Hamsa Venkat

Analyzing coherence for conceptual learning in a Grade 2 numeracy lesson

Abstract National and international evaluations of numeracy knowledge have shown that numeracy levels in South Africa are below the competencies specified in the curriculum. Within the broader context of ongoing poor performance in numeracy, a longitudinal research and development project – the Wits Maths Connect – Primary project (WMC–P) has been launched aimed at improving the teaching and learning of primary mathematics. As part of the baseline data collected for this project, the project team observed and videotaped a single numeracy lesson across the Grade 2 classes in the ten project schools, with a view to gaining insights about the nature of teaching and learning, and the classroom contexts of these activities. The analysis has been framed by the Systemic Functional Linguistics concept of coherence and the Variation Theory concept of structured variation. This paper presents evidence to illustrate, firstly, poor coherence in and across pedagogic communication and activities and secondly, random se...

Emerging pedagogic agendas in the teaching of Mathematical Literacy

Abstract This paper focuses on an emergent spectrum of pedagogic agendas in the teaching of mathematical literacy- a new subject in the Further Education and Training (FET) band—currently being implemented in schools in grades 10 & 11. It is argued that a range of pedagogic spaces are opened up as a result of the ‘newness’ of the subject. Thus we argue that the absence of precedents of what pedagogy and assessment should be like, have enabled a wide spectrum of interpretation of both the curriculum aims and the related pedagogic agendas for both individual lessons and lesson planning across the band. In this paper, we focus on 3 aspects—the emergence of the spectrum of agendas from our empirical data linked to Bernsteins theory, a delineation of the agendas themselves and a discussion of the different pedagogical issues arising within each agenda. We believe that the conceptualization of a spectrum provides a useful tool for teachers and researchers for thinking about, and investigating, the vast range of mathematical literacy agendas present in lessons taught as a result of current curriculum implementation in Grade 10 and Grade 11. The paper draws on the work of Bernstein (1982, 1996) as a framework for analysis.

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.

Exploring the nature and coherence of mathematical work in South African Mathematical Literacy classrooms

In this paper the mathematical working in a series of ‘litter project’ lessons from a South African Mathematical Literacy class is analysed in terms of Kilpatrick, Swafford and Findells (2001) five strands of mathematical proficiency. The analysis points to evidence of the life skills-oriented Mathematical Literacy frame opening up opportunities for engagement across aspects of all five strands, but shows that the emphases differ from the intra-mathematical emphases within the strands. I argue that this is due to the lack of centrality in the Mathematical Literacy frame of the ‘mathematical terrain’. The shifting of competence to the bridge between mathematics and everyday situations and problems retains mathematical coherence and connectedness. Both of these aspects are grounded in the mathematical tools and thinking that are needed to make sense of the everyday situation, rather than the more intra-mathematical connections and coherence that appear to be in focus within the strands of mathematical proficiency.

Primary Teachers' Experiences Relating to the Administration Processes of High-stakes Testing: The Case of Mathematics Annual National Assessments

In this paper we highlight teacher experiences of the administration of high-stakes testing, in particular, of the 2012 Annual National Assessments (ANAs). The exploration is based on data gathered across two primary numeracy teacher development projects in the Eastern Cape and Gauteng in the form of open-ended questionnaires designed to elicit teacher experiences of the 2012 Numeracy ANAs (at Grades 1–3) and Mathematics ANAs (Grades 4–6). Fifty-four teachers across 21 schools (including fee-paying and non-fee-paying schools) completed the questionnaire. Using a grounded approach to the analysis of data, we note that, while teachers state support for the purpose of the ANAs ,several concerns emerge in relation to their administration. These concerns fall largely into two categories: concern for learner experiences and concern for the implications of the administration processes (including the use of exemplars and the marking process) for teacher practices. The primary purpose of the paper is to raise awareness of the need for further discussion and research into the way in which ANAs result in possible unintended consequences.

Positions and purposes for contextualisation in mathematics education in South Africa

Abstract In this article, papers reviewed in the position paper (Venkat, Adler, Rollnick, Setati & Vhurumuku, 2009) relating to questions of contextualisation in mathematics education are analysed and used to develop a tentative framework consisting of two aspects. The first aspect relates to the position taken on contextualisation with three categories identified (‘advocacy’, ‘advocacy but…’ and ‘does not advocate’). The second aspect relates to the underlying purpose for which contextualisation is used with four key motivations emerging within the sample (‘mathematical’, ‘utilitarian’, ‘cultural affirmation’ and ‘critical democratic citizenship’). Taken together, the two aspects can be combined into a tentative framework which can be used as an analytical tool that allows for an initial dis-aggregation of the broader literature in the area of contextualisation in mathematics education, as well as for thinking about the design and use of contextualised tasks.

Pre-service Teacher Learning for Mathematical Modelling

Evidence has shown that teachers in South Africa often lack the capacity to both connect their mathematics to real-life contexts and struggle to see the internal connections between mathematical concepts. Situating our argument within the ‘critical competence’ and ‘utility’ perspectives, we focus on pre-service teachers’ initial mathematical modelling competencies in a professional development course. Using the notion of modelling competencies with specific reference to the didactic modelling process, we argue that the pre-service teachers’ initial mathematical modelling competencies are at early stages of development.

Primary Teachers’ Semiotic Praxis: Windows into the Handling of Division Tasks

The teaching of division is a complex task: division is difficult to teach in a connected and coherent way, given the diversity of models of division, and differences in their associated actions and utterances. This chapter focuses on the signs produced by teachers in their attempts to explain division. The signs produced follow from unifications between signifiers and signifieds located within what we are calling signification pathways. Our focus is on signification pathways that are co-produced by teachers and learners, and endorsed by the teacher. The data presented in this chapter exemplify categories within an emerging analytical framework of signification pathways when teaching division, which vary in the coherence of the signs that are involved. In this chapter we consider the possibilities and constraints of these signification pathways in relation to the semiotic system related to division from a mathematical interpretant perspective. The analysis makes visible limitations, ambiguity and incoherence across the signification pathways. The conclusion examines how the production of signs and the connection of signs in the signification pathway may lead to certain meanings about division that the teacher endorses as valuable in the teaching of division.

Professional Development Models for Whole Number Arithmetic in Primary Mathematics Teacher Education: A Cross-Cultural Overview

The goal of the chapter is to explore and discuss teacher education in different parts of the world and to emphasize the commonalities and differences not only in the panellists’ countries, but in a broad perspective. By looking at differences in the parts and processes of different educational systems, we can learn from each other and develop a more integrated perspective on teacher education. Most research studies in the field of primary mathematics teacher education at the international level focus on curricula within teacher education and on the knowledge a primary teacher needs for teaching well. WNA provides a context for developing understandings and constructing arguments that adhere to the practices and norms of more advanced mathematics. Two key issues frame the chapter: ways to increasing and deepening teachers’ mathematical understandings and developing tools that support their mathematics teaching. Examples from seven countries are accompanied by brief information about the organization of primary teacher education in each of them.

Connecting Whole Number Arithmetic Foundations to Other Parts of Mathematics: Structure and Structuring Activity

In this chapter, we attend to presentation/discussion of structure and structuring activities as two key routes through which whole number arithmetic can be connected to other mathematical content areas and to central mathematical processes and products like defining/definitions and generalizing/generalization. In the body of the chapter, we use literature to distinguish between approaches focused more on the presentation of structure and those oriented towards structuring activities, before presenting an overview and discussion of studies geared more towards one or other of these approaches. We incorporate studies that have been directed towards both students’ mathematical learning and mathematical (and pedagogical) teacher learning and conclude with commentary on biases towards structure-based or structuring activity-based approaches across these contexts. Our argument is that both approaches show promise for building towards stronger connections between whole number arithmetic and other mathematical areas, with a number of examples in each category included. Given the evidence of difficulties for so many children in many parts of the world in moving beyond the terrain of whole number, our findings suggest that attention to structure and structuring can provide important routes for bridging this chasm.