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用某种符号来表达，而最基本的符号是语言使用的数字名称系统。 当孩子们学习计数时，他们必须在弄清楚他们正在学习的特定数字名称系统的规则的同时，发展基本的数学概念。 由于语言表示数字的方式各不相同，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命名系统的语言结构与儿童发展对计数和基本算术的掌握之间的关系。 该研究将通过观察儿童如何学习用中文和英语进行计数，建立一个儿童对数字的表示以及数字命名系统结构如何影响数字的模型。 一些实验将研究幼儿（2.5 岁）的计数起源，看看这种基本数学技能在数字系统开始不同之前是否会发生变化。 还包括一项关于计数的纵向研究，以描述两国学习计数的僵局和平台是否有所不同。 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，中文通过在基数前面使用规则前缀（di'）来形成序数（例如第一，第二，第三等），这与英语的不规则序数系统（第一，该研究将探讨这种语言结构在儿童学习序数和基数概念区别方面所发挥的作用。最后，该研究将包括对中国和美国心算发展的研究。此前的研究表明，中国人。这项研究应该能够准确地描述美国儿童在各种数学任务上表现不佳的原因，从而为理解这些差异奠定了基础。中国孩子的优势表现出了一个具有明显现实意义的问题。 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。