n Ondersoek na visualisering en metakognisie met betrekking tot die onderrig-leer van gewone breuke
Common fractions and a good understanding thereof are fundamental to various life areas, including many mathematical topics (Dlamini, 2017:1; Gabriel, 2016:36), other school subjects and occupations later on (Fennell & Karp, 2016:648; Bruce et al., 2013). However, research indicates that many teachers and learners find the teaching-learning of fractions to be problematic and that learners' understanding of fractions is inadequate (Fennell & Karp, 2016:649). This is also true in the intermediate phase (Le Roux, 2013:38). Traditional methods for teaching and learning fractions may hamper learners' sufficient understanding (Mudaly & Rampersad, 2010:39). Consequently, this study focuses on the implementation of visualisations and metacognition with respect to the teaching-learning of fractions. These strategies are associated with more modern teaching-learning approaches and result in better understanding. Research on the links between visualisation, metacognition and fractions appears to be insufficient (Rogness, 2011). Literature encourages further research on the use of visualisation in mathematics education and points to the possible benefits (David & Tomaz, 2012:413). Metacognition supports the effectiveness of practices and is important due to the complex nature of the implementation of visualisations during the teaching-learning of fractions. This research involved an investigative and descriptive qualitative study to examine the use of visualisations, with the ultimate goal of improving the teaching of fractions. This would lead to a better understanding of fractions among learners. The sample was selected by means of purposive convenience sampling and included four mathematics teachers who teach in the intermediate phase. The teachers teach at one urban and one rural school in two different provinces. Data were collected by means of semi-structured individual interviews, video recordings, observations and field notes. The data were analysed using an inductive approach to content analysis to uncover how the participating teachers use visualisations and what kind of visualisations they use. The participants were subsequently probed on which metacognitive strategies they employed during the teaching-learning of fractions to establish a link between visualisation, metacognition and the teaching-learning of fractions. The findings show that the mathematics teachers regard the use of visualisations during the teaching-learning of fractions as important. They offered valuable information on the benefits, strategies and obstacles associated with the implementation of visualisations. The study, therefore, contributes to knowledge on the use of visualisations as it links with metacognitive practices during the teaching-learning of fractions in the intermediate phase. In summary, the teaching-learning of fractions benefits from the use of visualisations and metacognitive practices. The teachers applied planning, monitoring and evaluation as metacognitive strategies to regulate their implementation of visualisations in the teaching-learning of fractions. Visualisations supports learning and understanding by making abstract fractions content more concrete and accessible to learners (Dlamini, 2017:1), while metacognition contributes to more effective teaching-learning practices, better visualisations and ultimately better understanding (Jiang et al., 2016). Apart from certain barriers to the implementation of visualisations, effective visualisation can be valuable. Teachers should focus on exploiting the benefits of visualisations and on the most optimal implementation and facilitation practices to promote learners& understanding of fractions. However, the mere use of visualisations does not guarantee that learners learned and formed a good understanding. Effective teaching-learning involves more. Metacognition is therefore a crucial piece of this puzzle.
- Education