Mathematics In South Africa Research Articles

Mathematics in South Africa’s Intermediate Phase: Music integration for enhanced learning

Background: Embracing the influential role of music in education, teachers an cultivate an environment that fosters learners’ curiosity, creativity, and enthusiasm for acquiring knowledge. The first author, experienced in teaching Intermediate Phase music and mathematics, was keen to explore how to bridge the gap between the educational vision for 21st-century knowledge and skills and current teaching practices through the adoption of active music integration and appropriate pedagogy to full engage learners.Aim: The study aimed to explore how general teachers, with no previous formal music exposure perceived and engaged with the process of correlating concepts and learning experiences in music and mathematics.Setting: The research was conducted over nine weeks in three South African, Afrikaans-medium, middle-class governmental primary schools located in the Tshwane North district of the Gauteng province.Methods: This study employed a qualitative case study research approach and was situated within the pedagogical design of constructive alignment for effective teaching and learning.Results: The results underscore the significance of generalist teachers’ ability to effectively incorporate music into mathematics lessons without extensive musical training or instrumental skills.Conclusion: The article challenges the notion that musical expertise is a prerequisite for integration, highlighting the fact that generalist teachers can successfully incorporate music into mathematics instruction by fostering meaningful connections between the two subjects.Contribution: This article draws attention to the importance of constructive alignment in promoting independent thinking and the practical application of knowledge. These findings offer guidance for the development of pedagogical frameworks and instructional practices that prioritise meaningful teaching and learning experiences.

Mapping Design Principles to Instructional Realities in Early Grade Mathematics in South Africa: A Framework for Designing and Evaluating Learning and Teaching Support Materials

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.

ILearn? Investigating dialogical interaction with tablets in mathematics lessons

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

Language and multilingualism in the teaching and learning of mathematics in South Africa: A review of literature in Pythagoras from 1994 to 2021

This article presents a systematic review of research on language and multilingualism in mathematics education published in the South African journal Pythagoras from 1994 to 2021. This time frame was chosen as the year 1994 marked the acknowledgement of 11 official languages in the new democratic South Africa (including 9 indigenous languages), compared to only Afrikaans and English during the apartheid era. The review considers emergent themes in the included articles and examines what the articles reveal about mathematics education in South Africa. In addition to other findings, our corpus of literature indicates that research in this field of mathematics has been mostly undertaken in under-resourced schools and that research under the theme of multilingual education is at the forefront of research in South African mathematics education, while research on language policy needs more attention. Research on multilingual education in our corpus of literature also reveals great awareness of the value of seeing language as a resource, as well as the benefits that accrue when learners’ home languages are taken into account in mathematics teaching and learning. The gaps in research in the field of language and multilingualism in the teaching and learning of mathematics are also noted and recommendations for future research are made.

Exploring Teachers' Views on Code-Switching as a Communicative Technique to Enhance the Teaching of Mathematics in Grade 4

<p style="text-align:justify">The teaching and learning of mathematics in South Africa are conducted through the authorised Language of Learning and Teaching (LoLT). South Africa has eleven official languages, and English is a Language of Learning and Teaching (LoLT) from the Intermediate and Further Education and Training (FET) Phase. This study explores teachers' views on code-switching as a communicative technique to enhance teaching mathematics in Grade 4 in selected primary schools in South Africa. This qualitative single case study employed the interpretivist paradigm and social constructivism theory. A convenient purposive sampling technique was used to sample six grade 4 mathematics teachers from three primary schools in the Alexandra township in South Africa. Researchers collected data through the use of semi-structured interviews, which were later analysed and discussed using themes. Findings indicate that teachers often code-switch from LoLT (English First Additional Language) into Home Language (H.L.) to enhance learners' understanding of the mathematics concepts. Researchers suggested the integration of code-switching into the curriculum policy and followed by in-service training for Grade 4 mathematics teachers in code-switching.</p>

Opportunity to Learn Euclidean Geometry in Two Mathematics Textbooks of Tenth Grade in South Africa

Textbooks play a central role in the teaching and learning of mathematics. In some schools, textbooks serve as the only resource material available to teachers and students. Yet, little is known about the learning opportunities in mathematics textbooks in most countries. This study investigated the opportunities to learn Euclidean Geometry in two textbooks of tenth-grade mathematics in South Africa. It examined the content coverage, content organization, and the type of tasks used in teaching the topic in the textbooks. This study followed a case study research design and a qualitative approach. The Curriculum and Assessment Policy Statement's (CAPS) grade 10 Euclidean geometry curriculum and Gracin's mathematical activity types served as frameworks for the analyses. The data were analyzed following the deductive content analysis approach. The result shows that the contents of Euclidean geometry were well covered in both textbooks following the curriculum and the contents were presented in logical and sequential order to enhance learning. In addition, it was found that the tasks in the textbooks were predominantly of argumentation and reasoning type. It was concluded that the textbooks offer sufficient opportunities for learning Euclidean geometry as specified in the curriculum for the grade level. However, the inclusion of a wider range of tasks in the future editions of the textbooks was recommended.

A History of Mathematics in South Africa: Modern Milestones

A History of Mathematics in South Africa: Modern Milestones

Professor D.P. Mason (MASSAF, FRSSAF) on the occasion of his 75th birthday: A lifetime contribution to the development of Applied Mathematics in South Africa

Professor D.P. Mason (MASSAF, FRSSAF) on the occasion of his 75th birthday: A lifetime contribution to the development of Applied Mathematics in South Africa

Rethinking Learner-Centred Education: Bridging Knowledge Cultures

This article argues that learner-centred education needs to shift from a discussion only on pedagogical activities such as group-work and other cooperative learning strategies. It suggests that the focus of learner-centred education should be on the cultural world of the African child and how this influences the way in which he/she learns Western science. The African child often experiences cognitive dissonance/perturbation when learning Western science. The article draws on insights from the theory of collateral learning which was originally developed by Jegede. It argues that unless policymakers and teachers take into consideration the cultural frameworks of learners, there will not be a sound basis for improving school science and school mathematics in South Africa. Spending more on resources and increasingly testing learners, as is currently done in South Africa, will not improve school science in South Africa. Improving school science in part depends on rethinking leaner-centred education, which means critically looking at the important role that cultural frameworks of learners play in learning Western science.

Using code-switching as an empowerment strategy in teaching mathematics to learners with limited proficiency in English in South African schools

Teaching and learning mathematics in South Africa (SA) is characterised by serious challenges because the pass rate in Mathematics is always below the expected level. The introduction of the Curriculum Assessment Policy Statement (CAPS) ushered in new hope that the situation would improve. However, teachers still encounter challenges when they use English as the medium of instruction because learners fail to comprehend the challenging mathematical concepts presented to them in a language which is not their home language. This paper investigates how code-switching can be used as an empowerment strategy to help learners improve their performance in mathematics. Qualitative research methods were used to collect data and the findings reveal that code-switching can be successfully used to facilitate teaching and learning. Keywords: bilingual; code-switching; mathematical expressions; multilingual; paragon; perimeter

Multiplicative reasoning: An intervention’s impact on Foundation Phase learners’ understanding

Background: Given the context of low attainment in primary mathematics in South Africa, improving learners’ understanding of multiplicative reasoning is important as it underpins much of later math ...

Migrant Teachers’ Perceptions of the South African Mathematics Curriculum and Their Experiences in Teaching in the Host Country

This article investigates the tensions experienced by Zimbabwean immigrant teachers in teaching mathematics in South Africa. It explores their views on the South African mathematics curriculum and ...

Disentangling the language effect in South African schools: Measuring the impact of ‘language of assessment’ in grade 3 literacy and numeracy

The aim of this article is to exploit an unusual occurrence whereby a large group of South African grade 3 students were tested twice, 1 month apart, on the same test in different languages. Using a simplified difference-in-difference methodology, it becomes possible to identify the causal impact of writing a test in English when English is not a student’s home language for 3402 students. The article aims to address the extent to which language factors (relative to non- language factors) can explain the high levels of underperformance in reading and mathematics in South Africa. I find that the language of assessment effect is between 0.3 and 0.7 standard deviations in literacy and 0 and 0.3 standard deviations in numeracy. This is approximately 1–2 years worth of learning in literacy and 0–1 year worth of learning in numeracy. By contrast, the size of the composite effect of home background and school quality is roughly 4 years worth of learning for both numeracy (1.2 standard deviations) and literacy (1.15 standard deviations). These results clearly show that the ‘language effect’ should be seen within the broader context of a generally dysfunctional schooling system. They further stress the importance of the quality of instruction, not only the language of learning and assessment. The fact that the literacy and numeracy achievement of South African children is so low in grade 3 (prior to any language switch to English in grade 4) should give pause to those who argue that language is the most important factor in determining achievement, or lack thereof, in South Africa.

Learners’ errors in secondary algebra: Insights from tracking a cohort from Grade 9 to Grade 11 on a diagnostic algebra test

It is well known that learner performance in mathematics in South Africa is poor. However, less is known about what learners actually do and the extent to which this changes as they move through secondary school mathematics. In this study a cohort of 250 learners was tracked from Grade 9 to Grade 11 to investigate changes in their performance on a diagnostic algebra test drawn from the well-known Concepts in Secondary Maths and Science (CSMS) tests. Although the CSMS tests were initially developed for Year 8 and Year 9 learners in the UK, a Rasch analysis on the Grade 11 results showed that the test performed adequately for older learners in SA. Error analysis revealed that learners make a wide variety of errors even on simple algebra items. Typical errors include conjoining, difficulties with negatives and brackets and a tendency to evaluate expressions rather than leaving them in the required open form. There is substantial evidence of curriculum impact in learners’ responses such as the inappropriate application of the addition law of exponents and the distributive law. Although such errors dissipate in the higher grades, this happens later than expected. While many learner responses do not appear to be sensible initially, interview data reveals that there is frequently an underlying logic related to mathematics that has been previously learned.

Perceptions of Teachers and Learners about Factors that Facilitate Learners' Performance in Mathematics in South Africa

Under-performance in mathematics is a challenge in South African schools. The purpose of this study is to advance views expressed by teachers and learners on factors that facilitate learners' performance in mathematics. The participants in this research were educators and learners from historically disadvantaged schools from similar socio-economic backgrounds in the Limpopo Province. Ten rural schools participated in the study, all government schools, with schools selected on the basis of their accessibility and performance. They represent both high-performing and low-performing schools in mathematics. Data were collected from learner focus group interviews and individual teacher interviews. Perceptions expressed by educators and learners from high-achieving schools and from low-achieving schools are juxtaposed and point to factors such as learners' and teachers' commitment and motivation, attitudes and self-concept, learners' career prospects, learners' perceptions of peers and teachers and teachers' perceptions of learners. These factors appear to influence disadvantaged learners' decisions to persist and achieve in mathematics despite their difficult circumstances.

Instructional leadership for the improvement of science and mathematics in South Africa

The role of leadership in the improvement of teaching and learning has long been established in the literature. In recent years, there has been a proliferation of attempts to influence (or lead) classroom teachers, especially in the areas of science and mathematics. What remains unclear and somewhat contentious however, is what kinds of leadership matter for the improvement of learning and achievement in schools. This paper presents findings from a large-scale, qualitative research project on the leadership practices of 102 successful schools serving formerly disadvantaged children in South Africa. Data from a rich set of interviews with school administrators and subject specialists, document analysis, and school observations suggest that the more successful schools, in the group, distinguish themselves in the way they define and construct the overall goals of leadership around instruction and have developed fairly elaborate structures and processes for monitoring instruction (especially in mathematics and science). Using the framework of distributed leadership, we develop an account of how leadership for instructional improvement is constructed in the more successful schools in South Africa. We conclude the paper by puzzling over the rather strained (or non-existent) relationship between leadership and instruction in most (South African) schools, and explore why improvements in school achievement are rather rare among such schools serving the poor and (formerly) disadvantaged learners.

Study orientation and knowledge of basic vocabulary in Mathematics in the primary school

Whatever the reason, underachievement in mathematics in South Africa is endemic and tantamount to a national disaster. Despite the transformation of education in South Africa, failure rates in mathematics at school and university remain unacceptably high, and the number of learners who leave Grade 12 with a pass mark in both mathematics and physical science is unacceptably low. Relatively little has been written about inadequate performance of Grade 4 to 7 learners in mathematics in South Africa, and even less about possible solutions to the problem. South African primary school learners’ lack of basic mathematics and vocabulary skills in particular is a source of major concern. In the first national systemic evaluation of learners’ skills in English, mathematics and science in 2001 Grade 3 learners achieved an average of 30% in mathematics. In the follow-up studies, Grade 6 learners achieved a national average of 27% in mathematices, in 2004, while nationally eighty percent of Grade 3 and 6 learners achieved less than 50 percent for mathematics and Languages in 2008. The finding that so many primary school learners today are not numerate or literate has a direct influence both on the teaching and the learning of mathematics. Everything possible needs to be done to change this situation. During the past 15 years, the research focus in mathematics has shifted to an examination of the influence of social, cognitive and metacognitive, conative and affective factors on achievement in mathematics. In this regard, it is of particular importance that an ongoing investigation into “other” aspects that impact on achievement in mathematics is launched, rather than to restrict the investigation to mere assessment of objectives that are aimed at continually evaluating cognitive progress in mathematics. There is sufficient empirical evidence that an adequate orientation to the study of mathematics correlates positively with high achievement in mathematics on secondary and tertiary levels. The aim of this research was to investigate the extent to which the performance in study orientation (Study Orientation questionnaire in Mathematics (Primary)) and knowledge of basic vocabulary/terminology in mathematics (Mathematics Vocabulary (Primary)) (vocabulary as one aspect of language in Mathematics) of Grade 4 to 7 learners predict performance in mathematics (Basic Mathematics (Primary)). Three standardised questionnaires were administered, namely the Study Orientation questionnaire in Mathematics (Primary), or SOM(P), Mathematics Vocabulary (Primary) or (MV(P), and Basic Mathematics (Primary) or BM(P). The participants consisted of learners in Grade 4 to 7 (n = 1 103) in North-West Province with respectively Afrikaans, English and Tswana as their home language. Results from the data, by calculating intercorrelations and stepwise regression, confirmed that learners’ performance in mathematics (BM(P)) can be predicted through their performance in the knowledge of basic vocabulary in mathematics (MV(P)), their “maths” anxiety, study attitude towards and study habits in mathematics (SOM(P)). The results can be implemented to improve learners’ performance in mathematics when teachers identify inadequate knowledge of basic vocabulary in mathematics as well as study orientation (for example, “maths” anxiety, study attitude towards and study habits in mathematics) in the early years of schooling. Learners’ scores can be checked to identify those requiring aid, support, remediation and/or counselling. An analysis of individual answers (particularly those where learner’s replies differ significantly in respect of the answers usually given by good achievers in mathematics) could be extremely useful. Enculturing learners to the vocabulary of mathematical language is an aspect of instruction that needs specific attention. The three questionnaires, which are administered in this research, provide mathematics teachers with standardised tools with which to make a simple systematic analysis of a number of important background particulars, feelings, attitudes, habits and customs with regard to the learner’s academic orientation in mathematics, as well as to their knowledge of basic vocabulary in mathematics that could be remedied when inadequate.

The challenge of inadequate achievement in mathematics: Focus on a meta-approach

As is the case elsewhere in the world, all stakeholders in South Africa are deeply concerned about the level and scope of underachievement in mathematics, not only at Grade 12 level, but, indeed, at University, University of Technology and Further Education and Training levels. These concerns assume a deeper dimension in light of the fact that inadequate achievement in mathematics inevitably will have a ripple effect on the academic situation in any country: inadequate achievement in mathematics precludes learners from applying for admission to sought-after fi elds of study, which, in turn, prevents numerous learners from realising their true potential and, eventually, from being happy and successful in careers that they might otherwise have been able to execute successfully. It goes without saying that inadequate achievement in mathematics will impact negatively on the overall economic situation in any country (even more so in a developing country such as South Africa). Truth being, achievement in mathematics amounts to equipping oneself with survival skills. In this article, the spotlight shifts from a narrow and outdated focus on problems that are associated with inadequate achievement in mathematics to possible solutions for this disconcerting situation and the implied challenge it raises. The focus is thus on three levels that collectively underpin and impact on achievement in mathematics, viz. the macro level, the meso level and the micro level. The macro level refers mainly to the input by the national government (and, by default, the National Department of Education). In the fi rst instance, it is the responsibility of the state to provide adequate schooling facilities for all learners, irrespective of where they fi nd themselves. Furthermore, it is the duty of the state to ensure that every learner has access to basic facilities, including food, water, sanitation and housing. The state (via the National Department of Education) is also obliged to ensure that the basic philosophy that underpins mathematics education in the country is scrutinised continuously and that changes be made to existing teaching philosophy should these be recommended by the majority of stakeholders. Case in point: the implementation of Outcomes-Based Education (OBE) in South African mathematics classrooms has now already been under the spotlight for a number of years and there seems to be general consensus that it is essential to facilitate a number of basic changes to this philosophy and (especially) to the way in which it is implemented in South African classrooms. Teachers, for instance, constantly complain about matters such as an administrative overload, unacceptably high stress levels (brought about by factors broadly associated with OBE-related issues) and the fact that the laudable philosophy underpinning OBE is not consistently realised in practice. At the meso level, the spotlight falls on factors related to teacher training. For example, it seems highly advisable to optimise teacher training in mathematics, to facilitate training in emotional intelligence, to conduct a national audit on the number of mathematics teachers currently teaching mathematics (in terms of how many teachers are currently in the system, where these teachers fi nd themselves, their level of training, etc.) to determine training needs in mathematics and to facilitate a more equitable distribution of teachers across the country. For example, it is proposed that all graduating teachers be compelled to do community service in an effort to facilitate a better understanding of the challenges that teachers in various parts of the country face, thereby breaking down barriers between people. At micro level, the emphasis is on measures that might be taken to provide guidance to parents on how to assist their children in mathematics on the one hand and on practical ways in which to help learners in mathematics perform better in mathematics and leave school better equipped to deal with typical challenges at tertiary level on the other. It is hoped that this article will contribute to an improvement in the disconcerting situation to be found in mathematics classrooms across South Africa. I sincerely hope to have sensitised readers to the need not only to talk about the situation in mathematics in South Africa, but instead to start acting and in so doing to impact on the situation in practical ways.

New numbers in mathematics in South Africa

This article is a follow-up of a study conducted in 2000 by the same authors on trends in numbers of mathematics majors at South African universities. Data from 12 universities for the 2000–2007 period is investigated. The previously observed trend of general and dramatic decrease in numbers of mathematics majors appears to have been reversed and an increase of numbers is observed at all but one of the universities. Diversification into applied fields such as financial mathematics has aided in increasing numbers of mathematics majors and has been largely successful at universities that have ventured this way. Universities where mathematics teacher training is situated within mathematics departments also show a noteworthy increase in numbers. Of concern is the decrease in numbers of mathematics majors over the last 2 years.

The impact of the transition to outcomes-based teaching on university preparedness in mathematics in South Africa

Following the political changes of 1994 in South Africa, the decision was taken to replace the traditional skills-based education system at primary and secondary school level (Grades 1–12) with an outcomes-based education system (OBE). The implementation of the OBE system did not come without problems, giving rise to revised initiatives. The OBE approach, referred to as Curriculum 2005, was introduced into schools in 1998, for all learners in Grades 1–6 and progressively phased in after that. In 2002, the OBE system was put on hold for the two upper grades of these learners. Learners in these two grades reverted back to skills-based learning for their last three years of schooling, i.e. in Grades 10 – 12. The most senior of these learners that had been subjected to four years of OBE and another three years of the old system finished their schooling in 2005 and 2006 and entered university in 2006 and 2007. These groups are of interest. Students ahead of them had their full schooling in the old system and students two years younger were only subjected to OBE. These students are the “group in the middle”. This paper reports on what the impact is of the growing pains of such a new, inadequately planned education system on the mathematics preparedness of students entering university. This report will be extended in 2009 when the learners that have been fully subjected to the OBE system enter university.