Research topic Investigating how the use of visual models can enhance teaching of common fractions for conceptual understanding to grade 8 learners.

Research questions What are the selected grade 8 mathematics teachers’ experiences in working with visual models to enhance the teaching of common fractions? How did the selected grade 8 mathematic teachers’ conceptual understanding of common fraction change during the intervention? How did the teaching intervention influence grade 8 mathematic teachers’ conceptual understanding of common fractions?

Background and context According to MOE new syllabus, all school graduates in Namibia are expected to be numerate and the study of mathematics at the junior secondary level contributes to the learner’s ability to think logically, work systematically and accurately and solve real-world problems(Namibia. Ministry of Education, 2015). In my experience, fractions is one of the most difficult topics in mathematics, both to teach and learn. Learners in Grade 8 are expected to be able to compare and order fractions as well as to perform the four basic operations on fractions (Namibia. Ministry of Education, 2010, p. 9).

Background and context cont The term “fractions” can be used to refer to “any way of representing rational numbers, such as percentages, decimals and common fractions” (Hansen, 2015, p. 9). The present study is concerned with the development of common fractions. Common fractions refer to a representation of rational numbers in the form a/b (Hansen, 2015).

Background and context cont The teacher must be able to identify the needs of the learners and the learning that still needs to take place, and know how to shape learning experiences accordingly. Teaching strategies must therefore be varied and flexible within well- structured sequences of lessons (Namibia. Ministry of Education, 2015). Visualisation as the ability and the process and the product of creation, interpretation, use of and reflection upon pictures, images, diagrams, in our minds, on paper or with technological tools, with the purpose of depicting and communicating information, thinking about and developing previously unknown ideas and advancing understanding” (Arcavi 2003).

Theoretical framework The research will use constructivism theory oriented by interpretive paradigm. Constructivism theory concentrates on a holistic view of learning mathematics and focus on a deep understanding and strategies, rather than on facts and rote memorisation. The fundamental approach of this theory is that knowledge is constructed through the interaction with people and objects of inquiry (Bruner, 1961). Discovery learning an inquiry-based, constructivist learning theory that takes place in problem solving situations where the learner draws on his or her own past experience and existing knowledge to discover facts and relationships and new truths to be learned”(Champine, Duffy & Perkins, 2009). This then gain an insight to the purpose of my study that explore how can the use of visual models enhance teaching of common fractions in a group setting workshop.

Research design The study will be conducted using an intervention design drawing from qualitative and quantitative data ( mixed method). The research instrument: Survey, interviews and focus group interview. The study will have four phases Phase 1: Survey with at least 50 teachers in Khomas region, asking if teachers use visual models in their teaching.

Research design cont Phase 2: Teachers workshop, about five participants(non visualizer) will be selected from the survey. They will be introduced to the approach of teaching addition and subtraction of common fractions using visual models. The lessons and the materials will be planned together in the workshop. The workshop will be video recorded and the data generated will be used as the background of the research. Phase 3 : Teaching, fraction representation with model, addition and subtraction of common fractions, five selected mathematics teachers will each present a lessons on fractions to grade 8 learners using visual models. The lessons will be Video recorded and later interview each teacher based on the lesson taught. Phase 4: Focus group interview with the teachers, bring the teachers together to discuss their experience using visual models. Both interviews on phase 3 and 4 will be audio recorded.