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Over the years, several frameworks and lesson observation protocols have been developed to ensure objectivity and consistency when determining the quality of a mathematics lesson. Frequently, the frameworks do not agree on the benchmarks for assessing and describing the quality of a lesson. This puts mathematics education researchers in a dilemma when deciding the appropriate framework for analysing mathematics lessons. Instead of treating the frameworks as mutually exclusive, we are of the view that each framework has some unique aspects that contribute to the story about the quality of a mathematics lesson. In this paper, we examine how the Mathematical Quality of Instruction framework and the Mediating Primary Mathematics framework, as lenses, help us to see and describe various aspects of instructional quality from one episode of a mathematics lesson in Malawi. We notice that the two frameworks share some common criteria for describing the quality of a mathematics lesson, such as the focus on making mathematical connections and using multiple representations, but they also differ on other areas of emphasis, such as the use of artefacts in the Mediating Primary Mathematics framework, and the emphasis on errors in the Mathematical Quality of Instruction framework. As such, we conclude that both frameworks can be useful for discussing the quality of a lesson in a professional development setup. [ABSTRACT FROM AUTHOR]

The Old Mutual Mathematics Olympiad (OMMO) in Malawi is a national mathematics competition open to all final year secondary school students. In this paper, we analyse the results of the preliminary round of the competition from 2015 to 2020. We developed seven content areas for the OMMO based on core elements of the Malawi secondary school mathematics curriculum. We found that the OMMO is dominated by questions on the core element Number and numeration, particularly topics like number systems, indices and logarithms, linear equations and number patterns. We also analysed the general performance of students in these areas. We found that students performed well in topics like inequalities, trigonometry and mensuration and did very poorly on proportions, sets, coordinate geometry and geometric constructions, among other topics. These findings suggest that mathematics Olympiads can help diagnose areas that are difficult for students and hence enhance the teaching and learning of Mathematics, especially in Malawi and other countries with a similar mathematics curriculum. To take care of under-represented areas, future OMMO examinations need to be structured to adequately cover all the core elements. [ABSTRACT FROM AUTHOR]

While a consensus within the field exists that pre-service teachers need adequate knowledge and skills to become effective teachers in mathematics, less is known about how they understand the mathematical knowledge needed for teaching in elementary education. This paper explores how Malawian pre-service teachers understand the mathematical knowledge needed for teaching in primary schools. Written answers to a questionnaire survey, and data from six individual interviews collected at the beginning of the teacher-training programme will be presented. The analytical framework is based on the practice-based theory of mathematical knowledge for teaching, with a specific focus on the domains of the common, horizon and specialised content knowledge. The data revealed that, while taking theoretical courses, pre-service teaches develop only intuitive but complementary views of what is proposed by the theory, which is even the case with pre-service teachers with some prior teaching experience. Findings provide insights into the development of pre-service teachers' mathematical knowledge for teaching, and suggest that further research is needed on how pre-service teachers articulate their understanding of teaching in practice. [ABSTRACT FROM AUTHOR]