Mediating early number learning: specialising across teacher talk and tools?

In this paper we locate our work in the context of claims of poor performance amongstSouth African learners in primary mathematics, and gaps in the knowledge base of primarymathematics teachers. Our focus is on the analysis of three Grade 2 Numeracy teachers’actions with artifacts in the context of increasing resource provision in the South Africannational policy landscape. Using ideas of mediation drawn from the Vygotskian tradition,and developed by Michael Cole and Jim Wertsch, we identify actions with the artifacts thatsuggest shortcomings in teachers’ understandings of the mathematical structures thatunderlie the design of the resources. Drawing on the work on modeling and tool use in theDutch Realistic Mathematics Education tradition, we note disruptions in openings forpedagogy to provide ‘models of’ increasingly sophisticated strategies, which might providechildren with ‘models for’ working more efficiently (and ultimately ‘tools to’ think with),disruptions arising from teachers presenting only concrete unit counting based models ofearly number calculations. Within a policy context where improving the resource situationis a priority, we argue for more attention to longitudinal support to teachers to developunderstandings of number and its progression that allow them to see the significance of themathematical structures that are figured into the design of the artifacts that are increasinglyavailable for use

From what works to scaling up: improving mental strategies in South African Grade 3 classes

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 trialled one focus: adding and subtracting using jump strategies. Findings from pre- and post- test results of 1379 students show statistically significant gains in both the fluencies underlying calculating strategically and in items assessing strategic competency. The results indicate that scaling up this model into national implementation is feasible, and that the intervention package can support improvements in mental mathematics learning outcomes

Children doing mathematics with confidence in the early grades by 2030: what will it take?

In this chapter, we draw together the early grade mathematics (EGM) work reported on in this volume and in Volume 3, offering a bird’s-eye view of what we know. Pulling together the emerging themes that cut across the mathematics chapters and the factors identified as impeding progress, we reflect on what it will take to have South African children doing mathematics with confidence in the early grades by 2030. We note through this analysis that in the decade from 2010 to 2020, rates of curriculum coverage have improved, but teachers’ knowledge and their access to learning mathematics remain serious concerns. We have identified the following priorities for improving outcomes in mathematics learning: 1) mathematics-focused teacher-development programmes, 2) university-level capacity for mathematics-focused initial teacher education programmes, 3) school–university government partnerships for research design hubs, 4) more flexible working with the National Curriculum and Assessment Policy Statement (CAPS) and language policy, and 5) building capacity for school-based instructional leadership

Early grade mathematics in South Africa between 2000 and 2010: what did we know in 2010, and how did this set the stage for the 2010–2020 decade?

In this chapter we present a reflection on research and policy in early grade mathematics (EGM) in the 2000–2010 decade in order to consider the ground at the end of that decade, and how it laid foundations for the much broader raft of EGM-focused research studies, development policies, and projects that emerged between 2010 and 2020. Using Ball’s writing on the ‘essential circuits’ of education (curriculum, pedagogy, assessment, and the ‘hidden curriculum’), interlinked shifts were observed in all the circuits. In curriculum, there was a change from low to high levels of specification, amidst calls to reconsider specification in the face of gaps in teachers’ content knowledge and ongoing low attainment by learners. In pedagogy, attention to constructivist learner-centred approaches gave way, amidst evidence of gaps in awareness of progression and evaluation, to direct-instruction approaches linked to tighter specification in the curriculum. In assessment, there was evidence of rudimentary unit-counting approaches through the decade, and later, the introduction of national standardised tests. Increased data on how learners of EGM work came into view with these assessments. These changes reflected shifts in the hidden curriculum: the post-apartheid emphasis on using education to engender critical democracy reverted to traditional disciplinary goals in the face of ongoing demands for access to knowledge

A decade of the Wits Maths ConnectPrimary project (2010 –2020): Design research moving promising interventions to scale

In this chapter, we trace the movement – over the course of the 2010–2020 decade – of interventions developed within the Wits Maths Connect-Primary project (WMC-P), and the scaling-up of the project from ten schools to provincial and national contexts. The focus of key interventions, the rationales for them, and the ways in which this approach to expanding scale differs from the larger-scale policy interventions are discussed. Learning outcome data, usually in a pre-/post-test design model, from all the interventions in the WMC-P project are included. We discuss this evidence of impact, and reflect on what the outcomes suggest as critical areas for focus in the next decade. In-service capacity-building through work with subject advisors and pre-service primary teacher education form particularly important thrusts within the emphases going forward

Analysing the citizenship agenda in Mathematical Literacy school exit assessments

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

Analysing the citizenship agenda in mathematical literacy school exit assessments

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

Working Group Report: Task Design for Early Algebra

The focus of this newly established working group is on the complexities of designing tasks for engaging children in algebraic thinking. The working group aims to engage PME participants in interrogating the multiple ways in which robust task design supports teachers in facilitating children’s learning, within the topic of early algebra. The facilitators of the working group will present relevant theory from the distinct research fields of task design and early algebra, and participants will be invited to explore how insights from task design may be made manifest to address the specific needs of children engaging with algebraic thinking in elementary school