The objective of this thesis is to establish whether or not online, objective questions in elementary graph theory can be written in a way that exploits the medium of computer-aided assessment. This required the identification and resolution of question design and programming issues. The resulting questions were trialled to give an extensive set of answer files which were analysed to identify whether computer delivery affected the questions in any adverse ways and, if so, to identify practical ways round these issues. A library of questions spanning commonly-taught topics in elementary graph theory has been designed, programmed and added to the graph theory topic within an online assessment and learning tool used at Brunel University called Mathletics. Distracters coded into the questions are based on errors students are likely to make, partially evidenced by final examination scripts. Questions were provided to students in Discrete Mathematics modules with an extensive collection of results compiled for analysis. Questions designed for use in practice environments were trialled on students from 2007 – 2008 and then from 2008 to 2014 inclusive under separate testing conditions. Particular focus is made on the relationship of facility and discrimination between comparable questions during this period. Data is grouped between topic and also year group for the 2008 – 2014 tests, namely 2008 to 2011 and 2011 to 2014, so that it may then be determined what factors, if any, had an effect on the overall results for these questions. Based on the analyses performed, it may be concluded that although CAA questions provide students with a means for improving their learning in this field of mathematics, what makes a question more challenging is not solely based on the number of ways a student can work out his/her solution but also on several other factors that depend on the topic itself.

Research has shown that South African mathematics performance is extremely poor compared to other countries that participated in the Trends in Mathematics and Science Study in 2015 and 2016, respectively. Most of the competing countries were developing and were disadvantaged by their socio-economic status compared to the more economically vibrant South Africa. However, South Africa came last in the mathematics and science standardised tests commonly referred to as the Annual National Assessment and National Benchmark Test. The poor performance of the country’s learners in mathematics is exacerbated by the inability of veteran mathematics teachers to adopt technological teaching methods and innovations during teaching and learning. The Mathletics programme is a modern teaching tool that links every aspect of mathematics teaching and learning and gives individual learners the ability to successfully engage in mathematics learning activities. The learner gains mental mathematics skills to solve mathematical problems and is then able to apply the acquired mathematical skills to solve similar mathematical problems in any given situation. This study aimed to investigate and develop the professional status of veteran primary school mathematics teachers through participatory action research to improve their understanding of the application of Mathletics during teaching and learning. The data for my study was collected via audiotape, semi-structured interviews, and participant observations. The participants were veteran mathematics primary school teachers between the ages of 40 and 59 from the Gauteng Department of Education, Tshwane South District Circuit 2. The interviews and observations were conducted at times and venues preferred by the participants at their respective schools. The main research finding of the study shows that the majority of the participating veteran primary school teachers are not fully prepared in terms of skills, resources and methods to effectively respond to the recent technological teaching and learning transformations. As a recommendation, this study needs further research to benefit more schools and more teachers, so that participatory action research (PAR) can be a method for continuing professional development (CPD). / Dissertation (MEd)--University of Pretoria, 2020. / Humanities Education / MEd / Unrestricted