Both number system knowledge and estimation uniquely account for variance in all three third-grade arithmetic skills independently of each other and of domain-general factors¶

Claim · All claims
Evidence · 1 study · associational r2 · q3
Currency · newest study 2014 · checked against its sources 2026-10-24 (automated, 1 of 1 entry) · not reviewed by a person

Subclaims¶

q3 i? Number system knowledge and estimation each make unique contributions to basic calculation fluency, written arithmetic, and arithmetic word problems regardless of order of entry in fixed-order regressions. → Cowan 2014

Evidence¶

Cowan 2014¶

Cowan, R., & Powell, D. (2014). The Contributions of Domain-General and Numerical Factors to Third-Grade Arithmetic Skills and Mathematical Learning Disability. Journal of Educational Psychology, 106(1), 214-229. https://doi.org/10.1037/a0034097

q3 · i? · associational · r2

Fixed-order regression analyses with 258 third graders entering domain-general and numerical factors in different orders. Number system knowledge uniquely accounted for 12% and estimation 9% of variance in word problems when entered first, and both remained significant when entered last.

"Both number system knowledge and estimation uniquely account for variance in arithmetic word problems whether entered first or last: Model D-1, number system knowledge (12%, t = 8.57, p < .001) and estimation (9%, t = 7.39, p < .001)"

Discussion¶

Learner Variables¶

• Operations and Place Value — outcome: instruction changes it
• Prior Knowledge — predictor: learners who differ on it differ in outcomes

Related Claims¶

• Different domain-general factors uniquely account for variation in different arithmetic skills — related
• Preschool counting skills and number knowledge directly predict formal arithmetic skills in primary school, together accounting for 40–46% of variance — related
• Numeral comparison, but not quantity enumeration, uniquely accounts for variation in basic calculation fluency — reports the opposite