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Personal learning environments (PLEs) and personal learning networks (PLNs) are well-known concepts. A personal learning network cluster is a small group of people who regularly interact academically and whose PLNs have a non-empty intersection that includes all the other members. At university level PLN clusters form spontaneously among students and are known to last over an extended period of time. Little is known regarding the workings of these PLN clusters of students. The claim is that these PLN clusters are at the heart of student learning and are aligned with the current trend of a knowledge-pull community of learning. In this paper we investigate the activities and characteristics of PLN clusters in two different fields of study at a South African university, namely mathematics and computer science. We discuss the benefits that these clusters offer, investigate the mashup of activities and tools and we contrast experiences in the two fields of study. It is the commonalities rather than differences that are striking between the two groups of students. Although computer science students lean more towards digital communication, both groups impress with the pride they take in their PLN clusters and are vocal in describing the benefits that these clusters offer.

This article focuses on the unique contribution of the QT-clicker regarding formative and summative assessment in a large flipped first year statistics module. In this module, the flipped classroom as pedagogical model first substituted the traditional teaching model. QT-clickers were subsequently introduced to enable active and cooperative learning for face-to-face engagement inside the classroom. The various input capabilities of the QT-clicker, providing for the possibility of partial grade crediting, offer a distinguishing advantage. These clickers were initially only used for formative assessment, but soon extended to summative assessment. Two cohorts—2014 (no QT-clickers) and 2017 (with QT-clickers)—were compared. The intervention of using QT-clickers was evaluated along two lines: the pedagogical influence of the QT-clicker and the effect of partial grade crediting. Several general linear models (GLMs) were fitted to the data to investigate how QT-clicker use is related to the students’ examination performance. The outcome of the GLM models indicates that the association of higher examination marks with QT-clicker use holds for the 2017 cohort with and without partial credit. A qualitative component of the study reports on the student voice testifying to positive experience.

This article describes the authors' investigations into university student conceptions of mathematics over a number of years, with the goal of enhancing student learning and professional development. They 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. The authors found that for many students modelling is fundamental to their conception of 'What is mathematics?'. In a small number of students, the authors identified a broader conception of mathematics, that they have labelled Life. 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. [Author abstract]

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.

Internet education in mathematics is developing as a new mode of teaching with its own characteristics and possibilities, different from the traditional way of teaching. In a study presented in two parts, we attempt to capture the world of Internet teaching of undergraduate mathematics. In the first part of the study (Engelbrecht, J. and Harding, A.: 2004, \"Teaching undergraduate mathematics on the web 1: Technologies and taxonomy\"), we attempt to create some order in the huge number of activities that are available on the web with a graphical classification of the different types of web courses and discuss some of the technologies involved. In this, the second part of the study, we discuss attributes and implications of this mode of teaching/learning mathematics, also mentioning some of the benefits and concerns. Speculation about the future in such a fluid environment is both risky and fascinating but we nevertheless envisage some possible future trends. Research on this mode of teaching is sparse and open research questions are plentiful. We list possible research issues.

Research on undergradute mathematics education is a relatively new field that originated less than 20 years ago in the United States of America (USA), and that is known under the acronymn RUME (Research in Undergraduate Mathematics Education). In South Africa researchers in this field form a small but strong group that originated at the University of Pretoria. In this article a brief overview is firstly given on the international increase in interest and activities in this research field. Secondly the research field is viewed from a South African perspective. Examples of research projects are discussed, as well as the career path that leads to research in this field. Finally local activities and existing international ties are considered. The aim of this article is to give a South African overview of the research field and activities, hoping to motivate and stimulate research in this important and growing field.

Research on undergradute mathematics education is a relatively new field that originated less than 20 years ago in the United States of America (USA), and that is known under the acronymn RUME (Research in Undergraduate Mathematics Education). In South Africa researchers in this field form a small but strong group that originated at the University of Pretoria. In this article a brief overview is firstly given on the international increase in interest and activities in this research field. Secondly the research field is viewed from a South African perspective. Examples of research projects are discussed, as well as the career path that leads to research in this field. Finally local activities and existing international ties are considered. The aim of this article is to give a South African overview of the research field and activities, hoping to motivate and stimulate research in this important and growing field. Navorsing oor voorgraadse wiskundeonderrig is 'n betreklik nuwe veld wat sy beslag minder as 20 jaar gelede in die Verenigde State van Amerika (VSA) gekry het, en onder die akroniem RUME (Research on Undergraduate Mathematics Education) bekend staan. In Suid- Afrika vorm die navorsers in hierdie veld 'n klein, maar sterk groepie wat sy ontstaan aan die Universiteit van Pretoria gehad het. In die artikel word daar eerstens 'n kort oorsig oor die internasionale toename in belangstelling en aktiwiteite in hierdie navorsingsveld gegee. Tweedens word die navorsingveld vanuit 'n Suid-Afrikaanse perspektief beskou. Voorbeelde van navorsingsprojekte word bespreek, asook die beroepspad wat tot navorsing op die gebied lei. Ten slotte word plaaslike aktiwiteite en bestaande internasionale bande in oenskou geneem. Die doel van die artikel is om 'n Suid-Afrikaanse oorsig van die navorsingsveld en-aktiwiteite te bied in die hoop om navorsing oor hierdie belangrike en steeds uitbreiende veld te motiveer en te stimuleer.

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, the authors of this article 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. [Author abstract]

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 article reports on the impact of the growing pains of such a new, inadequately planned education system on the mathematics preparedness of students entering university. The measuring instrument was developed as part of the Alternative Admissions Research Project at the University of Cape Town. The sample population for the study consisted of students of the University of Pretoria, who registered for the first time from 2005-2007. In all but two topic areas student performances were on par with those in previous years. In geometry students outperformed their predecessors. However the areas of decline are of consequence in tertiary mathematics and for life skills in general. These were mathematical modelling and the topic of ratios and proportion. This report will be extended in 2009 when the learners that have been fully subjected to the OBE system enter university. [Author abstract, ed]

Internet education in mathematics is developing as a new mode of teaching with its own characteristics and possibilities, different from the traditional way of teaching. In a study presented in two parts, we attempt to capture the world of Internet teaching of undergraduate mathematics. In the first part of the study (Engelbrecht, J. and Harding, A.: 2004, 'Teaching undergraduate mathematics on the web 1: Technologies and taxonomy'), we attempt to create some order in the huge number of activities that are available on the web with a graphical classification of the different types of web courses and discuss some of the technologies involved. In this, the second part of the study, we discuss attributes and implications of this mode of teaching/learning mathematics, also mentioning some of the benefits and concerns. Speculation about the future in such a fluid environment is both risky and fascinating but we nevertheless envisage some possible future trends. Research on this mode of teaching is sparse and open research questions are plentiful. We list possible research issues.