National and international studies show that the standard of mathematics teaching and learning in South Africa is very low compared to other countries. These statistics are worrying because mathematics is one of the ‘gatekeeper’ subjects that determine learners’ access to higher learning and a better future. My study, aimed at exploring two Foundation Phase teachers’ selection and use of examples and representations when teaching number, forms part of a longitudinal study currently underway within the Wits Maths Connect Primary (WMC-P) Project. One of the broad aims of the WMC-P Project is to improve primary teachers’ mathematics content knowledge and also to see this translated into improved pedagogy on the ground. This qualitative study was carried out within the WMC-P Project’s 20-Day in-service training course and one of the ten government schools participating in the broader study. My study aimed to build on research that has been carried out on teachers’ use of examples and representations with a focus on the South African terrain. The dataset comprised of two Foundation Phase teacher’s pre-tests, course-work tasks, field notes, and transcripts of observed lessons. Data was analysed using an analytical framework based on current literature related to examples and representations within mathematics teaching. Findings from my study show possible associations between a higher content knowledge score and the extent of a teacher’s example space and more coherent connections between different representational forms. More studies around this topic are needed because research shows that teachers’ examples and representations in mathematics teaching are important for good teaching and conceptual understanding.

Research Report submitted to the Wits School of Education, Faculty of Science, University of the Witwatersrand, Johannesburg In partial fulfilment of the requirements For the degree of Master of Science (Mathematics Education) Johannesburg, 2017 / South Africa’s performance in mathematics education is ranked amongst the world’s worst. This performance is not only alarming at an international level, but also nationally. Annual National Assessments (ANA) conducted by the Department of Education have showed that the level of mathematics across the foundation and intermediate phase is poor with a pronounced dip in performance at a Grade 4 level (Department of Basic Education, 2014). Multiplication and division are common challenging areas that contribute to this poor performance. This is concerning as mathematics is globally recognised as a key competence for providing access to higher education and developing a country’s society and economy. My study, aimed at exploring multiplicative reasoning with Grade 4 learners through structured problem solving, is focused on the learning of multiplication and division within the context of an intervention concentrated on developing learners’ ability to model multiplicative situations. Shifts in the use of models were investigated following a smallscale intervention in which different modelling approaches (particularly ratio modelling) were introduced and developed. A control group was used to determine the usefulness of the intervention. Questions which I sought to answer were: (a) what kinds of multiplicative reasoning (models) are Grade 4 learners using prior to intervention, (b) what changes, if any, are seen in overall performance, across the intervention and control group, in the post-test, and, (c) what kinds of differences in model use were associated with the shifts in performance? The main dataset comprised of 61 pre- and post-test scripts across three Grade 4 classes in a former Model C school in a Johannesburg district. A sample of 15 interviews were also conducted across the classes. Document analysis and transcription notes were used to analyse data with a Realistic Mathematics Education (RME) framework informing my analysis. Findings from my study reveal that prior to intervention, Grade 4 learners presented limited multiplicative models which were predominantly confined to traditional algorithms. After the small-scale intervention, learners used a broader range of models with an emerging take up of ratio models. The success rate associated with the models presented by learners also improved. Limited and/or no changes in model use and their respective success rates were seen in the control group suggesting that the intervention program was useful. These findings suggest that, as a future recommendation, it would be worthwhile to investigate the outcomes of running a similar intervention in less privileged settings. / MT 2018

This study considered use of practical work as one of the strategies that may be used to teach and learn fraction concepts in primary school Mathematics. Although an educator and learners were participants in the study, the focus was mainly on the learners. The class educator’s perception of practical work was investigated and the results confirmed the assumption that most educators use minimal or no practical work when teaching learners fractions. The researcher carried out an experiment with learners to find out whether they saw any value in doing practical work. Data collection instruments used were an observation schedule which was collated by the researcher in teaching four lessons, written responses of learners to a series of activities they did as class work and their responses to interview questions. Data collected from learners confirmed that practical work did have value in the teaching of fraction concepts, especially addition of fractions. Other than confirming the value of practical work, much other valuable data emerged from the findings. The data have important implications for the teaching and learning of fractions, especially addition of fractions, teacher training in practical work and also further research. These are intended to improve teaching of fractions, particularly addition of fractions. / M. Ed. University of KwaZulu-Natal, Durban 2013.

Recent research has elucidated the sustained benefits of early mathematics instruction. With growing concern about the performance of South Africa’s senior learners in mathematics, it is imperative to look at long-term solutions within the education process. One such solution may be to focus on improved mathematics instruction as early as preprimary school. However, children at this young age are not typically suited to formal teaching. Alternative methods of mathematics instruction must be considered for maximum and effective impact. The study was conducted to test the notion that not all early methods of mathematics instruction are equal. During the empirical research approximately 200 preprimary school children in three different socio-economic environments (urban higher SES, township and rural) were tested after experiencing a teacher-guided play-based mathematics teaching intervention, or after experiencing a worksheet-based or free-flow play-based curriculum. The test performance of the participants was primarily compared to find relations between teaching methods and early mathematics performance. The study found that a teacher-guided play-based curriculum is superior to other curriculums in the instruction of mathematics in all educational settings, regardless of socioeconomic background. / Psychology of Education / M. Ed. (Psychology of Education)

Recent research has elucidated the sustained benefits of early mathematics instruction. With growing concern about the performance of South Africa’s senior learners in mathematics, it is imperative to look at long-term solutions within the education process. One such solution may be to focus on improved mathematics instruction as early as preprimary school. However, children at this young age are not typically suited to formal teaching. Alternative methods of mathematics instruction must be considered for maximum and effective impact. The study was conducted to test the notion that not all early methods of mathematics instruction are equal. During the empirical research approximately 200 preprimary school children in three different socio-economic environments (urban higher SES, township and rural) were tested after experiencing a teacher-guided play-based mathematics teaching intervention, or after experiencing a worksheet-based or free-flow play-based curriculum. The test performance of the participants was primarily compared to find relations between teaching methods and early mathematics performance. The study found that a teacher-guided play-based curriculum is superior to other curriculums in the instruction of mathematics in all educational settings, regardless of socioeconomic background. / Psychology of Education / M. Ed. (Psychology of Education)