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¶

Claim · All claims
Evidence · 1 study (2 entries) · associational r2 · q3 · i2 medium
Currency · newest study 2013 · checked against its sources 2026-10-20 (automated, 2 of 2 entries) · not reviewed by a person

Subclaims¶

q3 i2 Same-denominator items led to more accurate performance (90.3%) than same-numerator fractions (85.7%). → Mazzocco 2013 q3 i? Only the MLD group showed a negative correlation between accuracy on same numerator and same denominator problems over time. → 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 · i2 · associational · r2

A 2 (Item Type) × 2 (Format) × 5 (Grade) × 3 (MLD Status) ANOVA on 12 common-denominator and 12 common-numerator item pairs. The Item Type main effect was significant, "with same denominator items leading to more accurate performance (90.3%) than same numerator fractions (85.7%)".

"the main effect of Item Type (common numerator vs. common denominator) was significant, Wilks’ Lambda F(1, 118) = 8.22, p < .005, η2p = .065, with same denominator items leading to more accurate performance (90.3%) than same numerator fractions (85.7%), p < .005"

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 four-way interaction (Wilks’ Lambda F(8, 230) = 2.646, p = .01, η2p = .084) revealed the crossover. "Only the MLD group showed a negative correlation between accuracy on same numerator and same denominator problems", with MLD performance on common denominator items dropping annually despite a Grade 4 level comparable to TA.

"Only the MLD group showed a negative correlation between accuracy on same numerator and same denominator problems, such that the significant group differences that emerged on the former in the early grades disappear by Grade 8."

Discussion¶

Learner Variables¶

• Learning Disabilities and Developmental Differences — moderator: an instructional effect differs with it
• Proportional Reasoning — predictor: learners who differ on it differ in outcomes

Related Claims¶

• Participants required more time and committed more errors when comparing fractions with common numerators than with common denominators — 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
• 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
• 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 — related
• The comparison of decimal fractions undergoes developmental changes over the course of learning — related