11 research outputs found
A case study : exploring a DVD driven approach for teaching and learning mathematics, at secondary school level, with a framework of blended learning
No full textPost-apartheid South Africa is witnessing an education crisis of significant proportions. The new outcomes-based education system has failed to deliver and universities are suffering the consequences of under-preparation of learners for tertiary studies especially in mathematics. The educator corps is lacking and it has become common practice for universities to deploy augmented programmes in mathematics for secondary school learners in the surrounding areas. This thesis describes a particular approach of blended learning, devised for the Incubator School Project (ISP), an initiative of the Nelson Mandela Metropolitan University (NMMU) in the Eastern Cape of South Africa. The defining feature of this blended approach is that it incorporates DVD technology, which offers an affordable and accessible option for the particular group of learners and the schools they attend. The thesis poses the research question: How did the use of the DVD approach within a blended learning environment support the learning of mathematics? This case study explores the particular blended approach and reports six fold on the approach – qualitatively based firstly on a questionnaire completed by learners and secondly on interviews of learners, thirdly on the facilitators reports, fourthly quantitatively on learner performance before and after the intervention. Fifthly six schools are used as a case study where the mathematics performance of the learners who participated in the ISP is compared to those who did not participate in the ISP. Finally the scope of blending of this model is evaluated by means of a radar chart, adapted from an existing radar measure. This research revealed that using the DVD approach within a blended learning environment did lead to an improvement in learners perceptions about mathematics, an improvement in the manner in which they learned mathematics, an extension in their mathematics knowledge and provided learners with a supportive environment in which to learn mathematics. The elements which supported learning in this approach are presented. The findings of the study suggest that this approach impacted favourably on the mathematics learning and enhanced the mathematics learning and performance of these learners. Recommendations are offered for practice, teachers and schools and for further research possibilitie
Discussion Forums in Vector Calculus: Reflecting on the quality of engineering students’ online interactions
No full textUnlocking Complex Vector Calculus Concepts For Engineering Students Using Geogebra
No full textThere is an increasing drive to exploit the power of technology to improve students mathematical conceptual understanding. This work is motivated by the authors research presented at the SEFI 2022 conference which reported on students experienced difficulties with the double integral, a concept central to vector calculus. Some of the difficulties included visualising and sketching three dimensional surfaces and regions of integration and changing coordinate systems from rectangular to polar. Vector calculus is a crucial subject for engineering students, but its abstract concepts can be challenging to grasp. This curriculum proposal is a response to improve visualisation and conceptual understanding and is part of a larger project to develop an innovative, engaging and effective way for undergraduate engineering students at the University of Cape Town to learn vector calculus concepts supported by GeoGebra. The choice was made in favour of the easy to use, freely downloadable mathematical software, GeoGebra which presents a creative, visual and integrative way to experience and understand mathematical concepts.
Informing this curriculum development initiative is Vygotsky’s social constructivist perspectives with an emphasis on inclusivity, diversity and participant interactions. In this paper we discuss the above theoretical underpinnings with case studies on how to teach the double integral concept in GeoGebra for conceptual understanding. Additionally the benefits of using GeoGebra including its ability to engage students, promote critical thinking, and increase motivation will be discussed. This research will be of interest to those intending to use GeoGebra to improve the teaching and learning of vector calculus concepts
Towards Alleviating the Post-Apartheid Education Crisis in South Africa
No full textPost-apartheid South Africa is witnessing an education crisis of significant proportions. The new outcomes-based education system has failed to deliver, and universities are suffering the consequences of under-preparation of learners for tertiary studies. The educator corps is lacking, and it has become common practice for universities to deploy augmented programmes in mathematics for secondary school learners in the surrounding area. This chapter describes a particular model of blended learning, devised for the Incubator School Project (ISP), an initiative of the Nelson Mandela Metropolitan University (NMMU) in the Eastern Cape of South Africa. The defining feature of this blended model is that it incorporates DVD technology, which offers an affordable and accessible option for the particular group of learners. DVD technology was used as an ingredient in this blended learning approach since it is easily available to the majority of learners and to the schools they attend. This chapter describes the particular blended model and reports both qualitatively and quantitatively on its success: qualitatively, based firstly on a questionnaire completed by learners and secondly on interviews of educators; quantitatively, based thirdly on learner performance before and after the intervention and fourthly on a single school case study where the mathematics performance of the learners who participated in the ISP is compared to those who did not participate in the ISP. Finally, the scope of blending of this model is evaluated by means of a radar chart, adapted from an existing radar measure. The findings of the study suggest that the use of DVD technology in the blended learning approach impacted favourably on the mathematics learning and enhanced the mathematics performance of these learners.</jats:p
A blended learning Grade 12 intervention using DVD technology to enhance the teaching and learning of mathematics
No full textThis article describes the experiences and mathematics performance of Grade 12 learners selected to participate in a mathematics intervention project using digital video disk (DVD) technology within a blended learning context. Blended learning in the context of this study is defined as employing a variety of appropriate methods of delivery to enhance the teaching and learning process. DVD technology was used as an ingredient in this blended learning approach, since it is easily available and accessible to the majority of learners and the schools they attend. The study reported on here forms part of a larger study using action research methodology. This article reports on a single stage of the action research: implementing a change to improve the situation and observing the consequences of this action. Mathematics Incubator School Project (ISP) learners completed questionnaires with open-ended questions which pertained to their experiences of the blended learning approach. The observations of the facilitators were also recorded. A single school was used as a case study and the mathematics performance of learners who participated in the ISP was compared with that of those who did not. The findings suggest that use of DVD technology in this blended learning approach impacted on mathematics learning and enhanced the mathematics performance of learners
Students’understanding of double integrals - implications for the engineering curriculum
No full textMathematics plays a significant role in engineering students' education. To undergraduate engineering students, calculus concepts are foundational to their engineering courses. One such concept is the double integral. It is thus important to ensure that students not only learn this concept but also engage to understand it and are able to apply this knowledge in relevant engineering courses. This research paper focuses on the following two components: Firstly, the relevance of double integrals to the engineering curriculum. And secondly, students’ understanding of the double integral concept. We present the relevance of double integrals in the engineering curriculum by looking at the use of this concept in different engineering fields. We explored students’ understanding of double integrals and administered a test to 35 second year engineering students enrolled in an undergraduate Calculus III course. In a qualitative study, the performance of students was used to analyse the type of misconceptions they have in double integration. The findings reveal that the students encounter difficulties with graphical representation of surfaces and region of integration. In addition, students struggle with changing the order of integration and performing the integration process. While some of these errors are conceptual, others are really due to carelessness in the procedure
Profile, Performance and Language in Engineering Mathematics
No full textThere is a global concern for retention and success of students in higher education engineering programmes, in particular for students from under-represented communities. Low success in engineering programmes can be partly attributed to students failing mathematics or being unable to articulate mathematics in other engineering courses. This research explores how understanding the academic preparedness of engineering students in relation to their performance in university mathematics can direct curriculum changes to improve student success, driven by the research question: “How can the analysis of student data contribute to understanding student performance in calculus?” Data from engineering students in an extended curriculum programme at the University of Cape Town (UCT) were analysed to generate profiles from variables including gender, home language and performance in university admissions tests. Profiles were related to performance in three consecutive engineering mathematics courses. To determine which variables had the greatest explanatory power on engineering mathematics scores, relative importance analysis was applied. There was no evidence that weaknesses in terms of pre-university mathematics performance held students back from succeeding in the first two engineering mathematics courses at UCT, at least within the support context of the extended curriculum programme. When analysing according to engineering mathematics performance levels (e.g., fail versus first-class pass), academic literacy and, to a lesser extent, quantitative literacy emerged as having greater relative importance than pre-university mathematics in explaining the variance in engineering mathematics scores. The findings imply that interventions to improve the success of engineering students should include developing academic literacy practices, potentially in first- and second-year mathematics courses. We reflect on how the relative importance analysis of student data strengthens similar findings from other research on the importance of language in mathematics by highlighting the most important variables explaining students’ mathematics performance
The unexpected consequences of replacing corridor chats with an online community of practice
No full textThe unexpected consequences of replacing corridor chats with an online community of practice
No full textWe are four academics teaching mathematics at three different higher education institutions over two continents. Through fortnightly meetings to research how our practices changed as a result of the Covid-19 lockdowns, we formed a community of practice. The process of articulating our experiences and ideas, and reflecting on the recorded meetings and the written homework we set ourselves, was reassuring and motivational. We identified five assessment propositions to guide our mathematics teaching, which we summarize in this paper. A major proposition of assessment we embraced was the use of open book (or open-internet) assessment as a way to test for mathematical understanding. Our community of practice interactions influenced our teaching and assessment practices. We learnt more deeply about assessment by interrogating each other’s work, observing and identifying misconceptions or errors (made by ourselves and others), and learning different ways of solving problems through discussion. We noted that sustaining the community of practice required comfort in being confronted and criticized. The unexpected consequence of our community of practice was the push it gave us to think about why we teach what we teach, assess how we assess, and how we can make both more relevant to a changing world.</p
Lessons learnt and insights shared: The Diagnostic Mathematics Information for Student Retention and Success (DMISRS) Case Studies Dialogue on teaching first-year mathematics in South Africa
No full textThe Diagnostic Mathematics Information for Student Retention and Success (DMISRS) project was a collaborative project focused on first-year mathematics, which drew together lecturers in South African higher education institutions and other related organisations. Various themes were explored during the annual DMISRS symposia from 2018 to 2022. The project’s culmination was a final DMISRS symposium held in November 2023, which focused on the case studies that examine the sub-projects that have emerged over the years. The symposia have tackled critical themes, including collaborative practices and courses that influence graduation rates, the psychological well-being of students, and innovative solutions in first-year mathematics, such as assessments, performance metrics, blended learning approaches and curriculumdevelopment. The case studies offer valuable narratives of day-to-day interactions, teaching and learning activities, and shared resources or practices in first-year mathematics education experiences. They showcase successes and delve into challenges and their corresponding solutions, providing practical insights that empower the community of practice across diverse higher education institutions and contexts. As a capstone to the DMISRS project’s final symposium, the DMISRS team invited those who contributed case studies to take part in a panel discussion, referred to as the “DMISRS Case Studies Dialogue”, on a range of topics, including their own experiences in setting up and implementing innovations or conducting investigations, and their reflections on the impact of and the legacy of the workdone as part of this project.This paper captures that conversation as a dialogue among the contributorsdone as part of this project. This paper captures that conversation as a dialogue among the contributors.
