Primary mathematics in-service teaching development: elaborating 'in-the-moment'

A thesis submitted to the Wits School of Education, Faculty of Humanities, University of the Witwatersrand in fulfilment of the requirements for the degree of Doctor of Philosophy May, 2016This study investigates how primary school mathematics in-service teachers respond to learners’ offers, over time, during classroom interactions. The study was a follow-up to a one-year long in-service ‘maths for teaching’ professional development course in which 33 teachers participated in 2012. Four teachers from that course were tracked in this follow-up study. Data sources within this study consisted of two cycles of observations of lessons taught by the four teachers in 2013 and 2014, and an interim video-stimulated recall (VSR) interview with each teacher, with reflections guided by the structure of Rowland et al.’s ‘knowledge quartet’. A total of 18 lessons from the four teachers were video-recorded across the 2013 and 2014 observations. The notion of ‘elaboration’ was used in this study as an interpretive lens to examine and characterise responsive teaching actions in the South African context, with the focus narrowing over the course of the PhD to contingency situations within the knowledge quartet framework, focused on responses to learner offers. In the South African literature, the terrain of elaboration is characterised by extensive gaps in teachers’ mathematical knowledge, incoherent talk, and frequent lack of evaluation of learners’ offers in the classroom. Using a grounded theory approach, I propose an ‘elaboration’ framework with three situations of responsive teaching (breakdown, sophistication and individuation/ collectivisation), which can be used as a tool to support the development of more responsive teaching in the South African context (and perhaps in other contexts where similar problems prevail). In this way, the study has contributed in terms of identifying some important ‘stages of implementation’ (Schweisfurth, 2011) that might be required to move towards the ideals of more responsive teaching that are described in the international literature, and yet remain distant from the realities of South African schooling. Using the three markers of shifts (extent, breadth and quality) in elaboration recruited in this study, drawn from the ways in which the dimensions of responsive teaching were conceptualised, I report on the different patterns of shifts in elaboration by the four teachers. The results of this analysis indicated that all four teachers made shifts in their responses to learners’ offers from 2013 to 2014 lessons in at least one or more dimensions of responsive teaching, in relation to extent, breadth and quality of elaborations. Findings from VSR interviews indicated associations between shifts in teachers’ reflective awareness, and shifts in responsive teaching actions. Theoretically, the study contributes through characterising responsive teaching actions in contexts of evidence of limited evaluation within the elaboration framework, with a language of description for identifying and developing more responsive teaching actions in a resource constrained contex

Shifts in early number learning in South Africa

In this paper, we report on outcomes from the Structuring Number Starters intervention project focused on early grades’ number learning in South Africa. Using tests drawn from the Maths Recovery programme, a cross-attainment sample of Grade 2 students in six schools took part in oral interview assessments early in 2011, 2014 and 2018, with professional development activities for their teachers occurring across this period. Student outcomes point to increasing proportions, over time, of students able to use more sophisticated counting strategies, and to work with number structure for more efficient calculation

Shifts in early number learning in South Africa

In this paper, we report on outcomes from the Structuring Number Starters intervention project focused on early grades’ number learning in South Africa. Using tests drawn from the Maths Recovery programme, a cross-attainment sample of Grade 2 students in six schools took part in oral interview assessments early in 2011, 2014 and 2018, with professional development activities for their teachers occurring across this period. Student outcomes point to increasing proportions, over time, of students able to use more sophisticated counting strategies, and to work with number structure for more efficient calculation

Teaching for structure and generality : Assessing changes in teachers mediating primary mathematics

From a sociocultural perspective that a teacher’s use of mediational means is central to student learning, this paper presents an analysis of six teachers and their mediating, across a two-three year time gap. Drawing on the Mediating Primary Mathematics framework – developed to examine the type and quality of mediational means – we propose two composite assessments of quality of mediation – extent and depth – that indicate the extent to which teaching addresses mathematical structure and generality. The findings reveal a range of differences in these two assessments for each of the six teachers, but that all six teachers were more coherent in their use of mediational means in the later lesson than in the earlier one. These findings have implications for other schooling systems and researchers seeking to improve the quality of mathematics instruction

Mathematics and science teacher educators’ experiences of using the WhatsApp platform as a tool for supporting teaching during the Covid-19 pandemic

This article problematises the delivery of the curriculum after the sudden onset of lockdowns due to the outbreak of the COVID-19 pandemic that saw the sudden cessation of all face-to-face teaching and learning at a South African University. The article reports on how the otherwise neutral WhatsApp social media platform was appropriated to become a serious teaching and learning tool for pre-service mathematics and science students. The study draws predominantly on connectivism learning theory to understand how WhatsApp was used to continue the teaching and learning project during the lockdowns. The sample consisted of ten (n=10) maths and science teacher educators on whom data was collected through questionnaires. The article reports on the opportunities and challenges the WhatsApp platform provided as well as how it reshaped the teaching and learning of maths and science