Accuracy on approximate addition decreases as ratio approaches 1, with a stronger ratio effect on the non-symbolic task¶

Claim · All claims
Evidence · 1 study · associational r2 · q3 · i3 large
Currency · newest study 2011 · not yet checked against its sources · not reviewed by a person

Subclaims¶

q3 i3 Accuracy decreased when ratio approached 1 (ηp² = .53), and the ratio × task interaction showed the symbolic advantage only at ratios 4:6 and 4:7. → Bert De Smedt 2011

Evidence¶

Bert De Smedt 2011¶

Bert De Smedt, Camilla K. Gilmore. (2011). Defective number module or impaired access? Numerical magnitude processing in first graders with mathematical difficulties. Journal of Experimental Child Psychology, 108, 278–292. https://doi.org/10.1016/j.jecp.2010.09.003

q3 · i3 · associational · r2

Repeated measures ANOVA on approximate addition accuracy with ratio (4:5, 4:6, 4:7) and task as within-subject factors. "Accuracy decreased when ratio approached 1", the classic ratio effect, and the symbolic advantage held only at easier ratios; group membership did not affect the ratio effect.

"There was a main effect of ratio (F(2,120) = 66.65, p < .01, ηp² = .53, ε = 1.01), showing that accuracy decreased when ratio approached 1. A significant ratio × task interaction (F(2,120) = 10.94, p < .01, ηp² = .15, ε = 0.91) indicated that performance on the symbolic task was more accurate than on the non-symbolic task for the ratios 4:6 and 4:7 (ps < .01) but not for ratio 4:5 (p = .66)"

Discussion¶

Learner Variables¶

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

Related Claims¶

• Preschoolers' ANS task performance follows Weber's Law: accuracy decreases as numerical ratio approaches equality, and improves with age over six months — a narrower finding that bears on this claim
• Children succeed at non-symbolic approximate addition above chance with a ratio effect, without relying on non-numerical strategies — related
• Non-symbolic training improves collection comparison at ratios 1:2, 2:3 and 3:4, while symbolic training improves only ratio 1:2 — related
• In a number comparison task, adults outperform 6- to 7-year-old children in accuracy, Arabic numerals are easier than dot arrays, and easy 0.5 ratios are easier than difficult 0.8 ratios — related
• Group differences on symbolic tasks persist after controlling for number identification skill — related
• Characteristic distance effects occur in both nonsymbolic and symbolic single-digit approximate addition — related
• Response times in number comparison show group, notation, and ratio main effects, with a larger ratio effect for dot arrays than Arabic numerals — related
• Performance on the newly learned symbols shows canonical ratio effects, consistent with mapping novel symbols onto Approximate Magnitude System representations — related