Are the acuities of magnitude representations of different types and ranges of numbers related? Testing the core assumption of the integrated theory of numerical development

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.