Developing a built-in definition of fraction manipulative to enhance students’ conceptual understanding
DOI:
https://doi.org/10.29408/jel.v12i1.33341Keywords:
built-in definition of fractions, conceptual understanding, fraction learning, instructional media development, physical manipulatives, realistic mathematics education, square modelAbstract
This study addresses the challenge of students limited conceptual understanding of fractions by developing a physical manipulative called the Built-in Definition of Fraction (BDF). Using design research developmental studies, data were collected through written tests, questionnaires, and interviews. A total of 41 fifth-grade students participated in the study. The BDF and its accompanying student worksheet integrate dual visual-symbolic representations, that link each concrete action to its corresponding fraction notation and scaffold students in constructing their own understanding of fractions, offering a new approach to using fraction manipulatives. Validation results show that the manipulative is valid, practical, and effective in supporting student understanding of basic fraction concepts, equivalent fractions, and same-denominator addition, even with minimal teacher guidance. Student performance was high across visual-concrete tasks. However, a noticeable gap emerged in unlike-denominator addition between visual concrete performance (88%) and formal-symbolic procedures (77%). This finding highlights the need for additional scaffolding to help students transition more smoothly from concrete representations to abstract symbolic reasoning.
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