From Manipulation to Abstraction: The Impact of Flexible Decomposition on Numerical Competence in Primary School

TL;DR

This study demonstrates that a CPA-based instructional intervention significantly improves primary students' numerical competence, with high retention and robust effects confirmed through rigorous statistical analysis.

Contribution

It introduces a structured CPA progression approach for number decomposition, showing substantial learning gains in primary school students.

Findings

Experimental groups gained significantly more points than controls.

Retention rate exceeded 97% after four weeks.

Statistical analysis confirmed the robustness of the intervention effect.

Abstract

This study examines the effectiveness of a structured instructional approach to decomposition and recomposition of large numbers in six primary school classes (three Year 4 and three Year 5, N = 120) using a quasi - experimental design with a control group. The 12 - week intervention is grounded in the Concrete Pictorial Abstract (CPA) progression. The experimental groups achieved average gains of 34.0 points (Year 4) and 29.6 points (Year 5) out of 100, significantly higher than the control groups (16.4 and 11.1 points; p < .001). The Time Group interaction in the mixed ANOVA reached {\eta}^2p = .931. The ANCOVA with the pre - test as covariate estimated an adjusted difference of 18.25 points (F(1,117) = 2,978.10, p < .001, \eta^2p = .962), confirming the robustness of the effect after controlling for baseline differences. Four-week retention exceeded 97% in the experimental group. Internal reliability of the instrument was satisfactory (Cronbach's {\alpha} = .735).