Proposed Title An action research study investigating the role of visualisation tools to grow and develop connection making in teaching of algebra and geometry in junior secondary phase/grade 8.

Context/background The use of visualisation in mathematics plays a role in teaching mathematical problems by supporting the development of new ideas and promoting communication of results and understanding(Arcavi, 2003;Piggot & Woodham, 2011; Konyalioglu, 2008 and Rahim, 2009). Although many studies outlined the useful of visualisation in teaching and learning mathematics, many teachers are not using it, they prefer analytical approach since they believe that visualisation cannot lead to proofs (Einsberg & Dreyfus, 1991 cited in Konyalioglu et al. (2011). In my experience , the pressure in mathematics education, regarding teaching of mathematics increases, researchers are seeking new ways and tools to support the teaching of mathematics. This realisation provides the opportunities to create flexible, visualisation approach to teaching which aim to enhance conceptual understanding (Kilpatrick, Swafford and Findell,2001; Presmeg, 2011).

Context/background Cont. Acarvi (2003) summarises the definition visualisation as “the ability, 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 understandings”.

Context/background Cont. Namibia. Ministry of Education (2010) proposes that for learners to improve their learning of mathematics, teachers should adjust their approach to teaching by using a variety of teaching and learning materials. It is thus important that learners are able to use Mathematics in a sensible way and that teachers facilitate access to it by making meaningful connections.

Context/background Cont. Mhlolo, Venkat and Schafer (2012) defined connections as: A relationship between ideas or processes that one can use to link topics in mathematics; A process of making or recognising links between mathematical ideas;

The goals of the research Explore the types of connections in relation to visualisation tools which will be used by the teachers when teaching mathematics. Determine whether connections that teachers make in relation to visualisation tools can grow and develop teachers’ conceptual understanding.

Research Questions 1.In what way does the visualisation tools enable selected teachers to grow and develop connection making skills to teach for conceptual understanding? 1.1. what are the nature of connections in relation to visualisation tools that selected teachers make when teaching algebra and geometry ? 1.2.What are the perceptions of selected teachers on the importance of making connections in relation to visualisation tools?

Research question cont. 1.3. To what extent do the connections related to visualisation tools grow and develop teachers’ conceptual understanding?

Research design Action research which is located in the interpretive paradigm (Cohen, Manion and Morrison, 2011). It will be conducted using mixed methods: both qualitative and quantitative action study design. Research techniques : Questionnaires, interviews, observation and document analysis. The research will be conducted in Okahandja circuit, at four secondary schools which have grade 8 classes. 8 grade 8 mathematics teachers who are members of Okahandja Mathematics club will be involved in this study – community of practice This study is divided into 3 phases: Phase 1-Initial questionnaire : Given to teachers (during mathematics club session) to find out their level of understanding in making connections using visualization tools when teaching mathematics. Phase 2 – Design an intervention program according to the questionnaires outcome. - The concepts of visualisation, mathematical connection and conceptual understanding will be introduced in that program.

Research design cont. Phase 2 is divided into four cycles of teaching Each cycle is divided into four stages: Stage 1: Planning of teaching (Lesson planning) Stage 2: Implementation/teaching in schools(Lesson planned) Stage 3: Observation (Observe teachers teaching what they have planned). Stage 4: Reflection on the teaching

Stage 1: Planning of teaching Stage 2: Implement lesson planned Research design cont. Teaching cycles: Stage 1: Planning of teaching Stage 4: Reflection Cycle1: 2months Cycle2: 2months Cycle3: 2 months Cycle 4: 2 months Stage 2: Implement lesson planned Stage 3: Observation

Research design cont The data of the first cycle will be analysed and discussed before the second cycle. After every cycle teachers will be interviewed (Focus group interview). Phase 3 – Post questionnaires

Conceptual and theoretical framework Five components of mathematical connections in practice informed by Businskas, 2008 constitute the conceptual framework of this study. These are:  Different representation connections  Part-whole relationship connections  Implication connections  Procedural connections  Instruction-oriented connections This study will be framed within aspects of Wenger’s (1998), community of practice theory and Lave and wenger’s (1991) social learning theory and concepts of practices.