Delimiting and Leveraging Children's Natural Sense of Proportion

界定和利用儿童自然的比例感

• 批准号: 8757188
• 负责人: Percival Grant Matthews
• 金额: $ 7.53万
• 依托单位: UNIVERSITY OF WISCONSIN-MADISON
• 依托单位国家: 美国
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-07-17 至 2016-06-30
• 项目状态: 已结题
• 来源: https://reporter.nih.gov/project-details/8757188
• 关键词: 10 year old; 11 year old; 6 year old; Accounting; Adult; Age; Algebra; Area; Behavioral; Child; Cognition; Cognitive; Collection; Competence; Data; Detection; Development; Discrimination; Education; Educational process of instructing; Foundations; Goals; Instruction; Intervention; Knowledge; Learning; Length; Life; Measures; Methods; Nature; Neurosciences; Participant; Phase; Population; Population Intervention; Process; Protocols documentation; Regimen; Relative (related person); Research; Research Personnel; Sampling; Schools; Societies; Specificity; Stimulus; System; Teaching Method; Testing; Training; Training Programs; Wood material; abstracting; analog; base; cognitive system; design; developmental psychology; experience; high risk; high school; improved; insight; mathematical ability; mathematical learning; mathematics disability; public health relevance; screening; skills; therapy design

DESCRIPTION (provided by applicant): Mathematical competence is an important determinant of life chances. Recent research suggests that understanding fractions particularly understanding their relative sizes is critical for the development of mathematical competence. Unfortunately, children and adults often encounter considerable difficulties understanding fractions. To explain these widespread difficulties, many researchers have argued for an innate constraints account of fraction cognition. On this account, fractions are difficult to understand because they lack an intuitive basis, whereas whole number understanding can be grounded in our perceptual abilities to process numerosities (i.e., collections of countable objects). Thus, innate constraint theorists argue that fraction learning is challenging because it does not benefit from existing cognitive abilities similar to those that facilitate whole number learning and that fractions must instead be learned through adapting whole number understanding. In short, they argue that fractions are somehow less "natural" than whole numbers. The proposed research will investigate a competing hypothesis, the cognitive primitives' account, which integrates previously unrelated findings from neuroscience, developmental psychology and education. This hypothesis contends that cognitive systems tuned to the processing of non-symbolic fractions (such as the relative lengths of two lines or the relative areas of two figures) are present before children begin formal instruction. The existence of these primitive non-symbolic fraction processing abilities suggests that they might serve as a foundation for understanding the magnitudes of symbolic fractions. On this view, children may be equipped with cognitive mechanisms that support fraction concepts prior to formal education in the same way that the ability to process numerosities equips them to learn about whole numbers. If substantiated, this hypothesis can inform interventions designed to improve fraction learning and may contribute to the detection and treatment of math learning difficulties. To test the predictions of the cognitive primitives account, the project will use behavioral tasks to investigate children's (6-year-olds an 10- to 11-year-olds) abilities to perceive the magnitudes of non-symbolic fractions. It will also aim to develop a training program that pairs non-symbolic fractions with symbolic fractions to teach children about the magnitudes of symbolic fractions. These findings will have important implications for our understanding of number processing and for designing interventions that are optimal for promoting fraction learning. If perceptual sensitivity to non-symbolic fractions can provide a foundation for the acquisition of symbolic fraction knowledge, then instruction should attempt to exploit these primitive abilities. If deficits in these non-symbolic abilities contribut to math learning difficulties, then screening should include measures of non-symbolic abilities and interventions should be designed to strengthen these abilities.

描述（由申请人提供）：数学能力是生活机会的重要决定因素。最近的研究表明，理解部分特别了解其相对大小对于数学能力的发展至关重要。不幸的是，儿童和成人经常遇到很大的理解分数。为了解释这些普遍的困难，许多研究人员主张对分数认知的先天约束。因此，由于它们缺乏直观的基础，因此很难理解分数，而整个数字理解可以基于我们处理数字的感知能力（即，可计数对象的集合）。因此，先天的约束理论家认为，分数学习具有挑战性，因为它没有受益 从与促进全数学习的认知能力相似，而必须通过调整整数理解来学习分数。简而言之，他们认为分数比整数少于“自然”。拟议的研究将调查一个竞争性假设，即认知原始人的说法，该假设将神经科学，发育心理学和教育的先前发现。该假设认为，以前存在的认知系统调整为处理非符号分数（例如两条线的相对长度或两个数字的相对区域） 孩子们开始正式的指导。这些原始的非符号分数处理能力的存在表明它们可能是理解符号分数大小的基础。从这种角度来看，儿童可能会配备认知机制，以在正规教育之前支持分数概念，就像处理数字能力相同的方式使他们能够学习整个数字。如果得到证实，该假设可以为旨在改善分数学习的干预措施提供信息，并可能有助于对数学学习困难的检测和治疗。测试认知的预测 原始人说明，该项目将使用行为任务来调查儿童（6岁至11岁的孩子）能力，以感知非符号分数的大小。它还将旨在制定一个培训计划，该计划将非符号分数与象征分数配对，以向儿童传授象征分数的幅度。这些发现将对我们对数字处理的理解以及设计最佳促进分数学习的干预措施具有重要意义。如果对非符号分数的感知敏感性可以为获取符号分数知识提供基础，那么教学应试图利用这些原始能力。如果这些非符号能力的缺陷导致数学学习困难，那么筛查应包括非符号能力和干预措施的措施来增强这些能力。