The one-half advantage in fraction comparison emerges by Grade 4 for TA children and Grade 5 for LA children, but only at Grade 7 for children with MLD, who never exceed ~75% accuracy on one-half items¶

Claim · All claims
Evidence · 1 study (2 entries) · associational r2 · q3 · i3 large
Currency · newest study 2013 · checked against its sources 2026-10-18 (automated, 2 of 2 entries) · not reviewed by a person

Subclaims¶

q3 i3 One-half items were answered more accurately than non-half items overall (89.2 vs. 83.4%). → Mazzocco 2013 q3 i? The one-half advantage was absent for MLD children before Grade 7 and significant only in Grades 7 and 8. → Mazzocco 2013 (2)

Evidence¶

Mazzocco 2013¶

Mazzocco, M. M. M., Myers, G. F., Lewis, K. E., Hanich, L. B., & Murphy, M. M. (2013). Limited knowledge of fraction representations differentiates middle school students with mathematics learning disability (dyscalculia) vs. low mathematics achievement. Journal of experimental child psychology, 115(2), 371-387. https://doi.org/10.1016/j.jecp.2013.01.005

q3 · i3 · associational · r2

A 2 (Item Type) × 5 (Grade) × 3 (MLD Status) repeated-measures ANOVA tested the premise that one-half comparisons are easier. The Item Type main effect was significant with η2p = .333, "with more accurate performance on items that included representations of one-half" than non-half items.

"the predicted main effect emerged for Item Type, Wilks’ Lambda F(1, 119) = 59.41, p < .0001, η2p = .333, with more accurate performance on items that included representations of one-half vs. items that did not (correct responses = 89.2 vs. 83.4%, respectively)."

Mazzocco 2013 (2)¶

Mazzocco, M. M. M., Myers, G. F., Lewis, K. E., Hanich, L. B., & Murphy, M. M. (2013). Limited knowledge of fraction representations differentiates middle school students with mathematics learning disability (dyscalculia) vs. low mathematics achievement. Journal of experimental child psychology, 115(2), 371-387. https://doi.org/10.1016/j.jecp.2013.01.005

q3 · i? · associational · r2

Post hoc comparisons of the significant three-way interaction (Wilks’ Lambda F(8, 232) = 3.45, p = .001, η2p = .106) showed the one-half advantage appears by Grade 4 for TA and Grade 5 for LA, but "for the MLD group the one-half advantage does not emerge until Grades 7 and 8".

"for the MLD group the one-half advantage does not emerge until Grades 7 and 8 (ps < .005), and is quite absent prior to then (ps range from .134 to .689)."

Discussion¶

Learner Variables¶

• Learning Disabilities and Developmental Differences — predictor: learners who differ on it differ in outcomes
• Proportional Reasoning — predictor: learners who differ on it differ in outcomes

Related Claims¶

• Visual fraction models yield more accurate magnitude comparisons than Arabic numeral fractions for all ability groups, but the visual model advantage persists through Grade 8 only for children with MLD — related
• Children with MLD are less accurate than TA peers on symbolic fraction magnitude comparisons from Grades 4 to 8 and than LA peers from Grade 5, with no group differences in growth rates on the total score — related
• Group differences in fraction comparison accuracy persist when full scale IQ is included as a covariate — related
• Fraction pairs with common denominators are compared more accurately than pairs with common numerators, but children with MLD show a crossover, improving on common numerator items while declining on common denominator items — related
• The comparison of decimal fractions undergoes developmental changes over the course of learning — related