The Effects of Using Representations in Elementary Mathematics: Meta-Analysis of Research

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Author: Andrzej Sokolowski, Lone Star College, Houston, USA
Published: December 1, 2018

Citation: Sokolowski, A. (2018). The Effects of Using Representations in Elementary Mathematics: Meta-Analysis of Research. IAFOR Journal of Education, 6(3).


The current study provides a meta-analysis of global research on using representations to support the learning of mathematics in Pre-K through Grade 5. A total of 13 primary studies encompassing 1,941 subjects was analyzed. The weighted mean effect size for the 13 studies was reported to be ES = 0.53 (SE = 0.05). A 95% confidence interval around the overall mean – Clower = 0.42 and Cupper = 0.63 – proved its statistical significance and its relative precision. The calculated effect size signifies strong, robust support for the use of representations in Pre-K through Grade 5 mathematics classes and highlights the importance of providing students with opportunities to construct and explore transitioning between various forms of representations. Moderator analysis revealed differences among the effects due to a different type of representation, grade levels, and concepts taught. A synthesis of moderator effects allowed for a formulation of a general way of applying representations that produces maximum learning effects and that the teachers can adopt in their school practice. While the effect sizes provided a means of determining the most effective ways of applying representations, questions about how to develop students’ transitioning from one representation to another remain unsolved. A further discussion of the impact of the study findings beyond the boundaries of elementary mathematics classrooms follows.


meta-analysis, mathematical representations, internal and external representations, mathematics teaching and learning, elementary school

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