The effects of physical manipulatives on achievement in mathematics in grades K–6: A meta-analysis
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Even though there numerous books, articles, research studies, and other publications written since National Council of Teacher of Mathematics (NCTM) published Curriculum and Evaluation Standards of School Mathematics in 1989 have advocated the use of manipulatives in the teaching of mathematics, there is no conclusive evidence showing that the use of manipulatives helps students attain higher achievement in mathematics. The purpose of this meta-analysis is to investigate the overall effect of using manipulatives in mathematics instruction, compared to traditional instructional methods, on students’ achievement in mathematics in kindergarten through Grade 6. After formulating the research question, the following steps were undertaken: developing a coding form, gathering research studies by searching the literature, coding the appropriate information from each study, calculating effect sizes, and analyzing and interpreting the effect sizes. The coding form developed for this study included study characteristics such as year of publication, type of publication, study design, student ability level, SES of the students, type of community, type of measuring instrument, and duration of treatment. These nine study characteristics became the moderator variables of this study and it was found that they had a significant impact on the overall mean effect size. Eight electronic data bases and 12 peer-reviewed journals were searched to locate both published and unpublished studies conducted in the U.S. between 1989 and 2010. Eligible studies met the following search criteria: manipulative use was compared to manipulative nonuse, students were in kindergarten through Grade 6, sufficient information was reported for the calculation of effect sizes, and a control group/treatment group design was used. The search of online databases and education journals revealed 1035 articles about manipulatives and yielded 31 primary studies that met the search criteria. These studies represented 5288 students and produced 35 effect sizes. The mean effect size was 0.50 with a confidence interval between 0.34 and 0.65. These results indicate that students who used manipulatives during mathematics instruction had statistically significant higher mathematics achievement than students who were taught by traditional teaching methods. A 0.50 effect size can be interpreted to mean that students who used manipulatives scored one-half of a standard deviation higher on mathematics achievement tests than students who did not use manipulatives. This improvement in achievement implies that the average student who used manipulatives performed better than 69% of the students who did not use manipulatives. An implication of this research study is that there is evidence that student achievement in mathematics in kindergarten through Grade 6 can be improved as a result of using manipulatives. Implications for practice are that curriculum supervisors can confidently recommend policies that include manipulatives in the teaching of mathematics, teacher educators should guide future teachers in the proper use of manipulatives, and professional development personnel can encourage and prepare teachers to incorporate the use of manipulatives in their teaching practices.