Debbie Stott

The evolution of an instrument for researching young mathematical dispositions

In this paper, we share our experience of searching for ways in which to access learner dispositions and the evolution of an instrument that we have used as both a written and an interview instrument. We argue for the importance of understanding young learner mathematical learning dispositions in order to inform ways in which to support learning. As researchers, finding ways in which to access learner mathematical dispositions can be difficult, especially with young learners who struggle to articulate their stories. Mathematical learning dispositions are taken to include what learners say about learning and how they act when they learn. The focus of this paper is on gathering data in relation to the former. In order to illuminate what the instrument allows us to see we share some preliminary findings from our research. Our findings draw on evidence gathered, in interview form, from 16 learners in two grade 3 after school maths clubs and evidence gathered, in written form, from 614 grade 4 learners across 10 schools in the broader Grahamstown area. We interrogate the extent to which these articulated dispositions indicate constrained learning opportunities. The preliminary findings shared in this paper illuminate both what the instrument allows one to see as well as the limitations of the instrument.

Researching the Nature of Early Numeracy Progression in After-School Clubs

The setting up of after-school primary mathematics clubs has been a key intervention project of the South African Numeracy Chair project, Rhodes University, in which I participated as both a researcher and club coordinator. The clubs provide spaces for learner engagement that are free from several contextual constraints that teachers face in their classrooms, including large crowded classrooms and district-stipulated curriculum pacing. This chapter presents the findings of longitudinal research on developing mathematical proficiency of 12 learners across two such clubs. The chapter will report on the findings and offer insight into how mathematical proficiency developed for learners across over time, with a focus on combining the Learning Framework in Number and the strands of mathematical proficiency.

Attention Catching: Connection the Space of Joint Action and Togethering

In the context of after school mathematics clubs in South Africa, in this chapter I seek to gain a firmer and deeper understanding of the theoretical concepts of ‘space of joint action’ and ‘togethering’. I do this by connecting the notions of Meira and Lerman’s attention catching and Radford’s moments of poēsis, which are used as a combined lens to analyse data from two task-based interviews with 9 to 10-year old club learners. Using examples and non-examples, I analysed sustained sequences of attention catching as observed when participants paid attention to each other in a mathematical manner to enhance their understanding or sense making. I argue that the way in which participants take advantage of these sequences has a bearing on the way in which the space of joint action evolves and how togethering unfolds. The findings from this chapter contribute to calls for understanding the special work of mathematics teaching and may be pertinent in both classroom and out-of-school time contexts in South Africa and beyond.

Adapting Aspects of the Mathematics Recovery Programme for Use in Various South African Contexts

The Mathematics Recovery programme developed by Wright and colleagues has been successfully employed in the Australian context as a resource to enhance learner progression in number concepts. However, when such a resource is imported from a different context or country and used in a new context, it often needs to be adapted for use in a local context. Such adaptations in developing contexts illuminate both the usefulness and contextual adaptations of the tools for both analysis and developmental purposes, with the aim of informing teaching practice in numeracy in resource-constrained Southern African contexts. This chapter provides three cases as examples of adaptations and extensions that have emerged from the needs of the developmental researchers working with the Mathematics Recovery programme tools in a South African context.

Making sense of the ZPD : an organising framework for mathematics education research

The zone of proximal development (ZPD) is a well-known and frequently used notion in both educational research and practice with a wide and diverse range of interpretations. My aim in writing this theoretical article is not to provide a critical examination or an extensive literature review of the ZPD, but rather to highlight some significant issues surrounding the use of the notion in the mathematics education literature. Extending a series of questions contributed by Del Río and Álvarez, I have added an element about theoretical space enabling researchers who are not in psychology to use the questions to situate their own use of the ZPD within their theoretical perspective and to unpack their assumptions about each of the questions. More importantly, the paper exemplifies how the use of an organising framework assists in achieving some clarity on the different ways the notion is conceptualised in the educational literature. I propose that this framework could enable both researchers and educators to locate their own conceptualisation of the ZPD within the broader, complex space and to assist in achieving coherence between the theoretical and methodological perspectives they work with.