Children succeed at non-symbolic approximate addition above chance with a ratio effect, without relying on non-numerical strategies¶

Claim · All claims
Evidence · 1 study · associational r2 · q3
Currency · newest study 2010 · checked against its sources 2026-10-20 (automated, 1 of 1 entry) · not reviewed by a person · overdue for a recheck since 2015: baselines and conditions change

Subclaims¶

q3 i? In Experiment 1 children performed non-symbolic addition at 62.0% (chance 50%, t(40) = 7.20, p < .001) with a ratio effect (F(1, 40) = 15.37, p < .001); in Experiment 2 at 66.6% (t(61) = 12.12, p < .001) with a ratio effect (F(1, 61) = 45.80, p < .001). → Gilmore Camilla K. 2010

Evidence¶

Gilmore Camilla K. 2010¶

Gilmore Camilla K., McCarthy Shannon E., Spelke Elizabeth S. (2010). Non-symbolic arithmetic abilities and achievement in the first year of formal schooling in mathematics. Cognition. https://doi.org/10.1016/j.cognition.2010.02.002

q3 · i? · associational · r2

Experiment 1's task required approximate addition of two dot arrays and comparison of the sum to a third array across ratios 4:5, 4:6, 4:7, with dot size, array size and density correlated with number positively on half the trials and negatively on half. Appendix analyses ruled out alternative strategies.

"Children in the main experiment succeeded at the non-symbolic addition task (62.0%, chance = 50%, t(40) = 7.20, p < .001), showing the characteristic ratio effect (F(1, 40) = 15.37, p < .001; Figure 2a) and without resort to guessing strategies or reliance on non-numerical properties of the displays"

Discussion¶

Learner Variables¶

• Number Sense — outcome: instruction changes it

Related Claims¶

• Accuracy on approximate addition decreases as ratio approaches 1, with a stronger ratio effect on the non-symbolic task — related
• Characteristic distance effects occur in both nonsymbolic and symbolic single-digit approximate addition — related
• Brief practice on non-symbolic approximate numerical addition or comparison tasks speeds subsequent exact symbolic arithmetic in first graders compared with non-numerical magnitude tasks — related
• Kindergarten children's non-symbolic addition performance correlates with end-of-year mathematics achievement, independent of literacy (Experiment 1) — 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
• Kindergarteners perform significantly better in nonsymbolic than symbolic single-digit addition problem formats — related
• Preschoolers' ANS task performance follows Weber's Law: accuracy decreases as numerical ratio approaches equality, and improves with age over six months — 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
• Children with MLD and LA are less accurate than TA children on symbolic but not non-symbolic approximate addition — related