## Abstract

Difficulties in mathematics are argued to stem from impairments of a specialized system of numerical magnitude representation. This study investigates whether different measures of numerical magnitude understanding in kindergarten uniquely predict mathematical achievement concurrently and 6 months later, and also examines the relative explanatory of each aspect of magnitude understanding. It also examines the utility of such tasks as sensitive and specific predictors of children at risk of mathematical learning difficulties. Kindergartners (N = 215, M age = 74 months) were administered a number-line estimation task, a nonsymbolic numerical discrimination task, and a nonsymbolic to word mapping task. Multiple measures of math achievement were administered concurrently and upon entering formal education (M age = 80 months). Path analysis revealed that all 3 aspects of magnitude understanding had similar explanatory power in predicting concurrent and prospective math achievement; the only exception was that nonsymbolic numerical discrimination was not a significant predictor of concurrent mathematical reasoning. Of the 3 measures of magnitude understanding, number-line estimation was found to be the most accurate predictor of persistent mathematical difficulties. Approximately half of the children misclassified as having mathematical difficulties showed inconsistent mathematical achievement across the multiple measures. The implications for screening for mathematical difficulties and for designing interventions are discussed.

**Educational Impact and Implications Statement**

Insights into mechanisms that facilitate children’s early quantitative learning are critical to the development of interventions that put at-risk children on the path to numeracy. The current findings suggest that these mechanisms may include an approximate sense of magnitude (numerical discrimination), the ability to map between nonsymbolic and symbolic quantities (numerical estimation) and the ability to explicitly operate on these numerical symbols and understand the logical relations among them (number-line estimation). Evidence is provided showing the utility of a short and simple measure of number-line estimation in kindergarten as a tool for identifying children at risk of persistent mathematical difficulties.

Original language | English |
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Pages (from-to) | 911-928 |

Number of pages | 18 |

Journal | Journal of Educational Psychology |

Volume | 113 |

Issue number | 5 |

Early online date | 9 Oct 2020 |

DOIs | |

Publication status | Published - Jul 2021 |

## Keywords

- nonsymbolic
- symbolic mapping
- number-line
- sensitivity
- specificity