The Effectiveness of Physical and Technology-based Virtual Manipulatives in Enhancing Student Engagement: A Meta-analysis

Abstract

This meta-analysis investigates the effectiveness of physical and technology-based virtual manipulative instructional materials in enhancing students’ engagement across elementary, secondary, and tertiary education. Drawing on 10 empirical studies published from 2020 to 2024 that yielded 15 individual effect sizes, this study synthesized the quantitative data using Hedges’ g under a random-effects model. The overall pooled effect size was large and statistically significant, indicating substantial improvement in student engagement after using manipulatives. The included studies addressed a variety of mathematics topics, such as trigonometry, algebra, set theory, calculus, geometry, logic reasoning, and multiplication fluency. They also used diverse manipulatives: physical, technology-based, virtual, and combined approaches. Despite considerable heterogeneity, the robustness of the findings was supported by a Fail-safe N of 1564 and significant results from the equivalence test. Potential publication bias was suggested through Egger’s regression and Kendall’s tau tests, but the observed effect remained highly reliable. The results affirm the pedagogical value of manipulatives in promoting behavioral, cognitive, and emotional aspects in mathematics learning. The study recommends that educators and curriculum developers strategically incorporate both physical and technology-based virtual manipulatives into instructional design and encourages further research to explore moderating variables such as educational level, manipulative type, mathematics content, and intervention duration.