TY - JOUR

T1 - Reasoning About Fraction and Decimal Magnitudes, Reasoning Proportionally, and Mathematics Achievement in Australia and the United States

AU - Resnick, Ilyse

AU - Newcombe, Nora

AU - Goldwater, Micah

N1 - Publisher Copyright:
© 2023, PsychOpen. All rights reserved.

PY - 2023/3/31

Y1 - 2023/3/31

N2 - There is strong evidence from research conducted in the United States that fraction magnitude understanding supports mathematics achievement. Unfortunately, there has been little research that examines if this relation is present across educational contexts with different approaches to teaching fractions. The current study compared fourth and sixth grade students from two countries which differ in their approach to teaching fractions: Australia and the United States. We gathered data on fraction and decimal magnitude understanding, proportional reasoning, and a standardized mathematics achievement test on whole number computation. Across both countries, reasoning about rational magnitude (either fraction or decimal) was predictive of whole number computation, supporting the central role of rational number learning. However, the precise relation varied, indicating that cross-national differences in rational number instruction can influence the nature of the relation between understanding fraction and decimal magnitude and mathematics achievement. The relation between proportional reasoning and whole number computation was fully mediated by rational magnitude understanding, suggesting that a key mechanism for how reasoning about rational magnitude supports mathematics achievement: proportional reasoning supports the development of an accurate spatial representation of magnitude that can be flexibly and proportionally scaled, which in turn supports children’s mathematics learning. Together, these findings support using measurement models and spatial scaling strategies when teaching fractions and decimals.

AB - There is strong evidence from research conducted in the United States that fraction magnitude understanding supports mathematics achievement. Unfortunately, there has been little research that examines if this relation is present across educational contexts with different approaches to teaching fractions. The current study compared fourth and sixth grade students from two countries which differ in their approach to teaching fractions: Australia and the United States. We gathered data on fraction and decimal magnitude understanding, proportional reasoning, and a standardized mathematics achievement test on whole number computation. Across both countries, reasoning about rational magnitude (either fraction or decimal) was predictive of whole number computation, supporting the central role of rational number learning. However, the precise relation varied, indicating that cross-national differences in rational number instruction can influence the nature of the relation between understanding fraction and decimal magnitude and mathematics achievement. The relation between proportional reasoning and whole number computation was fully mediated by rational magnitude understanding, suggesting that a key mechanism for how reasoning about rational magnitude supports mathematics achievement: proportional reasoning supports the development of an accurate spatial representation of magnitude that can be flexibly and proportionally scaled, which in turn supports children’s mathematics learning. Together, these findings support using measurement models and spatial scaling strategies when teaching fractions and decimals.

KW - cross-national comparison

KW - decimals

KW - fractions

KW - magnitude representation

KW - mathematics achievement

KW - proportional reasoning

UR - http://www.scopus.com/inward/record.url?scp=85153311442&partnerID=8YFLogxK

U2 - 10.5964/jnc.8249

DO - 10.5964/jnc.8249

M3 - Article

SN - 2363-8761

VL - 9

SP - 222

EP - 239

JO - Journal of Numerical Cognition

JF - Journal of Numerical Cognition

IS - 1

ER -