Ansie Harding

Undergraduate students’ performance and confidence in procedural and conceptual mathematics

The general perception is that high school teaching of mathematics in South Africa tends to be fairly procedural and that students that enter university are better equipped to deal with procedural problems rather than conceptual. This study compares the conceptual and procedural skills of first-year calculus students in life sciences. Also investigated is students’ confidence in handling conceptual and procedural problems. The study seems to indicate that these students do not perform better in procedural problems than in conceptual problems. They are more confident of their ability to handle conceptual problems than to handle procedural problems. Furthermore the study seems to indicate that students do not have more misconceptions about conceptual mathematics than about procedural issues.

The influence of second language teaching on undergraduate mathematics performance

Understanding abstract concepts and ideas in mathematics, if instruction takes place in the first language of the student, is difficult. Yet worldwide students often have to master mathematics via a second or third language. The majority of students in South Africa — a country with eleven official languages — has to face this difficulty. In a quantitative study of first year calculus students, we investigated two groups of students. For one group tuition took place in their home language; for the second group, tuition was in English, a second or even a third language. Performance data on their secondary mathematics and first year tertiary calculus were analysed. The study showed that there was no significant difference between the adjusted means of the entire group of first language learners and the entire group of second language learners. Neither was there any statistically significant difference between the performances of the two groups of second language learners (based on the adjusted means). Yet, there did seem to be a significant difference between the achievement of Afrikaans students attending Afrikaans lectures and Afrikaans students attending English lectures.

Teaching Undergraduate Mathematics on the Internet: PART 1: Technologies and Taxonomy

The world wide web is becoming wider at an increasing rate. It is virtually impossible to take any kind of accurate snapshot of the state of its development. Undergraduate mathematics courses presented on the internet are relative newcomers to the race but nevertheless seem to be increasing in numbers also at a phenomenal rate. Internet education in mathematics is developing as a new mode of teaching with its own characteristics and possibilities, different from any traditional way of teaching. Research on this new mode of teaching is sparse and open research questions are temptingly plentiful. In a study presented in two parts, we try to capture the world of internet teaching of undergraduate mathematics with its myriad of possibilities. In this, the first part, we briefly list some of the technologies involved and we attempt to create some order in the huge number of activities that are available on the web. We give an overview of the scope of mathematics courses presented via the internet and attempt a graphical classification of the different types of web courses. In the second part (Engelbrecht, J. and Harding, A.: 2004a, Teaching undergraduate mathematics on the web 2: Attributes and possibilities) we discuss characteristics and implications of this mode of teaching/learning mathematics, list possible research issues and envisage possible future trends.

The Impact of the Transition to Outcomes-Based Teaching on University Preparedness in Mathematics in South Africa

Following the political changes of 1994 in South Africa, the decision was taken to replace the traditional skills-based education system at primary and secondary school level (Grades 1–12) with an outcomes-based education system (OBE). The implementation of the OBE system did not come without problems, giving rise to revised initiatives. The OBE approach, referred to as Curriculum 2005, was introduced into schools in 1998, for all learners in Grades 1–6 and progressively phased in after that. In 2002, the OBE system was put on hold for the two upper grades of these learners. Learners in these two grades reverted back to skills-based learning for their last three years of schooling, i.e. in Grades 10 – 12. The most senior of these learners that had been subjected to four years of OBE and another three years of the old system finished their schooling in 2005 and 2006 and entered university in 2006 and 2007. These groups are of interest. Students ahead of them had their full schooling in the old system and students two years younger were only subjected to OBE. These students are the “group in the middle”. This paper reports on what the impact is of the growing pains of such a new, inadequately planned education system on the mathematics preparedness of students entering university. This report will be extended in 2009 when the learners that have been fully subjected to the OBE system enter university.

Using Radar Charts with Qualitative Evaluation: Techniques to Assess Change in Blended Learning

When university academics implement changes in learning, such as introducing blended learning, it is conventional practice to examine and evaluate the impact of the resulting curriculum reform. Judging the worth and impact of an educational development is a complex task involving subtle differences in learning. Qualitative methods to explore these deep processes in learning include using interviews, observations and open-ended questionnaires targeting all stakeholders in the process, such as students, teachers, administration and technical staff. These evaluation tasks generate a mass of raw data that many faculty members in higher education are unaccustomed to analyzing. This article provides a framework using radar charts adapted from the field of organizational development. A modified six-zone radar chart was used to assess the extent of blended learning in order to compare changes in the learning environment. Data collection included interviews, classroom observations and electronic records generated during educational delivery over a 1-year period of time. A purposeful sample of online course data was collected by three participating universities in South Africa, Australia, and the United States.

Long-term retention of basic mathematical knowledge and skills with engineering students

This study focuses on the long-term retention of basic mathematical techniques in a first-year calculus course, involving a sample group of engineering students at the University of Pretoria. The study investigates which and how much of the basic mathematical knowledge and rote skills acquired in the first year of study is retained after a further two years of study. A quantitative and qualitative investigations show that, in general, there is a significant decline in performance over a two-year period. There are, however, areas in which students still performed reasonably well after the elapsed period or even showed improvement. The research is of diagnostic value in that it assists course designers in determining what basic mathematical skills and knowledge are retained after a period of two years in their teaching approach to and emphasis of different topics.

Is there Life after Modelling? Student Conceptions of Mathematics

We have been investigating university student conceptions of mathematics over a number of years, with the goal of enhancing student learning and professional development. We developed an open-ended survey of three questions, on “What is mathematics” and two questions about the role of mathematics in the students’ future. This questionnaire was completed by 1,200 undergraduate students of mathematics in Australia, the UK, Canada, South Africa, and Brunei. The sample included students ranging from those majoring in mathematics to those taking only one or two modules in mathematics. Responses were analysed starting from a previously-developed phenomenographic framework that required only minor modification, leading to an outcome space of four levels of conceptions about mathematics. We found that for many students modelling is fundamental to their conception of “What is mathematics?”. In a small number of students, we identified a broader conception of mathematics, that we have labelledLife. This describes a view of mathematics as a way of thinking about reality and as an integral part of life, and represents an ideal aim for university mathematics education.

Can you show you are a good lecturer

Measurement of the quality of teaching activities is becoming increasingly important since universities are rewarding performance in terms of promotion, awards and bonuses and research is no longer the only key performance indicator. Good teaching is not easy to identify and measure. This paper specifically deals with the issue of good teaching in mathematics at tertiary level–what good teaching is and how to measure it.

Implementing supplemental instruction for a large group in mathematics

The supplemental instruction (SI) programme has been well-established worldwide and the resulting success of the programme is indisputable. The University of Pretoria has decided on SI as the model to be used for addressing the underpreparedness of students entering the university, largely brought about by the changes in the curricula at secondary school level. The SI model was piloted in two courses, one in mathematics and another in chemistry, each consisting of more than a thousand students. This article addresses implementation issues of SI for such a large group of students in mathematics. It cautions would-be implementers to pitfalls and shortcomings of the SI model and suggests how the model could be adapted to answer the current needs. This article also shows that despite problems in strictly adhering to SI principles in the implementation of the programme, participants showed increased performance.

Evaluating the Success of a Science Academic Development Programme at a Research-intensive University

Academic development (AD) programmes for students not complying with the entrance requirements of mainstream programmes in science have been running at a number of universities in South Africa. In this study we contribute to the debate on criteria for the success of AD programmes, specifically in the context of research-intensive universities in South Africa. We identify five quantitative criteria for evaluating such a programme: retention, completion rate, migration to other faculties, comparison with other institutions and enrolment in graduate studies. Most of these criteria are relatively common in evaluating similar programmes whereas the extent of migration to other faculties is particular to this study. We illustrate the use of these criteria evaluating the BSc Four Year Programme at the University of Pretoria based on the group of students who registered for the programme in 2008. We found that around 15% of this group had completed their studies in the minimum time while the eventual completion rate of students getting degrees is expected to be in the order of 50%. The attrition rate across the four year science degree programme was high (43%), but the majority of students who terminated their studies did so during the first year. Of those still enrolled in their fourth year a high percentage of students remained in science-related programmes (79%). The fact that more than half of first graduates had enrolled for postgraduate programmes in 2012 is a criterion for success that is especially important for a research-intensive university.