if the PIs' hypothesis is true, then the development of integer understanding is an instance where perception-like representations arise from the application of abstract rules.
