A Meta-Analysis of the Efficacy of Teaching Mathematics with Concrete Manipulatives

Abstract

The use of manipulatives to teach mathematics is often prescribed as an efficacious teaching strategy. To examine the empirical evidence regarding the use of manipulatives during mathematics instruction, we conducted a systematic search of the literature. This search identified 55 studies that compared instruction with manipulatives to a control condition where math instruction was provided with only abstract math symbols. The sample of studies included students from kindergarten to college level (N = 7,237). Statistically significant results were identified with small to moderate effect sizes, as measured by Cohen's "d", in favor of the use of manipulatives when compared with instruction that only used abstract math symbols. However, the relationship between teaching mathematics with concrete manipulatives and student learning was moderated by both instructional and methodological characteristics of the studies. Additionally, separate analyses conducted for specific learning outcomes of retention (k = 53, N = 7,140), problem solving (k = 9, N = 477), transfer (k = 13, N = 3,453), and justification (k = 2, N = 109) revealed moderate to large effects on retention and small effects on problem solving, transfer, and justification in favor of using manipulatives over abstract math symbols. (Contains 7 tables and 1 footnote.)