# Richard BarwellUniversity of Ottawa · Faculty of Education

Richard Barwell

## About

104

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Introduction

My research has two main themes. In one theme, I look at language and discourse in the learning and teaching mathematics. I have studied how second language learners or bilingual learners participate in school mathematics, how mathematicians use language to talk about mathematics, and how researchers write about mathematical thinking. In the other theme, I explore the role of mathematics and mathematics education in recognising and responding to the ecological crisis now happening on our planet.

## Publications

Publications (104)

The importance of the role of language/discourse in the learning and teaching of mathematics is noted in many mathematics curricula and standards documents. In the research literature, this role has been widely theorised from a Vygotskian perspective. This perspective is limited by some of its underlying assumptions, including an instrumental and s...

For more than twenty years, research on the learning and teaching of mathematics in multilingual classrooms has deployed the notion of language as a resource. I review and critique the development and application of this notion, focusing particularly on the work of Jill Adler, Mamokgethi Phakeng (formerly Setati), Nuria Planas and Judit Moschkovich...

Research focused on learning mathematics in a 2nd language is generally located in individual 2nd-language contexts. In this ethnographic study, I investigated mathematics learning in 4 different second-language contexts: a mainstream classroom, a sheltered classroom for Indigenous students, a welcome class for new immigrants, and a French-immersio...

This book examines multiple facets of language diversity and mathematics education. It features renowned authors from around the world and explores the learning and teaching of mathematics in contexts that include multilingual classrooms, indigenous education, teacher education, blind and deaf learners, new media and tertiary education. Each chapte...

There is no shortage of urgent, complex problems that mathematics education can and should engage with. Pandemics, forest fires, pollution, Black Lives Matter protests, and fake news all involve mathematics, are matters of life and death, have a clear political dimension, and are interdisciplinary in nature. They demand a critical approach. The aut...

Our project aims to promote intercultural dialogue in school mathematics, by exploring the experiences of migrant students and teachers in mathematics classrooms. Although data collection was initially designed to be conducted in person, some ethical issues have emerged as it moved online, due to the COVID-19 pandemic. This poster explores a series...

Many mathematics curricula emphasise the importance of communication in mathematics classrooms, supported by an extensive body of research. In much of the world, this emphasis promotes specific communicational practices as necessary or desirable in order to support mathematical meaning-making and effective learning of mathematics. In this paper, we...

Rising rates of obesity are of widespread public concern and are targeted by public health policies around the world. In this chapter, we examine the origins of the most common definition of obesity, which is based on the Body Mass Index (BMI). We draw on Skovsmose’s concept of formatting, combined with an examination of the origins of the BMI, to...

Climate change is an urgent global challenge. Responding to climate change requires significant critical mathematical understanding on the part of all citizens. In this chapter, we consider what a critical mathematics education for climate change might look like. We draw on ideas from Skovsmose’s work, including the notion of formatting, as well as...

In this introductory chapter, we first set out our broad characterisation of critical math- ematics education, drawing on contemporary issues including, for example, global cli- mate change and rapid societal challenges. Critical mathematics education is driven by urgent, complex questions; is interdisciplinary; is politically active and engaged; i...

Metaphors are recognized as bridging scientists’ challenges in communication with the public. In mathematics, however, which often involves abstract concepts and relations, less attention has been paid to the role of metaphors in public communication. In this article we examine the metaphors appearing in the discourse of 10 mathematicians in five r...

While there are several studies analysing how mathematics education is portrayed in news media discourses, there has been little examination of the construction of different stakeholders (e.g. teachers, parents, curricula). In this paper, we report our analysis of a corpus of Canadian newspaper reports on mathematics education, focusing on the unde...

To make sense of issues related to mathematics and its teaching and learning, many researchers draw on social, historical, and cultural perspectives of learning and becoming. A wide range of applications and interpretations of this view reflects the vitality of this approach. The central purpose of this working session is to invite the participants...

With the fast-changing political world and speedy circulation of information from different sources and with different levels of accuracy, it is necessary for students to learn to think critically about the current issues of the world that are affecting the well-being of the inhabitants of planet Earth, including one of the most urgent threat to ou...

Mathematics education is often in the news and is often presented in controversial terms. The nature of news reporting influences public opinion, public policy and the context of mathematics teaching. In this study, we looked at how mathematics is framed in Canadian newspaper reports after the publication of recent PISA results. We analysed 26 arti...

The presence of migrant children in mathematics classrooms can create challenges for students and teachers, who may experience tensions, transformation and adaptation. Our recently launched research project aims to generate accounts of the experiences of student migration in Canadian mathematics classrooms, as well as the experiences of their teach...

The past two decades have seen an increased interest in education, especially in core areas such as mathematics, language and science. This is in part a consequence of the increase in the number of international comparisons of educational outcomes, such as PISA and TIMSS. Much research has focused on the contributions that curricula, financial reso...

This entry reviews research on language background in mathematics education. It looks at theoretical perspectives on language background, influence on mathematics attainment, as well as the role of language background in the learning and teaching of mathematics, mathematics teacher education, and research mathematics education.

Research on the learning of mathematics relies heavily on descriptions of such learning. In this article, I am interested in how the organisation of these descriptions of learning may be understood. To do so, I draw, in particular, on Bakhtin’s (1981) notion of the chronotope. Bakhtin’s work offers a way to go beyond the general category of ‘descri...

Much linguistic ethnography research examines language in classrooms, particularly in contexts of language diversity, such as second-language classrooms, multilingual classrooms, bilingual classrooms, Content and Language Integrated Learning (CLIL) classrooms, urban classrooms and complementary schools. Conducting such research is methodologically...

This chapter provides an overview of the journal For the Learning of Mathematics (FLM) from the point of view of its current editor and his immediate predecessor. It begins with a brief description of the nature of genres, especially in academic writing and more specifically in mathematics education. The aims of the journal and how these are situat...

Media reporting about mathematics education includes descriptions of different aspects of mathematics teaching, learning, curriculum and policies. As with any media reporting, such descriptions are not neutral. They reflect on and portray specific discourses and agendas about mathematics education, with quotations or experiences of different stakeh...

Mathematics Teaching 263, 31-34.
https://www.atm.org.uk/write/MediaUploads/Journals/MT263/1/MT26310.pdf

This article presents the results of an analysis of ethnographic data collected in three second language mathematics classrooms in Canada. The elementary school classes consisted of a group of indigenous students, a group of new immigrant students and a class in a French immersion programme. The focus of the analysis was on the sources of meaning s...

Planet Earth is beset by myriad environmental problems attributable to the unsustainable nature of human activities. These problems include climate change, species loss, pervasive pollution, and ecosystem degradation, all of which are examples of ‘post-normal situations’: they generate urgent, complex problems involving a high degree of risk and un...

Word problems are a commonly used genre of mathematics classroom tasks in which mathematical problems are presented in a realistic context. While word problems have been extensively researched as mathematical tasks, less attention has been paid to them as social texts. Research has, however, established differences in how students from different so...

In this chapter, I provide an overview of research on writing in mathematics classrooms, including some of the features of formal written mathematics, and with particular attention to English Language Learners. I introduce a Bakhtinian perspective on language, including an emphasis on the inherent tensions between standard or conventional forms and...

Teaching mathematics to students who are new to schooling and new to English, such as, in particular, refugee arrivals in Canada, is particularly challenging. In this chapter, we describe some aspects of our work with a group of teachers at a Catholic school in Toronto, in which we collaborated to find ways to support the many such students in the...

Climate change is one of the most urgent human concerns. Mathematics, in various degrees of complexity, is used to communicate climate change to scientists, politicians, policy makers, the general public and children. Drawing on ideas from critical citizenship and critical mathematics education, we ask how incorporating issues of climate change int...

There exist various situations in which mathematics is learned in a second language, including in the context of immigration, indigenous languages or immersion programs. Little research on this topic has examined mathematics learning across a range of such contexts. In this study, I collected ethnographic data in four different second-language math...

In this chapter, I report an analysis of the interaction of two grade 6 students in a second-language mathematics classroom in Canada. The two students are of indigenous heritage and attend an English-medium public school. The interaction arose during their work with the researcher on a textbook word problem about time zones. The analysis draws on...

While analysis of how children are constructed in mathematics education research discourses dates back to the 1980s, there has been much less analysis of the construction of children in media reporting about mathematics education. In this paper, we report our analysis of a corpus of Canadian newspaper reports on mathematics education, focusing on t...

In this paper we argue that the academic fields of critical mathematics education and post-normal science are complementary and can provide mutual benefits for the future. Post-normal science promotes the idea of extended peer communities, through which citizens participate with knowledge and insights in urgent and complex societal issues with conf...

An online survey was carried out in Norway and Canada to get a first impression of what teachers do in classrooms, and why, in relation to climate change and mathematics education. Barbosa’s perspectives of mathematical modelling inspired the questionnaire, in that his perspectives of modelling were exchanged for perspectives of climate change. We...

Research on the socio-political dimensions of language diversity in mathematics classrooms is under-theorised and largely focuses on language choice. These dimensions are, however, likely to influence mathematics classroom interaction in many other ways than participants’ choice of language. To investigate these influences, I propose that the notio...

Throughout much of her work, Jill Adler’s abiding interest has lain in the political implications of language in practice in mathematics classrooms, not solely because of the cultural importance ascribed to success in mathematics, but also because of there being some specific interactions of significance to be found within mathematics–language, our...

In the past few decades, language has become an active focus of investigation in educational research, including research in mathematics education. Such a focus is a symptom of a relatively recent paradigmatic shift whose chief characteristics are a new understanding of the student and an increasing awareness of the complexities of learning context...

This chapter provides the introduction to this ICMI Study 21 volume. It includes: a discussion of the place of this study and its topic within ICME; a discussion of what is meant by the study title; and a brief historical account of research on this topic in mathematics education. The chapter also recounts the various stages of the study, including...

Throughout the literature on mathematics teaching in multilingual, bilingual or second language classrooms and other contexts of language diversity, there has been a shift from thinking in terms of deficits and barriers to a discourse of dilemmas and tensions. While this work has highlighted the complexity of multilingual mathematics classrooms, it...

There is a growing awareness in the social sciences that globalisation has changed the nature of ‘diversity’. The old certainties of distinct ethnic groups, with distinct cultures, speaking distinct languages and living in distinct communities in specific locations are increasingly untenable. This shift is as applicable in mathematics classrooms as...

For this topic study group, 35 papers were accepted from a range of different cultural, linguistic and country contexts. The papers were discussed under specific thematic questions. These themes provide an organizing framework for this report that draws its content from the papers and the discussion in the TSG 30 sessions. The submissions illustrat...

Research on the learning and teaching of mathematics in contexts of language diversity has highlighted a number of common tensions that arise in a variety of contexts. These tensions can be explained by Bakhtin’s characterization of two sets of forces that are present in any utterance: centripetal forces represent the drive for unitary language, st...

The day-to-day business of being a science or mathematics teacher involves the continuous assessment of students. This, in turn, is an inherently discursive process. The aim of the present study is to examine some of the specific discursive practices through which science and mathematics knowing is jointly produced through classroom interaction. In...

Research on mathematics teacher knowledge, including work on mathematical knowledge for teaching, draws heavily on Shulman’s categories of teacher knowledge. These categories have been adopted, developed and modified by mathematics education researchers. This approach has led to some valuable insights. In this paper, I draw on discursive psychology...

Climate change is one of the most pressing issues of the 21st Century. Mathematics is involved at every level of understanding climate change, including the description, prediction and communication of climate change. As a highly complex issue, climate change is an example of ‘post-normal’ science – it is urgent, complex and involves a high degree...

Mathematics curricula increasingly emphasise the importance of mathematical communication. Students are seen as progressing from the use of a more informal or everyday form of communication to a more mathematical approach. There have, however, been very few studies of how mathematicians actually talk about mathematics. This paper reports analysis o...

What does linguistic or cultural diversity look like in a mathematics classroom? How does such diversity influence the teaching or learning of mathematics? In this chapter, I address these and related questions. Specifically, I draw on Bakhtin’s notion of heteroglossia to analyse the literature on teaching and learning mathematics in linguistically...

This chapter introduces the idea of ‘discursive demands’ as an overlooked aspect of the particular challenges faced by second language learners of mathematics. Discursive demands are defined as the interactional requirements arising in mathematics through which second language learners and their interlocutors jointly produce both cognition and cont...

Research in mathematics education is a discursive process: It entails the analysis and production of texts, whether in the
analysis of what learners say, the use of transcripts, or the publication of research reports. Much research in mathematics
education is concerned with various aspects of mathematical thinking, including mathematical knowing, u...

Mathematics classrooms are increasingly multilingual, whether they are found in linguistically diverse societies, urban melting pots or planned bilingual programs. The chapters in this book present and discuss examples of mathematics classroom life from a range of multilingual classroom settings, and use these examples to draw out and discuss key i...

A variety of perspectives on the nature and role of discourse in the teaching and learning of mathematics have been developed and applied in recent years. The conduct of research in mathematics education can also, however, be viewed from a discursive perspective. In this paper, I draw on discursive psychology, which has been described as an anti-co...

In this paper, we draw on our on-going collaboration to explore aspects of the role of multilingualism in mathematics classrooms through a comparison between two primary school mathematics lessons relating to arithmetic word problems. The data that form the basis of our comparison arise from two recently completed studies on the role of multilingua...

Book reviewed in this article: Learning discourse: discursive approaches to research in mathematics education C. Kieran, E. Forman & A. Sfard (Eds) Dialogue and learning in mathematics education: intention, reflection, critique H. Alrø & O. Skovsmose

This paper concerns the relationship between learning English as an additional language (EAL) and school mathematics. In bilingual education, Cummins has proposed a distinction between coercive and collaborative power-relations as an important consideration in the education of such students, advocating collaboration as a means to empower such stude...

Research into the teaching and learning of language and content in mainstream classrooms research tends to treat content as a fixed body of knowledge to be (re)constructed by learners. There is little research which seeks to understand how language and the curriculum are constructed and related in interaction by learners. In this paper, I report an...

The teaching and learning of language and curriculum content in the same classroom at the same time is an increasingly important area of research within bilingual education and related fields. This article introduces a special issue consisting of six research articles on this theme. The article maps out four dimensions of language and content integ...

There has been little research in the UK into how students learning English as an additional language (EAL) learn mathematics. This article reports results from a three‐year study of the participation of learners of EAL in Year 5 in an arithmetic word problem task. The research, drawing on ideas from discursive psychology, used discourse analysis t...

1. A dialogic perspective on learning in multicultural mathematics classrooms Approaches to the study of human interaction can be divided into two broad approaches that Linell (1998), for example, refers to as monologism and dialogism. Monologism is associated with a formalist perspective on social interaction, with communication seen as a kind of...

The preceding set of papers has explored various aspects of the role of language in mathematics education. The papers reflect the work of individual contributors. An important part of our collaboration, however, has been the conversation between us. This paper reflects on aspects of that conversation, as we draw together some of the themes that hav...

Mathematics is commonly seen as a discipline with no place for linguistic ambiguity. In this paper, the treatment of ambiguity in two data extracts is critically examined. Analysis draws on two contrasting models of the nature of mathematics and mathematical language. The formal model sees meaning as fixed and relating to language relatively unprob...

Mathematics is a central part of school curricula around the world. There has been much interest in linguistic aspects of the teaching and learning of mathematics, both from mathematics educators and from applied linguists. This short paper introduces a set of five articles exploring the intersection between these two communities. The articles all...

The effects of multilingualism have been an explicit focus of a number of PME research reports in recent years. These reports, however, are located in a wide range of socio-linguistic circumstances, making it difficult to compare findings and develop a clearer understanding of the relationship between the teaching, learning or understanding of math...

This paper provides an overview of some of the key ideas of discursive psychology and its theoretical and methodological approach
to the analysis of interaction. These ideas include a view of interaction as discusive practice, primarily structured by the
social action it performs, rather than by its content. The relevance of this approach to resear...

This paper presents a preliminary analysis from a study designed to investigate the participation of students learning English
as an additional language(EAL) in primary school mathematics. A key question for the study concerns how such students make
sense of mathematics classroom interaction. Primary data consists of two transcripts in which a 9-ye...

The notion of attention as a discursive practice has emerged as a key element of my approach to the analysis of students' participation in mathematics classroom interaction. The principal purpose of this paper is to describe and illustrate this approach, which draws on ideas from discursive psychology and conversation analysis and sees talk primari...

Despite plenty of practice, many students find interpreting and solving word-problems difficult. How can teachers work with students so that they learn to make appropriate sense (or should it be "inappropriate sense"?) of word-problems? One way to investigate how students make sense of word-problems is to ask them to write some of their own. The au...

interaction, including in classroom discourse. Edwards and Potter (1992), for example, highlight a number of rhetorical strategies or 'devices' and show how they can be used to strengthen claims, accounts or descriptions of reality and undermine possible alternative versions. In this paper, I take a rhetorical perspective to analyse an extract from...

In this paper, I want to consider the interface between linguistic ethnography and education, where that interface is represented by the relationship between the researcher and their classroom data. In particular, I want to argue that this relationship is complex: the interface is very blurred. The key issue I want to consider is that of reflexivit...