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Teacher quality in primary schools in South Africa is a serious concern, and how best to prepare teachers in initial teacher education—with regard to mathematics—remains an open and vexing question. There is a confluence of challenges facing the mathematics education community in South Africa: poor conceptual understanding of mathematics amongst teachers; poor attainment in Primary Teacher Education mathematics tests at both first and fourth year levels; and few initial teacher education programmes having evidence of improving knowledge for teaching mathematics. In addition, few lecturers in initial teacher education make explicit the theoretical tenets informing their course design for mathematics. In response to the latter challenge, this paper makes explicit the design choices made in the Emergent Number Sense first year mathematics module in Bachelor of Education degrees, used across six universities in South Africa. It then theorises the choice to commence the B.Ed mathematics programmes with two pathways into number knowledge: (1) a counting pathway, making use of discrete objects or events which can be quantified by counting in ones; and (2) a measurement pathway, making use of continuous extents which can be quantified by introducing a unit of measurement. Each has a distinct metaphor, strategy for the reification of the 10 and supporting representation. This offers the lecturers using the course in their own design trials, and initial teacher educators beyond the Maths4Primary Teachers collective, a conceptual framework for this design choice, which can now be critiqued and further improved. [ABSTRACT FROM AUTHOR]

This paper contributes to research in responsive teaching in a context of collaborative discussion using video stimulated recall (VSR) techniques. The aim was to gain deeper understanding of the kinds of teachers' reflective awareness that prompts changes (or lack of change) in responsive primary mathematics teaching. Using a case study methodology, I analysed the VSR interviews of two teachers who demonstrated different patterns of changes in responsive teaching. The findings revealed two distinct and complementary forms of evidence of states of awareness and reflections that support change in responsive teaching practices: (a) teachers acknowledging limitations of their practice; and (b) teachers expanding repertoires of tasks and example spaces. These two forms of evidence provide insights into ways of supporting primary mathematics teaching in the context of VSR techniques. The implication of these findings is that for effective use of VSR interviews, attention should be geared towards getting a teacher to acknowledge the limitations of her practice, and through reflection-oriented questions to encourage the teacher to expand task and example space to respond to the limitations noted within the teacher's practice. [ABSTRACT FROM AUTHOR]

The chain of progression from teacher education to qualification to classroom instruction and student engagement, and then to learning and achievement, is not as straightforward as often presented. Societal, political and economic pressures create either a positive climate or a stressful one for both teachers and students. Nevertheless it is safe to say that in a subject like mathematics, the importance of subject matter knowledge cannot be underestimated. Research in this area supports the presumption that formal qualifications in the subject, in this case mathematics, are necessary, as this focused engagement with mathematics provides the foundation for mathematics teaching and learning. The allocation of fully qualified teachers to schools has in the past been uneven, with the supposition that students at higher socio-economic levels are being taught by better qualified teachers. In South Africa the improvement of teacher qualifications has been identified as a core area of action with the relevant policy on teacher education renewed in 2007 and again in 2014. The focus of this paper is to understand the change in patterns of teacher qualifications, and the interrelationship with school contextual variables. The analysis is based on the Trends in International Mathematics and Science Study (TIMSS) data from 2003, 2011 and 2015, where teachers from the TIMSS sample provided contextual information. Descriptive statistics were calculated using the IEA IDB Analyzer. The results show that South Africa has made substantial progress in uplifting teachers' formal qualification levels and in reducing structural inequality within its education system. Out-of-field teaching of mathematics is still shown to be a common phenomenon and is unevenly distributed. [ABSTRACT FROM AUTHOR]

The Primary Teacher Education (PrimTEd) project was established in response to concerns about the pre-service preparation of primary teachers in South Africa. In order to inform the development of appropriate pre-service mathematics courses, an initial need in the PrimTEd project was to establish the nature of the mathematical knowledge of pre-service teachers both near the start and also near the end of their studies, through an online assessment. This paper describes the design of this PrimTEd online mathematics test and reports on the performance on the test of first-year and fourth-year primary mathematics student teachers, at three different universities. The overall performance of students together with the small differences between first and fourth year student performance indicate a need for student teachers to revisit primary school mathematics in a way that provides a deep understanding of key mathematical concepts in order to be better prepared for future teaching careers. [ABSTRACT FROM AUTHOR]

Paying attention to the planning of lessons represents a crucial teaching task. This paper analyses teachers' framing of lesson objectives and their descriptions of how they would introduce particular mathematics topics. Connections between the objectives and the instructional strategies employed, were also studied. The study involved 75 South African mathematics teachers who were teaching Grades 4-12, in the KwaZulu-Natal Province. These teachers completed a questionnaire asking them to reflect upon and describe their teaching practices with respect to a chosen topic. The findings revealed that setting up clear lesson objectives is not easily done with only 64.0% of the participants providing clear learning objectives. The findings also showed that teachers preferred introducing the topics using teacher-centred methods. It was also found that for more than half of the teachers, there were clear connections between lesson objectives and the introduction of the topic in the classroom whereas less than a quarter of them made connections between lesson objectives and teaching and assessment strategies. Teachers, as important drivers of education, should prioritize the setting of clear objectives around which coherent lessons can be developed so that their teaching can be more effective. [ABSTRACT FROM AUTHOR]

Although buoyed by the induction of a democratic government, and the high ideals of our constitution, the South African education system has in many ways not met the expectations of its people, in this case, the mathematics education community. With the birth of an expansive intended curriculum came the monitoring of the outcomes through systemic type testing, the so-called attained curriculum. In time, it became clear that the inevitable 'teaching to the test' would constitute a narrowing of the implemented curriculum. Two possible constraining influences of the systemic test were identified, namely, a narrowing of the curriculum, and reliance on only one source of external monitoring. To counteract these, a project titled Assessment Enhanced Teaching and Learning (AETL) has been initiated, involving Grade Nine mathematics teachers. The aim of the project is to provide intermittent markers of progress to the teachers and learners at strategic points throughout the year. Teacher involvement in the design and implementation of these formative assessment tasks is thus central to the project. In this paper, we report on a case study at one school in the Pretoria region, and explore the use of structured assessment tasks as an approach to professional development. The question posed here is, "How does the implementation of strategically designed assessment tasks support professional development and enable professional agency?" Our findings indicate a strong sense of agency motivated by the need to excel in systemic type testing. [ABSTRACT FROM AUTHOR]

In this paper we draw on two research projects in South Africa to describe and discuss the language practices of teachers in primary multilingual mathematics classrooms. We focus particularly on code-switching – moving across languages and discourses. We situate the paper in the policy and practice environment of post-apartheid South African education in which code-switching is encouraged. Through our descriptions and discussion, we argue that while at a general political and pedagogical level it makes sense for teachers to encourage and use code-switching as a learning and teaching resource, this is not a straight forward matter. We argue that different English language infrastructures present primary mathematics teachers with different challenges for communicating mathematics. Furthermore, we show how the movement across mathematical discourses relates to movement between languages in classroom communication. [ABSTRACT FROM AUTHOR]

Algebra is a key course in the secondary mathematics curriculum. As a prerequisite for post-secondary mathematics, science and engineering courses, it is considered a gateway course. Since mathematical knowledge for teaching involves more than content knowledge algebra, teachers must be able to do more than successfully complete algebraic problems. They should understand algebra deeply and flexibly so that they are able to mediate students’ ideas, make choices about representations of content and modify curriculum materials. Yet, little is known about how certain groups view algebra and its teaching. In order to determine the beliefs held by a group of South African mathematics teachers with historically disadvantaged backgrounds teaching in schools that were previously segregated through Apartheid, this paper reports on what the group felt are the most important features of algebra. [ABSTRACT FROM PUBLISHER]

The study reported in this paper investigated Teacher Educators' (TE) awareness of teaching in multilingual contexts and what support structures, at the teacher training institutional level, are available to TEs who are preparing pre-service teachers for teaching mathematics in multilingual contexts of learners whose first language is not the language of instruction. 12 TEs from 4 universities in a Province in South Africa were interviewed. Qualitative analysis of the interviews revealed that while Teacher Educators are mostly aware of teaching in a multilingual context, the pre-service teachers are unaware of the challenges ahead involved in teaching mathematics to multilingual learners. The study also revealed that at the university level, there are no structured courses that attend specifically to the needs of pre-service teachers who are being prepared for teaching mathematics in multilingual classrooms of learners who are not yet proficient in the language of instruction. The author argues that even though a course at the university level that attends to teaching mathematics in multilingual classrooms is essential, creating awareness of the multilingual context of teaching and what it entails should be a thread that runs through the entire teacher education (mathematics) curriculum. [ABSTRACT FROM AUTHOR]

In this paper the mathematical working in a series of 'litter project' lessons from a South African Mathematical Literacy class is analysed in terms of Kilpatrick, Swafford and Findell's (2001) five strands of mathematical proficiency. The analysis points to evidence of the life skills-oriented Mathematical Literacy frame opening up opportunities for engagement across aspects of all five strands, but shows that the emphases differ from the intra-mathematical emphases within the strands. I argue that this is due to the lack of centrality in the Mathematical Literacy frame of the 'mathematical terrain'. The shifting of competence to the bridge between mathematics and everyday situations and problems retains mathematical coherence and connectedness. Both of these aspects are grounded in the mathematical tools and thinking that are needed to make sense of the everyday situation, rather than the more intra-mathematical connections and coherence that appear to be in focus within the strands of mathematical proficiency. [ABSTRACT FROM AUTHOR]