# Jill AdlerUniversity of the Witwatersrand | wits · Wits School of Education

Jill Adler

B Sc, STD, M Ed, PhD

## About

118

Publications

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Introduction

Additional affiliations

January 2010 - present

January 2007 - December 2014

July 1997 - December 2002

## Publications

Publications (118)

We describe and use an analytical framework to document mathematics discourse in instruction (MDI), and interpret differences in mathematics teaching. MDI is characterised by four interacting components in the teaching of a mathematics lesson: exemplification (occurring through a sequence of examples and related tasks), explanatory talk (talk that...

This article reports an investigation into how students of a mathematics course for prospective secondary mathematics teachers in England talk about the notion of ‘understanding mathematics in depth’, which was an explicit goal of the course. We interviewed eighteen students of the course. Through our social practice frame and in the light of a rev...

In this paper, we focus on an initiative in England devised to prepare non-mathematics graduates to train as secondary mathematics teachers through a 6-month Mathematics Enhancement Course (MEC) to boost their subject knowledge. The course documentation focuses on the need to develop “understanding mathematics in-depth” in students in order for the...

In this paper we draw on two research projects in South Africa to describe and discuss the language practices of teachers
in primary multilingual mathematics classrooms. We focus particularly on code-switching – moving across languages and discourses.
We situate the paper in the policy and practice environment of post-apartheid South African educat...

One of the defining features of the current South African context is the breath-taking extent and pace of social, political and economic transformation desired by the country in this early post apartheid period. Rapid change produces both extreme and often contradictory conditions that in turn throw a spotlight onto complex social practices. What m...

Levering change is hard, and an incremental process. In the education process it requires an interaction between teachers, resources and learners. Levering change with human resources—teachers themselves, is a long term, time-intensive process requiring investment and commitment. The teacher–resources relationship is complex and not always optimal,...

Despite compelling arguments for the importance of revisiting school mathematics in pre-service mathematics teacher education, there is little indication of how such revisiting might be done, particularly at secondary level. We argue that revisiting provides three key opportunities for learning: (1) additional time on the mathematics that pre-servi...

This chapter focuses on mathematics teachers’ knowledgeable use of examples - their exempiflication - with explicit attention to principles of variation across example sets. We present a rationale for the co-ordination of principles of variation and exemplification, and then illustrate what and how we apply this in our professional development work...

We offer here some hypotheses about how teachers’ subject-matter knowledge is implicated in instruction through the lens of mathematical discourse in instruction (MDI) framework (Adler & Ronda, 2015).

This is a commentary on the special issue articles on rituals and exploration in mathematics teaching and learning. It explores the question of whether and how we can learn from research on rituals and ritualization, when these are typically associated with poor or even no learning of mathematics. The papers in the special issue show there is indee...

The Wits Maths Connect Secondary Project, a research-linked professional development project, included Lesson Study with teachers in school clusters. When two teachers shared their experiences of doing Lesson Study, they spoke spontaneously about how much they had learned about choosing and using examples in their teaching. Exemplification is a key...

Previous studies have reported the influence of professional development (PD) on participating teachers’ identities. However, what goes on in PDs, how and why they shape particular identities require further investigation. This study contributes in this direction by drawing on the notions of practice-linked identities and identity resources to exam...

The analytical approach for describing teachers’ Pedagogical Design Capacity (PDC) adopted in this chapter is part of a larger study investigating mathematics teachers’ use of a prescribed textbook. In this chapter, we describe teachers’ PDC through (i) the type of use of the curricular resource, that is, whether use is deliberate or tacit; as well...

Lesson Study (LS) is a collaborative learning space of professional development for teachers and researchers who support them. Teachers selected a lesson on “simplifying algebraic expressions with brackets in different positions” with Grade 10 learners in the context of a professional development project in South Africa. Structured by a discursive...

As a context for professional development, Lesson study (LS) has been used widely and differently around the world. Here, we look at LS as a community of practice (CoP) in which teachers and researchers work together on a specific object of learning. We highlight two ethical dilemmas that emerged in one cycle of LS in a project in South Africa, in...

What role does mathematics play in the teaching and research of some or all of the ‘disciplines’ of mathematics education, science education and the social sciences? This question was that to which I was asked to respond at the Academy of Science of South Africa’s workshop on the mathematical sciences, held in September 2016. As suggested by the ti...

The preceding quote from Mr T contains his instruction to the class for solving for x in x2> 36,
and follows after the main part of the lesson where he demonstrated and wrote up the
solution to the quadratic inequality exemplified by x2> 4. He instructed learners to write the
'answer'in a particular format. As he spoke of 'this format', he point...

This article reports a review of research in mathematics education in South Africa published in local and international journals in the period 2007–2015. The purpose of the review was to describe the landscape of mathematics education research in the country over the past (almost) decade. Findings indicate that the mathematics education research co...

This chapter provides a commentary on the Mathematics Education and Numeracy Chairs initiative in South Africa. The discussion is located, in the first instance, in the context of primary mathematics as an under-researched field in South Africa, and further in the ways in which South African research in this area speaks to and informs broader conte...

It is well known that learner performance in mathematics in South Africa is poor. However, less is known about what learners actually do and the extent to which this changes as they move through secondary school mathematics. In this study a cohort of 250 learners was tracked from Grade 9 to Grade 11 to investigate changes in their performance on a...

In Chapter 4, we analysed the opportunities made available to learn in Mr T’s lesson. We focused on three key elements of teaching. We first examined the examples and related representations for solving the quadratic inequality in the lesson. We then looked at how Mr T and his learners used language to name the mathematical ideas they were talking...

Research for Educational Change presents ways in which educational research can fulfil its commitments to educational practice. Focussing its discussion within the context of mathematics education, it argues that while research-generated insights can have beneficial effects on learning and teaching, the question of how these effects are to be gener...

The influences on governments for policy changes in schools range across many agencies, including the political party in power. When policies change, the sources of these influences are not always clear. The project whose work is presented in this special issue examines what these changes look like in terms of the differences in assessment tasks of...

In this paper, we propose an analytic tool for describing the mathematics made available to learn in a ‘textbook lesson’. The tool is an adaptation of the Mathematics Discourse in Instruction (MDI) analytic tool that we developed to analyze what is made available to learn in teachers’ lessons. Our motivation to adapt the use of the MDI analytic fra...

This chapter is inspired by the range of responsibilities that Michèle Artigue took on beyond her research work. It considers practically how she came to take on these responsibilities, as well as her goals and the impacts of her work. In the first section, Jean-Baptiste Lagrange reflects upon and draws lessons from the responsibilities taken on by...

Mathematical problems that make links to the everyday and to disciplines other than mathematics—variously referred to as practical, realistic, real-world or applied problems in the literature—feature in school and undergraduate mathematics reforms aimed at increasing mathematics participation in contexts of inequity and diversity. In this article,...

In this chapter we use a different lesson, a lesson that was taught by another teacher, Ms H, who also participated in the WMCS professional development (PD) project. It was taught more than a year after the video of Mr T's lesson was taken. In the intervening time, the WMCS teachers learned about the benefits of well-structured example sets for th...

We describe and use an analytical framework to document mathematics discourse in instruction (MDI), and interpret differences in mathematics teaching. MDI is characterised by four interacting components in the teaching of a mathematics lesson: exemplification (occurring through a sequence of examples and related tasks), explanatory talk (talk that...

I will develop and then reflect on two inter-related claims in this chapter. The first is that the sets of concepts that have emerged through research on mathematics knowledge for teaching (MKT), while relatively recent, have nevertheless proliferated. This is not surprising given that as part of educational knowledge, it is part of a horizontal kn...

It is wellknown that the majority of South African learners achieve extremely poorly in Mathematics. Many claim that one of the causes of this poor attainment is teachers’ weak knowledge of mathematics, and propose that improving teachers’ mathematical knowledge would improve learner attainment. However, the evidence-base for this proposed solution...

Purpose
– The purpose of this paper is to illustrate the methodology used by the authors to describe the enacted object of learning, a methodology where data production and analysis is rooted in a theorisation of pedagogy. The authors share how the authors used this methodological approach to provide a comprehensive description of the enacted objec...

In this chapter, we put Wenger’s communities of practice (CoP) theory to work to understand and describe pre-service mathematics teacher education practice in multilingual classrooms. Drawing on study data, we show how we expanded Wenger’s communities of practice theory into a framework that could productively analyse the nature of pre-service math...

In this paper, we put Basil Bernstein’s theory of pedagogic discourse to work together with additional theoretical resources to interrogate knowledge and practice in mathematics teacher education. We illustrate this methodology through analysis of an instance of mathematics teacher education pedagogic practice. While the methodology itself is our f...

In this chapter, we propose a framework for describing the opportunities for learning mathematics made available in a lesson and the nature of this mathematics. We name the framework Mathematical Examples, Tasks, and Talk (MET squared or MET2). The framework incorporates the core components of instruction - examples, tasks, and talk – but they are...

We illustrate an analytic framework for teachers’ mathematics discourse in instruction (MDI). MDI is built on three interacting components of a mathematics lesson: a sequence of examples and related tasks; accompanying talk; patterns of interaction. Together these illuminate what is made available to learn. MDI is grounded empirically in mathematic...

In this article, we share our combination of analytical concepts drawn from the literature with a set of grounded framing questions for thinking about differences in the nature of coherence and connections in teachers' mathematical discourses in instruction (MDI). The literaturebased concepts that we use are drawn from writing focused on transforma...

This paper proposes a reconceptualization of the psychological constructs of structural and operational conception. Drawing on Morgan, Moschkovich and Sfard, we present a theoretical perspective that views talking and looking operationally and structurally as ways of acting in a socio-political mathematical practice. We use transcripts of first-yea...

This chapter argues for attention to professional knowledge in use in descriptions of classroom practice and offers a methodology
to this end. It builds on previous work that conceptualised resources in use in school mathematics teaching and recent work
that focuses more directly on knowledge in use in practice, arguing that these shape the mathema...

This paper interrogates the recontextualisation of available assessment items developed for research purposes that measure mathematical knowledge for teaching, into scenarios for use in qualitative studies related to mathematics teachers' subject matter knowledge. It draws from interviews with teacher participants in the Wits Maths Connect-Secondar...

Teachers involved in action research in mathematics classrooms typically focus on their pedagogical practice, and rarely challenge the mathematical content of their teaching. The first part of this article supports this claim in terms of an analysis of the teachers-as-researchers movement. It then reports on a study where teachers were researching...

In this chapter, we discuss research that investigated what, how, and with what possible effects, mathematical knowledge and
related practices are constituted in and across a range of programmes, across diverse teacher training institutions in South
Africa. Our study includes three cases from three different teacher education sites where teachers w...

I begin this paper with a brief discussion of what can be considered systemic ‘problems’ in mathematics education before moving on to the research problem I am currently investigating. This broad introduction will help locate the QUANTUM research project – a study of the mathematical work of teaching – that forms the substantive part of this paper....

In their description of the mathematical work of teaching, Ball, Bass & Hill (2004) describe the mathematical problem solving that teachers do as they go about their work. In this paper we add to this description through our study of teaching of probability in a grade 8 multilingual classroom in South Africa. We use instances of teaching to highlig...

In this paper, I clarify the notion of mathematics for teaching (its matter) and argue that it matters (it is important), particularly for mathematics teacher education. Two examples from studies of mathematics classrooms in South Africa are described, and are used to illustrate what mathematics teachers use, or need to use, and how they use it in...

The QUANTUM research project in South Africa has as its central concern answering the question of what is constituted as mathematics in and for teaching in formalised in-service teacher education in South Africa and how it is constituted. Entailed in the question is an understanding that, in practice, selections of content in mathematics teacher ed...

In any education system, curriculum alone cannot fulfill reform demands imposed onto teachers to help learners make meaning of subject contents they learn. This paper revisits the notion of resources as explored in a mathematics teacher professional development project that focused on algebra learning. As a way to promote the use of manipulatives i...

I argue that mathematics teachers’ professional knowledge matters, and so requires specific attention in mathematics teacher education. Two examples from studies of mathematics classrooms in South Africa are described, and used to illustrate what mathematics teachers use, or need to use, and how they use mathematics in their practice: in other word...

In this paper, I examine resources and their use in school mathematics. I do so from the perspective of mathematics teacher education and with a view to the practice of school mathematics. I argue that the effectiveness of resources for mathematical learning lies in their use, that is, in the classroom teaching and learning context. The argument pi...

Initial mathematics teacher education is primarily concerned with knowledge–the acquisition of knowledge required for the
teaching of mathematics. Opinions as to what exactly comprises this knowledge and how it is best delivered and best learned
varies widely across different contexts. In what follows, we will look more closely at this concept of t...

Mathematics teacher education can be seen as directly related to activity in mathematics
classrooms and the success (or other) of students learning mathematics
worldwide. In what ways does what is published in the field of mathematics teacher
education inform us about key question and issues, about programmes for educating
teachers, and about resea...

In this paper, a review of journal articles containing South African research in mathematics and science education in the 2000 – 2006 period is undertaken, and used to identify significant clusters of research interest on the one hand and areas of under-representation of research on the other. In mathematics education, significant clusters were fou...

This paper describes and characterizes the science and mathematics education communities in South Africa by looking at their refereed outputs from 2000–2006. The publications under study are studies focusing on South Africa in local and international journals from 2000–2006. Our interest lies in looking more closely at the authors to understand how...

In this paper, I examine resources and their use in school mathematics. I do so from the perspective of mathematics teacher education and with a view to the practice of school mathematics. I argue that the effectiveness of resources for mathematical learning lies in their use, that is, in the classroom teaching and learning context. The argument pi...

In this paper, we consider our use of activity theory to examine empirical data from a study of reform in England – the implementation of the mathematics strand of the Key Stage 3 Strategy in two schools. Our concerns are largely methodological – we consider the aspects of reform that more traditional activity theory methods and foci were able to t...

We r eport on two c ase s tudies in whi ch we investigated m athematics for tea- ching. We were interested in the mathematical k nowledge teachers need to know, and know how to use, in order to teach mathematics well. The two case studies focused on t he t eaching of pr obability in Gr ade 8 a nd t he t eaching of functions in Grade 10. We discuss...

This paper describes some mathematical practices in and across school contexts in South Africa. Through this description,
I challenge a decontextualised notion of schooling and so too a decontextualised notion of mathematical practices in school.
Through examples of mathematical practices within and across school contexts in South Africa, I illustr...

In this paper we discuss our study of three instances of formalised in-service mathematics teacher education courses. We found that in varying ways, all courses draw in sensible experience by appealing to images of the teacher and teaching as a central resource for modelling the teaching and learning of mathematics. One of the courses also prioriti...

This paper reports on a study that investigated the kind of mathematical work a specific teacher does as he goes about his teaching. The study involved the pedagogic practice of one teacher teaching linear functions to his class of grade 10 learners in a secondary school in Gauteng, South Africa. Drawing on a theory of pedagogic discourse, we worke...

This article reports a review of research in mathematics education in South Africa published in local and international journals in the period 2007–2015. The purpose of the review was to describe the landscape of mathematics education research in the country over the past (almost) decade. Findings indicate that the mathematics education research co...

This article describes an investigation into mathematics for teaching in current teacher education practice in South Africa. The study focuses on formal evaluative events across mathematics teacher education courses in a range of institutions. Its theoretical orientation is informed by Bernstein's educational code theory and the analytic frame buil...

This paper reports a survey of research in mathematics teacher education from 1999 to 2003 done by an international team of five mathematics educators and researchers. The survey included published research in international mathematics education journals, international handbooks of mathematics education and international mathematics education confe...

In this paper we examine three instances of formalised in-service mathematics teacher education courses. We find that in varying ways, two of these courses prioritise the use of the visual as a central resource for the modelling of teaching mathematics and of the teaching and learning of mathematics. The way in which the visual is used produces an...

The changing landscape of post-apartheid education in South Africa has seen significant reform in the mathematics curriculum and marked growth in the community of researchers investigating mathematics education. The editors of this collection argue that a new agenda is required in mathematics education research in order to better understand the con...

Building on the work on ethics in educational research in recent publications, we present a framework for ethical practice
in mathematics education research. In particular, we discuss what are the implications of claiming or denying a particular
piece of research as acceptable within the community. We argue that researchers must be aware for whom t...

This article reports on an investigation that used concept mapping to explore first-year university students' understanding of key secondary mathematical concepts. The extent to which these students were able to make connections between concepts was a focus in the investigation. A concept map constructed by two students is presented and examined in...

In this paper we describe and discuss the language practices of mathematics, science and English language teachers and learners in a sample of urban and rural, primary and secondary schools in South Africa. We focus particularly on the reception and production of language through code-switching, exploratory talk and discourse-specific talk. We situ...

In this chapter I have highlighted both usual and often hidden issues in the research design and process, and so brought into view, the messy and often contradictory social relations constitutive of social research. I have explained why and how I viewed teachers’ knowledge of their practices — their knowledgeability — as an important point of depar...