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This paper focuses on the Southern African Association for Research in Mathematics, Science and Technology Education's (SAARMSTE's) role as a platform supporting research dissemination and connecting researchers in early grades mathematics (EGM) in the Southern African region. A review of the Long Papers in SAARMSTE over the last 20 years supports the finding of the other review papers in this Special Issue: that there has been substantial growth of attention to EGM since 2013. However, two distinctions are marked when looking at conference papers rather than journal papers. Firstly, there is a particularly large expansion of work in the last 5 years, with a broadening base of participation in this work. Second, looking across all the formats of conference presentations indicates SAARMSTE's role in supporting and building EGM as a key focus of research attention, and bringing together regional and international groups with interests in this area. Given that conference proceedings usually offer a broader picture of emerging interests than journal papers, we reflect on the range of foci of attention within EGM in the SAARMSTE Proceedings, and trends within this. These trends also help us to point to areas that are likely to be of key interest in the next decade. [ABSTRACT FROM AUTHOR]

The majority of children in mainstream (no fee, poorly resourced, African language dominant) public schools in South Africa fall significantly behind curricular norms in mathematics by Grade 3; the early learning gap grows across time. The provision of quality instructional materials is a well-recognised component of effective strategies to improve early grade mathematics in low- and middle-income contexts. However, there has been little explication of what constitutes quality instructional materials, nor long-term design work to contribute theory to this instructional design challenge. Across 15 years, the author has been working in an education design hub with teacher educators and teachers in the rural Eastern Cape, with the goal of improving early grade mathematics. The gains in mathematics performance have been among the most significant reported in research literature. This paper presents the design principles emerging from the work. Engaging the theoretical layers discussed by diSessa and Cobb, the paper contributes to design theory by emphasising the relationship between explicit instructional assumptions and design principles, integrating four ontological categories (motive, pedagogy, language use and mathematical meaning-making). Since 2011, the Department of Basic Education has provided learner workbooks to support teaching and learning in foundation phase mathematics at system scale. It is hoped that this paper will contribute to the ongoing development of this vital national resource. The paper makes explicit instructional assumptions and design principles (available for critique, adaptation, and refinement), and provides a more nuanced framework through which to assess and improve materials across time. [ABSTRACT FROM AUTHOR]

Among the problems identified at Technical and Vocational Education and Training (TVET) colleges, low achievement in mathematical subjects is the most prominent one. This paper documents a qualitative case study undertaken at TVET College in Gauteng with the purpose of exploring the National Certificate Vocational (NC(V)) Level 4 students' errors and associated misconceptions when answering optimisation questions in differential calculus. The participants were 60 students who were registered for a course in mathematics. Data were generated from the written student responses to two non-routine test items followed by interviews. Using the Newman error hierarchical model to analyse the data, it was discovered that students errors were conceptual and procedural as well as systematic and non-systematic. The literature also alluded to instructional approaches as some of the causes of students' misconceptions and the errors and that interventions should target students as well as the instructors. [ABSTRACT FROM AUTHOR]

This paper examines the conceptions of 'number sense' as promoted in pre-service primary mathematics education courses at 11 South African Higher Education Institutions through the texts used by academics or prescribed for students. While all the participating institutions agree that the development of primary school learners' 'number sense' is central to their mathematics methodology courses and that there is an overwhelming amount of research and literature on 'number sense' nationally and internationally, their conceptualisations of the nature of 'number sense' vary. Teacher educators, who develop pre-service teacher education courses, were asked to provide the texts, used to underpin the 11 universities' mathematics education modules in the Bachelor of Education (Foundation and Intermediate Phases) and Post Graduate Certificate in Education (Foundation and Intermediate Phases) programmes. These texts were analysed drawing on Whitacre et al.'s emphasis on three 'number sense constructs' identified as Innate Number Sense, Early Number Sense and Mature Number Sense. The results show that there is no common language of description for 'number sense' across the 11 universities. This research implies that there is a need to develop a consistent understanding of 'number sense' and how it is developed across institutions. [ABSTRACT FROM AUTHOR]

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]

Research on mathematical equivalence, and to some extent, on number structure in early grade mathematics, has shown that most students at primary and secondary levels understand these concepts instrumentally rather than relationally. The study reported in this paper uses a design research approach to explore both mathematical equivalence and number structure in a primary pre-service teacher education programme at a university in South Africa and reports on an intervention strategy intended to culminate in developing design principles comprising guidelines for the effective teaching of number structure and mathematics equivalence in primary pre-service teacher education programmes. The mixed method study comprises 70 first-year primary pre-service teachers (PSTs) and a teacher educator. The PSTs wrote pre- and post-tests, and were interviewed following the pre-test. Skemp's notion of relational and instrumental understanding guided the design of the intervention and the analysis of the data. The results from the study indicates that PSTs' understanding of the notion of equivalence is similar to what has been reported for students in schools, and that there were some learning gains in the post-test results. Based on the findings from the study in general, some emergent design principles are proposed. [ABSTRACT FROM AUTHOR]

This paper argues that the practice of teaching and learning is being re-defined as technology enables a re-imagining of what can be taught, and how it could be taught. In Namibia, demands on mathematics teachers to incorporate technology use into their teaching practice are often mismatched with the curriculum. This theoretical paper proposes meaningful mathematics teaching via technology, instead of a mere response to societal adoption of digital tools. The concept of meaningful teaching is viewed through a Vygotskian lens. Kilpatrick et al.'s five Strands of Mathematical Proficiency inform the interpretation of goals for teaching mathematics with technology. We discuss the gaps in current models for professional development for teaching with technology when we take the Namibian cultural historical context into consideration. Activity Theory is used to conceptualise a two-triangle embedded activity system of teachers and professional developers, and to reflect on nodal interactions. We conclude by proposing some principles for the design of professional development programmes that aim to support mathematics teachers in using technology in their teaching. The principles may be useful for professional development in other developing countries with uneven access to both technology and reformed mathematics curricula. [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]

Learning mathematics is as much about developing relationships with mathematics as the development of mathematics concepts and skills. Mathematics clubs usually support learners to develop relationships with mathematics through engaging with challenging mathematics problems, exploring mathematical ideas, and communicating and sharing their ideas. This paper reports on research on such a mathematics club. Data sources included learners' mathematics results, short written responses after club sessions and interviews with club learners. Data were analysed quantitatively and qualitatively. The study shows that club learners' school results improved relative to non-club learners, that learners' experiences of mathematics in club and class were very different from each other and that the club supported different relationships with mathematics than learners experienced in class. The study suggests that mathematics clubs can support learners' positive relationships with mathematics. [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]

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]

This paper seeks to explore the nature of dialogue within calculus lecture rooms. This paper reports on part of a larger study, in which the participants were two lecturers lecturing to 198 third year pre-service teachers at a University in South Africa. This qualitative interpretive study was framed within the ambits of social constructivism and aspects of Mortimer and Scott's framework were used to analyse dialogue in the lecture room. Data for this paper were generated through video-recorded lecture observations. Subsequently, a qualitative data analysis of the generated data revealed that dialogue within the calculus lecture rooms under study may be in the form of explanations and questioning. Questioning included questions that assess students' prior knowledge, probing, follow-up and guiding questions. The findings of this study are of value to both lecturers and students within higher education with implications for teaching and learning mathematics within higher education are presented. [ABSTRACT FROM AUTHOR]

This paper examines how seven teachers working in contexts of limited resources used the prescribed textbook for teaching, and the kinds of teacher–textbook relationships forged in the interactions. The study employs a sociocultural perspective to explore the processes by which teachers mobilise the affordances of the textbook to the teacher's practice, thereby advancing a particular way for studying and understanding better the teacher–textbook relationships in particular contexts. A methodological approach aggregating results for all teachers and looking for patterns of mobilisation across teachers allowed for the analysis of patterns of mobilisation regardless of the teacher. Findings point to generally tacit use of the textbook and a need for intervention on textbook use by teachers. The study makes recommendations for the production of educative guides as well as further research on the perceived role of the textbook in the teacher's practice. [ABSTRACT FROM AUTHOR]

Mathematics is frequently considered as value-free, centring entirely on abstract reasoning. However, more often than not, the teaching of values in mathematics classrooms takes place implicitly through the actions of the teacher. The role values play in mathematics learning is also a growing area of interest and is now viewed by many as a contributing factor in the advancement of the quality of mathematics performance. This paper reports on part of a larger study aiming to establish the components that Grade 8–10 learners from a mathematics-and-science-focus school in Johannesburg value as important in the learning of mathematics. A quantitative survey was used to collect data from 249 participants. Principal component analysis was employed to analyse the data. The main findings revealed seven components that learners appeared to value in the learning of mathematics. Knowledge about what learners value in the learning of mathematics can inform teachers' pedagogical practices and the inculcation of values in mathematics teaching, which may, in turn, improve the quality of learning of mathematics. [ABSTRACT FROM AUTHOR]

This paper reports on some aspects of an investigation on the impact of an instructional approach aimed at generating and maintaining students' interest in mathematics for secondary school students in displaced and re-settled communities in South Sudan. Two groups of Grade 11 students, an experimental group (E-group) and a control group (C-group), participated in the study. The E-group (n = 31) was taught using a Humour-supported Instructional Approach (H-SIA) and the C-group (n = 20) was taught using a Regular Instructional Approach. Preliminary indications from the pilot phase of the main study suggest that the method of instruction (H-SIA) generates and maintains at least similar levels of interest as the regular Regular Instructional Approach. The H-SIA also suggests some slight modifications and enhancement to the Interpersonal Competent Communication Model, the recommended existing guiding theory for humour communication in the classroom. It is concluded that H-SIA does indeed generate and maintain interest in mathematics in the classroom. Hence, it is recommended that mathematics teachers should consider infusing humour into their lessons to enhance students' interest in mathematics. [ABSTRACT FROM AUTHOR]

This paper reports on the professional development of four mathematics teachers in South Africa. The four teachers all participated in a Mathematical Thinking course before taking an Advanced Certificate in Education in mathematics. The research, which aimed to understand these teachers' ongoing professional development, took place two years after they had completed the Advanced Certificate in Education course, at a time when they were helping to run a subsequent Mathematical Thinking course, taking the role of teaching assistants. The teachers provided written 'stories' of their experiences during and after the two courses and were interviewed twice after the two courses; the first interview drew on the stories and the second drew on the first interview. The qualitative data gathered were analysed using a three-part framework of outcomes: personal, professional and cultural/social. In terms of personal outcomes, they reported renewed confidence and passion for teaching mathematics, changed beliefs and values, and acknowledged new learning experiences; they did not, however, report learning about mathematics, the curriculum or planning. In terms of professional outcomes, they reported changes in both their own classroom teaching practice and their approaches to leadership. Finally, there was little evidence of cultural/social outcomes, but participants reported on opportunities that had been offered to them and on new collaborations in their communities. We have called these 'community outcomes' and suggest that 'cultural/social outcomes' might be renamed 'community outcomes' so that it is extended to include these sorts of opportunities. [ABSTRACT FROM AUTHOR]