Exploring the Role of Physical and Virtual Manipulatives in Elementary Mixed Fractions Learning

Abstract

Understanding how different types of manipulatives influence children’s learning of mixed fractions can provide insight into effective instructional strategies and inform educational interventions. While both physical and virtual manipulatives are widely used in mathematics education, research comparing their relative effectiveness—particularly in relation to sequencing and retention—is still limited (Moyer-Packenham & Westenskow, 2013; Westenskow, 2013). The present study investigated whether sequencing physical and virtual manipulatives across two weeks influences children’s ability to identify, compare, and add mixed fractions. Twenty children were assigned to one of four groups: two groups used the same manipulative type across both weeks (physical or virtual), while the remaining two groups switched manipulative types between weeks. Pre- and post-tests were administered in Weeks 1 and 2 to assess performance across the three mixed fraction skills and to evaluate the effects of sequencing and retention. Although results were not statistically significant, descriptive analyses indicated that all groups improved in all skill areas using manipulatives. Non-sequencing groups generally achieving greater learning gains, while groups using virtual manipulatives demonstrated higher retention from Week 1 to Week 2. This study contributes to the growing literature on manipulative-based learning and highlights the need for further research on how sequencing and manipulative type affect children’s acquisition and retention of mathematical concepts.