Cognitive and Linguistic Bases for Mathematical Development

所有的数学概念都必须用某种符号来表达， 最基本的符号是数字名称系统 一种语言使用。 当孩子们学习数数时， 基本的数学概念，同时他们还能弄清楚 特定的数字名称系统的规则， 学习 因为语言表达的方式不同 数字，可以研究语言和文化如何 差异影响数学能力的发展。 本研究将研究语言学与语言学之间的关系， 数字命名系统结构与儿童发展 掌握计数和基本算术。 这项研究将产生一个儿童的模型， 数字的表示以及它如何受到结构的影响 通过观察孩子们是如何学会 用中文和英文计数。 一些实验将检查 幼儿（2.5岁）开始数数， 看看这种基本的数学技能是否在 数字系统开始不同的点。 还包括 将是一个计数的纵向研究，以描述是否 学习数数的僵局和停滞期在这两个国家是不同的。 国家 其他实验将研究特定的特征 数字系统影响儿童获得特定的 理念的 例如，汉语形成序数词（如 第一、第二、第三等。（通过使用常规前缀（di '） 基数的前面，与不规则系统相反 英语中的序数（第一，第二，第三， 第四，等等）。 这项研究将探讨这一作用， 语言结构在儿童概念学习中的作用 序数和基数的区别。 最后 研究将包括一项关于心理发展的研究， 中国和美国儿童的算术能力。 以前的研究 显示，中国儿童在一项 各种数学技能。 这项研究应该允许 精确描述算术技能的哪些方面 这些重大的差异。 美国儿童在一系列广泛的 数学任务使理解的基础， 中国孩子的优点表现出明显的实用性问题 意义 这些问题是基本的科学兴趣 同时，因为一个适当的发展模式， 数学能力必须能够解释 两组孩子的表现。 了解 美国人和英国人之间巨大差异的认知基础 中国儿童是弄清楚什么是最重要的一步。 这些差异的含义是为了理解和 促进认知发展。

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.