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Background: The study on which this article is based investigated the Mathematics Knowledge for Teaching (MKfT) that a well experienced Grade 2 teacher utilized when teaching counting. Aim: In this paper we share excerpts from one of the lessons of this Grade 2 teacher, which we analyzed to illuminate the various domains of MKfT and their interconnectedness in the teaching of counting. Setting: The research was conducted in a former Model C school in the Eastern Cape province of South Africa. Method: Using a case study methodology, 15 Grade 2 mathematics lessons were observed, video recorded and transcribed. Two formal interviews based on two selected video-recorded lessons were conducted to understand this teacher's practice. The data were analysed using Deborah Ball and colleagues' MKfT framework. Results: The study found that Foundation Phase mathematics teaching requires the knowledge and tactful employment of all six knowledge domains as described in the work of Ball and colleagues. The Knowledge of Content and Teaching (KCT) domain, was found to be essential in teaching counting in Grade 2. The other five domains supported and informed the KCT domain. Conclusion: We suggest from the insights gained here that research examining the MKfT that competent teachers draw on in teaching Foundation Phase mathematics could assist in developing curricula for in-service and pre-service teacher education programs.

Background: The underperformance of South African learners in literacy and numeracy is a source of concern, especially when learners move from Grade 3 to Grade 4. Aim: This article reflects on the reading and comprehension challenges of English language learners (ELLs) in the Grade 4 2013 mathematics Annual National Assessments (ANAs). Setting: The study took place in two primary schools that served relatively less affluent sectors of the community in the Eastern Cape. Learners were IsiXhosa speakers learning mathematics in English. Methods: A sample of 26 out of 106 isiXhosa-speaking Grade 4 learners in the two schools participated in task-based interviews (focused on ANA questions) in which reading and linguistic mediation was provided. While the broader study (from which this article derives) revealed learners' challenges in reading, comprehension, transformation and process skills, here the focus is on findings related to reading and comprehension skills, which are foundational to accessing written assessment items. Results: Interview excerpts show the negative influence poor English reading and comprehension skills had on learner access to questions and their subsequent performance in the ANA. Conclusion: The article challenges the validity of assessing ELLs' mathematical competence in English ANAs and draws implications for strengthening ELLs' language and mathematical proficiency in the Foundation Phase

In this paper, we share the results of the piloting of national diagnostic assessments for strategic calculation with Grade 3 learners in South Africa. The diagnostic assessment pilot intervention was focused on promoting strategic use of calculation strategies and aimed to move learners on from the concrete one-to-one counting methods that persist in this grade and into higher grades. Working with a broader team of mathematics education specialists, including international leaders in the field and department of education representatives, we designed a series of assessments that focus on key calculation strategies such as bridging through ten. Each assessment, comprised a pre- and repeat post-assessment, was accompanied by interim lesson starters for teacher use in eight 10-min mental mathematics sessions. These were designed to develop learner fluency in each of the focal strategies and related skills. The pre- and post-assessments allow teachers to track improvement in student learning. The pilot focused on the "bridging through ten" strategy in seven classes across the Eastern Cape and Gauteng provinces. Positive results indicate that the format of these assessments paired with the lesson starters is potentially useful for broader national trialling and implementation. This work feeds into the need for diagnostic assessments that inform teaching focused on strategic efficiency rather than simply accepting correct answers produced through highly inefficient methods.

This article addresses the question: Why teachers of mathematics have yet to 'take up' progressive roles? Drawing on the philosophy of critical realism and its methodological equivalent, social realism, we analyse interview and observation data of four grade 3 teachers, with the view to identifying the mechanisms conditioning the expression of teachers' identities. In so doing, we show how post-apartheid changes in systemic roles of teachers create contradictory tensions for teachers as these bring their own mathematical learning and teaching experiences into contradiction with the new post-apartheid roles they are mandated to enact. We examine how this contradiction, together with beliefs about mathematics, pedagogy and learners, is expressed in the teaching of grade 3 mathematics. We maintain that the complementarity between teachers' beliefs and old systemic roles provides an explanation for why teachers of grade 3 mathematics have yet to 'take-up' progressive roles. The implications point to the need for teacher development that creates enablers that lead to changes in classroom practices that align with policy-designated, progressive roles in teaching mathematics.

In this article we describe the design process for an after-school Grade 3 mathematics club, based on our experiences running a pilot club in a 2011 research and development project. Working from a sociocultural perspective, we show the progression from an initial multifaceted design to a much simpler, more learner-centred design that speaks directly to our research foci and one which is based on empirical evidence. Our experiences have brought to light the entwined and dialectical nature of the data collection and design processes and the significance of the post-club reflection sessions as a powerful data collection instrument for planning the club sessions. Furthermore, we identify and shape the zone of proximal development for the purposes of our club as the critical design concept for each club session for each learner.

The reported research attempts to trace possible reasons for third grade learners' limited progress in numeracy in a low socioeconomic status (SES) South African context. This is done through two lenses, both stemming from Sfard's commognitive (The term "commognition" has been offered by Sfard (2008) as an amalgam of "cognition" and "communication," thus expressing the unity of these concepts. Since its original appearance, some authors (including Sfard herself) have preferred using the word "communicational" to describe Sfard's framework. We chose to stick with "commognitive" because we believe it clearly points to the specific theoretical stance presented in Sfard (2008), whereas "communicational" might point to many other theories or frameworks that have something to do with human communication.) framework. One lens aims to analyze two learners' (Mina and Ronaldo (all names are pseudonyms)) mathematical and identity discourse both in one-on-one interviews and in a small group "math club" lesson led by the second author. The other examines the mathematical milieu in which these learners have participated through the analysis of a school mathematics lesson which exemplifies prevalent instructional practices in this milieu. Relying on the distinction between ritual and explorative participation, we show that while Mina was acting in an extremely ritualized manner, Ronaldo was more explorative in his actions. However, the milieu, as seen in the school lesson, encouraged almost exclusively ritual participation. Thus, while Mina was identified as a good student, Ronaldo was identified as an outcast or "troublemaker." We conclude by drawing implications to the tenacious nature of rituals in the mathematics classroom and the effects that these rituals may have on students' identities.

This article discusses the growing attention and research activity surrounding early grade mathematics (EGM) in South Africa and Malawi. The introduction of curriculum reforms and policy-linked interventions, such as the Teaching Mathematics for Understanding model and the Primary Teacher Education initiative, have led to increased research in this field. The article highlights the importance of foundational understandings of mathematics in addressing low performance in the subject. It also examines different approaches to EGM research, including large-scale interventions and projects that engage with the mathematics education literature base. The article concludes by emphasizing the need for ongoing attention to both larger-scale and smaller-scale intervention studies in order to improve mathematical outcomes. [Extracted from the article]

This paper focuses on patterns of post-apartheid learner migration between schools previously segregated along racial lines. South Africa’s shift away from cultural and linguistic isolationism and the ways this has impacted educational arrangements in this country, most particularly in relation to the language of learning and teaching, affects mathematics teaching and learning in complex ways. We focus on how changes in the demographic make-up of some schools have affected the teaching and learning of mathematics by drawing on two case study vignettes in historically different schools. The vignettes are used to illuminate our discussion and to raise key questions requiring further research. [ABSTRACT FROM PUBLISHER]