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¶

Claim · All claims
Evidence · 1 study · associational r1 · q3
Currency · newest study 2015 · not yet checked against its sources · not reviewed by a person

Subclaims¶

q3 i? Strong correlations between number line estimation and magnitude comparison appeared only for U.S. 6th and 8th graders and, to a lesser extent, Belgian 6th graders. → Torbeyns 2015 q3 i? Correlations between number line estimation and fraction arithmetic were relatively weak (r = -.23 to -.44), suggesting the two measure different competencies. → 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 · r1

Correlational analyses across the six Country × Grade groups (Table 3) showed inconsistent relations between the two magnitude tasks; the article states "magnitude comparison was correlated with general math achievement only in the U.S. samples", raising validity questions about the comparison task with fractions.

"although number line estimation and magnitude comparison are generally assumed to measure the same underlying construct, i.e., students’ magnitude understanding, strong correlations between the two was only present for U.S. 6th and 8th graders and, to a lesser extent, Belgian 6th 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¶

• 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 — 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 — 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
• The three estimation tasks do not represent the same construct in young children and should not be combined into composites — related