Multilingualism in Mathematics Classrooms: Global Perspectives

by Richard Barwell (Editor)

Overview

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 issues for the teaching and learning of mathematics and language. These issues relate to pedagogy, students’ learning, curriculum, assessment, policy and aspects of educational theory.

The contributions are based on research conducted in mathematics classrooms in Europe, South Asia, North America and Australia. Recurring issues for the learning of mathematics include the relationship between language and mathematics, the relationship between formal and informal mathematical language, and the relationship between students’ home languages and the official language of schooling.

Product Details

ISBN-13:	9781847692054
Publisher:	Multilingual Matters Ltd.
Publication date:	09/15/2009
Series:	Bilingual Education & Bilingualism Series , #73
Pages:	200
Product dimensions:	6.50(w) x 9.40(h) x 0.70(d)

About the Author

Richard Barwell is associate professor at the Faculty of Education, University of Ottawa, Canada. His research is located in the intersection of applied linguistics and mathematics education, with a particular focus on multilingualism/ bilingualism in the teaching and learning of mathematics. His research interests include mathematics classroom discourse, mathematics learning in multilingual settings and the relationship between learning language and learning curriculum content and his work has been published in peer-reviewed journals in applied linguistics, mathematics education and general education. Prior to his academic career, Dr. Barwell taught mathematics in the UK and in Pakistan, where his interest in language and mathematics first arose.

Read an Excerpt

Multilingualism in Mathematics Classrooms

Global Perspectives

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By Richard Barwell

Multilingual Matters

Copyright © 2009 Richard Barwell and the authors of individual chapters
All rights reserved.
ISBN: 978-1-84769-377-8

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CHAPTER 1

Multilingualism in Mathematics Classrooms: An Introductory Discussion

RICHARD BARWELL

Farida is a student in a medium-sized urban primary school in the United Kingdom. She has attended the school since she joined the nursery class and is now in Year 5 (9–10 years old). Her family, which is from Pakistan, lives near to the school and her parents work for long hours in the shop they run. At home Farida speaks Punjabi, Urdu and English at different times. When I first met Farida, she told me a bit about the mathematics she had recently been working on, including the following ('she' refers to her teacher, Miss T):

oh yeah, circle, and shapes and she talks about three Ds and two Ds like, but one face and hexadas she like says six sides yeah and, and, Miss T like, choose hepsadas, you have six sides, yeah? and pentagon has eight sides, um, and ummm, ummm ...

What mathematics can you see in what Farida says? What language issues might arise? If you were her teacher, what mathematics and what language would you want to work on with her? When she says 'pentagon has eight sides' is that a language issue? A mathematics issue? Both? Or just a slip of the tongue?! More generally, does multilingualism have any effect on the attainment of students like Farida in mathematics? How does multilingualism affect how such students participate in mathematics lessons? What role do students' different languages play in their learning of mathematics? What can we do as teachers' to support students like Farida? How can we balance teaching mathematics with teaching Farida the language of mathematics?

This book explores many of these questions, drawing on research and practice in a variety of different multilingual mathematics contexts. The book has two related aims. One is to give a sense of the diversity of what multilingual mathematics classrooms can be like. The case of Farida givessome sense of what multilingualism in one mathematics classroom in the United Kingdom might involve. The second aim of the book is to explore issues arising in these particular contexts in such a way that this exploration informs practice across contexts. This aim is not about providing simplistic generalisations or recipes for teaching. Language, learning and society are too complex for that. Rather, by discussing issues that arise in one context, readers will, I hope, encounter new perspectives and new ways of thinking about their own.

Later in this introduction, I introduce the nine contributions that make up the main part of the book. Before that, however, I want to set the scene. First, I provide an overview of research findings on a key question that is not significantly addressed in the chapters that follow: does multilingualism make any difference to students' attainment in mathematics. Second, I briefly highlight some of the key ideas that have emerged in previous classroom research concerned with multilingualism and the teaching and learning of mathematics, since these ideas have influenced much of the more recent work presented in this book. I cannot move on to address any of these points, however, without first clarifying the focus of the book.

What Makes a Mathematics Classroom Multilingual?

Farida's experiences illustrate the complexity of even defining what 'multilingualism in mathematics classrooms' might be about. In a time of migration, global mobility and concern for minority rights, multilingualism is ubiquitous, yet almost infinitely varied. From the linguistic diversity arising from immigration to cities like London or New York, to the multilingualism of a South African township, from the relocation of a doctor or business executive and their family to Milan or Adelaide or Bangalore to the millions of Chinese who have learned English without ever having left China, multilingualism has many faces. For this book, and in the context of mathematics classrooms, multilingualism simply refers to the presence of two or more languages (and so includes bilingualism). Such a presence may be overt or tacit. That is, mathematics classrooms are considered to be multilingual if two or more languages are used overtly in the conduct of classroom business. And mathematics classrooms are also considered to be multilingual if students could use two or more languages to do mathematics, even if this does not actually occur, as Farida experienced in the United Kingdom.

This definition of a multilingual classroom encompasses a wide range of situations. In the United Kingdom, Farida was considered to be a learner of English as an additional language (EAL), a label that privileges English and obscures the anonymous 'additional' languages. In some parts of the world, other terms, including English as a second language (ESL) or English language learner (ELL), would be used instead, although they have similar drawbacks. In such situations, multilingual students are expected to learn the language of schooling, occasionally in addition to some of their other languages, more usually with indifference to them. The definition also includes classrooms found in many parts of the world in which students routinely use a mixture of two or more languages both in school and in wider society, such as in bilingual education programmes in North America or in some schools in Wales, or as in highly multilingual societies like South Africa or India. In some of these situations, students are not necessarily learners of the official language of schooling; it is simply one of several languages in which they are proficient. Although the most common concern of teachers and researchers is with situations in which multilingual students are learners of the classroom language, it should not be overlooked that this need not be the case.

Multilingualism and Attainment in Mathematics

Perhaps the most fundamental question asked by teachers, policy makers and researchers alike is 'does it make any difference'? Does multilingualism have any effect on mathematical attainment? There have been few large-scale surveys of mathematics attainment that investigate multilingualism as a factor. This is, perhaps, because variations in language proficiency, language structure and background social, cultural and political conditions make it difficult to attribute any difference in performance in mathematics even partly to multilingual factors. It is difficult to say whether Farida's performance in mathematics is affected by her proficiency in English, the fact that she has spent time in two different countries, the fact that she is a member of what is regarded as a minority ethnic group in the United Kingdom, the educational or economic status of her parents or a host of other possible factors. Nevertheless, although far from conclusive, large-scale studies have led to the concern that, in many contexts, multilingual students tend to underachieve in mathematics (Cocking & Chipman, 1988; Hargreaves, 1997). In the United Kingdom, for example, Phillips and Birrell (1994) found that a sample of EAL students from South Asian backgrounds had lower mathematics attainment than monolingual students and that they made less progress in mathematics over a year. These findings were in contrast to the same EAL students' performance in literacy tests, where they did as well as their monolingual counterparts. In a much larger study conducted in South Africa, where there are 11 official languages, Howie (2002, 2003) compared the mathematics attainment and English proficiency of more than 9000 secondary school students using data collected for an international comparison of mathematics and science performance (called TIMSS-R). In South Africa, the vast majority of schools use English as the formal teaching language for subjects like mathematics, so English is the language for textbooks and examinations. In most mathematics classrooms, however, several different languages can be heard (see, e.g. Setati & Adler, 2000). Howie found that higher scores on the English proficiency test were correlated with higher scores on the mathematics test and that proficiency in English was the most significant factor in explaining differences in students' mathematics scores.

Even where mathematics attainment appears to have some connection with proficiency in a second language like English, as in Howie's study, it is not clear whether differences are a result of linguistic, cultural, social or economic conditions or some combination of these and other factors (Secada, 1992). One complication, for example, is that the tests used to measure mathematics attainment in the research described above are written in English, so that students' proficiency in English may obscure their attainment in mathematics. A further issue in reporting the attainment of multilingual students is that these studies implicitly take the majority or dominant perspective when considering what counts as attainment and what counts as mathematics, downgrading other forms of mathematical achievement as less valuable. Farida may be able to do arithmetic in Punjabi, for example, but this will never be tested at her school in the United Kingdom. She may be familiar with mathematical practices from her parents' shop, but these practices may not be recognised or considered in her mathematics lessons. Often, the only attainment that counts is that measured by standardised tests written in the societally dominant language.

The impact of multilingualism on mathematics attainment is far from straightforward and the role played by language in a mathematics classroom is complex. A number of different researchers have attempted to reduce this complexity by focusing in more depth on the relationship between language proficiency and mathematical attainment. Proficiency is a logical factor to consider. Language is unlikely to be an issue for a student who is fluent in the classroom language, although there may be related issues of a cultural and social nature. For a student who is new to or learning the classroom language, on the other hand, there are clearly challenges in participating in and learning mathematics. Between these two positions lie the majority of EAL students in the United Kingdom, for example, or students joining immersion programmes, such as in many African or Asian contexts. In Farida's case, we can speculate that some aspects of learning mathematics may be problematic. Her attempts to say the word 'hexagon' suggest that, for her, mathematical discussion may be more convoluted and involve more attention to the language and so less attention to the mathematics than for her monolingual peers.

Researchers interested in language proficiency and mathematics attainment have been influenced by the work of Cummins (2000a, 2001), especially his 'threshold hypothesis'. The threshold hypothesis states that for multilingual students, having low levels of proficiency in all their languages is a cognitive disadvantage. Being highly proficient in two or more languages gives cognitive advantages to students, while proficiency in only one language offers neither advantage nor disadvantage. A number of studies have been based on the assumption that any cognitive advantage or disadvantage will show up in students' levels of mathematics achievement.

A key early study was conducted by Dawe (1983) in the United Kingdom in which he investigated the threshold hypothesis by testing groups of around 50 students aged 11–14 years from four different language backgrounds: Punjabi, Mirpuri, Jamaican Creole and Italian. As measures of linguistic proficiency, he used tests of English reading comprehension and tests of competence in their first language (L1). For mathematical performance, Dawe used a test of deductive reasoning or logical thinking set in English and a test of logical connectives, that is problems involving words like 'if ... then', 'either ... or' and 'but'. By comparing scores on the linguistic tests with those on the mathematical tests, Dawe did find evidence to support Cummins' thresholds, particularly the lower threshold. Students who did not score highly on either English or their L1 did not generally score highly in the mathematics tests. He also found some evidence to support the upper threshold. Interestingly, this effect was strongest in the Mirpuri group, despite the relatively low social status of Mirpuri as a dialect of Punjabi.

Since Dawe's (1983) work, a number of other studies have provided further evidence that linguistic proficiency is related to mathematical attainment, in line with Cummins' ideas. Clarkson, for example, has conducted several studies in Australia and Papua New Guinea involving multilingual students in upper primary school (e.g. Clarkson, 1992, 2007; Clarkson & Galbraith, 1992). His approach involved testing students' linguistic proficiency in English and in their L1 as well as on different aspects of mathematics, including mathematical word problems. He used the scores from the linguistic proficiency tests to divide the students into three groups. The low–low (LL) group consisted of students with low scores in two languages and the high-high (HH) group consisted of students with high scores in two languages. In line with Cummins (2000a, 2001), the third group consisted of students with a high score in one language only, which he called 'one dominant'. Clarkson (1992, 2007; Clarkson & Galbraith, 1992) then looked at the mathematics scores of the three groups of students. The LL groups recorded significantly lower scores than the other two groups on at least some aspects of mathematics in each study, supporting the idea of a lower threshold. Clarkson's research also provides evidence to support the upper threshold, although the link is less strong than that for the lower threshold.

Overall, Clarkson's (1992, 2007; Clarkson & Galbraith, 1992) and Dawe's (1983) work seems to show that students' proficiency in both (or all) of their languages does make a difference to their performance in somemathematical tasks. Students who are highly proficient in two or more languages are likely to do better than average, while strong proficiency in at least one language appears to be an important factor in ensuring that multilingual students match monolingual students in mathematics attainment. In the case of the latter, it is important to note that this proficiency does not have to be in the classroom language; proficiency in other languages can be just as valuable. In Farida's case, for example, one way of enhancing her level of attainment in mathematics might be to support the development of her proficiency in Urdu and Punjabi.

The research discussed above provides the backdrop to the work presented in this book. While research shows that multilingualism does have an effect on performance in mathematics, it offers less in the way of explanation. Clarkson (2007) has suggested that proficient bilingualism enhances students' meta-cognitive skills in mathematics, that is, it allows students to think more effectively about their mathematical thinking. This idea is supported by experimental research in psycholinguistics (for a review, see Moschkovich, 2007) that suggests, for example, that the advantages of multilingualism include an enhanced capacity to analyse problems and select useful information, while ignoring other less useful features (e.g. Bialystok, 1992, 1994). As Moschkovich (2007) argues, however, there is a tendency to reduce questions about the role of multilingualism in the teaching and learning of mathematics to questions about individual cognition. As I have already implied, social factors are also likely to be important. In particular, the work discussed above says little about what goes on in multilingual mathematics classrooms and about how multilingualism is implicated in the process of teaching and learning mathematics. This focus is one that concerns all of the contributors to this book. Before introducing their specific contributions, I will discuss some of the research that has previously been conducted on multilingualism in mathematics classrooms and that has informed much of the work in the chapters that follow.

Multilingualism and Learning and Teaching Mathematics

Classroom research that investigates multilingualism and the teaching and learning of mathematics has led to the identification of a number of tensions that arise when teaching mathematics in multilingual classrooms (see, in particular, Adler, 2001). These tensions appear to have relevance across a wide range of contexts. In this section, I highlight three of these tensions:

• Tension 1: between mathematics and language;

• Tension 2: between formal and informal language;

• Tension 3: between students' home languages and the official language of schooling.

During research in the United States, both Khisty (1995) and Moschkovich (1999a) explored the question of what teachers can do to facilitate bilingual student participation in mathematical discussions. In her ethnographic study of three Spanish–English bilingual mathematics classrooms, Khisty (1995) found differences in how teachers attended to the language of mathematics, particularly where potential ambiguities arise in both Spanish or English. Teachers who seemed to be more effective paid more attention to the language of mathematics as well as to the mathematics itself. Moshchkovich (1999a), meanwhile, studied a third-grade class of Spanish-speaking EAL students taught by a bilingual teacher. She noticed a key element in how the teacher managed the discussion was to ensure that the focus stayed on mathematics, particularly by listening to the mathematical content, however it was expressed. These studies seem to suggest that in some situations, it is important to pay careful attention to how students express their mathematical ideas, while in others, it is important to engage carefully with the mathematics itself. Moschkovich (1999a) is critical of some 'advice' for teachers, which, she argues, focuses excessively on mathematical vocabulary and the use of real or 'concrete' objects to support students' learning. It may be that engaging with students' mathematics is more productive than simply teaching students vocabulary. We can see the force of this position in the case of Farida. As we saw in the opening extract, she has acquired a great deal of reasonably accurate vocabulary, but is perhaps still working on how to use some of it!

(Continues...)

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Excerpted from Multilingualism in Mathematics Classrooms by Richard Barwell. Copyright © 2009 Richard Barwell and the authors of individual chapters. Excerpted by permission of Multilingual Matters.
All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
Excerpts are provided by Dial-A-Book Inc. solely for the personal use of visitors to this web site.

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Table of Contents

1 Mathematics in multilingual classrooms: an introductory discussion Richard Barwell

2 Mapping the mathematical langscape Frank Monaghan

3 Somali mathematics terminology: a community exploration of mathematics and culture Susan Staats

4 Politics and practice of learning mathematics in multilingual classrooms: lessons from Pakistan Anjum Halai

5 Mathematical word problems and bilingual learners in England Richard Barwell

6 How language and graphs support conversation in a bilingual mathematics classroom Judit Moschkovich

7 Reflections on a medium of instruction policy for mathematics in Malta Marie T. Farrugia

8 Bilingual mathematics classrooms in Wales Dylan V. Jones

9 Bilingual Latino students, writing and mathematics: a case study of successful teaching and learning Kathryn Chval Lena Lic?n Khisty

10 Mathematics teaching in Australian multilingual classrooms: developing an approach to the use of classroom languages Philip C. Clarkson

11 Where next for multilingual mathematics classrooms? Richard Barwell

Editorial Reviews

The book adds significantly to the scholarly literature on linguistic diversity issues in mathematics education. This book also succeeds in capturing the powerful learning environments that teachers are intuitively creating, by analyzing classroom social interactions. This book will appeal to mathematics educators, teacher candidates, and researchers who are concerned with mathematics learning and teaching in multilingual classrooms. Also, this book will provide insights into second language educators, teacher candidates, and researchers who are interested in second language learning in content areas. The authors successfully described the complexity of teaching mathematics to linguistically diverse learners with the intent of sharing these insights with the international community of teachers and researchers who are concerned with multilingualism as a whole.

Miwa Takeuchi

The editor has astutely provided some of us who regard mathematics as a challenge with a book worth reading. The editor has collected a set of chapters which renders it possible to feel like an expert of a field one doesn't know about. It is this confidence and intellectual conceit which of course is a necessary step in a development of and not the closure of expertise in this important field.

Sinfree Makoni.

This timely book will greatly interest anyone seeking a better understanding of teaching and learning mathematics in linguistically diverse contexts. Researchers and educators of both mathematics and languages will find resources and inspiration in each chapter.

Prof. Mamokgethi Setati

The book does indeed provide an overview of interesting and important work that has been done by those who have initiated and developed research based on and in mathematics classroom practice; on the mathematics register, and on curriculum and policy...As a review of research and an elaboration of this for practice, it is, as I have said, a valuable resource for new researchers and practitioners.
Jill Adler
University of the Witwatersrand, South Africa and King's College, London, UK

Research in Mathematics Education

Not only does it provide insights into the nature of mathematical thinking in a socio-linguistic context, but it also provides countless ideas for developing classroom practice, and opportunities to reflect on the nature of the dialogue bilingual learners need to extend that mathematical thinking.
Catharine Driver, Cambridge Education @ Islington

NALDIC