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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 reports on a study that explored the subject and pedagogical content knowledge displayed by high school mathematics teachers in the Khomas education region in Namibia. The study was based on a quantitative approach using a survey design. A stratified random sampling method was used to select the participants in all the four school circuits in the region. The study population consisted of 79 Grade 12 mathematics teachers from public schools. A sample of 40 mathematics teachers took part in the study, completed a questionnaire and wrote a test. A Microsoft Excel spreadsheet was used to sort the data and produce graphs and tables. A paired t-test was also used to determine if a significant difference existed between the participants' subject content knowledge (mathematical knowledge in our context, (MCK) and pedagogical content knowledge (PCK). The findings revealed that the participants had some deficiencies on MCK topics such as quadratic equations, angles properties and numbers. They also portrayed weak PCK on fractions, simultaneous and linear equations. This shows that a significant difference exists between the teachers' MCK and PCK with tcalculated = 11.092 greater than the tcritical (between 2.712 and 2.704) at a significance level, α = 0.01 but also that the participants' MCK and PCK were moderately and positively correlated (r = 0.681, p < 0.01). This study recommends that mathematics teachers in the Khomas region be provided frequently with in-service training to strengthen their shortcomings regarding MCK and PCK (knowledge of mathematics tasks, knowledge of learners' misconceptions and difficulties, and knowledge of mathematics instructions). We also recommend further studies to determine how high school mathematics teachers' knowledge can impact learners' academic performance in other education regions in Namibia. [ABSTRACT FROM AUTHOR]

Reflective practice is a crucial element of professional growth that is gaining in popularity in teacher education, yet the ability to reflect is a skill that is neither natural nor easy to develop. This paper reports on an investigation that sought to establish if pre-service teachers at a South African university – in the process of learning to reflect on practice through analysing video-recorded lessons – reflected differently when reflecting on their own practice from the way they reflected on the practice of other teachers. Pre-service teachers were introduced to the Six Lens Framework as a tool to aid reflection on mathematics teaching. The authors compared two sets of reflections written by four pre-service teachers (PSTs) who participated in the study. One set was based on a video-recorded lesson of another teacher's practice while the other was based on a video-recording of their own practice. The study found that the PSTs' reflections in both cases were generally at the lowest level of the reflection spectrum. They mostly described classroom events rather than analysing the lessons to provide explanation suggestions, or reflectivity. We found, however, that all four PSTs reflected at substantially greater length on their own lessons than on those of other teachers. Furthermore, three of the four teachers' reflections on their own practice focused on mathematical rather than general aspects and provided more suggestions for improvement than their reflections on the practice of other teachers. [ABSTRACT FROM AUTHOR]