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.

所有数学思想都必须在某些符号中表达，并且最基本的表示法是语言使用的数字名称系统。 当孩子们学会计数时，他们必须在同一时间开发基本的数学概念，并确定他们正在学习的特定数字名称的规则。 由于语言在代表数字的方式上有所不同，因此可以研究语言和文化差异如何影响数学能力的发展。 这项研究将研究数字制度的语言结构与儿童发展的计数和基本算术的掌握之间的关系。 这项研究将通过查看儿童学习中文和英语的方式来产生儿童代表人数的代表及其如何受到数字命名系统结构的影响。 一些实验将检查很小的孩子（2.5岁）计数的起源，以查看这种基本数学技能是否在数字系统开始不同之前是否有所不同。 还包括对计数的纵向研究，以描述在两国学习计数的智能和高原是否有所不同。 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获取。 例如，中国人形成序数（例如第一，第二，第三等。（通过在基本数字前使用常规前缀（di'）与英语具有不规则数字的不规则系统相比（第一，第二，第三，第四，第四等）。研究将研究这种语言结构在儿童学习中的概念性差异中的作用，其中包括研究的概念和精神研究。美国的儿童以前的研究表明，中国儿童在多种数学技能上都超过了美国的同龄人。 这些问题也具有基本的科学兴趣，因为数学能力发展的适当模型必须能够说明两组儿童的表现。 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含义的重要步骤。