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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]

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]

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]