Number sequences are defined in terms of children’s abilities to construct and transform units. Children operating with the initial number sequence (INS) construct units of 1. They construct other numbers as strings of 1s and can count on, by 1s, from one number to a subsequent number. A critical benchmark in children’s further numerical development is the construction of units of units, or composite units. This development corresponds to the tacitly nested number sequence (TNS) wherein numbers are nested within other numbers. We report on a large-scale quantitative study of children’s available number sequences and their relationships with later mathematical development, such as multiplicative reasoning and fractions knowledge. This study involved 5747 children from three cohorts surveyed at the beginning of second grade in 2013, 2014, and 2015. We document strong relationships between children’s early construction of an INS and a TNS and the likelihood of their later development of multiplicative reasoning, a measurement meaning of fractions, and general mathematics achievement, while controlling for rote computational skills. Implications for teacher instruction are discussed.

数列是根据儿童构建和转换单位的能力来定义的。使用初始数字序列 (INS) 操作的儿童构建单位为 1。他们将其他数字构建为 1 的字符串，并且可以通过 1 从一个数字到后续数字进行计数。儿童进一步数字发展的一个关键基准是单元或复合单元的构建. 这种发展对应于默认嵌套数字序列 (TNS)，其中数字嵌套在其他数字中。我们报告了对儿童可用数字序列及其与以后数学发展的关系的大规模定量研究，例如乘法推理和分数知识。这项研究涉及 2013 年、2014 年和 2015 年二年级开始时接受调查的三个队列的 5747 名儿童。我们记录了儿童早期构建 INS 和 TNS 与他们后来发展乘法推理的可能性之间的密切关系分数的含义和一般数学成绩，同时控制死记硬背的计算技能。讨论了对教师教学的影响。