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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]

Education institutions globally, are increasingly driven to integrate innovative technologies in teaching spaces. While many studies have been conducted on e-learning, blended learning and m-learning, only a few studies have concentrated on the STEM preservice teachers' e-readiness for using online multimodal teaching methods in developing economic contexts. Therefore, the purpose of this paper is to examine the interplay of experiences, attitudes and technological pedagogical content knowledge (TPACK) self-efficacy as they influence STEM preservice teachers' e-readiness for implementing online multimodal teaching. This paper employed a descriptive online survey method and a stratified random sampling technique to collect data from 204 final-year STEM preservice teachers on a teacher training programme in South Africa. Statistical tools of confirmatory factor analysis, exploratory factor analysis, bivariate and correlation analysis were employed on the collected data. The results revealed that STEM preservice teachers have positive attitudes towards multimodal online learning. However, STEM preservice teachers do not feel confident in using multimodal online resources in their teaching. In addition, this paper found that experiences of online multimodal teaching impacted on preservice teachers' attitudes and resultantly, STEM preservice teachers' TPACK self-efficacy. The results and discussions inform the design for improvement in online multimodal teaching methods e-readiness and usage by preservice teachers. Recommendations include resource support, alignment of teacher training curricula and development of practicum practices for overall improvement of preservice teachers' experiences. [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]

Evidence in South Africa of poor performance on word problems points to particular challenges among learners relating to difficulties with, on the one hand, making sense of mathematical word problems and, on the other, moving beyond inefficient counting based calculation methods. While many studies in mathematics education in South Africa have tended to focus on one or the other issue, in this paper our focus is on a coding model that brings both interpretation of word problems and calculation into view simultaneously. This coding model was devised to capture and summarise learner work on solving additive relations word problems across pre-, post- and delayed post-tests around an intervention focused on improving additive word problem-solving. The coding model allowed for initial quantitative summarising of learner responses in ways that facilitated the tracking of shifts in learners' interpretations of the problem, their calculations and answers, while also pointing to salient avenues for more in-depth qualitative analysis. We argue through the analysis that the coding scheme afforded a holistic view of the profiles of learners' engagement across the three tests, thus opening a path away from the tendency towards the single-focus of analyses of word problems seen in many prior studies. [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 contributes to research in responsive teaching in a context of collaborative discussion using video stimulated recall (VSR) techniques. The aim was to gain deeper understanding of the kinds of teachers' reflective awareness that prompts changes (or lack of change) in responsive primary mathematics teaching. Using a case study methodology, I analysed the VSR interviews of two teachers who demonstrated different patterns of changes in responsive teaching. The findings revealed two distinct and complementary forms of evidence of states of awareness and reflections that support change in responsive teaching practices: (a) teachers acknowledging limitations of their practice; and (b) teachers expanding repertoires of tasks and example spaces. These two forms of evidence provide insights into ways of supporting primary mathematics teaching in the context of VSR techniques. The implication of these findings is that for effective use of VSR interviews, attention should be geared towards getting a teacher to acknowledge the limitations of her practice, and through reflection-oriented questions to encourage the teacher to expand task and example space to respond to the limitations noted within the teacher's practice. [ABSTRACT FROM AUTHOR]

This paper reports on a case study of South African Grade 12 learners' views about scientific inquiry. The study focuses on a non-fee-paying government school that receives curricular support and resources to specifically develop Science, Technology, Engineering and Mathematics (STEM) teaching in a low socioeconomic setting. Data were collected using the Views About Scientific Inquiry (VASI) questionnaire. The learners demonstrated high levels of understanding of some inquiry aspects, while other aspects were poorly understood. The best understood aspects relate to questions, data and conclusions, whilst the aspects related to multiple methods, previous knowledge and differences in interpretations were poorly understood. Results were compared with those of Grade 12 learners at other South African schools who also completed the VASI questionnaire. The findings suggest that the case study school's emphasis on STEM and high performance may support understandings of scientific inquiry in general, but at the same time encourages some naive views such as believing that scientific investigations are rigid processes, independent of human creativity. [ABSTRACT FROM AUTHOR]

Pedagogical content knowledge is considered a valuable knowledge base for all science teachers. Thus, promoting its development in all pre-service teacher programmes including a short 1 year Physical Science postgraduate certificate in education (PGCE) course is desirable. This paper focuses on the comparison of topic-specific pedagogical content knowledge (TSPCK) at a level of planning to teach between PGCE pre-service teachers (n = 8) and final (fourth) year traditional BEd pre-service teachers (n = 16). Both groups were exposed to an intervention targeting the development of TSPCK in Physical Science topics taught in South Africa's national secondary school curriculum. Data collected from both groups comprised pre–post intervention TSPCK tests and content representations tool for chemical equilibrium. The data analysis entailed the use of a criterion-based rubric for shifts in the quality of planned TSPCK and the content representations were analysed through an in-depth qualitative analysis. The findings revealed an improvement in the PGCE pre-service teachers' planned TSPCK to the same extent as for the BEd pre-service teachers. The PGCE pre-service teachers did not indicate being at an initial advantage in their TSPCK because of their strong content knowledge, but they showed a faster growth path in developing TSPCK. Recommendations made include the promotion of TSPCK discussion in the PGCE programme and a possible re-positioning of such discussions in the BEd programme. [ABSTRACT FROM AUTHOR]

This paper reports on a study conducted with Grade 11 learners as participants, in four public high schools in a rural district of the Eastern Cape Province of South Africa. The central objective was to investigate the mathematical discourses of Grade 11 learners related to the word, algebraic and graphic representations of asymptotes of the hyperbola and exponential functions. Commognition and social learning theories were referred to, with particular emphasis on the characteristics of the mathematical discourse, that is, word use, visual mediators, endorsed narratives and routines. The study adopted a qualitative research design, with exploratory, descriptive and interpretive elements complementing both its data collection and analysis processes. A purposive sampling strategy was opted for in the study. Data was collected by means of a test administered to a total of 112 Grade 11 participants from the selected four high schools. Data was thematically analysed by means of a developed Discourse Profile of the Hyperbola and Exponential Function adapted from the Arithmetic Discourse Profile. The study's findings revealed that, while there was evidence of learning functions, for these leareners, the process of de-ritualisation was not yet complete. There were also challenges in linking different representations of a function. Learners could work efficiently on procedure tasks, but struggled on action-oriented tasks. [ABSTRACT FROM AUTHOR]

Technology as a school subject has extensive entrepreneurship potential, especially when combined with the practical production aspects that form part of the intended curriculum. The South African Senior Phase Technology curriculum is silent on the topic of entrepreneurship and as a result, this potential is not reaching learners in a country with high levels of youth unemployment. This paper endeavours to address recommendations made in previous research, that entrepreneurship education should be developed as part of the South African Senior Phase Technology curriculum. Utilising the design process—described in the curriculum as the backbone for Technology methodology—as a point of departure, the current study aimed to develop proposals for the unpacking and scaffolding of entrepreneurship education in Technology, without deviating too far from the structure and content of the existing intended curriculum. Systematic qualitative document analysis and a consumer-based approach were used to align proposed entrepreneurship education with the curriculum definition and the original intentions of Technology education, which were to contribute to reducing unemployment in South Africa. The proposed structure and content for including entrepreneurship education in Senior Phase Technology will be presented to the Department of Basic Education for their consideration in subsequent curriculum modifications. [ABSTRACT FROM AUTHOR]

This paper reports on an investigation into management in Mathematics classrooms. Classroom management is contextualised in terms of the managerial actions required to manage classrooms effectively and the extent to which effective classroom management responds to contextual challenges. Relevant literature is reviewed, and theoretical perspectives with investigative value for classroom management are examined. Data was collected using individual semi-structured interviews with four Mathematics department heads and with five teachers per school, for the four focus group interviews. The interviews were audio-taped, transcribed and the data analysed using a process of abductive data analysis as suggested by McMillan and Schumacher (2010; Research in education: Evidence-based inquiry, 4th ed., Pearson Education). The participants in this study supported the use of different overlapping management styles. Teachers apply these styles by introducing useful and suitable management actions in their classroom practice. It was found that organising group work and motivating learners are actions that encompass the majority of functions related to the management of teaching and learning in Mathematics classrooms. Contextual influences like teachers' professional competencies, curriculum implementation, the maintenance of facilities and the availability of resources and learning materials were highlighted as factors that both support and constrain the effectiveness of classroom management. [ABSTRACT FROM AUTHOR]

The chain of progression from teacher education to qualification to classroom instruction and student engagement, and then to learning and achievement, is not as straightforward as often presented. Societal, political and economic pressures create either a positive climate or a stressful one for both teachers and students. Nevertheless it is safe to say that in a subject like mathematics, the importance of subject matter knowledge cannot be underestimated. Research in this area supports the presumption that formal qualifications in the subject, in this case mathematics, are necessary, as this focused engagement with mathematics provides the foundation for mathematics teaching and learning. The allocation of fully qualified teachers to schools has in the past been uneven, with the supposition that students at higher socio-economic levels are being taught by better qualified teachers. In South Africa the improvement of teacher qualifications has been identified as a core area of action with the relevant policy on teacher education renewed in 2007 and again in 2014. The focus of this paper is to understand the change in patterns of teacher qualifications, and the interrelationship with school contextual variables. The analysis is based on the Trends in International Mathematics and Science Study (TIMSS) data from 2003, 2011 and 2015, where teachers from the TIMSS sample provided contextual information. Descriptive statistics were calculated using the IEA IDB Analyzer. The results show that South Africa has made substantial progress in uplifting teachers' formal qualification levels and in reducing structural inequality within its education system. Out-of-field teaching of mathematics is still shown to be a common phenomenon and is unevenly distributed. [ABSTRACT FROM AUTHOR]

This paper examines student teachers' perceptions of their professional development while engaging in work-integrated learning at a teaching school in South Africa. Teacher educators often assume that practical aspects of pre-service education will be dealt with when student teachers are attached to schools for several weeks. However, the literature reports that such school experience is often sub-standard. This research surveyed student teachers' experiences in a teaching school providing a community of practice for student teachers. The theoretical framework underlying this study is the zone of proximal teacher development. Student teachers were placed in situations where they experienced prolepsis (expecting them to know more than they actually do). Student teachers had to plan lessons in groups and deliver the lessons to Life Sciences learners at the teaching school. Afterwards they attended a reflection session. Thirty-nine student teachers were part of the research over a two-year period. The data were obtained through individual interviews, focus group interviews, reflection sessions, a questionnaire and student reflection sheets. The data were coded inductively, arranged in categories which were collapsed into sub-themes. The sub-themes from each data source were triangulated to obtain seven main themes. Student teachers considered the teaching school approach very beneficial to their development of science subject knowledge, pedagogy, the use of scientific inquiry strategies and their application of pedagogical theory. The learners at the school, through their inquisitiveness, offered opportunities for prolepsis to take place. The community of practice that developed within groups of student teachers was seen as very supportive. [ABSTRACT FROM AUTHOR]

The Primary Teacher Education (PrimTEd) project was established in response to concerns about the pre-service preparation of primary teachers in South Africa. In order to inform the development of appropriate pre-service mathematics courses, an initial need in the PrimTEd project was to establish the nature of the mathematical knowledge of pre-service teachers both near the start and also near the end of their studies, through an online assessment. This paper describes the design of this PrimTEd online mathematics test and reports on the performance on the test of first-year and fourth-year primary mathematics student teachers, at three different universities. The overall performance of students together with the small differences between first and fourth year student performance indicate a need for student teachers to revisit primary school mathematics in a way that provides a deep understanding of key mathematical concepts in order to be better prepared for future teaching careers. [ABSTRACT FROM AUTHOR]

Patterns pervade our everyday life and are natural and familiar to children. Exciting new research in the field of Early Algebra describes the development of young children's algebraic thinking through the meaningful study of patterns. This paper contributes to this research by reporting on a case study of two primary schools in South Africa and looking at the capacity of learners for algebraic thinking in the early grades. Data was gathered using Grade 3 learner tests and focus group interviews based on pattern tasks. The data analysis process examined learners' pattern matching and building explanations related to each data collection instrument using Blanton, Brizuela, Gardiner, Sawrey and Newman-Owens's (2015. A learning trajectory in 6-year-old's thinking about generalising functional relationships. Journal for Research in Mathematics Education, 46, 511–558) levels of sophistication in learner's thinking about functional relationships. The results of the study suggest that young learners have the potential to think algebraically when offered opportunities to do so, particularly in terms of recursive and functional thinking when solving pattern problems. Traditionally instructional practice emphasises lengthy exposure to recursive thinking as a first route to algebraic thinking: this recent research suggests that young children also have the capacity to engage in functional thinking. Thus, we may need to rethink our approach to algebraic thinking through the development of a pattern-based approach to algebra. [ABSTRACT FROM AUTHOR]

A new Curriculum and Assessment Policy Statement (CAPS) was introduced in South Africa in 2012 to, among others, drive a learner-centred and constructivist approach to practical work in the high school subject Physical Sciences. This study investigates teachers' concerns with the implementation of practical work in Physical Sciences. A survey of 81 high school physical science teachers' concerns was conducted in a school district in South Africa. Participants were selected from 52 schools by means of convenience sampling. The seven stage concerns-based adoption model was used to identify teachers' stages of concern on the practical component of CAPS. The findings indicate that 69% of the participants (n = 47) had management concerns of high significance (p = 0.51), while the collaboration and consequence concerns were only slightly significant (p = 0.96). With regards to CAPS experience, respondents who had been implementing CAPS for less than three years had more personal concerns compared with those who had been executing it for three to four years. Equally, respondents with less experience with CAPS had marginally more management concerns compared with respondents with more experience. These trends were also observed with the collaboration and refocusing concerns suggesting that teachers with less CAPS experience worry more about their ability to manage practical work and to make laboratory activities workable in their contexts. The paper concludes with a discussion on the variety of concerns and how these might be addressed through targeted teacher professional development support. [ABSTRACT FROM AUTHOR]