We 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.
The study aims to identify areas of difficulty in learning about volumes of solids of revolution (VSOR) at a Further Education and Training college in South Africa. Students' competency is evaluated along five skill factors which refer to knowledge skills required to succeed in performing tasks relating to applications of the definite integral, in particular to VSOR. The paper reflects on reasons for the difficulties that students experience in this topic. The study reveals that many students are not competent in drawing graphs and in interpreting the region bounded by the given graphs. If the graphs are given, students have difficulty in selecting the representative strip that is used in approximating the bounded region. Although many students are able to produce the correct formula to calculate the volume, be it a disc, washer or shell, they find it problematic to draw the three-dimensional (3D) representation of the rotated strip and the generated solid of revolution. Students seem to succeed better with tasks requiring simple manipulation skills. The study illustrates how a measure (the skill factors) can be put into practice for establishing exactly where the problems lie when students underperform in the topic of VSOR. The results can serve as guide on how conclusions can be drawn by assessing the problematic situation through breaking it down along the framework of skill factors.
The Southern Hemisphere Conferences on the Teaching and Learning of Undergraduate Mathematics and Statistics have been taking place (with slightly shifting names) since 1997, located in South Africa, New Zealand, Australia and Argentina. Otherwise known as 'Delta' conferences, the 2015 conference, the tenth of its name, is Elephant Delta, with the theme 'Think Big!' The papers included in this special issue resonate with that theme in their global scope, their grain size of engagement with knowledge generation and in their disciplinary scope across mathematics, statistics and finance. These few, select, papers together with the conference Proceedings as well as the presentations themselves in Port Elizabeth, South Africa, November 2015, will form a body of work representing the researchers within this Delta community, a community which indeed Thinks Big. In their paper, 'Issues and trends: a review of Delta conference papers from 1997 to 2011', Henderson and Britton [1] categorized Delta papers published in the International Journal of Mathematical Education Science and Technology (iJMEST) and the Proceedings. When making a call for reviewers for this issue, in expectation of submissions, we adapted and modified this classification as two different categories:
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