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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]

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 considers the effects of both free optional mathematics learning support and engagement on the mathematics performance in a foundation mathematics subject of a cohort of engineering students entering university with poor mathematical skills. New engineering students were directed to either a foundation or standard mathematics subject based on the results of a placement test. For students in the foundation subject, it was found that high levels of learning support were associated with greater improvement over the semester. Some form of learning support was used by 57.9% of the students, a reasonably high proportion of the cohort. Some factors for this high level of use of learning support are considered. One possible factor, the placement test, appears to have had a positive effect. Engagement in the subject activities as measured by tutorial attendance and learning management system use was found to have a positive association with final mark. Students who utilized a high level of learning support were more likely to be more engaged with the subject, making it impossible to draw conclusions about improvements being solely due to the use of learning support. [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]

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]

There is a significant body of research that indicates that the use of tablets to learn mathematics in elementary school motivates students to learn. Low mathematical attainment in international benchmarking tests of mathematics in South Africa led the authors to investigate the potential that the mobility of the tablet provided for children to learn how to reason using what Mercer called 'exploratory' talk, a form of dialogical interaction indicative of reasoning. In this article the authors investigate two grade 6 classrooms in two schools where students are learning mathematics using tablets. In this multiple case study, the authors videotaped children during mathematics lessons where they used tablets to solve mathematical problems, and the data were transcribed. Findings indicate that the tablets across both contexts facilitate what Mercer calls exploratory talk, which is indicative of reasoning and, therefore, learning. [ABSTRACT FROM AUTHOR]

Girls performing well in mathematics at school do not necessarily enrol for mathematics courses at South African universities. Teachers could be transferring beliefs about the nature of mathematics favouring boys. This paper compared male and female pre-service teachers’ beliefs about the nature of mathematics. A quantitative, descriptive research approach was adopted. One hundred and twenty-six mathematics pre-service teachers, enrolled for an undergraduate teaching training programme at a South African university, completed a questionnaire. While both genders hold the same Platonist and instrumentalist beliefs, females embrace lower experimentalist beliefs than males. Research on differences between male and female pre-service teachers’ beliefs about the nature of mathematics could promote gender equity in mathematics teacher training and better facilitation of the subject, which might consequently encourage more girls to opt for mathematics-related careers. [ABSTRACT FROM AUTHOR]

Universal health coverage (UHC) aims to ensure people have access to the health services they need. Sixteen tracer indicators were developed for implementation by countries to measure UHC in the health system. South Africa uses 15 of the proposed 16 indicators. Operational managers in the public health care sector collect data and report on these indicators at a primary health clinic level. This qualitative study explored the knowledge and attitudes of managers toward data and UHC service indicators in a sub-district in Ugu, KwaZulu-Natal, South Africa. Operational managers saw data collection as information gathering, measuring performance and driving action. They understood UHC indicators as 'health for all' linking them to National Department of Health Strategic plans and saw the value of indicators for health promotion. They found the lack of training, inadequate numeracy skills, requests for data from multiple spheres of government and the indicator targets that they had to reach as challenging and untenable. While operational managers made the link between data, measuring performance and action, the limited training, skills gaps and pressures from higher levels of government may impede their ability to use data for local level planning and decision making. [ABSTRACT FROM AUTHOR]

Estimation equations based on different body segments are commonly used to predict height in patients whose height cannot be directly measured. This study aimed to assess the agreement between measured (reference) height and height predicted from published equations derived from measurement of body segments, in a South African public hospital setting. A descriptive cross-sectional study was undertaken. Medical, surgical, pulmonary, orthopaedic, cardiovascular and general wards at three public hospitals in Bloemfontein. Admitted patients, 20–50 years old; able to stand upright without assistance and without medical conditions or treatments affecting height. Stadiometer height, recumbent height, arm span, demi-span, ulna length, knee height, tibia length, fibula length and foot length were measured with standardised techniques. Height, predicted by 12 published equations, was compared with stadiometer height by 95% confidence intervals (CI) and Bland–Altman analysis. The median stadiometer height of the sample (n = 141; 38.3% female; median age 38.8 years, IQR 33.3–44.4 years) was 165.5 cm (males 169.3 cm; females 158.4 cm). Only a set of equations based on knee height and standardised on a large population of adults < 65 years in the United States estimated height without statistically significant deviance from the stadiometer height. Most standardised equations applied to hospitalised adults in a South African public health setting resulted in height estimations that differed significantly from height. Thus, equations standardised on other populations may not be suitable for the South African population, possibly due to differences in genetic and environmental factors. [ABSTRACT FROM AUTHOR]

This study, conducted in one high-achieving secondary school in a disadvantaged area in the Western Cape province of South Africa, asks whether mathematics teachers alter their "talk" across the face-to-face and computer-based lessons. Data were gathered through video recordings of teacher/student interactions across ten face-to-face and computer-based mathematics lessons conducted by two teachers. Findings indicate that the teachers studied significantly altered their "talk" across the two contexts, with a medium effect size. Further, a significant association at a medium effect level between any two of the three variables—location of lesson, "talk" type and scale of interaction—was found. In particular, teachers used significantly less mathematical talk in the computer lessons. As language is the primary mediator of conceptual acquisition (Vygotsky, 1978), this calls into question what mathematical concepts are learnt in a computer-based lesson. [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]

Using an arts based approach toward mathematics learning, a story, crossing the River was used in a multidisciplinary community engagement project in rural South Africa. Subsequently, the playing of the story highlighted key connections between mathematics and the arts. Play created the space, or 'stage', for the showcasing of the nature of mathematics. More importantly, similar to the notion of 'here' and 'now' in drama, play enabled access to mathematical thinking by inviting participants to converse about the problem at hand, while enrolled in respective characters entailed in the story. In the process, the activity challenged a long-standing argument that separates the two subjects and treats mathematics as a cognitive thinking and rational left-brain activity, while the arts are considered to be an affective, feeling and emotional right-brain activity. Through the teacher's comments, such as those linked to the 'performing mathematics', 'pedagogy' as well as 'the nature of mathematics', we learn that the crossing the river case study represents an attempt toward capturing the aesthetic nature of human cognition that needs to form part of mathematics teaching and learning. Accordingly, such interplay between arts and maths education provides an opportunity for engaging learners in such a way that the teaching of mathematics in isolation may never accomplish. Hence the argument of 'bringing learners to mathematics' as opposed to 'bringing mathematics to the learners', and adoption of an integrated learning approach that has play using an artistic creativity as an entry point. [ABSTRACT FROM AUTHOR]

A mathematical model, populated primarily with data from South Africa, was developed to model the numbers of children affected by maternal HIV, and the number who will experience long-term negative developmental consequences. A micro-simulation model generated two scenarios. The first simulated a cohort of women whose HIV status mimicked that of a target population, and mother–child dyads by way of age- and disease-specific fertility rates. Factors defining risk were used to characterize the simulated environment. The second scenario simulated mother-child dyads without maternal HIV. In the first scenario an estimated 26% of children are orphaned, compared to 10% in the absence of HIV. And a further 19% of children whose mother is alive when they turn 18 are affected by maternal HIV. School drop-out among all children increased by 4 percentage points because of maternal HIV, similarly population level estimates of abuse and negative mental health outcomes are elevated. Relative to HIV unaffected children, HIV affected have elevated risk of poor outcomes, however not all will suffer long-term negative consequences. Interventions to protect children should target the proportion of children at risk, while interventions to mitigate harm should target the smaller proportion of children who experience long-term negative outcomes.. [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]

The supplemental instruction (SI) programme has been well-established worldwide and the resulting success of the programme is indisputable. The University of Pretoria has decided on SI as the model to be used for addressing the underpreparedness of students entering the university, largely brought about by the changes in the curricula at secondary school level. The SI model was piloted in two courses, one in mathematics and another in chemistry, each consisting of more than a thousand students. This article addresses implementation issues of SI for such a large group of students in mathematics. It cautions would-be implementers to pitfalls and shortcomings of the SI model and suggests how the model could be adapted to answer the current needs. This article also shows that despite problems in strictly adhering to SI principles in the implementation of the programme, participants showed increased performance. [ABSTRACT FROM PUBLISHER]

The general perception is that high .school teaching of mathematics in South Africa tends to be fairly procedural and that students that enter university are better equipped to deal with procedural problems rather than conceptual. This study compares the conceptual and procedural skills of first-year calculus students in life sciences. Also investigated is students' confidence in handling conceptual and procedural problems. The study seems to indicate that these students do not perform better in procedural problems than in conceptual problems. They are more confident of their ability to handle conceptual problems than to handle procedural problems. Furthermore the study seems to indicate that students do not have more misconceptions about conceptual mathematics than about procedural issues. [ABSTRACT FROM AUTHOR]