Abstract
Through a search executed on Web of Science database with general keywords pertaining to ‘teaching fractions’ or ‘understanding fractions’ and ‘representation’, this study utilized PRISMA’s procedure in analysing previously published articles. This review reveals seven articles in inclusion criteria and seventeenth articles in exclusion criteria with reasons. The included articles were reviewed for (a) studies characteristics, (b) instructional focus, (c) representation elements: real-world situation, manipulative aids, pictures, spoken and written symbols, and (d) the outcomes of each study. The metadata was analysed to organise the outcomes. Most of these articles focus on grade 3 and above and Western countries’ urban area. The result indicates most studies emphasize both conceptual and procedural understandings. Multi representations utilize sequential or parallel concept related to fractions improve students’ knowledge, particularly in understanding fractions. Meanwhile, developing fraction learning through multiple explicit representations at the initial Grade level of fraction instruction is for elementary school. However, less attention has been given to explicit representations in learning fractions at such a level.
Highlights
Understanding fractions has been a global issue until today due to its importance as a foundation for mathematical knowledge and skills (National Council of Teachers of Mathematics [NCTM], 2007)
The selected studies emphasize on procedural knowledge, symbolic words, and part whole representations especially the area and length models
None of the selected studies were related to authentic problem context such as problem- or project-based learning (PBL) which was consistent with the result by Minarni, Napitupulu and Husein (2016)
Summary
Understanding fractions has been a global issue until today due to its importance as a foundation for mathematical knowledge and skills (National Council of Teachers of Mathematics [NCTM], 2007). Fractions’ understanding supports the knowledge of advanced concepts and procedures at higher levels (Aliustaoğlu, Tuna, & Biber, 2018; Bailey et al, 2015; Siegler, Thompson, & Schneider, 2011). Provided that failure of some students in understanding the concepts and procedures of fractions indicates diverse cognitive abilities between the students, it becomes the factor for students’ difficulties in solving problems, especially those involving fraction magnitudes. As a result, they fail to differentiate between the whole number and ratio representations (Hoch et al, 2018) during problem-solving They fail to differentiate between the whole number and ratio representations (Hoch et al, 2018) during problem-solving.
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