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The connections between citizenship education and mathematics education have been the focus of theoretical development and attention by educators interested in issues of justice, equity, power, criticality, and citizen engagement with societal issues, across schools, universities, and adult education levels. In this survey article, we contribute to new knowledge in the field by identifying and describing three interconnected layers of influence on the praxis of teaching and learning: (1) perspectives from citizenship education and mathematics education (e.g., kinds of citizenship, critical thinking in mathematics education); (2) institutional factors (e.g., policy, curricula, implementation within education systems); and (3) emerging influences (e.g., changing skill demands, innovations from communities of practice). In exploring the connections between citizenship education and mathematics education, we go beyond extant theory development and point to influences such as global disruptions, societal changes, systemic structures at the national and local levels, messaging in the media, and the role of teachers and learners. The holistic analysis of these influences enables identification of tensions and dilemmas, and issues of identity, autonomy, adoption, and systemic change. Together these point to multiple implications for educators, policy makers, and researchers aiming to enable informed and engaged citizens. [ABSTRACT FROM AUTHOR]

Assessments, in particular high stakes assessments, impact the nature of teaching and learning. Given this, the goal of citizenship if seen as important needs to feature within high stakes school exit assessments rather than only as part of curriculum and assessment policy rhetoric. South Africa's Mathematical Literacy (ML) curriculum foregrounds critical democratic citizenship. We analyse the ML Grade 12 exit assessments from their start in 2008 to 2020 to understand the emphasis placed on critical citizenship and how this emphasis has shifted over time. The literature base links critical citizenship orientations with reasoning and reflecting questions, so we focused on examination questions in this category. Our findings show shifts away from critical citizenship related agendas towards foregrounding a life preparation orientation for the self-managing person. Linked with this shift, we note a move away from general societal contexts towards more personal/individual contexts and moves from almost entirely national contexts to inclusion of global contexts. We noted movement from more open-phrased questions towards closed 'check figure calculated is valid'-type questions. Assessment memoranda suggest assessors view these questions as reasoning items, eroding the critical citizenship agenda. While increasing numbers of students are taking ML rather than Mathematics, average performance stands at around 40%. This points to limited and diminishing access to mathematical reasoning and reflecting for critical democratic citizenship. The paper highlights ways in which analysis of examinations over time can provide a window into the presence or absence of the citizenship agenda in mathematics education. [ABSTRACT FROM AUTHOR]

The COVID-19 pandemic continues to present severe challenges to the education sector more than 2 years after the first case was detected. We explore the strategies South African teachers used to support continued mathematics learning at home during the COVID-19 pandemic across different stages of the response to it and across different contexts. We explore these strategies, first, in relation to the initial shift to emergency remote teaching when learners needed to be reached in their homes under severe lockdown regulations, then through the gradual reopening of schools later as regulations were relaxed. Activity theory informs our perspective on the way in which teachers worked to mediate learning across school and home activity systems. Twenty-five Grade 4–7 mathematics teachers from the Eastern Cape responded to two questionnaires given at the start of the COVID-19 lockdown period and during the phased return to school. Questions focused on the strategies used to support mathematics learning. The results show that strategies focused on engaging caregivers through various technologies and getting resources into the home. WhatsApp, a free internet-based messaging service, was the most frequently used communication app across all types of schools for both messaging parents and sending instructional material and support in the form of videos, pictures and text messages. Department issued workbooks and teacher designed work packs were key resources sent to homes. Differences are evident in the range of use of different technologies across wealthier and poorer schools. Primary teachers' voices inform possible ways forward for the purpose of managing young student mathematical learning gaps and meeting ongoing learning needs. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Research that focuses on teacher identity is gaining traction as researchers argue that teachers mediate more than mathematical knowledge and skills in the classroom. This research tends to be underpinned by a social constructionist orientation, which foregrounds epistemology over ontology. This orientation is limiting for research that wishes to understand the base conditions that enable or constrain the expression (i.e. both communication and action) of teacher identity in teaching primary mathematics. The paper suggests that this requires research that explores the interaction between structure, culture and agency in the expression of teacher identity in teaching mathematics in primary school. The study argues that a social realist orientation is of value to research on teacher identity. From this perspective, teacher identity is defined as the manner in which teachers express their roles as teachers. As the paper is primarily theoretical, the exemplification is limited to two primary school teachers' expression of only one role namely effective communicator of mathematics. It demonstrates what social realism enables, that is, not illuminated in research underpinned by a social constructionist orientation. The argument made in this paper elucidates how social realism supports a deep analysis of the structural and agential conditions that enable and constrain teacher identities. [ABSTRACT FROM AUTHOR]

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]

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]

Identity research in mathematics education has become increasingly prominent over the past two decades. In the last few years, there have been several reviews of identity literature in the field of mathematics education generally, or specifically focused on mathematics learner identities or mathematics teacher identity. We begin our paper by summarizing the key findings of these reviews, pointing to various categorizations proposed by their authors, and the key critiques raised therein. We then report on our more recent review of identity literature in mathematics education published in the top twenty mathematics education journals over the past 5 years (47 articles in total). This review enables us firstly to speak descriptively about the extent to which the field is evolving (or not) in relation to earlier findings (dominant regions, focus of research, methods and perspectives used). Secondly, following deeper analysis of the papers, we speak to the way in which the field is addressing (or not) key critiques raised by reviews. Our analysis points to several theoretical, methodological and empirical absences and challenges requiring further engagement. We further highlight key absences in the research, particularly a lack of cross-national comparative studies and studies that connect learner and teacher identities. We then provide a summary discussion and analysis of the contributions of the present special issue papers and engage with how these take the field forward. Finally, we engage with the implications of our analysis and recommendations for future directions for research. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper proposes a transdisciplinary framework to allow for a multifocal exploration of classroom talk practices. It draws on data from a broader study of talk in South African Grade 4 mathematics classrooms where the language of teaching and learning (English) was the home language for neither the teachers nor their students. Lesson transcript data from one teacher’s lessons on fractions are used to demonstrate how working with three strands of conceptual insight from the disciplines of psychology, sociology and linguistics conduces to a potentially richer understanding of a teacher’s use of classroom talk in mediating her students’ mathematical understanding. By drawing on elements of Vygotsky’s sociocultural psychology, we make visible in the lesson data the ways in which this teacher used the ‘everyday’ in trying to navigate her students’ towards more ‘scientific’ conceptualizations of unit fractions. By then taking up aspects of Bernstein’s sociological work, we articulate, and make visible, how societal circumstances impinge on students’ access to exploratory mathematical discourse needed for epistemological access to abstract and generalized mathematical concepts. Finally, through Halliday’s work on the power of particular linguistic registers for meaning-making, we highlight challenges in learning mathematics in and through a second language and reveal the constraints placed on students’ opportunity to maximally exploit the distinct forms of meaning contained within the mathematics register. [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]

This article offers reflections on task design in the context of a Grade R (reception year) in-service numeracy project in South Africa. The research explores under what conditions, and for what learning purpose, a task designed by someone else may be recast and how varying given task specifications may support or inhibit learning, as a result of that recasting. This question is situated within a two-pronged task design challenge as to emerging gaps between the task designer's intentions and teacher's actions and secondly between the teachers' intentions and students' actions. Through analysing two teachers and their respective Grade R students' interpretations of a worksheet task, provided to teachers in the project, we illuminate the way explicit constraints, in the form of task specifications, can be both enabling and constraining of learning. In so doing we recast this 'double gap' as enabling productive learning spaces for teacher educators, teachers and students. [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]

South Africa's recent history of apartheid, its resultant high levels of poverty and extreme social and economic distance between rich and poor continue to play-out in education in complex ways. The country provides a somewhat different context for exploring the relationship between SES and education than other countries. The apartheid era only ended in 1994, after which education became the vehicle for transforming society and a political rhetoric of equity and quality education for all was prioritized. Thus education focused on redressing inequalities; and major curriculum change, with on-going revisions, was attempted. In this sense engagement with SES and education became foregrounded in policy, political discourse and research literature. Yet for all the political will and rhetoric little has been achieved and indicators are that inequality has worsened in mathematics education, where it is particularly pronounced. This paper proposes that continued research confirming poverty-underachievement links, which suggest an inevitability of positive correlations, is unhelpful. Instead we should explore issues of disempowerment and agency, constraints and possibilities, and the complex interplay of factors that create these widely established national statistics while simultaneously defying them in particular local contexts. Such research could shift the focus from a discourse of deficit and helplessness towards a discourse of possibilities in the struggle for equity and quality education for all. [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 "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]

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]