Early understanding of multi-digit numbers

位值概念和多位数是数学的基础;然而，许多 孩子们努力学习这些知识。对场所价值概念的理解不足， 一直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，而且适用于大部分有学习障碍的儿童。 正常发育的儿童比例。因此，重要的是要了解发展的 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。 最近关于位置价值概念的研究表明，儿童对 在接受学校的正式培训之前，在学前阶段学习多位数字。这些 多位数知识的先驱可以作为儿童学习的重要基石， 一入学就掌握位置价值的概念。然而，至少有两个差距， 我们目前对地方价值概念发展的理解。第一，如何早期 对多位数的理解与学校正规训练的位值概念有关吗？ 第二，儿童是如何在这么小的时候就获得部分的多位数知识的？ 年龄在第一？拟议研究的目标是填补这些空白， 文学有三个目标。目的1检验了多位数的早期知识 数字预示着后来学校学习的地方价值概念。我建议进行一次 3-一项为期一年的纵向研究，以衡量儿童对多位数字的早期理解， 幼儿园开始和结束，一年级和二年级。这项研究将测试如何早期知识， 数字名称和书写数字，以及其他个体差异测量（例如，年龄， 性别、社会经济地位、数字感、家庭接触数字）与十进制学习有关 小学的原则。目标2检验了获得早期知识的假设， 多位数是一种统计学习形式，在此期间，儿童提取潜在的 结构，通过稀疏的 共现数据。一项培训研究旨在让儿童随意体验 多位数字在吸引人的和儿童友好的活动中（例如，图画书阅读，iPad 游戏）。同样的孩子在接受统计学的学习训练后也会得到正规的学校教育 训练后，使我们能够评估和提供因果证据的假设，早期 知识为儿童接受正式的学校培训做好准备，使他们了解地方价值概念。知识 从这项研究中获得的信息将对以下方面产生影响：a）确定早期知识的作用， 多位数，帮助儿童在学校学习以10为基数的记法; B）将 从关于数字词和多位数的稀疏共现数据的统计学习， 位置值的早期部分知识; c）记录早期学习中的差异 环境（或投入）可能会导致以后学校表现的发展不平等。

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.