Craig Pournara

Mathematics and science teacher education in South Africa: A review of research, policy and practice in times of change

Abstract The social, political and educational policy changes in South Africa provide a backdrop to this paper. Its authors report recent (2000–2006) research into the education of science and mathematics teachers in this country. International research trends provide a frame for the survey. Findings suggest that most of the research in both science and mathematics teacher education consists of small scale qualitative studies, generally conducted in urban contexts and among teachers participating in formal in-service programmes. In science teacher education, research emphases appear to have shifted towards process skill development, nature of science (NOS) and indigenous knowledge systems (IKS) while still acknowledging the importance of content knowledge. In mathematics teacher education research, there is a strong emphasis on the specificity of mathematical knowledge for mathematics teaching and teacher learning, with curriculum reform recently in focus in both mathematics and science teacher education literature. Gaps in the research have also been identified, including the education of primary mathematics and science teachers, teacher education for life sciences and the education of teachers in and for rural contexts. The authors argue for further research into mathematics and science teacher education and conclude with a research agenda focused on an examination of teacher education practices, investigations into primary teacher education, studies into life sciences teacher education and empirical research across diverse schooling contexts, with particular attention being paid to rural education.

Developing a new pre-service secondary mathematics teacher education programme: Principles for content selection and emergent tensions

The recent shift of teacher education into the higher education sector, coupled with the introduction of the Bachelor of Education degree has provided opportunity for innovation in the area of pre-service teacher education. In this article I discuss the conceptualisation, development and implementation of a new pre-service secondary mathematics teacher education programme at one university in South Africa. I outline two sets of principles for content selection – one set focused at the programme level and the other at the course level. I discuss four key issues that have emerged in the implementation of the programme and suggest ways of taking these forward.

Learner Participation in the Functions Discourse: A Focus on Asymptotes of the Hyperbola

The study investigated learners’ mathematical discourse on the hyperbola from a commognitive perspective, and focused on algebraic, graphic, and numeric representations of the hyperbola. Task-based interviews were conducted with five Grade 10 learners from a township school. Learners’ mathematical discourse was analysed by means of the Discourse Profile of the Hyperbola, which was adapted from the Arithmetic Discourse Profile of Ben-Yahuda et al. We found that, while learners’ graphs were mainly mathematically correct, their word use was colloquial and their interpretation of the mediators and their narratives were generally visual. Taken together, this suggests that their routines were ritualised. Learners’ tables of values did not show asymptotic behaviour yet they drew graphs showing two asymptotes. However, four learners tended to talk as if there were only one asymptote and they had difficulty in seeing the axes as asymptotes.

Designing Mathematics Tasks for the Professional Development of Teachers Who Teach Mathematics Students Aged 11–16 Years

This workshop focuses on identifying and developing tasks that are appropriate to use in professional development with mathematics teachers of 11 – 16 year olds who self-identify as being “non-specialists” in mathematics. The professional development of this group of teachers tends to get overlooked because of the focus on senior secondary mathematics and primary mathematics. Many non-specialist teachers of mathematics lack confidence in their knowledge of mathematics and yet they play a pivotal role in the mathematical education of students. There is much still to be learned about what constitutes appropriate professional development for them from both a mathematical perspective and in terms of pedagogy.

Defining the Problems of Mathematics Education, Getting the Description Right and Making It Count: Jill Adler’s Contribution and Beyond

In 2003, Jill Adler and Stephen Lerman published a chapter entitled “Getting the description right and making it count: Ethical practice in mathematics education research”. They use the context of mathematics education in southern Africa to illuminate and open up a conversation about the ethical, methodological and political challenges faced by researchers in this and other similar contexts. These challenges relate to defining what counts as a problem in mathematics education, making the research “count” both locally for the participants and more broadly for the mathematics education community, and producing descriptions that are “right” in the sense that they are rigorous, valid, comprehensive and respectful. In this chapter we review how Jill has responded to these challenges in her own research over the past 20 years. We ask: How does respect for practice, democracy, truth and persons play out in her research descriptions? Are they right? For whom and how do they come to count? We also draw on our own research histories of working with Jill to reflect on how her research practice has impacted the postgraduate supervision space.

Talking Time, Seeing Time: The Importance of Attending to Time in Financial Mathematics

Through analysing a critical incident where a small group of pre-service secondary mathematics teachers work together on an annuities problem, we gain insight into the ways in which students make use of timelines and attend to time in their talk. Drawing on Lave and Wengers notion of transparency, I argue that it was only when time became visible for the students, that they were able to resolve the impasse they had reached in working with the timeline. I propose the notion of pre-visible to describe the ways in which a newcomer makes use of a resource in an intuitive way when s/he still lacks awareness of how the resource is typically used in the practice. I discuss five issues pertaining to the use of timelines in working with annuities: the changing role of the timeline; attending to discrete points in time vs intervals; explicit attention to time on the timeline; explicit attention to time in students’ talk; and potential problems associated with the use of month-names on a timeline. I make recommendations for teaching based on these findings.

Pre-school children's performance on repeat-pattern tasks

AbstractThis study explored the performance of eight pre-school children on a range of tasks involving repeat patterns. Task-based interviews were conducted where children were required to produce their own pattern, to copy and extend a given pattern, and to complete missing parts of a pattern. The findings show that most children were able to copy and extend a repeat pattern, but few could produce their own repeat pattern. While most children tended to focus on ‘what comes next’, some children paid attention to pattern structure, but were not able to isolate the pattern element. Evidence is provided of inconsistent performance by individual children across tasks, which provides new insights into childrens developing sense of repeat patterns.