3 research outputs found
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 Vygotskyâs 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
Studentsâunderstanding 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, studentsâ 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 studentsâ 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
The 13th Southern Hemisphere Conference on the Teaching and Learning of Undergraduate Mathematics and Statistics
NgÄ mihi aroha ki ngÄ 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 yearâs 2021
participants are unable to set foot in TÄmaki 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 MÄori 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.
NgÄ manaakitanga,
Phil Kane (The University of Auckland | Waipapa Taumata Rau) on behalf of the Local
Organising Committ