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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]

This article discusses the growing attention and research activity surrounding early grade mathematics (EGM) in South Africa and Malawi. The introduction of curriculum reforms and policy-linked interventions, such as the Teaching Mathematics for Understanding model and the Primary Teacher Education initiative, have led to increased research in this field. The article highlights the importance of foundational understandings of mathematics in addressing low performance in the subject. It also examines different approaches to EGM research, including large-scale interventions and projects that engage with the mathematics education literature base. The article concludes by emphasizing the need for ongoing attention to both larger-scale and smaller-scale intervention studies in order to improve mathematical outcomes. [Extracted from the article]

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]

Participating in classroom mathematics conversations, particularly engaging with the opinions of others, can improve learners' mathematical comprehension. Teachers can use a variety of invitation and follow-up moves to encourage student engagement. The study aimed to explore teacher follow-up on learners' initial responses to teacher questions and building on learner ideas in Grade 9 mathematics classrooms. A qualitative approach and descriptive case study design were utilised. Data were collected from three schools in the same circuit in South Africa through classroom lesson observations, face-to-face teacher interviews and researchers' field notes. Three Grade 9 mathematics teachers, one from each school, were purposively selected, and the selected teachers' already established Grade 9 classes, with a maximum of 30 learners each (owing to the COVID-19 health protocol), were automatically involved. Cognitively guided instruction, a learner-centred approach that uses social constructivism as a research paradigm, guided this study. The exploration was supplemented by Brodie's conceptual framework on teacher follow-up moves. The findings revealed that the three teachers followed up on learner contributions and used different follow-up moves, namely insert, elicit, press, maintain and confirm. The study showed hybrid teacher moves. Although more teacher moves were skewed towards elicit and insert, which are closer to traditional practices, there is an indication of moving towards the press, maintain and confirm, which are reform-oriented moves. In addition to these moves identified by Brodie, acknowledging or praising the learner for responding was another move that emerged in this study. [ABSTRACT FROM AUTHOR]

This article draws on the notion of epistemic agency to illustrate how the enactment of shared epistemic agency is enabled or hindered in a mathematics classroom for student teachers. I used data from an ethnographic study that was conducted in a third-year class of mathematics for educators. Data was drawn from verbal interactions that took place between mathematics student teachers, and between student teachers and myself as their lecturer, as they worked on class tasks. A narrative mode of analysing data was employed to synthesise data from critical incidents, while excerpts of these incidents represented data. From this analysis, I argue that, with extended wait time by a facilitator, students' disposition of epistemic virtues and vices may enable or hinder enactment to epistemic agency, respectively. In article, those vices presented themselves as epistemic stinginess, prejudices against answers by peers and epistemic disclaimer. The epistemic virtues were presented as impartiality and intellectual courage. I further suggest that the recommended wait time of 1–3 during classroom questioning and answering should be extended for classes where epistemic practices are encouraged. [ABSTRACT FROM AUTHOR]

The aim of this study was to investigate the quality of the Annual National Assessment (ANA) Grade 6 Mathematics assessment instrument, administered in the year 2012 guided by the main question: to what extent does the 2012 Grade 6 Mathematics assessment instrument provide meaningful and consistent information for making appropriate interpretations? The responses to 29 questions, comprising 56 items, from 546 learners' scripts were coded individually, recaptured and analysed. The analysis shows that the Annual National Assessment was not well targeted, that is, the mean of the item and the mean of the person measures were not approximately equivalent. Specifically, in relation to this cohort, and taking into account the many factors that influence performance, we recommend that for reliable inferences to be made from test results, the quality of the assessment instrument should first be established. [ABSTRACT FROM AUTHOR]