(SGER) The Educational Neuroscience of Integer Understanding

学习理论的一个基本问题是，人们如何建立在一个成熟的知识体系之上，从而超越这个体系。为了开发一种从一开始就合作的教育神经科学，pi们正在数学学习的背景下解决这个问题。到12岁时，孩子们比较自然数的流利程度已接近成人水平。儿童行为数据和成人功能磁共振成像和行为数据表明，这些比较依赖于神经过程，也比较知觉的大小。大约在这个年龄，孩子们开始接触整数，它建立在自然数的基础上，但超越了自然数。pi的初始行为数据表明，儿童最初通过应用规则来理解负数。例如，要确定一个负数和一个正数中哪个较大，他们只需注意哪个有负号。相比之下，成人的行为数据表现出一种被称为分类感知的感知现象的特征，因此零已成为进行比较的重要边界。使用功能磁共振成像，发展和教学数据的组合，pi正在测试规则和众所周知的自然数的长期组合是否演变成参与感知过程的整数表示。如果是这样，这将为教育神经科学如何为教育和神经科学贡献新的理论提供一个范例。例如，普遍的观点认为抽象规则产生于感知表征，但如果pi的假设是正确的，那么整数理解的发展就是一个实例，其中类似感知的表征产生于抽象规则的应用。

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.