Early understanding of multi-digit numbers

对多位数字的早期理解

• 批准号: 9567447
• 负责人: Lei Yuan
• 金额: $ 5.9万
• 依托单位: TRUSTEES OF INDIANA UNIVERSITY
• 依托单位国家: 美国
• 财政年份: 2017
• 资助国家: 美国
• 起止时间: 2017-11-01 至 2020-10-31
• 项目状态: 已结题
• 来源: https://reporter.nih.gov/project-details/9567447
• 关键词: 5 year old; 6 year old; Age; Books; Child; Consequentialism; Correlation Studies; Data; Data Reporting; Development; Digit structure; Exhibits; Exposure to; Foundations; Frequencies; Future; Gender; Goals; Home environment; Individual; Individual Differences; Inequality; Instruction; Knowledge; Lead; Learning; Learning Disabilities; Letters; Light; Link; Literature; Longitudinal Studies; Machine Learning; Maps; Mathematics; Measurement; Measures; Names; Nursery Schools; Only Child; Performance; Population; Preschool Child; Procedures; Public Health; Reading; Reporting; Research; Risk; Role; Sampling; Schools; Source; Structure; System; Testing; Text; Training; Training Programs; Work; base; design; early experience; educational atmosphere; elementary school; experience; experimental study; first grade; formal learning; grasp; junior high school; kindergarten; mathematical ability; mathematical learning; mathematics disability; second grade; socioeconomics; success

Place value concepts and multi-digit numbers are the foundations of mathematics; however, many children struggle at acquiring this knowledge. Poor understanding of the place value concepts has been linked to difficulties in mathematics learning through the elementary and middle school grades, and it is present not only for children with learning disabilities but also for a large proportion of normally developing children. It is, thus, important to understand the developmental mechanisms of multi-digit number learning and potential sources of early experiences that allow some children to readily grasp the concepts while others continue to struggle. Recent research on place value concepts has suggested that children have partial knowledge of multi-digit numbers at the preschool period, before receiving formal training from schools. These precursors of multi-digit number knowledge can serve as important stepping-stones for children to master the concept of place value once entering schools. However, there are at least two gaps in our current understanding of the development of place value concepts. First, how does early understanding of multi-digit numbers relate to formal school training of the place value concepts? Second, how do children come to acquire partial knowledge of multi-digit numbers at such a young age in the first place? The goal of the proposed research aims at filling these gaps in the literature with three specific aims. Aim 1 tests the hypothesis that early knowledge of multi-digit numbers is predictive of later school learning of the place value concepts. I propose to conduct a 3-year longitudinal study to measure children’s early understanding of multi-digit numbers at the start and end of kindergarten, 1st and 2nd grades. The study will test how early knowledge of number names and written numerals, as well as other individual difference measurements (e.g., age, gender, SES, number sense, home exposures to numbers), relate to the learning of base-10 principles in grade school. Aim 2 tests the hypothesis that acquiring early knowledge of multi-digit numbers is a form of statistical learning, during which children extract latent structures that govern the mapping between number words and written numerals through sparse co-occurrence data. A training study is designed to give children casual experiences with multi-digit numbers in engaging and child- friendly activities (e.g., picture-book reading, ipad games). The same children in the statistical learning training will also be given formal school training afterward, allowing us to assess and provide causal evidence for the hypothesis that early knowledge prepares children for formal school training of the place value concepts. The knowledge gained from this research will have implications for: a) determining the role of early knowledge of multi-digit numbers in preparing children to learn about base-10 notation at schools; b) linking statistical learning from sparse co-occurrence data about number words and multi-digit numbers to early partial knowledge of place value; c) documenting how differences in early learning environment (or input) may contribute to developmental inequalities in later school performances.

位值概念和多位数字是数学的基础；然而，许多 孩子们很难获得这些知识。对地方价值概念的理解不足 与小学和中学数学学习困难有关 它不仅适用于有学习障碍的儿童，也适用于大量 正常发育儿童的比例。因此，了解发育过程非常重要 多位数学习的机制和早期经验的潜在来源 有些孩子很容易掌握概念，而另一些孩子则继续挣扎。 最近对位值概念的研究表明，儿童对以下内容有部分了解： 在学前阶段，在接受学校正式培训之前，就已经掌握了多位数的数字。这些 多位数字知识的先驱可以作为儿童学习的重要踏脚石 进入学校后掌握位​​置价值的概念。但至少还有两点差距 我们目前对位值概念发展的理解。首先，如何早 对多位数字的理解与学校对位值概念的正规培训有关吗？ 其次，孩子们是如何在这么小的年纪就获得部分多位数知识的？ 首先年龄？拟议研究的目标旨在填补这些空白 具有三个特定目标的文学。目标 1 检验以下假设：早期的多位数知识 数字预示着以后学校学习的位值概念。我建议进行一次 为期 3 年的纵向研究，旨在衡量儿童对多位数数字的早期理解 幼儿园、一年级和二年级的开始和结束。该研究将测试早期知识如何 数字名称和书面数字，以及其他个体差异测量（例如年龄、 性别、SES、数感、家庭接触数字），与 10 进制的学习相关 小学时的原则。目标 2 检验以下假设：获取早期知识 多位数字是统计学习的一种形式，在此过程中，孩子们提取潜在的 通过稀疏控制数字词和书面数字之间映射的结构 同现数据。一项培训研究旨在为孩子们提供休闲体验 参与和儿童友好的活动（例如图画书阅读、iPad 游戏）。同样接受统计学习培训的孩子也将被送入正规学校 随后进行培训，使我们能够评估早期的假设并为其提供因果证据 知识使儿童为地方价值概念的正规学校培训做好准备。知识点 这项研究的成果将对以下方面产生影响： a) 确定早期知识的作用 多位数字帮助孩子们在学校学习 10 进制表示法； b) 链接 从数字词和多位数字的稀疏共现数据中进行统计学习 早期对位值的部分了解； c) 记录早期学习的差异 环境（或输入）可能会导致以后学校表现中的发展不平等。