Psychology

Rational number conceptualization predicts mathematics achievement: Quantity matters

Document Type

Article

Abstract

Knowledge integration is a crucial part of learning as concepts are built over time and modality. In mathematics, rational numbers are a particularly difficult concept that requires integration across notations to understand the quantity represented by fractions and decimals (e.g., ½ and 0.5). We investigated how 5- to 14-year-old children conceptualize rational numbers, whether it differs across development (Study 1), and whether the conceptualization is related to math achievement (Study 2). A novel Numerical SpAM task was created to document children's unprompted rational number conceptualization. We found that most children organized rational numbers either by notation or quantity, with quantity becoming more common after age 10. Quantitative conceptualization predicted higher math achievement compared to notation, regardless of age. Moreover, conceptualizing rational numbers by quantity across distinct notations (e.g., 1/2 and 0.5) was related to children's math achievement. Implications for numerical understanding as well as general cognition are discussed.

Publication Title

Cognitive Development

Publication Date

7-2022

Volume

63

ISSN

0885-2014

DOI

10.1016/j.cogdev.2022.101195

Keywords

cognitive development, knowledge organization, memory integration, numerical development, rational numbers, semantic organization

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