Fraction magnitude understanding, measured by number line estimation, predicts general mathematics achievement beyond fraction arithmetic skill in 5 of 6 Belgian, Chinese and U.S. grade samples, though not among Chinese 8th graders¶

Claim · All claims
Evidence · 1 study · associational r2 · q3
Currency · newest study 2015 · checked against its sources 2026-10-23 (automated, 1 of 1 entry) · not reviewed by a person

Subclaims¶

q3 i? In 5 of 6 Country × Grade combinations (all except Chinese 8th graders), adding number line estimation to fraction arithmetic accuracy considerably increased explained variance in mathematics achievement. → Torbeyns 2015 q3 i? When number line PAE was entered first, adding fraction arithmetic increased explained variance in the U.S. sample only. → Torbeyns 2015

Evidence¶

Torbeyns 2015¶

Torbeyns, J., Schneider, M., Xin, Z., & Siegler, R. S. (2015). Bridging the Gap: Fraction Understanding is Central to Mathematics Achievement in Students from Three Different Continents. Learning and Instruction. https://doi.org/10.1016/j.learninstruc.2014.03.002

q3 · i? · associational · r2

Hierarchical regression analyses in the cross-sectional study of 187 Belgian, Chinese, and U.S. 6th and 8th graders tested four models predicting mathematics achievement, measured by country-specific tests: Flemish standardized achievement tests in Belgium, the school-reported state PSSA in the U.S., and the mid-term mathematics examination score in China. The article reports that adding number line estimation "considerably increased the explained variance" in 5 of 6 combinations, all except Chinese 8th graders; no effect size is printed for this finding. The authors call the evidence clear for Belgian 6th and 8th graders, Chinese 6th graders and U.S. 8th graders, less straightforward for U.S. 6th graders (fraction arithmetic and number line estimation were equally important), and absent for Chinese 8th graders, for whom neither fraction magnitude understanding nor fraction arithmetic predicted achievement, possibly because of their high performance and small variance on the fraction tasks.

"When fraction arithmetic accuracy was first entered as a predictor of mathematics achievement, adding number line estimation considerably increased the explained variance in overall mathematics achievement in 5 of the 6 Country × Grade combinations (all except among Chinese 8th graders)."

Discussion¶

Learner Variables¶

• Number Sense — predictor: learners who differ on it differ in outcomes
• Proportional Reasoning — predictor: learners who differ on it differ in outcomes

Related Claims¶

• On 0-1 fraction number line estimation, Belgian and Chinese students estimate far more accurately than U.S. students, with no Country × Grade interaction — related
• The relation between fraction magnitude understanding and mathematics achievement is a general cognitive characteristic, not attributable to specifics of the U.S. educational system, though instruction quality may strengthen or weaken it — possibly the same claim (merge candidate)
• On the more difficult 0-5 number line task, Chinese students estimated more accurately than Belgian students, who in turn estimated more accurately than U.S. students — related
• Fraction magnitude comparison correlated with general math achievement only in the U.S. samples, indicating number line estimation and magnitude comparison tap partly different aspects of fraction magnitude understanding — related
• Number line estimation and numerical magnitude comparison correlate with mathematics achievement (r = .24 to .44), with number line estimation more strongly related in older children — a broader claim this one bears on
• A combination of specific mathematical cognition measures predicts subsequent mathematics achievement better than prior mathematics achievement scores alone — related
• Fractions knowledge is a critical domain-specific predictor of mathematics achievement in later grades — related