From manipulation to measurement reasoning: Rethinking virtual manipulatives for primary mathematics

Abstract

Understanding relationships among measurable quantities is an important aspect of learning primary mathematics; however, measurement instruction may emphasise procedures rather than how quantities are related and change together. This study developed and conducted a preliminary classroom-based evaluation of the Virtual Manipulative Model of Measurement Relationships (VM-MR Model), implemented through the VM Measurement Y6 digital environment. The model was designed around three measurement relationships—length–mass, length–volume of liquid, and mass–volume of liquid—and three design principles: dynamic representation, guided exploration, and relational explanation. A quasi-experimental pre-test–post-test comparison-group design was employed with 60 Year 6 pupils from two intact classes in a Malaysian primary school. Thirty pupils received instruction using the VM-MR Model, while 30 pupils received textbook-based instruction covering the same measurement content. Both groups received 12 hours of instruction over six weeks. Pupils’ Understanding of Relationships Among Measurable Quantities (URMQ) was assessed using a 15-item test, and the data were analysed using a two-way mixed ANOVA. The mean URMQ score of the VM-MR group increased from 31.33% at pre-test to 74.53% at post-test, while the comparison group increased from 29.33% to 61.07%. A significant Time × Group interaction was found, F(1, 58) = 17.67, p < .001, ηp² = .233, indicating different patterns of change between the two instructional groups. Significant Time × Group interactions were also found across all three measurement-relationship domains. These findings provide preliminary classroom-based evidence that virtual manipulation can be purposefully structured around explicit opportunities for measurement reasoning rather than digital interactivity alone.