Karin Brodie

Forms and substance in learner-centred teaching: teachers' take-up from an in-service programme in South Africa

Abstract In this paper we examine the ways in which teachers, enrolled on an in-service programme in South Africa, have taken up learner-centred practices. We introduce the notions of forms and substance in learner-centred teaching and describe how these are developed in the programme. We then analyse the teachers’ practices in these terms, using data from classroom observations and interviews. We argue that teachers take up learner-centred practices in different ways. The majority of teachers took up the forms without the substance, but some managed to be substantively learner centred.

The power of professional learning communities

Abstract In this paper I share some key principles and examples from the Data Informed Practice Improvement Project. The project develops an innovative model of mathematics teacher development, with three main strands: teachers work with data from their classrooms, they use this data to understand and engage with learner errors in mathematics, and they do this collectively in professional learning communities, with facilitation from members of the project team. I describe each of these strands and present three examples that show how the strands work together to support teacher learning in professional communities. These examples illuminate a key achievement of the project: a focus on learner errors in professional learning communities can develop powerful conceptual knowledge of mathematics among teachers at the same time as developing teachers’ knowledge for teaching and teaching practices.

Pressing dilemmas: meaning‐making and justification in mathematics teaching

Meaning‐making and justification are two important goals of current reforms in mathematics education. Working with learners to develop meaning‐making and justification through communication and discussion in class can create dilemmas for teachers, particularly dilemmas between seemingly compatible reform goals. Drawing on previous descriptions of teaching dilemmas, I identify dilemmas observed in the classrooms of two reform‐oriented South African teachers. Two key dilemmas are whether or not to press particular learners’ meanings and whether to take up or ignore learner contributions. I show how these dilemmas are supported by the ‘press’ move of reform pedagogy and how these two dilemmas come together to create a third overarching dilemma: the dilemma between working with learners’ meanings and encouraging justification.

Mathematical Reasoning Through Tasks: Learners’ Responses

In this chapter, I focus on the use of tasks to teach mathematical reasoning. Chapter 1 argued that particular features of tasks can support mathematical reasoning (Am Educ Res J 33(2):455–488, 1996) and using such tasks in mathematics classrooms is a necessary condition for supporting learners’ reasoning. Using appropriate tasks is, however, not a sufficient condition because how learners respond to tasks and how learners and teachers interact around tasks is crucial in creating opportunities for learning mathematical reasoning. In this chapter, I explore learners’ reasoning on a task that made higher-level cognitive demands and the teacher’s responses to the learners’ reasoning. I illuminate some of the strengths and challenges in the learners’ responses to the tasks as well as in the teacher’s practices in trying to work with these.

Learner Resistance to Teacher Change

The previous chapters have described a range of ways in which five teachers shifted their pedagogies to take account of learner contributions and to teach mathematical reasoning. The analysis has pointed to both successes and challenges in their teaching and has shown that a new curriculum and new pedagogies place new and increased demands on teachers and learners. Increased demands can lead to resistance on the part of both teachers and learners. In this chapter, I focus on learners’ resistance to their teacher’s changing pedagogy.

Learning Mathematical Reasoning in a Collaborative Whole-Class Discussion

Chapter 3 focussed on how learners responded to tasks in groups and how the teacher worked in whole-class discussion to try to develop discussion around the tasks. It showed that although the tasks were of higher-level cognitive demand, in fact it was difficult for both the teacher and learners to maintain the level of cognitive demand as they interacted with the tasks. The teacher was able to develop discussion in one case, in which the task demands were maintained. In this chapter, I focus more directly on collaborative learning in a whole-class discussion and show how this collaboration influenced the mathematical reasoning of one learner. I focus also on the role of the teacher in creating and maintaining whole-class discussions and the role of learners in co-producing each other’s learning.

Developing Diagnostic Competence Through Professional Learning Communities

In many countries, it is becoming increasingly common for teachers to analyse data from learners’ tests and classroom work in order to improve their practice in response to what learners need to learn. In order to use data well, teachers need to develop diagnostic competence, which has been defined as the ability to respond in a didactically sensitive manner to learners’ mathematical productions. In this chapter we look at the extent to which mathematics teachers enact elements of diagnostic competence in professional learning communities and their classroom practice. We analyse data from one professional learning community over a two-year period and show that there were features of diagnostic competence in the teachers’ conversations and that three of four teachers shifted their diagnostic competence in practice.

Learning in Professional Learning Communities: Shifts in mathematics teachers’ practices

Professional learning communities as a form of teacher development have been in existence internationally for some time now and more recently in South Africa. Although strong claims have been made for their influence on teacher practices, very few research studies have investigated these claims. This paper presents a case study that connects teacher-learning activities in a professional learning community to shifts in teaching practices. Four high school mathematics teachers’ practices were analysed before, during and after their participation in a professional learning community. The results show that two teachers made modest shifts in three of the five key dimensions of their lessons and one of the two teachers sustained these shifts. The two other teachers did not make major shifts in their teaching. The shifts are linked to learning activities in the professional learning community, which involved the teachers in conversations about learners’ errors and learners’ learning needs, and designing lessons to address these needs. Findings from the study indicate how teacher-learning activities in a professional learning community can support shifts in teachers’ teaching and explain why changes differ among teachers.

Contexts, Resources, and Reform

This chapter provides a contextual description of the five classrooms in the book and locates them against a more general contextual background of the contexts of schooling in South Africa. It argues that while reform practice is difficult to instantiate in well-resourced contexts, it is even more difficult in classrooms of low socio-economic status, with fewer resources. At the same time, if reforms do mitigate achievement gaps, then if they are poorly distributed across rich and poor, inequity may increase, rather than decrease. The five classrooms in the study are described in terms of the material and human resources; learners’ knowledge, as a key aspect of human resources is described and the tasks that the teachers used are also described.

Teaching Mathematical Reasoning: A Challenging Task

This chapter presents an overview of current literature on mathematical reasoning, and learning and teaching mathematical reasoning. Much of this literature informed the research in this book and I present an extensive review to situate our work in the field. The main aims of the chapter are to (1) argue for the centrality of mathematical reasoning in mathematics education; (2) describe how current theories of learning inform discussions of mathematical reasoning and (3) outline possibilities and constraints for teaching mathematical reasoning in secondary school classrooms. The argument is twofold, first that teaching and learning mathematical reasoning is a challenging task for both teachers and learners, second, even given the challenges, it is a task that is well worth undertaking, because developing mathematical reasoning is key to developing sound mathematical knowledge and proficiency.