The dose–response relation for K-3 intensive mathematics interventions is linear, with no support for a nonlinear (quadratic) curve¶

Claim · All claims
Evidence · 1 study · quant-synthesis r? · q3
Currency · newest study 2025 · not yet checked against its sources · not reviewed by a person

Subclaims¶

q3 i? A quadratic nonlinear model was not more parsimonious than a linear model for modeling the relation between intervention dosage and effect sizes in K-3 mathematics interventions. → Anna H. Miller 2025

Evidence¶

Anna H. Miller 2025¶

Anna H. Miller, Daniel R. Espinas, Daniel McNeish, & Marcia A. Barnes. (2025). Dosage Response in Intensive Mathematics Interventions for Early Elementary Students With or At-Risk for Mathematics Learning Disability. Educational Psychology Review, 37, 91. https://doi.org/10.1007/s10648-025-10070-y

q3 · i? · quant-synthesis · r?

Meta-analytic model comparison of 164 effect sizes from 24 studies, fitting a re-parameterized quadratic mixed-effect model against a linear meta-regression. The authors report the linear model was more parsimonious, with "a likelihood ratio test comparing the models was not significant (χ 2(1) = 0.20, p = .66)".

"The BIC from the quadratic model (BIC = 479.1) was larger than the BIC of a linear model (BIC = 474.2), the R2 values were essentially identical between the models (linear R 2 = 23.2%, quadratic R2 = 23.4%), and a likelihood ratio test comparing the models was not significant (χ 2(1) = 0.20, p = .66)."

Discussion¶

Learner Variables¶

• Time and Continuity — moderator: an instructional effect differs with it

Related Claims¶

• Instructional focus (number and operations vs. word-problem solving) and intervention implementer (researcher vs. school personnel) did not significantly predict effect sizes or moderate the dose–response relation — related
• Outcome proximity moderates the dose–response relation: distal outcomes outperform proximal outcomes at dosages at or below 5.43 h, while proximal outcomes exceed distal outcomes at or above 22.6 h — related
• Dosage significantly predicts intervention effects in a linear model (β = 0.03 per hour), but the dosage main effect is no longer significant after controlling for moderators — related
• A discrete time trend model fit the reading fluency data significantly better than a linear time trend model — related