Perceptual and Cognitive Mechanisms of Developing Fractions Knowledge: A Cross-Sequential Approach

项目摘要 数学能力是现代社会生活机会的重要决定因素， 分数是建立数学能力的基本技能。尽管分数很重要 知识，儿童和成人往往遇到相当大的困难理解分数。解释 对于这些普遍存在的困难，许多研究人员主张用先天限制来解释。他们提出 分数很难，因为它们不对应于我们大脑中预先存在的任何类别， 整数，对应于可数事物的集合。因此，他们认为分数概念是 具有挑战性，因为它们不能从现有的认知能力中受益，而是必须通过 适应儿童对整数的理解。 该研究小组提出了一个竞争性的假设，即认知基元解释， 神经科学、发展心理学和教育学的研究成果。我们认为， 我们称之为比率处理系统（RPS）的原始能力被调整为非符号的处理 分数-如两条线的相对长度或两个图形的相对面积-并且是偶数 在正式的指导之前。根据这一观点，儿童具有支持分数的认知机制， 处理可数集合的能力使他们能够学习整数。 为了检验这些相互竞争的假设的预测，本项目将跟踪两组儿童（第二组）。 5年级至8年级）使用行为和脑成像方法来（a）追踪 非符号分数处理能力的发展，（B）决定如何符号分数知识 建立在这些能力和（c）调查是否在RPS预测以后的数学个体差异 成就为了测试这些非象征性结构的敏锐度或招募是否在 分数困难以及一般数学学习困难，研究小组将比较行为 在一系列认知任务上的表现和神经活动。 这项研究对我们理解数字处理和设计 最适合分数学习的教育实践。提高分数的理解将有助于 孩子们在获得高阶数学能力方面清除了一个关键障碍， 教育，就业，甚至健康的结果。如果非符号分数的认知基元可以 为符号分数能力的获得提供基础，那么教学应该试图招募 这些原始人。如果这些原始的缺陷导致数学学习困难，那么筛查应该 包括衡量非象征性能力的措施，并应设计干预措施来解决这些能力问题。

Project Summary Mathematical competence is an important determinant of life chances in modern society, and knowledge of fractions is a foundational skill for establishing mathematical competence. Despite the importance of fraction knowledge, children and adults often encounter considerable difficulties understanding fractions. To explain these widespread difficulties, many researchers have argued for an innate constraints account. They propose that fractions are difficult because they do not correspond to any preexisting categories in our brain, unlike whole numbers, which correspond to sets of countable things. Thus, they argue fraction concepts are challenging because they do not benefit from existing cognitive abilities and instead must be learned through adapting children's whole number understanding. The study team proposes a competing hypothesis, the cognitive primitives account, which integrates previously unrelated findings from neuroscience, developmental psychology and education. We argue that a primitive ability that we dub the ratio processing system (RPS) is tuned to the processing of non-symbolic fractions—such as the relative length of two lines or the relative area of two figures—and is present even before formal instruction. On this view, children are equipped with cognitive mechanisms that support fraction concepts in the same way that the ability to process countable sets equips them to learn about whole numbers. To test the predictions of these competing hypotheses, this project will follow two cohorts of children (2nd graders until 5th grade and 5th graders until 8th grade) using behavioral and brain imaging methods to (a) trace the development of non-symbolic fraction processing abilities, (b) determine how symbolic fraction knowledge builds on these abilities and (c) investigate whether individual differences in the RPS predict later math achievement. To test whether the acuity or recruitment of these non-symbolic architectures plays a role in fraction difficulties as well as general math learning difficulties, the study team will compare the behavioral performance and neural activity on a battery of cognitive tasks. This research has important implications for our understanding of number processing and for designing educational practices that are optimal for fraction learning. Improving fractions understanding would help children to clear a critical hurdle in the acquisition of higher-order mathematical competencies that impact educational, employment, and even health outcomes. If cognitive primitives for non-symbolic fractions can provide a foundation for the acquisition of symbolic fraction ability, then instruction should attempt to recruit these primitives. If deficits in these primitives contribute to math learning difficulties, then screening should include measures of non-symbolic abilities and interventions should be designed to address these abilities.