Abstract The current study tested whether the magnitude representation acuities of different types and ranges of numbers, as proposed in the integrated theory of numerical development ( Siegler, 2016 ), are significantly related to each other. A sample of 123 kindergarteners was assessed four times over the period from kindergarten to fourth grade on magnitude representation acuities of different types and ranges of numbers (nonsymbolic numerical magnitude in kindergarten, small whole-number magnitude in grade 1, large whole-number magnitude in grade 2, rational number magnitude in grade 4). The children were also evaluated for their mathematics achievement, intelligence, working memory capacity, reading skills, attention level, and multiplication skills. The results showed that the magnitude representation acuities of different types and ranges of numbers were significantly related to each other, and these numerical magnitude representation acuities were either directly or indirectly related to children’s mathematics achievement in grade 4. The findings from this work provide empirical support to the core assumption of the integrated theory of numerical development and highlight the significance of numerical magnitude representations at an early developmental stage to the acquisition of more advanced numerical magnitude representations in later elementary school years.

中文翻译：

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不同类型和范围的数字表示的幅度表示的敏锐度是否相关？检验数值开发综合理论的核心假设

摘要 目前的研究检验了数值发展综合理论(Siegler, 2016) 中提出的不同类型和范围数字的震级表示敏锐度是否彼此显着相关。对123名幼儿园儿童的样本，从幼儿园到四年级，对不同类型和范围的数字量级表示能力进行了四次评估（幼儿园为非符号数字量级，一年级为小整数量级，大整数量级为2级，4级有理数级）。还评估了孩子们的数学成绩、智力、工作记忆能力、阅读技能、注意力水平和乘法技能。