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This paper explores Grade R teacher expressions of themselves as teachers of numeracy, and as teachers working in the transition phase of schooling, after their participation in a research-informed numeracy-focused professional development (PD) intervention. The Early Number Fun (ENF) programme had 33 teachers from 17 Eastern Cape schools participating monthly over 18 months. Inclusion of Grade R to schooling is relatively new following policy changes in Early Childhood Development. In-service support tends to be subsumed within the Foundation Phase without attention to the specialised nature of Grade R that emphasises learning through play. ENF focused on the development of specialised teacher knowledge to support the development of early number sense through play, particularly with conceptual manipulatives. Data sources include three pre-, during, and post-PD questionnaires. Findings reveal that participation in ENF, and access to multiple research informed numeracy resources, supported teachers in their relationship with numeracy and the teaching thereof. Questionnaire responses indicate greater confidence in themselves as knowledgeable teachers of numeracy and that belonging to the ENF community supported navigation of positive professional identities within the mixed messages of policy. The findings contribute to the community-supported field of Grade R PD research and early numeracy teaching and learning. In concluding we discuss implications of this research for Grade R PD and for policy. [ABSTRACT FROM AUTHOR]

Reflective practice is a crucial element of professional growth that is gaining in popularity in teacher education, yet the ability to reflect is a skill that is neither natural nor easy to develop. This paper reports on an investigation that sought to establish if pre-service teachers at a South African university – in the process of learning to reflect on practice through analysing video-recorded lessons – reflected differently when reflecting on their own practice from the way they reflected on the practice of other teachers. Pre-service teachers were introduced to the Six Lens Framework as a tool to aid reflection on mathematics teaching. The authors compared two sets of reflections written by four pre-service teachers (PSTs) who participated in the study. One set was based on a video-recorded lesson of another teacher's practice while the other was based on a video-recording of their own practice. The study found that the PSTs' reflections in both cases were generally at the lowest level of the reflection spectrum. They mostly described classroom events rather than analysing the lessons to provide explanation suggestions, or reflectivity. We found, however, that all four PSTs reflected at substantially greater length on their own lessons than on those of other teachers. Furthermore, three of the four teachers' reflections on their own practice focused on mathematical rather than general aspects and provided more suggestions for improvement than their reflections on the practice of other teachers. [ABSTRACT FROM AUTHOR]

This special issue comprises seven studies and a commentary piece, which relate to various aspects of rituals and the "ritual-exploration" dyad in learning, teaching and learning-to-teach mathematics. The theme of the special issue arose from Sfard and Lavie's (Cognition and Instruction, 23(2), 237–309, 2005) "ritual" vs. "explorative" dyad, on which a Working Session was held during the PME conference in 2016. Three central themes are addressed in the papers of this special issue: (1) the logic of ritual, and why rituals are so persistent in mathematics classrooms; (2) the co-existence of rituals and explorations, including the question of whether rituals and explorations are a binary or a continuum; and (3) alternative theoretical conceptualisations of the ritual-exploration dyad, focusing in particular on what can be learned about rituals from social and critical theory, as well as socio-linguistics. In this introduction, we first give an overview of each of the papers and its unique contribution. We then synthesise the answers given by the papers to the three themes described above. [ABSTRACT FROM AUTHOR]

This paper illuminates challenges confronting teachers and students at the literacy/numeracy interface in contexts where students have not developed sufficient English language proficiency to be learning mathematics through English but, due to socio-politically and economically driven perceptions are being taught in English. We analyse transcript data of classroom talk in a South African grade 4 mathematics lesson on fractions. Together with interview data, the lesson data highlight some of the consequences students' diminished access to their home language appear to have on their access to mathematical meaning-making. [ABSTRACT FROM AUTHOR]

From a Marxian/Vygotskian perspective, learning is social in origin and it happens in the presence of others that are more knowledgeable. Extending this view to the learning of mathematics, such learning also becomes inseparable from the presence of others (people and artefacts). Researchers over decades have studied different interactions to see how such learning with others occurs, what is the role of the (more knowledgeable) other, and if at all this role alternates between the participants. In this paper, we looked at a 5-year-old's (Lila) interaction with her mother (Mellony) and a television remote control as Lila attempted to count in threes using the three by three physical layout of the numbered buttons 1-9 on the remote control. We specifically looked at the emergence of the Zone of Proximal Development (ZPD) as Lila's attention was caught by the properties of the remote control and by her mother's questions. We also pay attention to how the role of the more knowledgeable other alternates among the participants. Our findings suggest that Lila, at times, used resources provided by the physical properties of the remote control and sometimes, used resources provided by Mellony to think about the task of counting in threes. In Lila's interaction, we interpreted a multi-directional ZPD as the role of the more knowledgeable other alternated between Mellony, Lila and the remote control. [ABSTRACT FROM AUTHOR]

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 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 , 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. [ABSTRACT FROM AUTHOR]

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]

The article "Exploratory mathematics talk in a second language: a sociolinguistic perspective", written by Sally-Ann Robertson and Mellony Graven, was originally published electronically on the publisher's internet portal (currently SpringerLink) on 16 August 2018 without open access. [ABSTRACT FROM AUTHOR]

The article "Rituals and explorations in mathematical teaching and learning: introduction to the special issue", written by Einat Heyd-Metzuyanim and Mellony Graven, was originally published electronically on the publisher's internet portal (currently SpringerLink) on 21 March 2019 without open access. [ABSTRACT FROM AUTHOR]