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This paper focuses on the Southern African Association for Research in Mathematics, Science and Technology Education's (SAARMSTE's) role as a platform supporting research dissemination and connecting researchers in early grades mathematics (EGM) in the Southern African region. A review of the Long Papers in SAARMSTE over the last 20 years supports the finding of the other review papers in this Special Issue: that there has been substantial growth of attention to EGM since 2013. However, two distinctions are marked when looking at conference papers rather than journal papers. Firstly, there is a particularly large expansion of work in the last 5 years, with a broadening base of participation in this work. Second, looking across all the formats of conference presentations indicates SAARMSTE's role in supporting and building EGM as a key focus of research attention, and bringing together regional and international groups with interests in this area. Given that conference proceedings usually offer a broader picture of emerging interests than journal papers, we reflect on the range of foci of attention within EGM in the SAARMSTE Proceedings, and trends within this. These trends also help us to point to areas that are likely to be of key interest in the next decade. [ABSTRACT FROM AUTHOR]

Gender inequality is strongly linked with poor performance in science and mathematics for female students in secondary schools owing to socio-economic and cultural issues as well as learning strategies. According to the Certificate of Secondary Education Examination results of 2021 in Tanzania, the failure rate for female students was higher than that for male students, and such failure in chemistry was associated with inadequate knowledge about the tested concepts, failure to identify the requirements of the respective questions and lack of adequate mathematical skills. Real practical sessions are integral parts of chemistry to enhance the learning environments for both female and male students. However, the real laboratory practices especially for chemistry are challenged with the costs of the construction of physical laboratory infrastructure and reagents, and the time-consuming and physical demands on personnel during real practical sessions. Thus, this study explores gender-based effects of the chemistry virtual laboratory against a paper-based approach towards a real chemistry practical in Tanzanian secondary schools. The results indicate that the combined exposures of virtual laboratory and paper-based practicals improve real practical performance for both female and male students. Moreover, the performance of real practical practices progressively improved for female students when they were first exposed to the virtual laboratory and then the paper-based practical. Such improvements can be associated with the virtual laboratory providing interactive learning environments which support female students to connect and engage. [ABSTRACT FROM AUTHOR]

The majority of children in mainstream (no fee, poorly resourced, African language dominant) public schools in South Africa fall significantly behind curricular norms in mathematics by Grade 3; the early learning gap grows across time. The provision of quality instructional materials is a well-recognised component of effective strategies to improve early grade mathematics in low- and middle-income contexts. However, there has been little explication of what constitutes quality instructional materials, nor long-term design work to contribute theory to this instructional design challenge. Across 15 years, the author has been working in an education design hub with teacher educators and teachers in the rural Eastern Cape, with the goal of improving early grade mathematics. The gains in mathematics performance have been among the most significant reported in research literature. This paper presents the design principles emerging from the work. Engaging the theoretical layers discussed by diSessa and Cobb, the paper contributes to design theory by emphasising the relationship between explicit instructional assumptions and design principles, integrating four ontological categories (motive, pedagogy, language use and mathematical meaning-making). Since 2011, the Department of Basic Education has provided learner workbooks to support teaching and learning in foundation phase mathematics at system scale. It is hoped that this paper will contribute to the ongoing development of this vital national resource. The paper makes explicit instructional assumptions and design principles (available for critique, adaptation, and refinement), and provides a more nuanced framework through which to assess and improve materials across time. [ABSTRACT FROM AUTHOR]

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

This paper explores Grade R teacher expressions of themselves as teachers of numeracy, and as teachers working in the transition phase of schooling, after their participation in a research-informed numeracy-focused professional development (PD) intervention. The Early Number Fun (ENF) programme had 33 teachers from 17 Eastern Cape schools participating monthly over 18 months. Inclusion of Grade R to schooling is relatively new following policy changes in Early Childhood Development. In-service support tends to be subsumed within the Foundation Phase without attention to the specialised nature of Grade R that emphasises learning through play. ENF focused on the development of specialised teacher knowledge to support the development of early number sense through play, particularly with conceptual manipulatives. Data sources include three pre-, during, and post-PD questionnaires. Findings reveal that participation in ENF, and access to multiple research informed numeracy resources, supported teachers in their relationship with numeracy and the teaching thereof. Questionnaire responses indicate greater confidence in themselves as knowledgeable teachers of numeracy and that belonging to the ENF community supported navigation of positive professional identities within the mixed messages of policy. The findings contribute to the community-supported field of Grade R PD research and early numeracy teaching and learning. In concluding we discuss implications of this research for Grade R PD and for policy. [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]

Among the problems identified at Technical and Vocational Education and Training (TVET) colleges, low achievement in mathematical subjects is the most prominent one. This paper documents a qualitative case study undertaken at TVET College in Gauteng with the purpose of exploring the National Certificate Vocational (NC(V)) Level 4 students' errors and associated misconceptions when answering optimisation questions in differential calculus. The participants were 60 students who were registered for a course in mathematics. Data were generated from the written student responses to two non-routine test items followed by interviews. Using the Newman error hierarchical model to analyse the data, it was discovered that students errors were conceptual and procedural as well as systematic and non-systematic. The literature also alluded to instructional approaches as some of the causes of students' misconceptions and the errors and that interventions should target students as well as the instructors. [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]

This paper examines the conceptions of 'number sense' as promoted in pre-service primary mathematics education courses at 11 South African Higher Education Institutions through the texts used by academics or prescribed for students. While all the participating institutions agree that the development of primary school learners' 'number sense' is central to their mathematics methodology courses and that there is an overwhelming amount of research and literature on 'number sense' nationally and internationally, their conceptualisations of the nature of 'number sense' vary. Teacher educators, who develop pre-service teacher education courses, were asked to provide the texts, used to underpin the 11 universities' mathematics education modules in the Bachelor of Education (Foundation and Intermediate Phases) and Post Graduate Certificate in Education (Foundation and Intermediate Phases) programmes. These texts were analysed drawing on Whitacre et al.'s emphasis on three 'number sense constructs' identified as Innate Number Sense, Early Number Sense and Mature Number Sense. The results show that there is no common language of description for 'number sense' across the 11 universities. This research implies that there is a need to develop a consistent understanding of 'number sense' and how it is developed across institutions. [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]

Learning mathematics is as much about developing relationships with mathematics as the development of mathematics concepts and skills. Mathematics clubs usually support learners to develop relationships with mathematics through engaging with challenging mathematics problems, exploring mathematical ideas, and communicating and sharing their ideas. This paper reports on research on such a mathematics club. Data sources included learners' mathematics results, short written responses after club sessions and interviews with club learners. Data were analysed quantitatively and qualitatively. The study shows that club learners' school results improved relative to non-club learners, that learners' experiences of mathematics in club and class were very different from each other and that the club supported different relationships with mathematics than learners experienced in class. The study suggests that mathematics clubs can support learners' positive relationships with mathematics. [ABSTRACT FROM AUTHOR]

Topic-specific pedagogical content knowledge (TSPCK) enables teachers to transform pedagogically difficult content for specific science topics into forms more easily understood by learners. In science teaching, there is evidence pointing to poor learner performance in key chemistry topics such as stoichiometry. This paper reports on the changes in pre-service teachers' (PSTs) planned TSPCK in stoichiometry. This follows after the practicum that explicitly targeted the development of planned TSPCK for stoichiometry in the methodology class for physical sciences. The study followed a mixed-methods research design and case study as a research strategy. The participants were 10 PSTs in their final year of study for a Bachelor of Education. Quantitative and qualitative data were collected as a set of tests on TSPCK, applied both pre- and post-practicum, using TSPCK tools developed and validated in an earlier study. In both cases, data were analysed using the Rasch method. The distribution of both person and item measures was valid for measuring PSTs' planned TSPCK. In each test, they fell within the conventional fit statistical range of −2 to +2. All of the reliability indices had values ≥ 0.6 and hence were considered to be acceptable. The findings in this study indicated a measured improvement in the quality of TSPCK among the PSTs. In addition, PSTs experienced TSPCK components used in planning to teach stoichiometry at different levels of difficulty. This paper recommends further research exploring how such practicum programmes facilitate changes in PSTs' planned TSPCK and what agencies contribute to these changes in planned TSPCK. [ABSTRACT FROM AUTHOR]

This paper argues that the practice of teaching and learning is being re-defined as technology enables a re-imagining of what can be taught, and how it could be taught. In Namibia, demands on mathematics teachers to incorporate technology use into their teaching practice are often mismatched with the curriculum. This theoretical paper proposes meaningful mathematics teaching via technology, instead of a mere response to societal adoption of digital tools. The concept of meaningful teaching is viewed through a Vygotskian lens. Kilpatrick et al.'s five Strands of Mathematical Proficiency inform the interpretation of goals for teaching mathematics with technology. We discuss the gaps in current models for professional development for teaching with technology when we take the Namibian cultural historical context into consideration. Activity Theory is used to conceptualise a two-triangle embedded activity system of teachers and professional developers, and to reflect on nodal interactions. We conclude by proposing some principles for the design of professional development programmes that aim to support mathematics teachers in using technology in their teaching. The principles may be useful for professional development in other developing countries with uneven access to both technology and reformed mathematics curricula. [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 an aspect of a larger research study conceptualised within a teacher development project in Mthatha, Eastern Cape Province. The project was initiated with the objective to develop appropriate skills to use dynamic geometry software (DGS) effectively and strategically as a teaching and learning tool for mathematics. The study reported in this paper aims specifically to ascertain how selected mathematics teachers integrated co-developed technologically aided visualisation tools in the observed lessons. The case study involved two teachers from different schools. The data sources were the classroom observations followed by stimulated reflective interviews with the teachers. The data were analysed to study the use of DGS visualisation tools in relation to Kilpatrick's framework of teaching proficiency. The lessons evidenced a displayed alignment with the elements of teaching proficiency in the context of teaching geometry. The dynamic visualisation opportunities offered by DGS proved to supplement the teaching repertoire for the participating teachers. Pedagogical practices influence the use of DGS, as evident from the lessons when the participating teachers incorporated collaboratively developed GeoGebra applets into their classrooms. We argue that the collaborative engagement between teachers appears to be a positive way forward in closing the gap between having access to technology and adapting it for effective use in mathematics classrooms. [ABSTRACT FROM AUTHOR]

This paper addresses the important question of the nature of the subject matter (content knowledge) that should be a base for a science teacher education curriculum. We present our argument in two parts. Firstly, we report an argument conceptualising the nature of content knowledge for science teaching that we called TerSCK. This is followed by a presentation on the shape of a science teacher education curriculum for developing TerSCK, introduced as a TerSCK-based teacher education curriculum. Our conceptualisation argument is built on a systematic analysis of previous qualitative arguments about the nature of content knowledge for teaching school science subjects. It is influenced by Deng's foundational work critiquing the grip of the doctrine of academic disciplines in theorising content knowledge for teaching, as the base from which teachers pedagogically transform their content knowledge. While acknowledging this criticism, we present the appropriate content knowledge for science teachers (TerSCK) to reflect the complex relationship between the academic and the school science kinds of content knowledge through three of Deng's relational dimensions: logical, epistemological and social dimensions that constitute TerSCK. Drawing on Schwab's curriculum faces, these relational dimensions of TerSCK were translated into a TerSCK-based curriculum comprising five elements: (i) the fundamental concepts of the topic within the discipline; (ii) interconnections between the concepts that make up the fundamental concepts; (iii) tensions from the process of extracting the discipline fundamentals into the school curriculum constraints; (iv) scientific and other modes of inquiry from non-science disciplines; and (v) cultivating social agency. We close our argument by illustrating the implementation of the TerSCK-based curriculum using the organic chemistry topic. Our recommendations call for further studies exploring the validation of a TerSCK-based curriculum across different science topics. [ABSTRACT FROM AUTHOR]

Creating awareness of environmental sustainability issues through formal education may be an effective way to help citizens deal with these issues. Teachers, however, have not been sufficiently trained on how to teach with sustainability concerns in mind. For this study, a purposively selected group of six chemistry teachers was exposed to an online professional development intervention (PDI) whose content draws on collective pedagogical content knowledge (cPCK) about the extraction of metals and mining as related to environmental sustainability. This paper reports on a study that explores the transfer of knowledge from cPCK to personal PCK (pPCK), and from pPCK to enacted PCK (ePCK). Data were collected using a pre- and post-PDI questionnaire, interviews and a lesson plan template. These tools were used to capture the teachers' pPCK and ePCK. During the analysis of the data, a validated PCK rubric and a master content representation created by experts were used. The PCK components of knowledge of curricular saliency, student thinking and conceptual teaching strategies constituted the lens through which the researchers investigated the chemistry teachers' PCK. The findings of this study revealed that the intervention enhanced the quality of the teachers' ePCK about extraction of metals, by informing their pPCK. It also showed that despite being exposed to the same intervention, the PCK of all the teachers did not develop to the same extent. Four of the six participants showed a positive gain in the quality of their PCK across all three components, while the other two only showed a positive gain on two of the three components. The differences in PCK development within the context of chemistry teaching were attributed to the presence of amplifiers and filters. The study contributes to both theory and practice, highlighting the need for research-informed continuous professional development of teachers in education for sustainability and suggesting ways to infuse sustainability into their teaching of chemistry. [ABSTRACT FROM AUTHOR]

Mathematics is frequently considered as value-free, centring entirely on abstract reasoning. However, more often than not, the teaching of values in mathematics classrooms takes place implicitly through the actions of the teacher. The role values play in mathematics learning is also a growing area of interest and is now viewed by many as a contributing factor in the advancement of the quality of mathematics performance. This paper reports on part of a larger study aiming to establish the components that Grade 8–10 learners from a mathematics-and-science-focus school in Johannesburg value as important in the learning of mathematics. A quantitative survey was used to collect data from 249 participants. Principal component analysis was employed to analyse the data. The main findings revealed seven components that learners appeared to value in the learning of mathematics. Knowledge about what learners value in the learning of mathematics can inform teachers' pedagogical practices and the inculcation of values in mathematics teaching, which may, in turn, improve the quality of learning of mathematics. [ABSTRACT FROM AUTHOR]

This paper argues that there is a gap in the research on teaching and learning mathematics, and thus a need for research into effective teaching practices. From a selective review of literature, reasons are examined as to why less emphasis appears to have been placed on generating knowledge about teaching and effective mathematical teaching practices than on mathematics teachers and their knowledge. Possible reasons for this lack of attention to teaching include assumptions that, as researchers, we already know what effective teaching is or that if teachers embrace certain principles about teaching or learning, then effective teaching will necessarily ensue. Arguing that both of these positions neglect to address important aspects of developing knowledge about effective teaching, the paper raises a number of questions that research might address in moving the balance more towards examining the actual practices that might characterise effective teaching. [ABSTRACT FROM AUTHOR]

This study focuses on science, technology, engineering and mathematics (STEM) education teachers’ perspectives on integrating indigenous knowledge systems (IKS) into a multidisciplinary STEM framework to promote sustainability. The aim is to understand how integrating the values, ethics and worldviews of the global community can contribute to a sustainable mindset. Through an examination of the research background and pedagogical foundations, as well as a review of existing literature, it becomes evident that teachers’ perspectives are pivotal in fostering a sustainable mindset among students. To encourage social dialogue that has the potential to evolve teachers’ perspectives, a 6 month workshop focused on dialogic argumentation was provided to a group of basic education and university STEM teachers. The workshop aimed to explore the evidence- and reasoning-based arguments that influenced their perspectives regarding the role of IKS in STEM education. Analysis of data collected through questionnaires and interviews yielded the following findings: (a) initially, most teachers had mixed feelings about the role of IKS in STEM education for sustainable development; (b) a significant number of teachers reported that the dialogic argumentation workshop helped them transition from a negative to a positive attitude towards acknowledging the complexity of the role of IKS in promoting various approaches to achieving sustainability goals; and (c) several others, particularly university teachers, attributed IKS with the potential to enhance reflective reasoning in order to solve complex sustainability problems. The implications of these findings for classroom practice, particularly in terms of utilising IKS to enhance STEM teacher education, are highlighted in the paper. [ABSTRACT FROM AUTHOR]

This paper seeks to explore the nature of dialogue within calculus lecture rooms. This paper reports on part of a larger study, in which the participants were two lecturers lecturing to 198 third year pre-service teachers at a University in South Africa. This qualitative interpretive study was framed within the ambits of social constructivism and aspects of Mortimer and Scott's framework were used to analyse dialogue in the lecture room. Data for this paper were generated through video-recorded lecture observations. Subsequently, a qualitative data analysis of the generated data revealed that dialogue within the calculus lecture rooms under study may be in the form of explanations and questioning. Questioning included questions that assess students' prior knowledge, probing, follow-up and guiding questions. The findings of this study are of value to both lecturers and students within higher education with implications for teaching and learning mathematics within higher education are presented. [ABSTRACT FROM AUTHOR]

Sub-Saharan Africa secondary school science curricula recognise language as the most important communication tool for learners' biology learning outcomes. Despite this prominent goal, learners' scientific literacy at secondary school appears to be insufficient to cope with classroom teaching and learning of biology. This paper presents a review of literature regarding the way English as the language of instruction and inquiry-based learning strategies affect biology learning in Sub-Saharan Africa secondary schools. The scope of the review included journal articles, books and book chapters published in the period from 2005 to 2020 on the English language of instruction in biology education in Sub-Saharan Africa. We established criteria for first article searches indexed in Scopus, African Journals Online, the Education Resources Information Center, Web of Science and Psych Info as recognised index systems for science education. We considered studies related to the understanding of learners' language backgrounds, language-in-education policy and pedagogical language strategies (practice) that mediate learning. In this case, 53 studies were identified after removing redundancies; 27 studies satisfied the inclusion criteria when screened by key words and abstract and reviewed for eligibility; and only nine were selected after evaluating the full texts. The review analysis suggests that there is a gap in the corpus of literature on what and how pedagogical language strategies should be utilised to support meaningful learning of biology in multilingual settings. Poor learners' academic achievement and conceptual engagement in biology at secondary school level were the main effects reported by the reviewed literature. Less is still known about the effect of the use of inquiry-based learning strategies on learners' conceptual engagement in multilingual biology classrooms. We recommend formulating a clear policy articulation on the use of bilingual instructions in teaching and learning of biology at the secondary school level; assessing teacher and learner performance over pedagogical language strategies; and evaluating the contribution of IBL strategies in addressing language barriers in biology learning for higher order thinking skills in Sub-Saharan Africa secondary schools. [ABSTRACT FROM AUTHOR]

This paper reports on a study that explored the subject and pedagogical content knowledge displayed by high school mathematics teachers in the Khomas education region in Namibia. The study was based on a quantitative approach using a survey design. A stratified random sampling method was used to select the participants in all the four school circuits in the region. The study population consisted of 79 Grade 12 mathematics teachers from public schools. A sample of 40 mathematics teachers took part in the study, completed a questionnaire and wrote a test. A Microsoft Excel spreadsheet was used to sort the data and produce graphs and tables. A paired t-test was also used to determine if a significant difference existed between the participants' subject content knowledge (mathematical knowledge in our context, (MCK) and pedagogical content knowledge (PCK). The findings revealed that the participants had some deficiencies on MCK topics such as quadratic equations, angles properties and numbers. They also portrayed weak PCK on fractions, simultaneous and linear equations. This shows that a significant difference exists between the teachers' MCK and PCK with tcalculated = 11.092 greater than the tcritical (between 2.712 and 2.704) at a significance level, α = 0.01 but also that the participants' MCK and PCK were moderately and positively correlated (r = 0.681, p < 0.01). This study recommends that mathematics teachers in the Khomas region be provided frequently with in-service training to strengthen their shortcomings regarding MCK and PCK (knowledge of mathematics tasks, knowledge of learners' misconceptions and difficulties, and knowledge of mathematics instructions). We also recommend further studies to determine how high school mathematics teachers' knowledge can impact learners' academic performance in other education regions in Namibia. [ABSTRACT FROM AUTHOR]

Over the years, several frameworks and lesson observation protocols have been developed to ensure objectivity and consistency when determining the quality of a mathematics lesson. Frequently, the frameworks do not agree on the benchmarks for assessing and describing the quality of a lesson. This puts mathematics education researchers in a dilemma when deciding the appropriate framework for analysing mathematics lessons. Instead of treating the frameworks as mutually exclusive, we are of the view that each framework has some unique aspects that contribute to the story about the quality of a mathematics lesson. In this paper, we examine how the Mathematical Quality of Instruction framework and the Mediating Primary Mathematics framework, as lenses, help us to see and describe various aspects of instructional quality from one episode of a mathematics lesson in Malawi. We notice that the two frameworks share some common criteria for describing the quality of a mathematics lesson, such as the focus on making mathematical connections and using multiple representations, but they also differ on other areas of emphasis, such as the use of artefacts in the Mediating Primary Mathematics framework, and the emphasis on errors in the Mathematical Quality of Instruction framework. As such, we conclude that both frameworks can be useful for discussing the quality of a lesson in a professional development setup. [ABSTRACT FROM AUTHOR]

The aim of this paper is to analyse the reasoning and symbolisations used by sixth grade Moroccan students in solving a task based on figurative patterns. Our analysis aims at identifying the systems of actions elaborated by the students to give the general expression of the sequence, according to their perceptions of the sequence of its patterns. The results of this study show that the students can produce a wide variety of generalisations, without using the letter, by resorting to verbal expressions, the majority of which remain in the class of a factual or contextual generalisation. However, several students were not able to determine the general term of the sequence in the question, through an expression that is detached from the context of the situation. This study also contributes to raising the consciousness of Moroccan teachers and researchers of mathematics didactics about the important role played by algebraic thinking, in particular the generalisation coming from an activity based on the figurative patterns, which generates several equivalent and meaningful numerical or algebraic expressions. This article also sheds light on ways for programme designers to enrich primary school curricula, by proposing arithmetic activities with algebraic potential, like the one proposed in our study. [ABSTRACT FROM AUTHOR]

It has recently been suggested that pedagogical content knowledge (PCK) has a concept-specific nature, beyond the topic-specific level of PCK. This paper reports a case study of three pre-service teachers' reported PCK about three fundamental concepts within the topic of electrostatics, namely electrostatic force, electric field and electric field strength. The aim of the study was to compare the quality of the PCK of each of the individual participants across these fundamental concepts. Data was collected using a content representation tool and a lesson planning form prescribed by the participants' teacher training institution. A topic-specific PCK model was adopted as the framework for this study. The model asserts that the content of a particular topic is transformed for instruction through five components, namely learners' prior knowledge, curricular saliency, what is difficult to teach, representations including analogies and conceptual teaching strategies. Guided by the model, we designed a rubric to assess the concept-specific PCK of the participants on a four-point scale. The results of the study indicated that the PCK of the participants varied across the fundamental concepts of electrostatics, with each participant reporting better PCK for a different concept. The results of the study imply that describing PCK at concept level is appropriate and recommend that PCK should be strengthened at concept level during teacher training to ensure that it develops across all of the concepts within a topic. [ABSTRACT FROM AUTHOR]

This paper is about using a 'Two-Eyed Seeing' approach as the process of co-learning for incorporating elements of indigenous knowledge into school science teaching. Two groups of 150 Form 3 integrated science learners drawn from six high schools in Mutare, Zimbabwe, comprised the study sample. One group of learners, the control group, was taught the concepts of forces in structures in the traditional way. The other, the experimental group, was prepared using a context-based Two-Eyed Seeing framework. A mixed-method but primarily quantitative research approach involving a pre-test–post-test control group quasi-experimental design was used to investigate the achievement differences between the two groups of learners. A content knowledge test (CKT) and a paper-and-pencil theory of practical skills test (PST) were administered to the two groups prior to and following instruction. The analysis showed that the experimental group produced significantly better results than the group following the traditional approach (CKT, F = 131.593, p < 0.0001; PST, F = 116.350, p < 0.0001). Focus group interviews indicated that achievement differences were strongly linked to the pairing of indigenous knowledge and technology as relevant pedagogical contexts with the school science content knowledge, which resulted in intrinsic motivation for meaningful learning. The qualitative data complemented the quantitative data. [ABSTRACT FROM AUTHOR]

The Old Mutual Mathematics Olympiad (OMMO) in Malawi is a national mathematics competition open to all final year secondary school students. In this paper, we analyse the results of the preliminary round of the competition from 2015 to 2020. We developed seven content areas for the OMMO based on core elements of the Malawi secondary school mathematics curriculum. We found that the OMMO is dominated by questions on the core element Number and numeration, particularly topics like number systems, indices and logarithms, linear equations and number patterns. We also analysed the general performance of students in these areas. We found that students performed well in topics like inequalities, trigonometry and mensuration and did very poorly on proportions, sets, coordinate geometry and geometric constructions, among other topics. These findings suggest that mathematics Olympiads can help diagnose areas that are difficult for students and hence enhance the teaching and learning of Mathematics, especially in Malawi and other countries with a similar mathematics curriculum. To take care of under-represented areas, future OMMO examinations need to be structured to adequately cover all the core elements. [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]

In this paper, illustrative excerpts from mathematics lessons are analysed to examine mathematical and multilingual moves between representations within Sepedi and English medium classrooms. Duval's theory of representational registers and the literature on multilingual practices help foreground similarities within and differences between the instructional practices of four teachers—two teaching in the medium of Sepedi and two in English—as they move between mathematical and multilingual representations in the teaching of numbers. The findings show patterned differences on the basis of the medium of instruction, with the Sepedi medium instruction indicating, primarily, 'restatement' moves between the oral and the symbolic modes of representation, whilst the English medium instruction incorporated a higher incidence of mathematical moves between oral, concrete, iconic and symbolic number-based modes of representation. The evidence of broader use of mathematical representational moves as observed in the English medium lessons offers insights into how and, perhaps, why learners' knowledge development and understanding of early number in English medium classrooms may emerge in ways that are different from the knowledge developed in the Sepedi medium classes. These patterned differences are important to understand in a South African context where language of instruction continues to be associated with differences in mathematical outcomes in ways that, as previously documented, relate to socio-economic disadvantage. [ABSTRACT FROM AUTHOR]

Reflective practice is a crucial element of professional growth that is gaining in popularity in teacher education, yet the ability to reflect is a skill that is neither natural nor easy to develop. This paper reports on an investigation that sought to establish if pre-service teachers at a South African university – in the process of learning to reflect on practice through analysing video-recorded lessons – reflected differently when reflecting on their own practice from the way they reflected on the practice of other teachers. Pre-service teachers were introduced to the Six Lens Framework as a tool to aid reflection on mathematics teaching. The authors compared two sets of reflections written by four pre-service teachers (PSTs) who participated in the study. One set was based on a video-recorded lesson of another teacher's practice while the other was based on a video-recording of their own practice. The study found that the PSTs' reflections in both cases were generally at the lowest level of the reflection spectrum. They mostly described classroom events rather than analysing the lessons to provide explanation suggestions, or reflectivity. We found, however, that all four PSTs reflected at substantially greater length on their own lessons than on those of other teachers. Furthermore, three of the four teachers' reflections on their own practice focused on mathematical rather than general aspects and provided more suggestions for improvement than their reflections on the practice of other teachers. [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]

The study in this paper reports on whether an online homework system in combination with a flipped classroom has a positive effect on success rates of first year statistics students. Departing from a traditional teaching model (Baseline), the technology-based intervention strategies implemented were firstly the Aplia™ interactive online homework system (Phase 1) and then, in addition, the flipped classroom (Phase 2). In the flipped classroom model, the transfer of information took place by pre-reading and pre-class Aplia™ homework assignments. This approach intended to allow more quality time to be spent on revisiting difficult concepts and engaging in problems inside the lecture hall, thus enhancing the learning process. The average final marks of the three cohorts were compared using an ANOVA test. Chi-square tests were used to evaluate the effects of the changing teaching models from Baseline through Phase 1 to Phase 2. The success rates of three different cohorts (n = 1485, 1343 and 1466 respectively), consisting of only first-time statistics students with a Grade 12 mathematics mark of at least 60%, were assessed. For Phase 1 compared with the Baseline the increase in the success rate was insignificant, but the success rates for Phase 2 compared with both Phase 1 and Baseline improved significantly with a small to medium effect size, because of the very large samples. The practical importance of this is that the number of successful students increased by more than 100 from Phase 1 to Phase 2 and more than 130 from Baseline to Phase 2. A significant relationship was also found between the different cohorts and their mark distributions, confirming that the online homework system in combination with the flipped classroom in particular is effective in increasing the success rate. [ABSTRACT FROM AUTHOR]

This paper reports on key aspects of a short in-service programme improving science teachers’ pedagogical content knowledge to teach for the affective domain. The affective domain refers to outcomes that involve changes in feelings, values, appreciation, interests, motivations or attitudes that might result from a learning experience. The intervention adopts a socio-scientific issues instructional strategy aimed at enhancing the participants’ capacity to promote these attributes in their teaching practice. Twenty-two science teachers from seven public schools in Johannesburg participated in a short intervention programme that explored creative ways of highlighting the practical relevance of science content, especially for the learners. Data were collected through questionnaires, interviews and observations and analysed qualitatively using Krathwohl’s taxonomy of affective learning outcomes and Saldana’s code-to-theory model. The emerging themes suggest that the intervention enabled the participants to develop more nuanced understandings and capabilities for privileging the needs of the affective domain in the teaching of science. The paper argues that, in the design and teaching of science lessons, the core content could be wrapped in contemporary social issues which learners can readily relate to and presented in ways that deliberately aim to excite students in order to promote their sustained engagement with both the content and social issues in more meaningful ways. [ABSTRACT FROM AUTHOR]

In this paper we report on the findings of a study on Advanced Level Chemistry students’ approaches to investigations from a learning perspective in the Zimbabwean educational context. Students’ approaches to investigations are inextricably linked to the quality of learning and performances in these practical activities. An explanatory mixed-methods design was adopted. Quantitative data were collected by administering a survey questionnaire to 50 students from two schools. Qualitative data were collected by means of four classroom observations and eight focus group discussions involving 32 of the 50 students. The quantitative data were subjected to descriptive statistical analysis while the textual qualitative data were subjected to thematic content analysis. Marton’s approaches to learning theory was used to make sense of the findings. The students were found to be predominantly strategic in their approach to investigations. Their approaches were influenced by contextual factors such as instructional strategies and prior Chemistry practical experiences, but success in examinations dominated. The findings of this study provide useful insights to curriculum designers on the enactment of the Chemistry practical component with respect to investigations. A shift from the traditional high-stakes final examination to a school-based continuous assessment of investigations might be a viable move towards a deep approach to investigations and greater emphasis on developing process skills. [ABSTRACT FROM AUTHOR]

The emphasis on programming and robotics owing to the unfolding of the Fourth Industrial Revolution on the African continent has led the South African National Department of Education to propose a new subject in Grades R to 9. Hence, the training and development of pre-service teachers is crucial so that they can respond to the skills needed in the Digital Age. This preliminary study set out to explore and gauge pre-service teachers' experiences of programming and robotics. Programming is perceived as being difficult and challenging because of its abstract nature. Block-based programming has gained popularity in introducing the novice to programming concepts. This paper presents a case of nine computer science pre-service teachers from a South African university and their experiences of physical computer programming using Scratch for Arduino. Data was collected from unstructured observations during a practical session followed by a semi-structured group interview. The meaningful implementation of physical computing was supported by Rogers's (Freedom to learn: A view of what education might become, Charles Merrill, 1969) experiential learning theory. A prominent finding was that physical programming affords the opportunity to learn electronics and programming simultaneously, making programming relevant and interesting. Programming with Scratch for Arduino takes advantage of the fact that an Arduino is a physical device when paired with Scratch, further making these concepts accessible in a concrete manner. [ABSTRACT FROM AUTHOR]

Research findings show that inquiry-based science education has positive effects in improving learning of both science content knowledge and scientific inquiry (SI) skills. As a result, various science curricula, including that of Namibia, recommend the use of an inquiry-based approach in science teaching. However, the implementation of an inquiry-based teaching approach remains a concern in Namibian science classrooms, particularly in poorly resourced schools. This paper reports the outcome of a small-scale interventionist research project which involved three experienced Life Science teachers. The teachers were exposed to an intervention that explicitly focused on supporting them with the pedagogical content knowledge (PCK) needed to facilitate inquiry-based learning in their classrooms. An indigenous technology, the production of a traditional non-alcoholic beverage (oshikundu) was used in the intervention. The Topic-Specific PCK model by Mavhunga and Rollnick provided the analytical framework for this study. Additionally, the principles of classroom inquiry together with the model of inquiry-based science instruction predict–explain–explore–observe–explain were used to scaffold teachers towards the PCK for inquiry-based teaching. Findings from the study revealed that prior to the intervention workshop some science teachers had inadequate PCK for inquiry-based approach. Except for concern over time constraints, the study established that all five components of teachers' PCK of an inquiry-based approach improved after the intervention. Furthermore, teachers recognised and recommended the use of the PEEOE model for inquiry-based science teaching. The process of making oshikundu was established as a suitable resource to conduct practical investigation in poorly resourced schools. This study thus recommends more interventions based on locally available indigenous technology to improve science teachers' PCK for inquiry-based science teaching. [ABSTRACT FROM AUTHOR]

This paper presents the results of a study on the integration of modelling and simulation tools in mechanical design. Indeed, optimisation of the design process often uses modelling and simulation tools in mechanical design activities. Thus, to meet the needs of the labour market, training situations in this field use communication and information techniques. In particular, digital tools are used for the development of virtual models intended for sizing and optimisation, and/or validating the behaviour and performance of a system, component or process. However, their use in the teaching–learning activities of mechanical design gives rise to many problems. These problems are often related to the educational use of these tools, the ergonomics of their interfaces, and their appropriation by students. This research presents the main results of a quantitative study on the learning of mechanical design. A survey using a questionnaire was conducted among 67 first-year tertiary students enrolled in the University Diploma of Technology programme in Science and Industrial Techniques in Morocco. The results of the study identified a number of factors that promote the efficiency of student mechanical design learning using modelling and simulation tools. [ABSTRACT FROM AUTHOR]

The world we live in is increasingly multimodal, necessitating multiliteracy for learners to engage meaningfully with knowledge and skills. While verbal language is the primary medium for constructing, communicating and learning scientific knowledge and concepts, visuals can help learners to gain knowledge that they may not develop from verbal explanations alone. Verbal and visual semiotic modes have the potential to function in a complementary way, working together to strengthen meaning. This paper explores the dynamics of verbal–visual intersemiotic complementarity in the classroom practice of three junior secondary physical science teachers in the Oshana region of Namibia. It reports on a qualitative case study employing Systemic Functional Linguistics in the analysis of multimodal discourse. The results revealed how the content selections in the verbal and visual modes of the science teachers' practice are related in terms of the meanings and their relationships through all five intersemiotic sense relations. The results also showed that some teachers consistently employed fewer visuals. The results further highlighted low frequency of the use of intersemiotic antonymy (opposites) and hyponymy (hierarchy) by each teacher compared with intersemiotic repetition, synonymy (synonyms) and meronymy (whole–part relationships). It is recommended that Namibian science teacher training programmes incorporate intersemiotic complementarity in order to help teachers harness the full potential of this approach. [ABSTRACT FROM AUTHOR]

This paper examines how seven teachers working in contexts of limited resources used the prescribed textbook for teaching, and the kinds of teacher–textbook relationships forged in the interactions. The study employs a sociocultural perspective to explore the processes by which teachers mobilise the affordances of the textbook to the teacher's practice, thereby advancing a particular way for studying and understanding better the teacher–textbook relationships in particular contexts. A methodological approach aggregating results for all teachers and looking for patterns of mobilisation across teachers allowed for the analysis of patterns of mobilisation regardless of the teacher. Findings point to generally tacit use of the textbook and a need for intervention on textbook use by teachers. The study makes recommendations for the production of educative guides as well as further research on the perceived role of the textbook in the teacher's practice. [ABSTRACT FROM AUTHOR]

This paper presents the findings of a study that explored the link between teachers' views on the challenges to inquiry-based science teaching (IBST) practice in the chemistry classroom and their need for professional development. The study used a multiple case study design and collected data using interviews. Participants were purposively selected. In all, eight chemistry teachers in six schools participated in the study. Five out of six cases we studied reported that the challenges the schools faced impeded the implementation of IBST. These challenges included lack of awareness of the IBST strategy, limited laboratory facilities and equipment, insufficient textbooks and overcrowded classes. In all, the views of teachers from the six cases suggested that, before embarking on the implementation of inquiry-based science teaching, it is vital to first consider a given school's teaching and learning resources, teacher capacity and motivation as essential factors that support the effective implementation of such innovation. Teachers' voices in all six cases also suggested that IBST implementation requires teacher development that focuses on their actual teaching needs and contextual challenges to optimise innovation outcomes. Three relationships between school implementation context and preferred professional development initiatives emerged. Teachers in private schools with or without resources and independent of class sizes require government-initiated and expert-led provision. Teachers at government schools with limited resources and large classes suggest expert-led workshops with a focus on sharing experiences during the workshops and on return to school. Teachers at government schools with previous access to centralised professional development and sufficient school resources (including improvised materials) indicate the need for in-school support from a professional learning community to strengthen the implementation of IBST. [ABSTRACT FROM AUTHOR]

Motivation and interest affect students' learning especially in Physics, a subject learners perceive as abstract. The present study was guided by three objectives: (a) to adapt and validate the Science Motivation Questionnaire (SMQ-II) for the Ugandan context; (b) to examine whether there are significant differences in motivation for learning Physics with respect to students' gender; and (c) to establish the extent to which students' interest predicts their motivation to learn Physics. The sample comprised 374 randomly selected students from five schools in central Uganda who responded to anonymous questionnaires that included scales from the SMQ-II and the Individual Interest Questionnaire. Data were analysed using confirmatory factor analyses, t-tests and structural equation modelling in SPSS-25 and Mplus-8. The five-factor model solution of the SMQ-II fitted adequately with the present data, with deletion of one item. The modified SMQ-II exhibited invariant factor loadings and intercepts (i.e. strong measurement invariance) when administered to boys and girls. Furthermore, motivation for learning Physics did not vary with gender. Students' interest was related to motivation for learning Physics. Lastly, although students' interest significantly predicted all motivational constructs, we noted considerable predictive strength of interest on students' self-efficacy and self-determination in learning Physics. Implications of these findings for the teaching and learning of Physics at lower secondary school are discussed in the paper. [ABSTRACT FROM AUTHOR]

In this paper we focused on university mathematics students' mental constructions on the concept limit of a sequence. The aim was to explore the nature of the mental constructions and to contribute to Action–Process–Object–Schema (APOS) theory in terms of instructional strategy for teaching limit of sequences. The belief that understanding students' mental constructions in learning mathematics leads to improved instructional strategy guided this study. Maple software was applied in the learning of limit of sequences to foster students' understanding of the topic. Thirty university students took part in this study. The data was collected through the test questions and interviews. The results revealed that in most cases, the preliminary genetic decomposition could be used to appropriately describe students' constructions of their responses. Furthermore, many students operated at an action/process/object level with the exception of a few students who were not able to operate at these levels. It was also revealed that few students carried out procedures effectively without the conceptual understanding of the concept limit of a sequence. It is recommended that the preliminary genetic decomposition be extended to include aspects necessary for conceptual understanding of the limit of sequences in modified genetic decomposition, such as prerequisites, concepts which include rules of inequalities and properties of the modulus function. These concepts are required for the understanding of proving or disproving the given limits of a sequence. [ABSTRACT FROM AUTHOR]

Learners in general struggle when working with word problems. South African learners in particular have an added barrier owing to the many official languages that have been legislated. The South African Department of Basic Education, through its curriculum statements, envisages that problem solving will play a fundamental part in mathematics teaching and learning. Whilst this has been embraced by teachers of mathematics, learners still experience difficulties when solving chosen word problems. This empirical, qualitative study explored 28 Grade 9 learners' use of visualisation when solving word problems. After all the due ethical clearance protocols were observed, one class of learners completed a task-based exercise and five learners were interviewed. The results showed that when learners drew a diagram that represented the problem, they were more likely to solve it. Those learners who drew no diagram, or drew an incorrect one, failed to arrive at a suitable solution. An important finding is that the visualisation technique is a powerful tool when working with the solving of problems in mathematics. [ABSTRACT FROM AUTHOR]

The topic of resources for learning mathematics commonly becomes of interest during times of disruption and rapid change in education. The considerable research on undergraduate mathematics students' resource use largely focuses on learning resources in the form of material technologies and texts. Concerned that contemporary decisions about resourcing for learning in mathematics may take the form of simply adding material resources, we identify the need for research that is designed around a broader notion of learning resource, and which focuses on what resources students use, as well as how they use multiple resources individually and together towards accessing mathematics. Thus, in our qualitative study of undergraduate mathematics students' resource use, we adopt a socio-cultural notion of resources as material, human, spatial, temporal and linguistic, and of resource use as transparent. We investigate six students' resource use, reported in weekly learning logs and focus group interviews. We show that students used material technologies and texts, and human and linguistic resources in three spaces − the live lecture, informal study and tutorial − with study time available for mathematics central to their choice of resources and how they used them. How students put these multiple resources to work (or not) towards accessing mathematics involved complex, agentic, individual work. Students' use of the lecturer's writing on the chalkboard, talk and gestures to make lecture notes in the live lecture is an example of this. Our findings offer insights into how lecturers can select learning resources, and also support students to use these towards accessing mathematics. [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 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]