Cognitive and Linguistic Bases for Mathematical Development

数学发展的认​​知和语言基础

• 批准号: 8909566
• 负责人: Kevin Miller
• 金额: $ 24万
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-08-15 至 1993-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8909566&HistoricalAwards=false
• 关键词: Cognitive; Linguistic; Bases; Mathematical; Development

All mathematical ideas must be expressed in some notation, and the most basic notation of all is the system of number names a language uses. When children learn to count, they must develop basic mathematical concepts at the same time that they figure out the rules of the particular system of number names they are learning. Because languages vary in the way they represent numbers, it is possible to study how linguistic and cultural variation affects the development of mathematical competence. This research will study relations between the linguistic structure of number-naming systems and children's developing mastery of counting and basic arithmetic. The research will produce a model of children's representation of number and how it is affected by the structure of number-naming systems by looking at how children learn to count in Chinese and English. Some experiments will examine the origins of counting in very young children (2.5 years old), to see whether this fundamental mathematical skill varies before the point where the number systems begin to differ. Also included will be a longitudinal study of counting, to describe whether impasses and plateaus in learning to count differ across the two countries. Other experiments will examine how specific features of the number systems affect children's acquisition of particular concepts. For example, Chinese forms ordinal numbers (such as first, second, third, etc.( by using a regular prefix (di') in front of the cardinal number, in contrast to the irregular system of ordinal numbers that English has (first, second, third, fourth, etc.). The research will examine the role this linguistic structure plays in children's learning the conceptual distinction between ordinal and cardinal numbers. Finally, the research will include a study on the development of mental arithmetic in Chinese and American children. Previous research shows that Chinese children outperform their American peers on a variety of mathematical skills. This research should allow the precise description of which aspects of arithmetic skill account for these substantial differences. The poor performance of American children on a wide array of mathematical tasks makes understanding the basis for the advantages Chinese children show a question of obvious practical significance. These questions are of basic scientific interest as well, because an adequate model of the development of mathematical competence must be able to account for the performance of both groups of children. Understanding the cognitive bases for large differences between American and Chinese children is an essential step in figuring out what the implications of these differences are for understanding and promoting cognitive development.

所有的数学思想都必须用某种符号来表达，而最基本的符号就是一种语言使用的数字名称系统。当孩子们学习数数时，他们必须发展基本的数学概念，同时他们也要弄清楚他们正在学习的特定数字名称系统的规则。由于语言表示数字的方式不同，因此研究语言和文化差异如何影响数学能力的发展是可能的。本研究将研究数字命名系统的语言结构与儿童计数和基本算术的发展之间的关系。这项研究将通过观察儿童如何学习中文和英文数数，得出儿童对数字的表征以及数字命名系统结构如何影响儿童对数字的表征的模型。一些实验将检查非常小的孩子（2.5岁）计数的起源，看看在数字系统开始不同之前，这种基本的数学技能是否会发生变化。还将包括一项关于数数的纵向研究，以描述两国在学习数数方面的僵局和停滞是否有所不同。其他实验将研究数字系统的特定特征如何影响儿童对特定概念的习得。例如，汉语的序数（如第一、第二、第三等）与英语的不规则序数系统（第一、第二、第三、第四等）形成了鲜明的对比（通过在基数前面使用规则前缀（di'））。本研究将探讨这种语言结构在儿童学习序数和基数概念区分中的作用。最后，本研究将包括对中美儿童心算发展的研究。此前的研究表明，中国孩子在各种数学技能上都优于美国同龄人。这项研究应该允许精确的描述哪些方面的算术技能解释这些实质性的差异。美国儿童在各种数学任务上的糟糕表现，使得了解中国儿童优势的基础问题显得具有明显的现实意义。这些问题也具有基本的科学意义，因为数学能力发展的适当模型必须能够解释这两组儿童的表现。了解美国和中国儿童之间巨大差异的认知基础是弄清楚这些差异对理解和促进认知发展的影响的重要一步。