Investigating teachers’ experiences of using multiple representations to teach fractions for conceptual understanding in 'Grades 5-7': a Namibian case study

This study investigated teachers’ experiences of using multiple representations to teach fractions for conceptual understanding in ‘grades 5 – 7’. Three teachers were involved in the study and the main goal was to explore how teachers might work with the additional tools of multiple representations to improve the teaching of fractions for conceptual understanding. Different types of multiple representations such as written mathematical symbols, descriptive written words, pictorial representations, manipulations, concrete reality, oral representations, and experience-based representations and videos or power point presentations were examined. This investigation was carried out through a focus group workshop developed by the researcher and though observations of fraction teaching which took place in schools. The research focused on the teachers working to develop their use of multiple representations to teach fractions and how they implemented what they learned in the workshop into their own classroom teaching. This study was conducted using a qualitative case study design and was oriented in the interpretive paradigm. The three participating teachers in the focus group workshop were observed and interviewed individually. The purpose of observing teaching before the workshop was to observe how the selected teachers taught fractions and in particular to observe which types of representations they used and how these were used to enhance the conceptual understanding of the learners. Post teaching took place after the focus group workshop and the different multiple representations which were used in different lessons were observed and analyzed. The purpose of the interview was to gain an understanding of the teachers’ views of using multiple representations when teaching fractions for conceptual understanding. The data showed that teachers who participated in the focus group workshop worked positively to develop their use of multiple representations to teach fractions. They made sense of fractions and were able to look at representations in different ways to develop the meaning and concepts of fractions. Teachers developed an understanding of working with multiple representations and were able to make connections among concepts and the use of concrete representations. Teachers also developed their lesson plans effectively to involve a variety of teaching methods and multiple representations, despite the limited time available to them. Moreover, teachers used different modes of representation to improve learner engagement in learning activities. Lastly, teachers used multiple representations to teach in ways that improved the learners’ conception of fractions. On the basis of this research, it can be concluded that in-service workshops for teachers on the integration of multiple representative tools in the teaching of ‘Grades 5 – 7’ fractions could provide a valuable contribution to further developing the teaching of fractions in schools