Early Grade Mathematics: Directions of Growth in the Research Field

Early grade mathematics (EGM) has received substantial policy attention in the last decade. In South Africa, the introduction of the ‘CAPS’ curriculum in 2011 was followed by the rollout of the now widely used national workbooks and there have been further policy-linked interventions like the Teaching Mathematics for Understanding model (Department of Basic Education, 2019) and the Primary Teacher Education (PrimTEd) initiative. Alongside these policy directions, there has been extensive research activity linked to interventions. These include the large-scale Gauteng Primary Mathematics and Language Strategy (Fleisch et al., 2016) and the more recent Bala Wande study (Mpofu et al., 2021), the work of longitudinal projects within the two Numeracy Chairs at Wits and Rhodes Universities and the Magic Classroom Collective in South Africa (see chapters in Venkat & Roberts’ (2022) book for overviews of these projects), as well as the series of EGM-focused projects led by Mercy Kazima in Malawi (e.g. Longwe et al.’s (2022) recent paper). Both review papers in this Special Issue (Morrison et al., 2023; Graven and Venkat, 2023) quantify, detail and disaggregate this growth in research interest from a low base in the previous decade. They note the more recent turn of interest towards initial teacher education within the South African PrimTEd study. Similar packages of curriculum reform and research attention have been seen in Malawi. This growth in attention reflects the growing acknowledgement that the concerns with low performance in mathematics at school exit levels have their roots in much more fundamental and foundational understandings of mathematics. As Taylor (2021) noted recently in relation to South African outcomes in mathematics:

the roots of the country’s paucity of graduates in the mathematical and physical sciences lie deep in the primary school. (p. 2)

In looking at the larger scale interventions, Venkat and Graven (2022) recently noted two rather different approaches. On one side, there are projects that tend to be large scale from the outset, located within the policy- and change-oriented research fields, and focused on changing the routines and norms of curriculum coverage in the early grades. On the other side, there are projects that explicitly connect and engage with the evolving mathematics education literature base in the early grades. These projects have worked longitudinally and broadened into scale over time through increasing the number of participating schools/personnel or developing materials and training packages that can be used beyond the intervention study sites. Venkat and Graven (2022) describe the latter approach in terms of ‘building your timber’ as this model pays explicit attention to the need to build capacity for implementing interventions in systems where this capacity is acknowledged as limited.

A key motivation for this Special Issue is a focus on the latter category of research in the EGM field. The collection of papers in the Special Issue reports or reflects on studies guided substantively by the mathematics education research base. The review papers point to emerging clusters within recent work focused on early grade mathematics—initial teacher education (ITE) being one of these and reflected on in four articles in this issue. Westaway et al. (2023), drawing from their work in the PrimTEd project, note that while there is general agreement on the importance of number sense, there is the lack of a common understanding of what number sense is when analysing number content across 11 different ITE programmes. They argue that there is a need for developing a common language of description.

Roberts and Porteus (2023), in a second paper drawn from the PrimTEd study, argue that there is a lack of explicitness among primary teacher education lecturers on the theoretical underpinnings of their course design. In the paper they make explicit the design choices underpinning the first year ‘Emergent Number Sense’ module, built around two pathways into number knowledge, namely a counting and a measurement pathway. Understanding these pathways provides teacher educators with a conceptual framework for considering their design choices. Also focused on design issues in ITE, Essien et al.’s (2023) article suggests several design principles for developing ITE courses that build an understanding of number sense. Their article is based on the data from a design research study with 70 first-year pre-service teachers and one lecturer, focused on the notion of equivalence and number structure learning and teaching in ITE. Going beyond number teaching and learning, Bansilal et al.’s (2023) article considers the understandings of measures of central tendency among a cohort of primary ITE students, and finds that while there were computational strengths, the students encountered difficulties with unpacking procedures and working with examples of learner errors.

Both review articles also note that the largest clusters of work in early grade mathematics in the region are currently located in South Africa and Malawi. However, Graven and Venkat’s (2023) review of SAARMSTE conference papers shows a broader regional spread of small-scale work reported through this outlet. Some of this work reflects growth in postgraduate studies focused on early grade mathematics. Two articles in this issue emerge from this growth: Long and Graven’s (2023) paper studies changes in the professional identities of Grade R teachers related to numeracy during the course of an 18-month professional development (PD) intervention. Through analysis of 33 Grade R teachers’ pre-, during and post-questionnaires they found that participation in the PD and the related access to key age-appropriate research informed numeracy resources supported teachers in their teaching and in their relationship with numeracy. Furthermore, being part of the PD community supported navigation of positive professional identities within the mixed messages of policy. Tshesane and Venkat’s (2023) article follows from the first author’s doctoral study in which he designed and taught a sequence of intervention lessons on additive reasoning. The focus in this article is on the coding scheme utilised for analysing learner responses to a varied set of additive word problems pre, post and delayed-post around the intervention. The succinctness of their approach allows for the translation of large numbers of item responses into a numerical code form in which numbers of appropriate/inappropriate/absent models, appropriate/inappropriate/absent calculations and correct/incorrect/no answer responses can be efficiently summarised. The authors note the holistic view of learners’ performance on problem solving offered through this approach.

Our sense is that the extent of challenges on the ground, and the critical role of EGM in changing the landscape of mathematical outcomes, necessitates ongoing attention to both larger-scale and smaller-scale intervention studies. The former provide proof of probability that an intervention is likely to work at scale; the latter offer explorations of what is possible under more specific conditions. While some would argue that the emphasis should be on the former, we would argue instead for both lines with a focus on core and high leverage mathematical ideas. Early number and number structure/pattern, addressed in a number of ways in the last decade in the research base, represent key foci, and form the empirical base of several of the interventions that are reported on in this issue: Long and Graven’s Early Number Fun programme with Grade R teachers; Tshesane and Venkat’s focus on additive problems; and the emphasis on understanding/developing number sense in initial teacher education in Westaway et al. and Essien et al.’s articles.

At the same time, there are also indications of a maturing field. Porteus’ (2023) paper in this issue reflects on more than a decade of intervention work with an offer of design principles for considering the development of learning and teaching support materials for early grade mathematics. Located in schools where home languages form the medium of instruction, Porteus notes the need to embed insights into mathematical ideas for teachers within teaching and learning materials. Similarly, Bansilal et al.’s paper, in going beyond the emphasis in research on number teaching and learning, offers insights into the nature of ITE students’ understandings of a broader range of topics.

In Graven and Venkat’s review paper, the role of the SAARMSTE Conference in providing a platform for bringing together regional research in EGM is acknowledged and evidenced in the increasing prevalence of EGM work in the conference proceedings across the last two decades. Our proposal to AJRMSTE for this Special Issue came on the back of our appreciation for the space that SAARMSTE as an organisation has offered for the growth of an EGM field that had a very small footprint in universities and conference presentations across the region two decades ago. This Special Issue stands testament to a now thriving research field of work that is critical to shifting the dial on learning outcomes in mathematics, albeit with greater emphasis in some parts of the region than others.

Acknowledgement

The publication of this Special Issue on Early Grade Mathematics in Open Access format is made possible by a generous donation from The Zenex Foundation.