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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 examines whether tobacco expenditure leads to the crowding out or crowding in of different expenditure items in South Africa. We apply genetic matching to expenditure quartiles of the 2010/2011 South African Income and Expenditure Survey. Genetic matching is a more appealing approach for dealing with the endogeneity of tobacco expenditure that often plagues studies using systems of demand equations. Further, genetic matching provides transparent measures of covariate balance giving the analyst objective means of assessing match success. We find that the poorest tobacco consuming households in South Africa consistently allocate smaller budget shares towards food items than non-smoking households. Specifically, we find that dairy, fruits, nuts and oils are displaced in favour of tobacco expenditure in the two poorest quartiles. Unsurprisingly, food items are never displaced for households in the top two quartiles, given these households’ greater access to resources. Like other studies in the literature, we find that tobacco expenditure consistently crowds-in alcohol across all quartiles confirming the strong complementarities between the two. [ABSTRACT FROM AUTHOR]

TB is rated as one of the world’s deadliest diseases and South Africa ranks 9th out of the 22 countries with hardest hit of TB. Although many pieces of research have been carried out on this subject, this paper steps further by inculcating past knowledge into the model, using Bayesian approach with informative prior. Bayesian statistics approach is getting popular in data analyses. But, most applications of Bayesian inference technique are limited to situations of non-informative prior, where there is no solid external information about the distribution of the parameter of interest. The main aim of this study is to profile people living with TB in South Africa. In this paper, identical regression models are fitted for classical and Bayesian approach both with non-informative and informative prior, using South Africa General Household Survey (GHS) data for the year 2014. For the Bayesian model with informative prior, South Africa General Household Survey dataset for the year 2011 to 2013 are used to set up priors for the model 2014. [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]

Although buoyed by the induction of a democratic government, and the high ideals of our constitution, the South African education system has in many ways not met the expectations of its people, in this case, the mathematics education community. With the birth of an expansive intended curriculum came the monitoring of the outcomes through systemic type testing, the so-called attained curriculum. In time, it became clear that the inevitable 'teaching to the test' would constitute a narrowing of the implemented curriculum. Two possible constraining influences of the systemic test were identified, namely, a narrowing of the curriculum, and reliance on only one source of external monitoring. To counteract these, a project titled Assessment Enhanced Teaching and Learning (AETL) has been initiated, involving Grade Nine mathematics teachers. The aim of the project is to provide intermittent markers of progress to the teachers and learners at strategic points throughout the year. Teacher involvement in the design and implementation of these formative assessment tasks is thus central to the project. In this paper, we report on a case study at one school in the Pretoria region, and explore the use of structured assessment tasks as an approach to professional development. The question posed here is, "How does the implementation of strategically designed assessment tasks support professional development and enable professional agency?" Our findings indicate a strong sense of agency motivated by the need to excel in systemic type testing. [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]

South Africa exhibits one of the largest pro-girl gaps in education, yet the reasons behind this gap are poorly understood. This paper analyses South Africa's pro-girl gap in Grade 4 reading and Grade 5 mathematics achievement. I make use of Oaxaca-Blinder decomposition analysis to decompose the observed gender gaps into their explained and unexplained components, separately by school socio-economic quintile. This approach allows me to present new evidence that part of the country's pro-girl gaps in reading and mathematics are due to girls progressing through the early grades faster than boys. I also find that South African girls score higher on the constructs aimed at tapping student attitudes toward reading (reading self-efficacy and enjoyment, and engagement in reading lessons), and that these differences contribute significantly to the pro-girl gap in PIRLS reading achievement. Interestingly, despite outperforming boys in the TIMSS mathematics assessment, South African girls do not display more positive attitudes toward mathematics. The results suggest much more needs to be done to understand the reasons behind boys' disadvantage in the early grades, since much of the pro-girl achievement gap in Grade 4 reading and Grade 5 mathematics can be attributed the pro-girl advantage in grade completion in earlier grades. • South African girls outperform boys in both PIRLS and TIMSS. • This is partly due to girls progressing faster through the early grades. • Girls also display more positive attitudes toward reading than boys. [ABSTRACT FROM AUTHOR]

This study quantifies a year's worth of mathematics learning in South Africa (0.3 standard deviations) and uses this measure to develop empirically calibrated learning trajectories. Two main findings are (1) only the top 16% of South African Grade 3 children are performing at an appropriate Grade 3 level. (2) The learning gap between the poorest 60% of students and the wealthiest 20% of students is approximately three Grade-levels in Grade 3, growing to four Grade-levels by Grade 9. The paper concludes by arguing that the later in life we attempt to repair early learning deficits in mathematics, the costlier the remediation becomes. [ABSTRACT FROM AUTHOR]

There is consensus in the international mathematics teacher education literature that teachers should, at the most basic level, have mastery of the content knowledge they are required to teach. In this paper we test this assumption empirically by analyzing the South African SACMEQ 2007 mathematics teacher test data which tested 401 grade 6 mathematics teachers from a nationally representative sample of primary schools. With items matched to curriculum grade bands, findings indicate that 79% of grade 6 mathematics teachers showed content knowledge levels below the grade 6/7 band, and that the few teachers with higher-level content knowledge are highly inequitably distributed. [ABSTRACT FROM AUTHOR]