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This article explores the power of language to either include or exclude certain groups of students from genuine opportunities for mathematical sense-making. The substantial increase worldwide in the number of students learning mathematics through a language other than their primary language makes this a particularly urgent issue. This paper focuses on the South African situation, where, because English is widely perceived as the language of opportunity, it is, by grade 4, overwhelmingly the chosen language of learning and teaching. The epistemological and pedagogical consequences of this choice are evidenced in the poor performance of the country's students on national and international assessments of mathematical proficiency. Drawing on research literature around language immersion education models and the extent to which these align with certain key principles of second language acquisition, this position paper motivates for a stronger and more sustained commitment to providing students, particularly those from marginalized and vulnerable communities, with opportunities for becoming both bilingual and biliterate. Empirical data from two South African grade 4 mathematics classrooms are used to illuminate aspects of the mathematical sense-making challenges students and their teachers face without such commitment. [ABSTRACT FROM AUTHOR]

In this paper, we describe how we came to use timed fluency activities, along with personal learner reflections on those activities, in our after-school maths club as a complementary research and developmental tool for assessing the changing levels of learners' mathematical proficiency over time. We use data from one case-study after-school maths club. Not only did the activities provide us as researchers, and mentors, with a quick way of tracking, evaluating, encouraging and valuing learner progress, but also with a mechanism for the learners to practise the fluency they were developing through other activities of the club. More importantly, the use of learner reflections assisted learner buy-in and reduced the stress related to such timed assessments. This alleviated, to some extent, our ethical unease with the use of such instruments. We have subsequently extended this research and development tool in all clubs that we run and continue to research their affect and effect in order to gain deeper understanding of the research and development opportunities enabled by such activities. [ABSTRACT FROM AUTHOR]

This paper is part of a broader study that draws on Wenger's (Wenger, E.: 1998, Communities of Practice: Learning, Meaning, and Identity, Cambridge University Press, New Work) social practice perspective to investigate teacher learning. The study extends Wenger's complex model of interrelated components of leaning (as meaning, practice, identity and community) to describe and explain teacher learning that occurs within a mathematics senior-phase in-service program that was stimulated by curriculum change. The study uses qualitative ethnography in which the researcher performs the dual role of both coordinator and researcher of the in-service practice. In a longitudinal study the phenomenon of confidence emerged in teachers' descriptions and explanations of their learning. In this paper I explore this phenomenon both empirically and theoretically. The extension of Wenger's (1998) theory to include the overarching and interacting component of confidence is embedded in and derived from data analysis of 10 teachers' learning, over a 2-year period, during a time of radical curriculum change. Since it would be incoherent within this framework to draw on psychological explanations of confidence I set out to explore confidence from within a social practice frame in a way that is grounded in data of the teachers in this study. The paper offers a concept of confidence in relation to teacher learning as 'learning as mastery', and confidence as both a product and a process of learning. Teachers can at once state their confidence as mathematics teachers, and their confidence to admit to what they do not know and still need to learn. It is argued that this is a primary condition for ongoing learning in a profession like mathematics teaching. In addition, the paper provides a critique of the applicability of Wenger's work to the context of teacher education and in particular highlights the absence of the notion of confidence within his work. [ABSTRACT FROM AUTHOR]

The article focuses on the notion of the zone of proximal development (ZPD) to explain five-year old girl Lila Rose's discovery of counting threes while using television remote. It cites the reference of Rose and her mother Mellony in conceptualisation of the ZPD as bi-directional and collaborative. It mentions several theories related to the emergence of ZPD in context to learning activities.