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Problem-solving and enquiry-based learning are integral in the Mathematics and Science curriculum in South Africa through online-based assessment. Online assessment has rapidly gained recognition because of technology. In this paper, the authors explored the views of online baseline assessment among Senior Phase First-year Mathematics Student Teachers. The researchers adopted a qualitative research method. Data was collected from the participants using an online Google form developed into a questionnaire. The participants in this study were first-year students enrolled for the Bachelor of Education in Mathematics at a university in a rural province of South Africa. The first-year student teachers were exposed to the senior phase baseline assessments through the licensed online Computer Aided Mathematics Instruction (CAMI) tool. One hundred and sixteen (116) senior-phase student teachers completed the online questionnaire. This study used convenience sampling since it was the most appropriate method to conveniently invite the participant. The findings revealed that first-year student teachers were enthusiastic and motivated to write the baseline assessment on computers for the first time. The result also showed that several first-year student teachers experienced difficulties solving mathematics problems using computers. This study recommends more intensive research on student teachers' views on online assessment regarding gender and time.

Background: The presence of African women in mathematics has been nearly invisible. The underrepresentation of African women in this field is a result of their historical socio-political marginalisation. The mathematics discipline is politicised, racialised, and gendered to systematically oppress African women. The mathematics fields continue to be a masculine and white male dominated field, which reinforces and preserves masculine culture which is hostile and unwelcoming to women. African women mathematicians are further oppressed because of their racial and gendered identities in fields that are ideologically founded on proving the racial, gendered, social, cultural, and intellectual inferiority of Africans. Aim: The article aims to exemplify the lived experiences of African women doctoral students in the mathematics disciplines in South African universities. The article critically interrogates the factors that influence the participation, progression, and retention of African female doctoral students in the mathematics disciplines. Setting: The article comes from a larger study which investigated the reasons why African doctorate students do not become academics after they receive their doctorates in science, technology, engineering and mathematics (STEM) disciplines in South African universities. This paper focuses on the experiences of 10 African female doctoral students at five universities in South Africa. The universities were selected because they ranked in the top five in South Africa. Two of the institutions are historically Black universities and the rest are historically white institutions, with one historically Afrikaner-speaking university--between 2019--2021. Methods: This article employed a qualitative research methodology, where semi-structures interviews were conducted with 10 African female doctoral participants in mathematics disciplines in five South African universities and is underpinned by the theory of intersectionality. Results: The findings reveal how interlocking systems of oppression continue to influence the recruitment, retention, and progression of women in the mathematics discipline, thereby providing insight into the mechanisms that need to be altered and/or put in place to actively recruit African female doctoral students and retain them in academic positions. Conclusion: The article concludes that despite the mathematics field proclaiming neutrality and objectivity nevertheless, African women still experience racism, sexism, and classism. The experiences of African women in mathematics are vital to understanding the reasons why there is a high attrition rate of African women in the mathematics discipline in academia and why they do not become academics when they could transform this discipline.

Learners' participation in mathematics decreases during their transition from primary to high school. This is despite adolescents' cognitive growth equipping them with enhanced cognitive ability; to learn mathematics. Hence low participation in mathematics does not result from cognitive deficiency. Rather, lack of motivation to learn mathematics may be the factor. According to self-determination theory, motivation results from nurturing three human basic needs: autonomy, connectedness and competence. Since identity is linked to autonomy, identities in mathematics learning impacts motivation to learn the subject. Hence, this paper reports on the action research intervention which took advantage of adolescents' preoccupation with identity formation. In line with continuous cycles of action research, the intervention is the pilot of the ongoing study that seeks to enhance mathematics learning by utilizing non-cognitive factors that resonate with the characteristics of adolescents. The paper reports on how the autonomy to form their identities in mathematics learning, impacted the adolescents' learning and attitude towards mathematics. Qualitative results show that learners lived up to their self-formed identities and this enhanced their motivation to learn mathematics. Further studies that forge positive identities in mathematics classrooms to enhance motivation to learn mathematics are recommended.

When embarking on our journey of learning in mathematics, we may envision a linear path of modules for acquiring mathematical knowledge and understanding to reach a predetermined outcome. However, this is a partial representation since the outcome and path are developing and adapting and our learning is continuously emerging. In this paper, our journey of learning in mathematics is re-envisioned as a complex adaptive system with agents, internal diversity, internal redundancy, decentralised control, sources of disruption and sources of coherence. As will be illustrated through the adaptive cycle of a complex adaptive system, learning may emerge between phases of destabilisation and development. For this emergence there needs to be openness to embrace a disruption, reflection to interpret the disruption, connection to respond to the disruption and inspiration to grow and adapt in response to the disruption. There also needs to be a balance between individual and collective learning. Through navigating these cycles along our journey of learning there may be emergence of learning experiences within and beyond mathematics.

This paper reports on an exploration of students' learning derived from the implementation of learning materials developed in a previous collaborative project. The purpose of the study was to examine the development of third-year students' understanding of the Reimann Sum. These concepts were taught to undergraduate teacher trainees wishing to specialize in the teaching of mathematics in the FET (further education and training) school curriculum. The learning materials were developed by mathematics teacher educationists from the University of Witwatersrand, the UKZN (University of KwaZulu-Natal) and the Nelson Mandela Metropolitan University. A group of 31 students participated in the project. The study adopted the APOS (action-process-object-schema) approach within constructivism, as a theoretical framework. Data were generated from students' responses to the collaborative tasks. A genetic decomposition of the Reimann Sum is offered and used as a basis for the analysis. This paper, specifically, reports on the investigation of students' responses based on a learning theory within the context of advanced mathematical thinking and makes a contribution to an understanding of how these students constructed the concepts in a collaborative way. Appended is "The Worksheet with Instructional Tasks." (Contains 5 tables.)

Pre-service secondary mathematics teachers have a poor command of the exact language of mathematics as evidenced in assignments, micro-lessons and practicums. The unrelenting notorious annual South African National Senior Certificate outcomes in mathematics and the recognition by the Department of Basic Education (DBE) that the correct use of mathematical language in classrooms is problematic is reported in the National Senior Certificate Diagnostic Reports on learner performance (DBE, 2008-2013). The reports further recognise that learners do not engage successfully with mathematical problems that require conceptual understanding. This paper therefore highlights a need for teachers to be taught and master an exact mathematical language that for example, calls an "expression" an "expression" and not an "equation". It must support the call of the DBE to use correct mathematical language that will support and improve conceptual understanding rather than perpetuate rote procedural skills, which are often devoid of thought and reason. The authentic language of mathematics can initiate and promote meaningful mathematical dialogue. Initial teacher education programmes, as in the subject methodologies, affords lecturers this opportunity. The language notions of Vygotskian thought and language, Freirian emancipatory critical consciousness and Habermasian ethical and moral communicative action frame the paper theoretically. Using a grounded approach, after examining examples of student language in a practice based research intervention, the design and development of a repertoire of language categories, literal, algebraic, graphical (Cartesian) and procedural (algorithmic) emerged from three one-year cycles of an action research methodology. The development of these repertoires of language was to assist teachers in communicating about mathematical objects through providing a structured framework within which to think and teach. A course model encompassing small group discussions, an oral examination and a self-study action research project, that helped sustain the teaching of an exact mathematical language, is presented. This is supported by student reflections on the usefulness of implementing them.

This paper reports on the findings of a baseline study that fed on to a broader investigation exploring ICT integration in the teaching of functions. The baseline study was premised on the observation that the notion of function, despite being a fundamental and central idea in the mathematics school curriculum, presents pedagogical challenges to both teachers and learners. The study used the qualitative case study design to investigate Grade 11 mathematics learners' errors and misconceptions under hyperbolic functions at a rural high school in the Limpopo province of South Africa. Informed by the constructivist APOS theory conception levels, learners' errors were detected from their written responses in a diagnostic test. The learners were then individually interviewed during task-based interviews to infer on the misconceptions underlying their errors. Qualitative analysis of the data revealed the following categories of misconceptions: algebraic, conceptual, asymptotic, graphical, and notational misconceptions. The study established that errors, if diagnosed and corrected, are springboards and milestones to the formulation and construction of proper mathematical ideas. To resolve learners' misconceptions, this study recommends that teachers should use explorative and discovery pedagogical strategies to enable learners realize their own misconceptions and self-correct. Based on the findings of this study, the integration of Information and Communication Technologies (ICTs) in teaching functions as an intervention strategy will be explored.

In this paper, I argue that the establishment of after-school mathematics clubs in early grades holds rich potential for supporting the development of increasingly participatory and sensemaking maths learning dispositions. Within the South African Numeracy Chair project, lead by the author, multiple after-school mathematics clubs have been set up for learners in Grades 3-6 across Eastern Cape schools. These clubs are a complementary initiative to teacher development, aimed at improving low levels of numeracy learning across the majority of schools in the province. Two sources of data, learner interviews and teacher questionnaires, from one case study club, are shared in this article to illuminate the potential such clubs hold in developing increasingly participatory mathematics learning dispositions.

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]

It is argued in this paper that there is an absence of literature relating to research on learner mathematical dispositions, particularly with young learners. Drawing on Kilpatrick, Swafford and Findell's (2001) five interrelated strands of mathematical proficiency, which include: conceptual understanding, procedural fluency, strategic competence, adaptive reasoning and productive disposition, it is argued that there has been little engagement with productive disposition in the field of mathematics education and how we might access and assess this strand. Despite competence in all strands being essential for mathematical proficiency, literature and assessments that seek to establish learner levels of mathematical proficiency have tended to focus on the first four and have neglected the last; productive disposition. Finding ways in which to access student mathematical learning dispositions can be challenging, especially with young learners who struggle to articulate their views. An instrument is shared that the author has designed with doctoral fellow, Debbie Stott, in order to access and assess the productive disposition of learners participating in maths clubs run within the South African Numeracy Chair. The findings that emerge in one Grade 3 club with six learners is shared. These findings are related to the data collected through instruments that assess the other four strands of mathematical proficiency. This enables a holistic picture of learner's mathematical proficiency as intended in the conceptualisation of the interrelated five strands of proficiency.

This paper analyses student teachers' meta-narratives associated with 'doing' mathematics. The quality of the vocabulary associated with the doing of the mathematical objects of a sample of 56 multilingual third-year mathematics methodology students preparing to be secondary teachers was explored and assessed. Sfard's theoretical concept of 'pronounced foci' and her 'critical categories' for determining if a narrative was mathematical were used to analyse the data. Meta-narratives refer to the written mathematical metacognitive monologues that manifested students' thinking while they were doing the mathematical objects. Students were required to write, in language suitable for teaching, a description of the procedure which led to a solution. The procedures and their associated meta-narratives provided data for a mixed-method analysis in this case study. The absence of a mathematical vocabulary presented difficulties when students engaged in meta-narratives. The data also show that inexact mathematical vocabularies are not culturally specific since the 11 English mother tongue students demonstrated a similar lack of command of mathematical language as their peers. Meta-narratives revealed mathematical misconceptions that may not have been detected without them. For two of the three mathematical objects there is a significant but moderate positive correlation between correct vocabulary and correct procedure. The findings support the need for mathematical vocabulary (and language) to be a teaching focus when preparing teachers for their careers and that the assessment of tasks is not completely achieved by evaluating only the procedural 'doing' of mathematics.

There is not just one mathematics taught at university level, nor is there one group of students. Mathematics is taught differently depending on the discipline and the perceived background of the student. There is engineering mathematics for the students heading towards engineering degrees, life science mathematics for those heading towards biology degrees and so on. This paper considers the phases of transitions that students experience as they embark on a course of study and then go on to professional life. We make inferences about the ways the curriculum should be designed to alleviate the difficulties of these phases as well as to take account of the capabilities that graduates will require in the workplace. It is not only where students are coming from that affects their learning but where they are heading to, in combination with their perceptions of that destination. (Contains 1 table and 1 figure.)

One challenge for an optimal design of the mathematical components in engineering education curricula is to understand how the procedural and conceptual dimensions of mathematical work can be matched with different demands and contexts from the education and practice of engineers. The focus in this paper is on how engineering students respond to the conceptual-procedural distinction, comparing performance and confidence between second and fourth year groups of students in their answers to a questionnaire comprising conceptually and procedurally focused mathematics problems. We also compare these students' conceptions on the role of conceptual and procedural mathematics problems within and outside their mathematics studies. Our data suggest that when mathematical knowledge is being recontextualised to engineering subjects or engineering design, a conceptual approach to mathematics is more essential than a procedural approach; working within the mathematical domain, however, the procedural aspects of mathematics are as essential as the conceptual aspects.

This paper presents an enrichment case study to showcase a possible avenue for attending to the needs of academically strong mathematics students. We report on a group of university students who were presented with the opportunity of exploring a specific first year mathematics topic deeper, using an inquiry-based learning approach as part of an enrichment programme. Following the intervention, students completed a questionnaire and a few were interviewed to establish their experiences of the enrichment programme. We discuss the successes and pitfalls of the intervention and report on the impact it had on the participants.

This study focuses on the mathematics department at a South African university and in particular on teaching of calculus to first year engineering students. The paper reports on a cause-effect analysis, often used for business improvement. The cause-effect analysis indicates that there are many factors that impact on secondary school teaching of mathematics, factors that the tertiary sector has no control over. The analysis also indicates the undesirable issues that are at the root of impeding success in the calculus module. Most important is that students are not encouraged to become independent thinkers from an early age. This triggers problems in follow-up courses where students are expected to have learned to deal with the work load and understanding of certain concepts. A new model was designed to lessen the impact of these undesirable issues.

The research interest underpinning this paper concerns the type of mathematical knowledge engineering students may acquire during their specialised education in terms of the conceptual and procedural dimensions of doing and using mathematics. This study draws on interviews with 25 qualified engineers from South Africa and Sweden regarding their views on the role of mathematics in engineering education, with special focus on the conceptual and procedural aspects of mathematical knowledge. A thematic analysis of the interview data led to the identification of two main themes. According to the conceptual view a predominantly conceptual approach is needed and valued more than procedural skills, while the balanced view emphasises a balance of conceptual understanding and procedural fluency as well as links between them. It is suggested that the mathematical education of engineers would need to be more conceptually oriented to prepare for the demands at the workplace.

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]

"Personal learning environments" (PLEs) and "personal learning networks" (PLNs) are well-known concepts. A personal learning network "cluster" is a small group of people who regularly interact academically and whose PLNs have a non-empty intersection that includes all the other members. At university level PLN clusters form spontaneously among students and are known to last over an extended period of time. Little is known regarding the workings of these PLN clusters of students. The claim is that these PLN clusters are at the heart of student learning and are aligned with the current trend of a knowledge-pull community of learning. In this paper we investigate the activities and characteristics of PLN clusters in two different fields of study at a South African university, namely mathematics and computer science. We discuss the benefits that these clusters offer, investigate the mashup of activities and tools and we contrast experiences in the two fields of study. It is the commonalities rather than differences that are striking between the two groups of students. Although computer science students lean more towards digital communication, both groups impress with the pride they take in their PLN clusters and are vocal in describing the benefits that these clusters offer.

In this paper we offer a theoretical discussion on the mathematical content knowledge development of secondary school mathematics teachers. We discuss relevant studies from literature and use different views and conceptions of school mathematics to propose a model to develop or transform the mathematical content knowledge of secondary school mathematics teachers in such a way that they are able to reconsider their beliefs about the nature of school mathematics. In the model we view mathematics teaching as a kind of problem solving where mathematical content knowledge has to be unpacked and communicated after teachers have reflected on the components of the model, namely different kinds of mathematical knowledge (procedural and conceptual), cognitive processes (problem solving, reasoning, communication, connections and representations) involved in doing mathematics, and working in different problem contexts.

The classroom is a micro-culture where socio and socio-mathematical norms of interactions are fostered by an instructor who represents the mathematics community. Informed by the "emergent approach" developed by Cobb and Yackel (1996) that explains how mathematical growth takes place in the social context of classrooms, I explored the enactment of these norms in small groups' interactions that were not directly influenced by an instructor. I used audio recorded and later transcriptions of groups of undergraduate mathematics students' discussions on class tasks that were analysed using Polkinghorne's (1995) narrative analysis. Using excerpts from the discussions I argue that with a broadened view on socio-mathematical norms, and interpretations of interactions that focus on "learning in the moment", enactments of norms are seen in students' (a) contributions to discussions through initiating discussions, (b) taking responsibility for raising and offering answers, (c) acceptance of arguments that are efficient to the self. (Contains 1 figure and 2 tables.)

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]

In South Africa, there is no adequate research that explored mathematics learning and teaching within rural schools and classrooms. Various literature posits that mathematics education research has virtually over-concentrated on urban and township schools and consistently ignored rural contexts and schools. Arguments exist that rural education and rural education research have been understudied in South Africa. Presumably, this would include mathematics education research as well. This paper explores the relationship between witchcraft beliefs, which is considered as an entrenched cultural phenomenon, and learners' mathematics learning within rural classrooms. In this paper, the local influences include that the learners end up not demonstrating their full understanding of mathematics contents because of the beliefs that if they exhibit their knowledge of the subject, they may be bewitched. Cultural Relativism was used to theorise the study within qualitative critical phenomenology as a methodology for the study. The study comprises 12 mathematics learners from a rural Acornhoek region in Mpumalanga Province, and data were collected using individual semi-structured interviews while the collected data were analysed using Critical Discourse Analysis. Findings from this study illuminated that local beliefs and knowledge such as witchcraft exert significant influence on schools and learners' learning, including learners' not demonstrating their optimum understanding of mathematics. [ABSTRACT FROM AUTHOR]

Given the importance of mathematics performance of learners and the challenges in South Africa, it is important that the expertise of all role-players, including the subject advisors who visit the teachers to guide and support them, is used to its full potential. While some studies have explored the experiences of teachers in this regard, literature on the experiences of mathematics subject advisors is scant. Furthermore, little has been published on the experiences of subject advisors within the context of rural areas with a low population, such as the Northern Cape Province. This article addresses the gap by exploring the deeper understanding of mathematics subject advisors’ experiences when conducting school support visits. Taking a qualitative research approach, I conducted semi-structured interviews with six mathematics subject advisors from the four phases (foundation, intermediate, senior, and further education and training) in all five of the education districts of the Northern Cape Department of Education (Frances Baard; Z.F. Mgcwawu; Pixley Ka Seme; Namakwa; and J.T. Gaetsewe). Through Husserl’s phenomenological theoretical framework, complemented with Gibbs’ reflective cycle and Colaizzi’s seven steps of data analysis, participants were found to have had both good and bad experiences when conducting school support visits. Experiences included positive attitudes from educators and schools in general, and good curriculum implementation and teaching and learning practices. However, participants were sometimes received with hostility, and observed poor curriculum implementation and teaching and learning practices. Noteworthy is some negative union influence, lack of specialisation in mathematics by foundation phase departmental heads, lack of coherence in communication, and lack of cooperation and collaboration amongst district officials. If the concerns raised by mathematics subject advisors in this paper are not addressed, these may have a negative impact on the experiences of subject advisors and, by implication, on learner performance as well as education in general. [ABSTRACT FROM AUTHOR]

Mathematics is a core subject in South Africa. Studies have shown that the performance of learners on this subject is not encouraging. Many factors have been alluded to by scholars as contributing factors to this poor performance. The gap between theory and practice of mathematics teaching can be bridged by the use of appropriate learning styles, availability, and utilization of instructional. This paper finds out the relationship that exists among learning styles, instructional materials, and mathematics performance of Grade 6. The choice of Grade 6 is important because it is the last grade level of primary school before a learner can enter secondary school level in South Africa. The study adopted a correlational research design of a quantitative approach. Stratified sampling techniques were used to select 1225 learners from Grade 6 schools within Buffalo City Metropolitan Education District. The data revealed among others that in Buffalo City, availability and utilization of instructional materials have no significant relationship with the mathematics performance of selected grade 6 learners (B=.023, t=.804, P=0.05) while students learning styles (visual, auditory, and kinesthetic) have a significant relationship with grade 6 learners Mathematics performance (B=-.113, t=-3.886, p<0.05). The study concluded that one of the most fundamental issues to consider in improving Mathematics performance is the understanding of the learners' learning styles and effective use of appropriate instructional materials for teaching Mathematics. [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 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]

There is concern over the learning and teaching of mathematics in South Africa. The aim of this study was to explore high school mathematics teachers' conceptual difficulties in trigonometry and coordinate geometry. The participants were in-service teachers (n = 236), who were enrolled in an in-service programme at a South African university. The research instrument was based on a previous Grade 12 national mathematics paper. The study used Duval's theory on semiotic systems to try to understand the teachers' difficulties experienced with the content. Ethical clearance was obtained from the university research office for the collection of data. All participants provided informed consent to participate in the study. The study used a mixed methods approach where the quantitative data was first analysed. Thereafter a content analysis was conducted on 50 scripts to gain insight into the areas which presented challenges to the teachers. The results showed that the teachers obtained an average of 55% overall in the items. The average for the trigonometry and coordinate geometry was 52% and 61% respectively. The study suggests that teachers need more support in mastering the Grade 12 content and developing representational fluency. [ABSTRACT FROM AUTHOR]

This paper focuses, empirically, on the developments seen in a group of South African early grades' mathematics teacher educators in the course of a university-provincial education department partnership project. This project sought to support the district Mathematics Subject Advisers to support, in turn, teachers to implement an intervention consisting of a sequence of four lessons focused on multiplicative reasoning. Outcomes based on pre- and post-tests administered by the Subject Advisers suggested substantial pre- to post-test improvement at the student level. Subject Adviser observations and reflections pointed to successes in engendering more dialogic conversations between mathematics teachers and mathematics teacher educators focused on mathematics and its teaching and learning. The 'double move' of increasing overlap between the subject adviser and teacher communities, coupled with evidence that implementing the intervention had enabled the Subject Advisers to develop their mathematical and pedagogical understandings, provides a useful way of considering development in the capacity of mathematics teacher educators to support mathematics teaching and learning. [ABSTRACT FROM AUTHOR]

Since 2016, all the second-year Intermediate Phase students at the University of the Free State (UFS), South Africa, who have enrolled for the MTBI2503 module have been exposed to family math (FM) activities during six compulsory contact sessions. The main aim of the FM training sessions for student-teachers was to expose them to reallife and hands-on mathematics teaching and learning. It was decided by the key role players that the FM program should be subjected to formative evaluation. A self-constructed questionnaire was used as an assessment tool. The first section of the questionnaire focuses on the generics of the program (FM training program per se, content, training outcomes, course material, and assessment). This paper reports on data from the second section of the questionnaire and aims to answer the following research question: Are MTBI2503 students satisfied with the way the UFS adapted the FM program to make provision for Intermediate Phase students' specific expectations and needs? Statements relating to the FM program are evaluated using five-point Likert scale items. Overall, the rating of the contact sessions, teaching and learning, facilitators, and personal experiences of the students are high. It was concluded that an awareness of the inherent educational value of the FM program for Intermediate Phase students may have a positive influence on future initial teacher training programs in South Africa. [ABSTRACT FROM AUTHOR]

This paper is centred around a framework for studying teaching—Mediating Primary Mathematics (MPM)—developed in the context of the teaching of Whole Number Arithmetic (WNA) in South Africa. Findings from the analysis of four WNA lessons are used to illustrate how the application of the MPM framework can measure nuanced differences in the meditational means—both artefact- and human-based—employed by teachers. Detailed analysis of differences observed across these lessons shows that the mathematics taught can go beyond localized procedures and counting-based methods, and engage learners in mathematical activity that involves affordances for making connection and generalizing, particularly with respect to counting with composite units, a key developmental stage in WNA. [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]

One of South Africa’s identified priorities is the implementation of ICT in education. To this end a phased implementation plan was initiated in 2004 for ICT to be implemented into schools across the country over eight years. During this time South Africa also participated in three international studies undertaken by the International Association for the Evaluation of Educational Achievement (IEA) focusing on ICT in Education. Each of these permitted the country to benchmark its progress in terms of other countries and their implementation of ICT in education. The latest study, SITES 2006 provides a useful set of indicators against which South Africa can evaluate its progress with regard to its implementation of ICT. This paper seeks to evaluate South Africa’s readiness to integrate ICT into mathematics and science classrooms. This was done using a number of indicators of “sustainable change” derived from SITES 2006 and then comparing these to countries such as Chile, Thailand and Norway, the former two with similar context and conditions and the latter with contrasting conditions. The findings reveal that whilst South Africa has made some progress since 1998 in terms of the implementation of ICT in education, that the majority of schools are still in their infancy regarding the acquisition of ICT and most of those who have access are still in the process of trying to integrate the ICT into their teaching and learning. It would appear that more fundamental needs in South Africa’s education system have dominated its priorities. [ABSTRACT FROM AUTHOR]

The study reported on here was conducted to explore four Grade 7 mathematics teachers' understanding of the relationship between the objectives indicated in the CAPS for teaching different topics/concepts and instructional time stipulated for doing so. Seven lessons were studied in 4 primary schools in the Vhembe district of the Limpopo province, South Africa. A constructivist philosophical approach was used. The data collection methods included interviews and classroom observations. The main finding indicates teachers' understanding of instructional time as either a regulatory or a teaching tool. The ability to translate instructional time into social time depends on the level of teachers' curriculum literacy. Consideration of how CAPS objectives could be fulfilled based on the topic/concept to be taught and the stipulated instructional time, influenced the learners' conceptual understanding, procedural fluency, and competency in mathematics. The conclusion underscores the importance of instructional time as both an essential authoritative regulatory tool and signal of a pedagogic device and communication required to advance the instructional objectives. [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 paper reports the findings of an evaluative study of an initiative, in its sixth year of implementation, enhancing the learning and teaching of mathematics in 20 disadvantaged secondary schools in KwaZulu-Natal (KZN), South Africa, twenty years after democracy. Findings highlight the importance of initial and ongoing professional development for under-qualified teachers. Support and strategies that have enhanced the achievement in mathematics of learners in these still underresourced schools, are described. [ABSTRACT FROM AUTHOR]

The aim of this paper is to discuss the barriers that learners encounter when learning mathematics and to explore an approach that will simplify the teaching of mathematics in Foundation Phase. A qualitative research design within the interpretive paradigm was used. Five professionally qualified Grade 3 mathematics teachers were sampled from five primary schools in the Tshwane South District in South Africa. The data was collected through lesson observation, interviews and focus groups. The data was analysed by reading transcripts to identify patterns that emerged from the data; these patterns were developed into categories. The participants in this study included Grade 3 mathematics learners. Grade 3 learners were selected because they have already done all the mathematics computations. The research revealed that the main barriers to understanding mathematics relate to language, an inability to solve word sums, being unable to carry over to the tens/hundreds, and confusing multiple signs and addition signs. Recommendations were that the teachers should not handle too many aspects at any given time. Until the teachers are sure that the learners have mastered one element or function, such as addition, they should not move to the next section. [ABSTRACT FROM AUTHOR]

This paper reports on an investigation on the real-life situations students in grades 8 and 9 in South Africa and Albania prefer to use in Mathematics. The functioning of the instrument used to assess the order of preference learners from both countries have for contextual situations is assessed using Rasch modeling techniques. For both the cohorts, the data fit the Rasch model. The differential item functioning (DIF) analysis rendered 3 items operating differentially for the two cohorts. Explanations for these differences are provided in terms of differences in experiences learners in the two countries have related to some of the contextual situations. Implications for interpretation of international comparative tests are offered, as are the possibilities for the cross-country development of curriculum materials related to contexts that learners prefer to use in Mathematics.

This study investigated how high school mathematics teachers in South Africa integrate GeoGebra, a free dynamic mathematics software program, into their teaching practices. The research explored teachers' perceptions of the training they received for the GeoGebra software, their ability to create and implement GeoGebra-based lessons, and their confidence in using it in the classroom. The study employed an interpretive research paradigm to gather insights through unstructured interviews with four purposefully selected teachers from South Africa's Northwest Province. Despite the absence of a structured training program, the study findings indicate teachers' enthusiasm for adopting GeoGebra. The study underscores the need for the Department of Basic Education to enhance support to address potential obstacles and the importance of aligning GeoGebra training with existing guidelines for integrating information and communication technologies within the Department of Basic Education and school management. In summary, this study provides valuable insights into how professional development impacts high school mathematics teachers' incorporation of GeoGebra, with implications for the design and implementation of future programs aimed at helping teachers integrate technology into their instructional practices. [ABSTRACT FROM AUTHOR]

Learners are often tasked with activities that require them to solve problems in mathematics classrooms. Problem posing is one of the teaching strategies that can enable learners to appreciate the mathematics concepts to be extracted from familiar or everyday situations. However, problem posing, as a teaching and learning strategy, is mostly under-utilised, despite its potential to enhance mathematics learning. This article explores how Grade 11 learners pose Mathematics and Mathematical Literacy questions from a 2010 FIFA World Cup soccer match and determines the extent to which the questions posed by learners mirror the given soccer context. The study involved 42 participants, comprising 22 Mathematics and 20 Mathematical Literacy learners from a high school in the Soshanguve township in Tshwane, South Africa. Participants were selected through purposive sampling. Data were collected through a written task in which learners were given a scenario in the form of an extract from a 2010 FIFA World Cup soccer match report. The qualitative findings of the study show that learners were generally capable of posing or formulating questions based on the real-life soccer context provided. The analysis showed that (a) Mathematics learners formulated more questions with more mathematical terms in them than Mathematical Literacy learners did, and (b) Mathematical Literacy learners formulated questions that were more aligned to the analysis of the game than was the case with Mathematics learners. We argue that learners' responses to the task were consistent with how they were socialised with the Mathematics and Mathematical Literacy discourse. [ABSTRACT FROM AUTHOR]

The unsatisfactory mathematics performance of South African learners has long been a concern. South Africa is ranked among the lowest performing countries in mathematics, calling for a rethinking of the way the subject is being taught. Mathematics needs to be contextually relevant and interesting for learners to be motivated to learn. Ethnomathematical games provide a means of making mathematics meaningful to learners because of the potential mathematical knowledge embedded in them. Playing gamesis a fun way of learning, and indigenous games are an integral part of learner culture. The aim of this article is to explore the games played by community elders to determine how the games can be used in the classroom. We employed observations and interviews to collect data from community elders on the indigenous games. This article is framed by the following research question: which indigenous games, with mathematical relevance are played by community elders, and what mathematical skills and knowledge are identifiable in the games? The study offers four (4) main findings that are relevant to address the crisis in mathematics teaching and learning. Thisstudy identified various ethnomathematical games and various mathematical operations embedded in them. Based on these findings, recommendations are made to use ethnomathematics to improve the mathematics performance of learners in the intermediate phase. A further recommendation is that mathematics teachers need to be trained in alternate methods of mathematics instruction such as the use of indigenous games. Future research comprises the piloting of indigenous games in intermediate phase mathematics classrooms. [ABSTRACT FROM AUTHOR]

The introduction of progression policy, which prohibits the repetition of a grade to more than once within each of the four phases of Basic Education, was enforced in South Africa in the Further Education and Training phase in 2013, but appropriate strategies which could be applied to support progressed learners are not addressed. This research was qualitative by nature and approached according to the interpretative paradigm. It was a comparative case study, which investigated strategies to support Grade 12 progressed Mathematics learners using Information Communication Technologies in comparison with other strategies that do not apply ICT instructional technologies. Data collection strategies were semi-structured interviews, questionnaires and support policies. The study population was sixteen FET Mathematics educators from five schools in Ekurhuleni North district. The findings indicated that connectivism, when incorporated into teaching and learning, becomes an effective support tool for progressed learners. ICTs within networks makes teaching and learning more learner centred, improves participation, learner attainment and pass rate. Learners are able to learn at their own pace, in their most convenient set-up and they manage what they learn, how they learn, with whom they learn and what information they require. The study found that there are greater benefits of using ICT instructional technologies in a connectivist classroom to support progressed learners, but that traditional support strategies cannot be ruled out due to the socio-economic challenges schools under research experienced. The findings further indicated that there is a dire need of a comprehensive support policies, strategies and guidelines to support progressed and low-ability learners in Mathematics both digitally and non-digitally. [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]