A Triadic Programme Combining Universal Design for Learning, Multilevel Instruction and Manipulative Mathematics in Second-Grade Primary Education: A Quasi-Experimental Study of Mathematical Competence and Attitudes

Abstract

Evidence on programmes that combine manipulative mathematics, Universal Design for Learning (UDL) and multilevel instruction is scarce, particularly for primary students with and without specific learning difficulties (SpLD). This study examined whether a six-session triadic programme was associated with gains in mathematical achievement and attitudes towards mathematics in second-grade students. A quasi-experimental pre-test/post-test design with a non-equivalent control group was used in four schools in Castilla y León (Spain); in each school, one classroom received the programme (n = 69) and one received traditional instruction on the same content (n = 69). Mathematical fluency, calculation and mathematical competence were primary outcomes; competence sub-domains and four attitude items adapted from the TOMA-3 were secondary outcomes. Analyses of covariance controlling for pre-test scores and school, with corrections for multiple testing and cluster-level sensitivity analyses, showed higher adjusted post-test scores in the experimental group on all primary outcomes (adjusted differences of 4.99 and 5.14 raw-score points in fluency and calculation and 1.84 points in competence; ηp2 = 0.60–0.69; all p < 0.001) and on all secondary outcomes. Exploratory analyses indicated a smaller, though still positive, adjusted effect in the single state-subsidised school and no reliable differences by sex; comparisons involving the eight students with SpLD were imprecise. Group membership and pre-test score were the only substantial predictors of post-test achievement. Given the non-random assignment of classrooms, the short duration and the absence of follow-up, the findings are interpreted as associations that warrant replication in randomised designs rather than as definitive causal effects.