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Using Manipulatives to Enhance Students’ Comprehension and Engagement
Swieter, Kenneth
Swieter, Kenneth
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Abstract
Mathematics is a subject in both primary and secondary education that plays a critical role in developing foundational academic skills. Because of this, mathematics instruction should actively engage students in constructing their own understanding, helping them develop conceptual knowledge through hands-on, interactive lessons that promote self-discovery of concepts. Fractions are the building blocks for conceptual understanding in later subject areas such as algebra and proportional reasoning. The purpose of this study was to examine how manipulatives, taught through the Concrete–Representational–Abstract (CRA) model, could support students’ conceptual understanding and achievement when learning to divide fractions while keeping them engaged. The study design used was a mixed-methods approach, incorporating pre- and post-tests, surveys, and focus group interviews; the pre- and post-test data, in conjunction with the survey, supported quantitative analysis, while the survey and focus groups contributed to qualitative insights. The findings showed that manipulative use when teaching fraction division enhances conceptual understanding and achievement while keeping students actively engaged in the lessons. The researcher concluded that using manipulatives when teaching dividing fractions not only improved academic achievement and strengthened conceptual understanding, but that increased engagement also contributed to these outcomes. These findings suggest that teachers should incorporate manipulatives more consistently within instruction to support both understanding and engagement, particularly when teaching abstract mathematical concepts. Future research should examine the effectiveness of manipulative use across different grade levels and mathematical topics.
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Date
2026-04-27
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Publisher
University of Wyoming Libraries
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Keywords
Manipulatives,Comprehension,Engagement,Plan B,Mathematics
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Attribution-NoDerivatives 4.0 International