Issues in Mathematics Teaching

Peter Gates

• Publisher: Routledge
• Year: 2002
• ISBN:
  9781134555765
• Edition: 1
• Topic: Education
• Subtopic: Education General

This book presents the key debates that the mathematics teacher will need to understand, reflect on and engage in as part of their professional development. Issues in Mathematics Teaching is suitable for those at initial training level right through to practising mathematics teachers. Its accessible structure enables the reader to pursue the issues raised as each chapter includes suggestions for further reading and questions for reflection or debate.

Part I Setting the scene; raising the issues

DOI: 10.4324/9780203469934-2

1 What is an/at issue in mathematics education?

Gates Peter

DOI: 10.4324/9780203469934-3

The introduction to the issues

Those of us with an interest in—and indeed a passion for—teaching mathematics learn pretty quickly not to divulge this information too readily in public places. One has to be careful responding to the apparently innocent ‘and what do you do?’ question for fear of throwing the hairdresser into a rant about how they never enjoyed maths, could never do it or understand all those letters. You then find that you are being looked at a bit askance in order to examine what other defects or peculiarities you might have. Hating mathematics is as much a national pastime as complaining about the weather and mathophobia is so acceptable that one can readily make light of it—as I just have, but of course, it is a very serious matter, that has serious implications for very many children. Mathematics is not just a complex collection of skills, concepts and ideas that we endeavour to pass on to the next generation. As many chapters in this book will go on to argue, mathematics serves as a ‘badge of eligibility for the privileges of society’ (Atweh, Bleicher and Cooper 1998:63). Being successful at mathematics brings with it opportunities and riches; one stands a better chance of higher paid careers if one holds a higher qualification in mathematics. In addition, of course the converse is true. In order to keep certain sectors of the population away from such success, they have to be made to fail at mathematics. However, I am running away with myself here and need to develop this argument a little more.

Of course, many children enjoy mathematics—usually more so between the ages of 5 and 11 than 11 and 16 it has to be said, but there's another story! For many pupils, mathematics is a series of challenges and hurdles, which they face with passion and determination. For many others however, mathematics is a daily experience of continued failure and irrelevance. Mathematics education fails too many children; it fails children on the margins of society, it fails children from ethnic minorities, and it fails children from social and cultural backgrounds that are different from the majority of mathematics teachers.

In 1982, one submission to the Cockcroft Report into the teaching of mathematics in schools, Mathematics Counts, said ‘Mathematics lessons in secondary schools are very often not about anything. You collect like terms, or learn the laws of indices, with no perception of why anyone needs to do such things’ (Department for Education and Science 1982: para 462, p. 141). This seems to me to sum up what must be many children's experience of the subject. Mathematics is about all manner of things, but about nothing at all. It is about things that seem quite divorced from our everyday lives, interests or needs. Yet while this might reflect what goes on in many classrooms, it is a rather naïve description because it merely takes some of the surface features of the mathematics classroom and ignores the underlying complexity and the unintended outcomes of that complexity. Paradoxically, it is exactly because someone can say ‘mathematics lessons are not about anything’ that the situation is more worrying—showing how the processes of exclusion, rejection and de-motivation are hidden, obscured and misinterpreted.

Part of that complexity lies in the role that schools play in the construction of one's identity—forging how one compares oneself to others during some particularly difficult times for young people—growing independence, the embarrassment of puberty and the frustrations of adolescence. So, in this gradual process of self-awareness and self-efficacy what are the issues for mathematics teachers? What do we need to think about? In a book titled Issues in Mathematics Teaching, one might naturally expect a bunch of mathematicians to begin with the definitions, and I'll not disappoint. ‘Issues’ is the easy one, so I will start there. To be an issue means to be important and requiring of a decision; to be at issue implies something is under discussion due to disagreement; to take issue implies to disagree, whereas to issue forth means to expound. This book then is an opportunity for some writers to expound on matters about which there is likely to be some disagreement and which are under debate. As for defining ‘mathematics’ and ‘teaching’, little will be gained by opening that can of worms because the terms are so contentious and so slippery. I will ‘leave it as an exercise for the reader’—as it used to say in my university mathematics books. Defining such terms is really only useful insofar as it engages you in discussion with others. Coming to understand and define what it means to teach mathematics requires a long-term professional commitment of critical engagement in debate, not a textbook definition.

The background to the issues

It can hardly be contested that we live in an uneven and unjust society where access to education and to justice depend on the capital one can appropriate and accumulate— particularly through the benefits the education system bestows on some individuals. There is ample evidence in the academic and research literature in education to support this contention such that it is hardly now contentious. Yet, unfairness, injustice and prejudice are not abstract concepts of some macro-social analysis of an internecine class war. They are felt through the disappointment, hopelessness and frustrations of ordinary people as they get though their everyday lives. They exist in the knots in the pit of the stomach and the tears in the eyes. Injustice exists in the disappointments many children face when they are not endowed with financial resources to have what other children have and take for granted. Injustice exists in the frustration, anger and self-depreciation when a pupil is placed in a low set for mathematics based on some assessment procedure over which they have no control and which they feel is unfair. Injustice is a process that goes on all around us, even when—and arguably especially when—we do not look for it or recognise it.

I have spent many years in a variety of classrooms as a mathematics teacher, and continue to do so in my current role as tutor to student teachers, and what I see often upsets me, and I guess it was this which, to some extent, encouraged me to put this book together. I feel uncomfortable when I see children labelled as ‘less able’ placed into ‘bottom sets’ and fed diets of at worst, tedium, or at best, irrelevant and uninteresting exercises. I feel uncomfortable when the majority of pupils I see in those bottom sets seem to have had very similar life experiences reflecting varying degrees of deprivation. I feel uncomfortable when I can see they realise that there really is no point in working hard to learn mathematics because the structure of the school means they cannot achieve high GCSE grades whatever they do. I feel frustrated when I see mathematics envisaged by pupils, parents and teachers as little more than a collection of techniques to be captured rather than an approach to understand and to tackle society's ills. Finally, (for now) I feel angry when I hear teachers criticise parents for not being interested enough in their children to come to parents’ evenings when, of course, ‘these are just the ones you want to see!’. Well that may be so, but they clearly don't want to see you very much—and that ought to be where we begin to ask questions.

However, this book is not about my feelings; this is about those children who give up on mathematics; because many of the children who give up on mathematics (or better, those whom mathematics gives up for sacrifice) give up on society. OK. You might think this is a bit extreme, but it is my contention that mathematics education in schools plays a significant role in organising the segregation of our society, and conversely as a mathematics teacher, you will play your part too.

Sue Willis is an Australian who works in mathematics education, and who in a book titled Real Girls Don't do Maths provocatively argued:

Mathematics is not used as a selection device simply because it is useful, but rather the reverse.

(Willis 1989:35)

Hence she claims mathematics is not useful because it is useful; it is not useful because of what it helps you do. Mathematics is useful because it is organised and conceptualised in such a way that certain people can't do it. Now that is certainly a challenging and controversial claim—one you might take issue with or one you believe is right on. It certainly is an issue whichever way you look at it.

So, what makes something an issue in mathematics teaching? Let me give you one classic example—setting by ability. Why is setting an issue? Well, the answer to this will be obvious if you spend any time looking at the make-up of the different ability groups in any comprehensive school. Furthermore, setting is a mechanism for legitimising the very process of differential privileging of cultural background. We know from a great deal of international research that setting does not actually have an effect on raising overall standards—though the likelihood is that you will not accept my argument here. You might prefer the argument put to me by Alan Brown, a head of mathematics:

I think it's probably only fair to say that I have a fairly high degree of scepticism about a lot of the qualitative and quantitative research. I think it tends to be done by people who, with the best will in the world, have an axe to grind. The people who've argued about mixed ability tend to be people who've moved out of the classroom.

(Gates 2000:299)

Which puts me firmly in my place (and as it happens all the other contributors to this book too). I don't intend here to argue the merits or demerits of this issue, because that type of controversy and disparity of perspective is in the nature of an issue—and because I don't expect any chapter in any book to radically alter deeply held beliefs on its own. What I hope this book does is to raise issues and expose the underlying values that need to be confronted. What is important is that you recognise the controversies, and enter into them with an awareness of what is at stake. When it comes down to it, it is a matter of whose side you are on and that is for you to decide by considering your own values. Of course, this book, like any other similar book, is deeply saturated with values. The difference here, that all contributors have striven to ensure, is that our values are somewhat more explicit and transparent than many others you might read. This does not make the book less useful, on the contrary. Because you will be able to ascertain from whence each writer is coming, you will be better placed to consider, evaluate and position yourself.

Actually, all the contributors to this book are qualified classroom teachers, trained and experienced either at primary or at secondary level, with decades of classroom experience between them, and they have something important to say about that experience. For half of the contributors in this book, the chapters they have written also derive directly from their own doctoral research studies.

About the issues in this book

Of course, any book represents someone's selection of material to include, and this book is no exception. We are not suggesting the issues we have written about are the only issues that are currently important in mathematics teaching, but they are the issues that engage the twenty-one of us who have contributed to the book. The importance of our selection is not only in its content, but is in the way that the politics of mathematics teaching is being made explicit throughout the book. We discuss a wide sweep of issues, and provide sources and resources for those wanting to know more. In an overview of many of the contemporary issues in mathematics education, Peter Bailey concludes that teachers of mathematics can play a crucial role in making the world a fairer place’ (Bailey 1999:84), and that is our starting point—which surely must be of interest to us all.

Our focus in this book is on teaching mathematics in schools, but no one interested in children's learning of mathematics can overlook the significant issue of the difference between doing mathematics in schools and being mathematical outside of school. This is a fast-growing area of study—and is something that teachers ought not ignore (though it will have to remain as the subject of another book). The number of studies of adults and children doing mathematics outside of school show that lack of competence in one context (usually school) is no indicator of lack of competence in the other. See for example the work of Mary Harris, (Harris 1991), Gelsa Knijnik (Knijnik 1996), Madelena Santos (Santos and Matos 1999), Jean Lave (Lave 1988) and Terezinha Nunes (Nunes, Schliemann and Carraher 1993). It is perhaps interesting that so many of these studies are carried out by female researchers in mathematics education. One small way of marking the contribution that women make to the academic literature is to identify gender through the use of first as well as second names. This is a practice utilised throughout this book.

The social context of mathematics education

The chapters forming Part II—Issues in the Social Context of Mathematics Education, really cover a broad sweep of contemporary issues at the heart of current debates about the teaching and learning of mathematics; social justice (Chapter 2), language, social class and social inclusion (Chapter 3), gender (Chapter 4) and ethnicity (Chapter 5) all have a central place in these debates, yet have not all had a central place in mainstream literature on mathematics education. However, in addition to these broad, macro-issues, there are chapters here that look more into the personal dimension of mathematics teaching—pupils’ perspectives and emotions on their learning (Chapter 6), one's own values as a teacher (Chapter 7) and the ways in which one's values influence one's teaching style in the context of the current teaching of numeracy (Chapter 8).

In Chapter 2, ‘Mathematics Teaching in the Real World’, Tony Cotton discusses the relationship between mathematics education and social justice, an area in which Tony's work is well known. Tony's work—and his discussion of it in this chapter—is important because it helps us understand the nature of social exclusion and its manifestation in and through mathematics education. Furthermore, Tony offers some blueprints for strategies that we might incorporate into our teaching to try to make a difference. What comes across in Tony's chapter—and this issue is picked up at several other points in this book—is that pupils have a view, they have a right to a view, and a right to be listened to, and that no school, department or teacher can claim to be socially just without listening to and acting on those views. Of course, for this to be successful, effective channels of communication need to be established between the dominant voice of the teachers and the oft-suppressed voices of the pupils.

Robyn Zevenbergen problematises the idea that language is merely a means of communication. In Chapter 3, ‘Language, social class and underachievement in school mathematics’, she claims that the language forms an...

Table of contents

• Cover Page
• Half-Title Page
• Series Title Page
• Title Page
• Copyright Page
• Table of Contents
• List of tables
• List of figures
• Contributors
• Glossary
• PART I Setting the scene; raising the issues
• PART II Issues in the social context of mathematics education
• PART III Issues in the teaching and learning of mathematics
• Part IV Issues in the assessment of mathematics
• Part V Issues in the Culture of Mathematics Teaching
• Subject Index
• Author Index