Personal learning network clusters : a comparison between mathematics and computer science students

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.http://www.ifets.infoam201

Interventions to improve teaching and learning in first year mathematics courses

In keeping with the national mandate of increasing graduates in the sciences in South Africa, a concerted effort in improving the first year experience becomes imperative. First year mathematics courses commonly provide the base knowledge necessary for progression in different degree programmes at university. Success in mathematics courses influences throughputs, retention and graduation rates of various degree programmes. Due to the highly complex and integrated nature of issues pertaining to improving teaching and learning in these courses, a multi-dimensional approach was conceptualized and implemented at the University of Pretoria. This paper reports on the development of a coherent framework, and the process and strategy for improving student success through a number of teaching and learning interventions in the first year mathematics courses, addressing the different dimensions of the framework. The process embarked upon resulted in a coherent, resource-focused approach with a replicable model for similar contexts.University of Pretoria.http://www.tandfonline.com/loi/tmes202016-08-30hb201

Strategies involved in teaching large groups of undergraduate students

The study is set at a large, research-intensive university in South Africa. The teaching model in mathematics for entry level students is that of large group teaching, with up to five hundred students per group. The principles required for the success of large group teaching in mathematics, as identified by the teachers involved, are classified hierarchically into two broad categories. The first category concerns organisational principles and the second involves social principles based on the human element. The study shows that organisational fluency such as suitable and well-equipped venues, and the skilful use of technology is essential. What also emerges is the importance of ‘soft’ skills such as knowledge of large group thinking, and the ability to deploy strategies to build a group identity and group coherence, as well as for making the individual feel recognised. The recommendation is for these skills to be developed to cultivate an environment within which large group learning is optimised.http://www.journals.co.za/content/journal/jedsam2018Mathematics and Applied MathematicsScience, Mathematics and Technology Educatio

Does the chalkboard still hold its own against modern technology in teaching mathematics? A case study

The purpose of this case study is to explore the integration of technology into teaching at a mathematics department at a large South African University. Both quantitative and qualitative data were collected from staff teaching undergraduate mathematics. The study shows that many staff members feel that chalkboards are still more suitable than technology for teaching mathematics. This finding supports the idea of a strong subject culture. Age does not emerge as a determinant for preference of either technology or the chalkboard, although gender and academic qualifications do. Subject culture is strongly rooted under the male members of staff, while female staff members feel more positive towards the use of technology in teaching. Use of chalkboards has decreased significantly over the past 10 years, while the use of modern technologies has increased accordingly. Teaching of large groups has necessitated the use of technology in the classroom. Despite the strong subject culture, a shift in attitude towards technology use in teaching is noticed and there is a definite trend of moving towards using new technologies.http://www.tandfonline.com/loi/tmes202019-02-08hj2019Mathematics and Applied MathematicsScience, Mathematics and Technology Educatio

The use of personal response systems to renegotiate the didactical contract in tertiary mathematics education

Challenges experienced by first-year students transitioning from secondary to tertiary mathematics education are examined through the lens of the didactical contract. The didactical contract describes the expectations of both lecturer and students about their mutual obligations towards teaching and learning. First-year students’ beliefs about the nature of mathematics and mathematics teaching/learning need to be challenged to renegotiate the didactical contract at tertiary level. The study focuses on how to elicit and confront transitioning students’ beliefs in order to support their learning and influence a shift in the didactical contract. A Likert scale questionnaire was deployed at the beginning of students’ first year to gauge their beliefs about mathematics and mathematics teaching/learning and redeployed near the end of the first semester (or term) to observe possible changes in their beliefs and hence the didactical contract. The intervention consisted of personal response system (PRS) sessions regularly incorporated into the traditional transmission mode lecture to flip the classroom and create a student-centred learning environment, aimed at influencing students’ beliefs in order to make them aware of their own learning and their responsibility for learning. Questionnaire data were quantified and compared for the before and after surveys. There is evidence of a shift towards students taking ownership of their learning and a renegotiation of the didactical contract. Qualitative data generated by focus group interviews confirm the role of the PRS sessions in influencing student beliefs and the didactical contract.https://journals.co.za/journal/newgenam2023Science, Mathematics and Technology Educatio

Student enrichment in mathematics : a case study with first year university students

This paper presents an enrichment case study to showcase a possible avenue for attending to the needs of academically strong mathematics students. We report on a group of university students who were presented with the opportunity of exploring a specific first year mathematics topic deeper, using an inquiry-based learning approach as part of an enrichment programme. Following the intervention, students completed a questionnaire and a few were interviewed to establish their experiences of the enrichment programme. We discuss the successes and pitfalls of the intervention and report on the impact it had on the participants.http://www.tandfonline.com/loi/tmes20hj2017Mathematics and Applied MathematicsScience, Mathematics and Technology Educatio

Review of a predator-prey model with two limit cycles

It is well-known that the Lotka–Volterra predator-prey model has a family of periodic orbits, but does not possess limit cycles and therefore the model is said to be structurally unstable. The Lotka–Volterra model is a special case of a much larger group namely the quadratic population models and it can be shown that none of them can produce limit cycles. The surprising finding is that by combining two quadratic models a quadratic population model with two limit cycles is uncovered. Although the model looks simple at first glance it provides a rich source of dynamics and deserves attention. In this paper, we revisit a model that has its origin in the work of Dubois and Closset. A set of two quadratic population models interact as piecewise defined differential equations. The model has been discussed by Ren Yongtai and Han Li, cryptically written and showing some linguistic and typographical errors, but providing an excellent vehicle for developing skills in mathematical modelling, differential equations and technology for the young researcher. We explore the model in clearer detail and supplement the theory with rich graphical illustration. The paper has the purpose of providing an example of how a young researcher, such as a postgraduate student in biomathematics, can expand on an existing model by making use of current technology.http://www.tandfonline.com/loi/tmes202019-08-20hj2018Mathematics and Applied Mathematic

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.http://www.tandfonline.com/loi/tmes20nf201

Cause–effect analysis : improvement of a first year engineering students’ calculus teaching model

This study focuses on the mathematics department at a South African university and in particular on teaching of calculus to first year engineering students. The paper reports on a cause-effect analysis, often used for business improvement. The cause-effect analysis indicates that there are many factors that impact on secondary school teaching of mathematics, factors that the tertiary sector has no control over. The analysis also indicates the undesirable issues that are at the root of impeding success in the calculus module. Most important is that students are not encouraged to become independent thinkers from an early age. This triggers problems in follow up courses where students are expected to have learned to deal with the work load and understanding of certain concepts. A new model was designed to lessen the impact of these undesirable issues.http://www.tandfonline.com/loi/tmes202017-06-30hb2016Mathematics and Applied Mathematic