A case study : exploring a DVD driven approach for teaching and learning mathematics, at secondary school level, with a framework of blended learning

Post-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 possibilities

Unlocking Complex Vector Calculus Concepts For Engineering Students Using Geogebra

There 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

Students’understanding of double integrals - implications for the engineering curriculum

Mathematics 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

A blended learning Grade 12 intervention using DVD technology to enhance the teaching and learning of mathematics

This 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.We are grateful to SASOL for the funding that supported the 2007 ISP and this research.http://www.pythagoras.org.z

A blended learning Grade 12 intervention using DVD technology to enhance the teaching and learning of mathematics

This 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.We are grateful to SASOL for the funding that supported the 2007 ISP and this research.http://www.pythagoras.org.z

The 13th Southern Hemisphere Conference on the Teaching and Learning of Undergraduate Mathematics and Statistics

Ngā mihi aroha ki ngā tangata katoa and warm greetings to you all. Welcome to Herenga Delta 2021, the Thirteenth Southern Hemisphere Conference on the Teaching and Learning of Undergraduate Mathematics and Statistics. It has been ten years since the Volcanic Delta Conference in Rotorua, and we are excited to have the Delta community return to Aotearoa New Zealand, if not in person, then by virtual means. Although the limits imposed by the pandemic mean that most of this year’s 2021 participants are unable to set foot in Tāmaki Makaurau Auckland, this has certainly not stopped interest in this event. Participants have been invited to draw on the concept of herenga, in Te Reo Māori usually a mooring place where people from afar come to share their knowledge and experiences. Although many of the participants are still some distance away, the submissions that have been sent in will continue to stimulate discussion on mathematics and statistics undergraduate education in the Delta tradition. The conference invited papers, abstracts and posters, working within the initial themes of Values and Variables. The range of submissions is diverse, and will provide participants with many opportunities to engage, discuss, and network with colleagues across the Delta community. The publications for this thirteenth Delta Conference include publications in the International Journal of Mathematical Education in Science and Technology, iJMEST, (available at https://www.tandfonline.com/journals/tmes20/collections/Herenga-Delta-2021), the Conference Proceedings, and the Programme (which has created some interesting challenges around time-zones), by the Local Organizing Committee. Papers in the iJMEST issue and the Proceedings were peer reviewed by at least two reviewers per paper. Of the ten submissions to the Proceedings, three were accepted. We are pleased to now be at the business end of the conference and hope that this event will carry on the special atmosphere of the many Deltas which have preceded this one. We hope that you will enjoy this conference, the virtual and social experiences that accompany it, and take the opportunity to contribute to further enhancing mathematics and statistics undergraduate education. Ngā manaakitanga, Phil Kane (The University of Auckland | Waipapa Taumata Rau) on behalf of the Local Organising Committ