Jill Adler

Between Languages and Discourses: Language Practices in Primary Multilingual Mathematics Classrooms in South Africa.

In this paper we draw on two research projects in South Africa to describe and discuss the language practices of teachers in primary multilingual mathematics classrooms. We focus particularly on code-switching – moving across languages and discourses. We situate the paper in the policy and practice environment of post-apartheid South African education in which code-switching is encouraged. Through our descriptions and discussion, we argue that while at a general political and pedagogical level it makes sense for teachers to encourage and use code-switching as a learning and teaching resource, this is not a straight forward matter. We argue that different English language infrastructures present primary mathematics teachers with different challenges for communicating mathematics. Furthermore, we show how the movement across mathematical discourses relates to movement between languages in classroom communication.

Teachers as Researchers in Mathematics Education

This paper explores the ways in which teaching, learning and research are conceptualised by various members of the mathematics education community and makes an argument for research-like activities by teachers as a means to professional development. Such development is viewed as a prerequisite for changes in the processes and quality of mathematics education for school students. Examples from Australia and South Africa, two different ex-colonial contexts undergoing rapid social change, are used to illustrate the need for change and the importance of active participation of teachers in research activities associated with their professional practice.

A Participatory-Inquiry Approach And The Mediation Of Mathematical Knowledge In A Multilingual Classroom

This article describes and analyses a short teaching episode in a multilingual secondary mathematics classroom in South Africa where the teacher is using a participatory-inquiry approach. The episode is used to illuminate the general claim that such an approach, because of the particular communicative demands it places on teachers and learners, can create specific dilemmas of mediation. Teachers are often aware of dilemmas they face. However, what can be obscured is how a participatory-inquiry approach can inadvertently constrain mediation of mathematical activity and access to mathematical knowledge.

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.

Getting the Description Right and Making It Count: Ethical Practice in Mathematics Education Research

Building on the work on ethics in educational research in recent publications, we present a framework for ethical practice in mathematics education research. In particular, we discuss what are the implications of claiming or denying a particular piece of research as acceptable within the community. We argue that researchers must be aware for whom they advocate, thus making it count. We present a map with which researchers should engage the ethics of their practice, and we suggest that they must consider whether they are getting the description right.

Modelling Teaching in Mathematics Teacher Education and the Constitution of Mathematics for Teaching

In this chapter, we discuss research that investigated what, how, and with what possible effects, mathematical knowledge and related practices are constituted in and across a range of programmes, across diverse teacher training institutions in South Africa. Our study includes three cases from three different teacher education sites where teachers were enrolled in in-service upgrading programmes. Our focus is on what comes to be the content of mathematics for teaching; that is, the mathematical content and practices offered in these courses, and how this occurs. In the chapter, we describe our observations and the analytic resources recruited to that end, building on our previous work. We argue that three different orientations to learning mathematics for teaching are exhibited across our cases and present different opportunities for learning mathematics in and for teaching.

An Investigation into Mathematics for Teaching: Insights from a case

Abstract This paper reports on a study that investigated the kind of mathematical work a specific teacher does as he goes about his teaching. The study involved the pedagogic practice of one teacher teaching linear functions to his class of grade 10 learners in a secondary school in Gauteng, South Africa. Drawing on a theory of pedagogic discourse, we worked from the assumption that pedagogic judgement is a necessary element of pedagogic communication, operationalised through evaluation (in the broad sense), and requiring appeals to some or other ground to substantiate meaning. We studied ‘evaluative events’ in this practice, and the kinds of appeals made by the teacher over time. We argue that these provide for a systematic description of mathematics for teaching in use in this practice. Implications for developing our understanding of the specificity of mathematics used in teaching are drawn, as well as for mathematics teacher education in a context of curriculum change.

A Framework for Describing Mathematics Discourse in Instruction and Interpreting Differences in Teaching

We describe and use an analytical framework to document mathematics discourse in instruction (MDI), and interpret differences in mathematics teaching. MDI is characterised by four interacting components in the teaching of a mathematics lesson: exemplification (occurring through a sequence of examples and related tasks), explanatory talk (talk that names and legitimates what comes to count as mathematics in a particular lesson), learner participation (interaction between teacher and learners and amongst learners) and the object of learning (the lesson goal). MDI is grounded empirically in mathematics teaching practices in South Africa, and theoretically in sociocultural theoretical resources. The MDI framework allows for nuanced descriptions of mathematics teaching and interpretations of differences in what is mathematically made available to learn.

Mathematics and science education research, policy and practice in South Africa: What are the relationships?

Abstract In this paper, a review of journal articles containing South African research in mathematics and science education in the 2000–2006 period is undertaken, and used to identify significant clusters of research interest on the one hand and areas of under-representation of research on the other. In mathematics education, significant clusters were found relating to: questions of relevance, language issues, mathematics teaching and learning, and mathematics teacher education. In science education, specific clusters of research focused on: tertiary science teaching and learning, school level science teaching and learning, and relevance issues focused on the nature of science and indigenous knowledge systems. Our classification of articles highlighted the paucity of research at the primary level, in rural contexts, and dealing with issues related to language use in multilingual classrooms. Our overview of articles also provided examples of research that linked the issues arising within specific clusters, and considered the consequences of these linked issues for teaching and learning. We conclude by noting examples of research findings within our review that have impacted on policy and practice, and point also to areas where further research appears necessary.

Professionalism in process: mathematics teacher as researcher from a South African perspective

Abstract The ‘teacher as researcher’ movement highlights the concept of ‘teacher as researcher’ and claims a key role for teachers in the production of knowledge about teaching. It constitutes teaching as an inquiring process, and as a powerful context and practice for professional development. This paper explores the potential of the teacher as researcher movement for the professional development of mathematics teachers in South Africa. It argues that themovement has particular historical roots in contexts of professionalism very different from South Africa. It proposes that the notion ‘teacher as inquirer’ is more inclusive of the very diverse teaching conditions in South Africa. It also argues that such a conception of the teacher could contribute to a more general theorisation of the teacher as researcher movement.