arXiv2026
This study examines a structured instructional approach to the decomposition and recomposition of large numbers in six primary school classes (three 4th-grade and three 5th-grade, N = 120), using a quasi-experimental pre-test/post-test design with a control group and a four-week delayed post-test. The 12-week intervention follows the Concrete-Pictorial-Abstract (CPA) progression. The experimental groups achieved mean gains of 34.0 points (4th grade) and 29.6 points (5th grade) out of 100, against 16.4 and 11.1 points in the control groups (all p < 0.001). The Time x Group interaction in the mixed ANOVA gave partial $η^2$ = 0.931. An ANCOVA with the pre-test as covariate estimated an adjusted difference of 18.25 points, 95% CI [17.59, 18.92], F(1, 117) = 2,978.10, p < 0.001, partial $η^2$ = 0.962. The advantage was present on all five components of the test. At the delayed post-test the experimental groups retained 93.7% of their gain, against 78.6% in the control groups. Internal consistency of the instrument at pre-test was acceptable (Cronbach's $α$ = 0.735). The effects are unusually large, and the limits of the design that bear on their interpretation are discussed.