An investigation of the use of multiple representations in teaching fractions at primary school level in Swaziland.
Dlamini, Thab’sile Priscilla.
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This study aimed at identifying the kinds of representations primary school teachers commonly use in teaching fractions, how they use them and their reasons for using them. The study drew on the teaching model by Ball, Thames and Phelps (2008), who claim that representations play a crucial role in developing learners’ understanding of mathematical concepts. Learners frequently make errors and teachers are required to identify the source of those errors and find ways of remediating them, usually by using multiple representations. The study is framed by Vygotsky’s (1978) social constructivism and Lesh, Post and Behr’s (1987) typology of representations in primary mathematics; namely, verbal, pictorial or diagrammatic representations, concrete models, experience-based metaphors and symbols. Through classroom observations and interviews, the researcher sought to understand teachers’ motivations for using particular representations in teaching the concept of fractions. Findings from this study revealed that teachers use all the representations suggested by Lesh et al. (1987); however, it confirmed results from other studies that symbolic and spoken language tend to dominate in most classrooms. Teachers also preferred using the rectangular area model to the circle model. The study highlighted the need for teachers to exercise caution when using metaphors, so as to avoid the metaphor itself becoming the focus of the lesson. Teachers used the various representations available to them as scaffolds upon which to build learners’ understanding of fractions, often through engaging them in group activities or demonstrations in which learners became active participants. Most of the representations were used to make the fraction concept concrete, to make the lesson interesting and exciting and to accommodate the different learning styles within the classroom. The researcher recommends that teachers in the intermediate phase introduce operations on fractions using either concrete or virtual manipulatives or real-life problems. It is also suggested that teachers give learners opportunities to come up with the rules for performing operations on fractions themselves, using multiple representations which enable them to observe patterns and draw conclusions.