|dc.description.abstract||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
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
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.||en_US