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Introduction
Current institution
Additional affiliations
January 1995 - December 2008
January 2011 - present
January 1995 - December 2008
Position
- R&D officer; lecturer; senior lecturer - associate professor
Description
- Prior to 2009 I worked as an academic at Wits for eight years preceded by six years of working in In-service primary and secondary mathematics teacher education projects
Education
January 1998 - January 2002
Publications
Publications (191)
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 t...
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 h...
In this article, South Africa provides an “outlier” case that
illuminates the tensions that exist between locally responsive
mathematics education interventions, aimed at tailoring
initiatives to vastly unequal contexts of schooling, and the
systemic “one size fits all” interventions of the state. I draw
on the experiences of two teachers involved...
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,...
In this paper, I argue that the establishment of after-school mathematics clubs in early grades holds rich potential for supporting the development of increasingly participatory and sensemaking maths learning dispositions. Within the South African Numeracy Chair project, lead by the author, multiple after-school mathematics clubs have been set up f...
In this article we investigate the transparency of language in learning place value in either a Southern African indigenous language (isiXhosa, Setswana, Oshiwambo or Emakhuwa) or a European-based language (Afrikaans, English, German or Portuguese). Since language is a key mediator in developing place value understanding, it is important to investi...
Drawing on a broader study which sought to model mental mathematics strategies to first-year pre-service teachers (PSTs), this paper explores their recognition, demonstration, and explanation of the bridging through ten strategy. Data, in the form of post-intervention tasks from 23 PSTs, included three varying learner work examples and solving a ca...
This brief history of SEMT provides details of the life of the Symposium on Elementary Mathematics Teaching (SEMT), which, as its name suggests, focuses on the teaching of mathematics to children within the range of 5 to 12 years of age. The first SEMT symposium was in 1991, with the participation of some 39 educators and researchers, and since the...
In South Africa and in many other parts of the world, decolonising the curriculum has become a valued goal, while frameworks that would systematically support the decolonising project through instructional design are not broadly available. In this conceptual paper we bring readers to consider one framework for instructional design, the theory of Re...
This chapter elaborates and reviews the professional development (PD) model of the South African Numeracy Chair Project (SANCP), Rhodes University from inception (2011) to date. The Chair’s development mandate is to run PD with local primary teachers of mathematics in partner schools. The PD model evolved in a grounded way over time, informed by te...
Background: National and international assessments show South Africa’s underperformance in mathematics. As many learners already fall behind in the early grades, where foundational number sense should be established, addressing the challenges of number sense in the Foundation Phase (FP) is important. Research recognises the need to better develop p...
Background: South African teachers’ mathematical knowledge for teaching and number sense are markedly low, evidenced in national and international research. There is a call for supporting teachers in developing their knowledge and confidence in teaching mathematics.
Aim: The aim of this article is to share how pre-service teachers (PSTs) used the...
Background: This article critically examines the nature of isiXhosa translations in mathematics learning materials, specifically focusing on the doubling and halving unit within the ‘South African Grade 3 Mental Starters Assessment Project (MSAP): Teacher Guide’. Teaching in home languages is encouraged in the Foundation Phase, but unfamiliar stand...
Background: South African learners face the double disadvantage of living in low socio-economic conditions with access to few resources and attending schools with challenging learning conditions. Mathematics performance reflects such conditions with extreme performance gaps between wealthier and poorer learners. The need for early intervention is i...
It is widely accepted that children whose home environment is supportive of their school learning experience an academic advantage and that parents are influential in whether or not their children experience success in mathematics. In this oral communication we focus on primary school mathematics teacher practices, in the post-Covid context, that e...
In this position paper we investigate the role of language in learning place value concepts in either a Southern African indigenous language (isiXhosa, Setswana, Oshiwambo, and Thimbukushu) or a European based language (Afrikaans, English or German). Given the importance of place value in the early years of schooling, it is important to understand...
In this paper we compare the primary grades' (1-3) mathematics curricula of South Africa, Namibia, Malawi, and Kenya with a focus on place value (PV). PV is the basis for much content within the primary mathematics number strand. Our findings point to some similarities and differences between the four curricula that we explored, focusing on the fol...
In response to the conference theme of ‘rethinking relevant research’, we highlight an ethical dilemma in the space of design-research. The first author’s doctoral study, which sought to design and research tasks integrating mathematics and music, highlighted a situation where the roles of doctoral supervisors became blurred. The supervisors and do...
We explore the potential of merging numeracy and literacy, through using number stories to stimulate mathematical engagement with young, marginalized learners in their communities. Our data emerges from the Family Maths Storytime Programme (FMSP) run in partnership with teachers in two South African schools. The FMSP conducted sessions with caregiv...
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...
In this article we share the findings emanating from a 20 year (2003–2022) review of South African Early Grade Mathematics (EGM) research articles published in key international and local/regional journals. The review shows a substantial increase in the volume of published EGM articles in the second decade (2013–2022), nationally and internationall...
In this research, we ask: How are mathematics teachers engaging with parents in the post-Covid context? Early grade (Grades R, 1 and 2) mathematics teachers (38) completed a questionnaire that probed for responses about how they are engaging with parents and the practice of giving homework in the post-Covid context.
In this paper we compare the early years mathematics curricula of Germany, South Africa, and Australia in relation to the place value concept. Place value is an important topic as it underpins much of the number work completed by learners in the early years of schooling. We found that there were differences between the three curricula that could be...
This paper reports on a key representation, a triple number line, designed as part of the first author’s doctoral study. The study sought ways to represent multiple constructs of fractions in the context of merging music and mathematics to support learners’ understanding of fractions. A problem scenario was designed guided by Realistic Mathematics...
In this paper I share aspects of the work of my team, over the past twelve years as the incumbent South African Numeracy Chair at Rhodes University in Makhanda, South Africa. This is one of two National Research Foundation Chairs established to merge development with research in the search for sustainable solutions to persistent challenges in prima...
Ongoing concern about poor learner performance in mathematics has led to wide-ranging research on the subject, globally and in South Africa. Among the remedies identified is the reformation of pre-service teacher (PST) education programmes in a way that supports the acquisition of professional skills for pre-service teachers. Developing PSTs’ refle...
The research paper reports mathematics learner identities of a group of high school learners who participated in our after-school mathematics clubs that our project ran when they were in primary school. What is captured here is one quite typical story of a learner’s mathematical journey, written by the learner when in secondary school. We conceptua...
In 2011, in response to the increasing awareness of the need to address challenges in mathematics education from the early grades of learning, two South African Numeracy Chairs were established. One of these is headed by Professor Venkat at the University of the Witwatersrand (Wits) in Gauteng and the other is headed by the first author of this cha...
This paper shares insight from the three authors’ recent twelve-month task design journey. The journey represents an important part of the first author’s doctoral study. The aim of the study is to explore integrating mathematics and music in ways that support young learners’ development of fractional reasoning. The global COVID-19 pandemic meant th...
This book brings together the first book collection of African research in mathematics education in multilingual societies andchronicles current research in different linguistic contexts across the African continent, (including Algeria, Namibia, Malawi, Morocco, Rwanda, South Africa) on issues of multilingualism in mathematics education, but more i...
International research on storytelling in mathematics holds that
stories offered as explanations by teachers, and stories told and
retold by children, help both affect and attainment in mathematics.
In the South African early grade mathematics context, we have paid
attention to diversity of linguistic expression and what this offers in
bilingual a...
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 c...
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...
This paper emerges from a broader study that investigated the strategies employed by teachers to continue mathematics teaching and learning during South Africa’s COVID-19 lockdowns and through subsequent phased and partial re-opening of schools. In this paper, we focus on teacher views of the role of parents in these efforts gathered through two qu...
This paper shares results from a national ‘familiarisation trial’ of a mental
mathematics intervention focused on assessing and encouraging strategic calculation
methods with Grade 3 students in South Africa. Successful smaller pilots refined the
intervention into 6 foci and this paper draws on assessment results from the four
provinces that triall...
This paper derives from the early phases of the first author’s doctoral study. Eight primary school teachers at a school in South Africa’s Eastern Cape Province were invited to be part of a community of practice in which strategies for using music to support the teaching and learning of fractions would be explored. Wenger’s theory of community of p...
This paper reflects on the task design process of a design research study around integrating music and the teaching of fractions. The paper focuses on Phase One of the research study that involves the initial task design. The task design process was informed by curriculum aims, Realistic Mathematics Education theory, literature reviewed and author...
It is a privilege to have the opportunity to write this ‘greeting chapter’ for Professor Gabriele Kaiser’s Festschrift. While I write a personal story and greeting I know that this story and the sentiments herein are echoed by other South African colleagues of mine in mathematics education who had the opportunity to engage with and learn from Gabri...
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 r...
The coronavirus disease 2019 (COVID-19) pandemic and the resulting school closures in South Africa necessitated a major shift in how to support learners’ ongoing mathematics learning. For 10 weeks learners were strictly confined to their homes with restrictions that prohibited seeing any person outside of their household. The only means to access l...
This paper explores the mathematical identities of one high school learner who participated in an after-school mathematics club in primary school. What is captured here is the story of one learner's mathematical journey, written several years after his mathematics club participation, as a grade 10 learner. We foreground Martin's (2009) definition o...
Background: Mathematics education is a significant issue in the South African context. Learners’ achievement levels are markedly low as suggested by both national and international studies. The teaching and learning of fractions in particular have been identified as challenging.
Aim: The aim of this article is to share some of the outcomes derived...
Family members (parents, grandparents, aunts, siblings and cousins) and members of the community (such as elders, teacher aides, neighbours, etc.) play a significant role in shaping children’s interest and participation in numeracy and literacy practices (Goos in APMC 9:18–20, 2004).
The argument running through this book is that numeracy is an applied form of literacy and that its teaching must be integrated into the repertoire of school practices. While there are obvious differences between literacy and numeracy, in the Early Years numeracy is inseparable from the teaching of literacy. This is the case in multilingual classro...
Here, we explore briefly, through examples, how age- and context-appropriate narratives in the form of rhymes and stories can enhance and enable numeracy and literacy learning, particularly for learners for whom there are vast differences between their home and school environments.
This book draws on both in and out of school literacy practices with teachers and families to enhance the numeracy of early learners. It provides highly illustrative exemplars, targeted for learners up to approximately eight years of age whose home language differs from the language of instruction. It identifies the challenges faced by these learne...
One of the key concerns in this third section of the book is the scaffolding of learners so that they can engage with the academic language of mathematics. In the previous section, the focus was on building the literacy and reading skills of underserved Early Learners. It was recognised that this cohort of learners typically comes to school with li...
Our collective experience from decades of working in classrooms and other learning environments is that most educators focus on literacy rather than numeracy in the resources displayed in the classroom. The field of numeracy is often restricted to an obligatory poster displaying numbers or number facts and/or a poster about shapes and solids. To fi...
Big books are especially valuable when teaching takes place in a foreign language (Colville-Hall and O’Connor in Foreign Language Annals 39:487–506, 2006). This chapter extends the previous chapter by focusing exolicitily on incorporating a multilingual focus. For the learners in the two contexts on which we have focused, where the language of inst...
Throughout our careers, we have been guided by critical pedagogy and socio-cultural perspectives on learning. It is our firm view that learners are marginalised in subtle ways by practices that serve to reproduce the status quo. In our research, we have sought to identify these practices and propose new ones, in order to challenge prejudicial hegem...
In Chap. 10, we highlight the importance of partnering with families and communities to support early learning with a particular focus on numeracy. We offer some guiding principles and practical suggestions as to how this can be achieved. In this chapter, we focus on ways to get learners to initiate engagement with numeracy ideas learned in school...
In Chap. 4, we described how to use readily available maths-rich stories and rhymes to engage children in learning numeracy and literacy simultaneously. In this chapter, we discuss how to design and create maths-rich stories that can be tailored to the needs of both your curriculum and your learners.
From a Vygotskian perspective, tools and signs are inseparable parts of the teaching and learning of mathematical concepts. The central purpose of this discussion group is to examine this sign/tool-mediated view of learning and concept formation in relation to Vygotsky's notions of:
To make sense of issues related to mathematics and its teaching and learning, many researchers draw on social, historical, and cultural perspectives of learning and becoming. A wide range of applications and interpretations of this view reflects the vitality of this approach. The central purpose of this working session is to invite the participants...
Updated Encyclopedia entry on Mathematics Teacher Identity
Background: English is the dominant language in South African schools although it is the home language for less than 10% of the population. Many schools have yet to embrace the Language in Education Policy’s advocacy of additive bilingualism. This has led to a majority of the country’s children learning and being assessed through a language in whic...
In this lecture we reflect on the design of an instructional sequence that introduces the concept of fractions through measurement activities. In particular we focus on the creation of the story on which this sequence is centred. The ‘Fraction as Measure’ sequence has been researched and refined over more than a decade in Mexican and Australian cla...
In this chapter, I argue that establishing multidirectional learning opportunities that bring together communities of researchers, teachers, and teacher educators (including government departmental officials), aimed at learning for all participants, is needed for addressing challenges of mathematics education in contexts stubbornly resistant to cha...
A key intervention of the South African Numeracy Chair Project (SANCP) since 2011 has been the introduction of mathematics (or maths) clubs, which occur in the out-of-school time space. In 2016 the maths club concept was developed into a 15-week Pushing for Progression (PfP) teacher development programme which supports primary school mathematics te...
This paper reports on preliminary use of an analytic framework to research the mathematical identities of one high school learner who participated in an after-school mathematics club in primary school. We draw on Solomon (2009) who views one's mathematics identities as: beliefs about oneself as a mathematical learner; beliefs about the nature of ma...
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.
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.
In this chapter, we provide a conceptual overview of the field of identity in mathematics education based on a recent State of the Art review and our co-editing of a collection of 15 papers in this field, published in ZDM in 2019. We take as our starting point Sfard and Prusak (Educ Res 34(4):14–22, 2005) definition of identity as a collection of r...
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 focuse...
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...
A key intervention of the South African Numeracy Chair Project (SANCP) since 2011 has been the introduction of mathematics (or maths) clubs, which occur in the out-of-school time space. In 2016 the maths club concept was developed into a 15-week Pushing for Progression (PfP) teacher development programme which supports primary school mathematics te...
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 u...
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 intercon...
This research explores the mathematical learner identities of high school learners who participated in after-school mathematics clubs during their primary schooling. In response to a range of challenges in mathematics education in South Africa, the South African Numeracy Chair Project established a number of these clubs for Grade 3 learners in 2012...
The dominant image of fractions in many South African mathematics classrooms is that of a whole that is ‘fractured’ into equal parts. Cortina, Visňovská and Zúñiga (2014) argue that this approach can become a didactical obstacle when teaching fractions and propose an instructional sequence that rather uses length measurement activities to introduce...
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 d...
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 whi...
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 summar...
The aim of this paper is to discuss an approach to instructional design in which we intertwine mathematics education research with development, draw insights from collaborations across international contexts, and place educational equity firmly at the centre of our work. Using an example of the instructional sequence on 'Fraction as Measure,' we il...
A mathematical story and activity book that guides a parent (a teacher) in introducing the need for fraction units by engaging children in activities of measuring various lengths with increasing precision.
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The Storybook is available in better print quality (under Creative Commons licence CC BY-NC-ND 4.0) a...
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: T...
Writing for FLM conversational style
In this study we sought to establish whether an instructional sequence focused on fractions as measures was effective in supporting a group of South African Grade 3 students’ understanding of fractions. The sequence is centred on a story that utilises ‘nonsense’ words to describe fractions. The students in this study had already been introduced to...
In this study we sought to establish whether an instructional sequence focused on fractions as measures was effective in supporting a group of South African Grade 3 students’ understanding of fractions. The sequence is centred on a story that utilises ‘nonsense’ words to describe fractions. The students in this study had already been introduced to...
We draw on our work with designed instructional sequence on Fractions as Measures across three international contexts and explore the functions of the design features related to the stories embedded within the sequence. We discuss functions that relate to how stories support students' meaningful engagement in classroom mathematical activities, focu...
Research suggests mathematical stories can support mathematical learning. We discuss an unexpected outcome caregivers of reception year learners (Gr R age 5-6yrs), participating in a mathematics story-time program, shared in interviews. The program, implemented with Gr R learners' caregivers in two South African schools, explained and demonstrated...
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...
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 teac...
The focus of research presented in this snapshot paper is on the use of measurement as a context for teaching the inverse order relationship of unit fractions. It seeks to investigate the effectiveness of a sequence of lessons with this focus, developed by Cortina and Visnovska (2015), that has been trialled in Australian and Mexican schools with p...
This article investigates the participation enablers and learning affordances identified by teachers through participation within an in-service community of practice (CoP) of primary teachers called the Numeracy Inquiry Community of Leader Educators (NICLE) in the Eastern Cape. The article draws on three qualitative sources of data: the annual teac...
South Africa, as a result of its apartheid history, is a nation of extreme socioeconomic and educational inequality. Three aspects of this context are important in understanding why it is essential that educational research and development be intertwined. The first is South Africa's post-apartheid (1994) education context in which performance and o...
Plenary panel for ICTMA - Prof Gabriele Kaiser (Chair); Prof Alan Schoenfeld (USA); Prof Angeles Dominguez (Mexico) ; Prof Mellony Graven (SA); Prof Peter Galbraith (Australia),28th July 2017 Cape Town.
ICTMA plenary panel - Relations of Mathematical Modelling to Problem Solving, Interdisciplinary
Teaching and Numeracy
In the context of learner reliance on using one-to-one counting methods to solve basic operation problems, this paper investigates learner progression in a common assessment across three research projects in South Africa. These projects focus on learner progression in mathematical proficiency in after-school maths clubs as part of a broader maths c...
Questions
Question (1)
I have been looking for seminal articles on how some of the bureaucratic systems of Education, with quality management systems and highly prescribed lesson formats and so forth have constrained possible interventions aimed at increased quality and equity – particularly in mathematics education. I recall many years ago in England that highly structured lesson systems pushed some of the best teachers out. I would love to read further on research that has looked into how bureaucratisation of teachers work can get in the way of the core business of teachers and their focus on student learning.
