A research report submitted to the Faculty of Science, in partial fulfilment of the requirements for the degree of Master of Science, University of the Witwatersrand. Johannesburg, October 2016. / This research study makes an attempt at intervening in the Grade6learners’ use of models and strategies in solving addition and subtraction word problems based on Realistic Mathematics Education (RME) theory. RME theory advocates for the provision of understandable contexts that learners can relate with to support them in developing models and strategies, with specific reference to the empty number line model in assisting learners to develop an understanding of the structure of number and to work flexibly in solving addition and subtraction word problems. It is in understanding the models and strategies learners are using that we can begin to understand how the learners need to be supported in order to operate at the appropriate mathematics levels for their grade. Participants in this research study, forty boys and girls doing grade six, all with a weaker mathematical background, wrote the same tests in the form of pre test, post test and the delayed post test. After writing the pre test, the learners attended a series of six intervention lessons before writing the post tests. The intervention lessons encouraged learner engagement with word problems and the development of models as representations of problem situations and strategies which represent learner’s manipulation of models in an RME-advocated approach. Learner responses were analysed aiming at the identification of models and strategies they employed, as well as the correctness and success in solving the problems. The analysis found out that mainly there have been some improvements in the repeat sittings from predominantly using the column model with a lot of incorrect answers to using the empty number line with more correct answers. I would therefore encourage the maximum participation of teamwork amongst teachers for identifying and using efficient models and strategies in order to promote performance levels in mathematics through developing an understanding of the structure of number and working flexibly in solving addition and subtraction word problems. / LG2017

This study examines the teaching and early learning of addition in primary classrooms. The relationship between teaching and learning is examined at the level of classroom interaction, in the completion of mathematical tasks. The mathematics lessons of two classes in each of two schools were observed over a period of six months, involving four teachers and the 4, 5 and 6 year old children in their classes. The mathematical focus of the study was the learning of addition, one of the first formal mathematical concepts taught in school. This formed a basis for exploring the factors involved in the teaching of mathematics to young children, and their learning. The methodology is qualitative, with participant observation the main method of data collection. Detailed fieldnotes were taken of all mathematics lessons observed; short unstructured interviews with teachers were carried out before and after the lessons. The children's understanding of number concepts and addition was assessed at both the beginning and the end of the observation period. The data was analysed using a grounded theory approach, which produced patterns of recurring variables. Analysis of these variables, influenced by the theoretical perspectives of the researcher, provided analytical pictures of teaching and learning, from which the findings emerged. The study highlights the complexity of the classroom for teachers and young children, where curriculum considerations, understanding of the mathematics concepts, social interaction and integration into the community of the classroom, vie for attention. It indicates that children are more likely to make sense of mathematics when the number curriculum is taught with a view to its complexity, rather than broken down into simple steps; the problems young children have learning to use mathematical symbols; and that the use of story is important in helping especially the youngest children understand mathematics. This was a small scale study, but provides a 'thick description' of teaching and early learning of addition, which can form a basis for future studies. Key Words: addition, early mathematical development, primary school, constructivism, socio-cultural theory, situated cognition, symbols, real world scripts, narrative.

published_or_final_version / Education / Master / Master of Education