Developing Numeracy in the Secondary School

A Practical Guide for Students and Teachers

Howard Tanner, Sonia Jones, Alyson Davies

• Publisher: Routledge
• Year: 2020
• ISBN:
  9781134139255
• Edition: 1
• Topic: Education
• Subtopic: Education General

As the National Numeracy Strategy (NNS) extends into secondary schools this book for trainee and practicing mathematics teachers provides practical guidance on developing effective strategies for the teaching of numeracy at KS3 and 4 based on the DfEE requirements.

The teaching and learning approaches suggested in the NNS are analyzed and explained using case-study examples from secondary schools. Many of these ideas were developed by teacher inquiry groups in the Raising Standards in Numeracy project.

The book includes examples of pupils' work; lesson plans and pupil activities; ideas for using ICT to enhance mathematics; teacher guidance on both teaching and assessment; and ideas for developing numeracy across the curriculum.

This book offers an introduction to the subject of numeracy accompanied by lesson ideas and practical guidance. It will prove a valuable resource for all trainee and new mathematics teachers.

SECTION 1

Issues in numeracy and mathematics teaching and learning

In this section, after exploring the various definitions of numeracy, we consider the findings of some of the significant studies into the teaching of mathematics conducted in the UK and overseas. Their recommendations are contrasted with advice offered by official sources and we consider how they impact on fundamental issues in the teaching of mathematics such as the development of mathematical thinking.

CHAPTER 1

What is numeracy?

Introduction

The zeitgeist in Britain and much of the Western world at the turn of the century has focused on standards of numeracy and literacy in schools. The standards achieved in such key skills have long been a subject of discussion among the profession, politicians and the public. They were brought to the centre ground of UK politics by the ‘great debate’ initiated by James Callaghan in his Ruskin College speech of 1976 and have remained there ever since.

Key international studies such as the Third International Mathematics and Science Study (TIMMS: Beaton et al. 1996) and its follow up studies (Stigler et al. 1999; Mullis et al. 2001; OECD 2000) generated league tables and data about teaching approaches. The league tables focused the minds of politicians, who often view such matters in much the same way as football, and motivated a flurry of curriculum development worldwide. We will examine some of the lessons to be learned from international comparisons in Chapter 2.

However, schools in the UK had not been untouched by the spirit of the times and developments in numeracy had already begun. Certainly there had been an increased interest in mental arithmetic in English primary schools during the 1990s (Brown et al. 2000) and by the middle of the decade, a number of large and influential projects were investigating the teaching of numeracy (Askew et al. 1997; CIMT 1997; Straker 1997; Reynolds 1998a, 1998b). One of the most significant was the National Numeracy Project (NNP) under Anita Straker which was set up in October 1996 with a budget of £2.8 million. It conducted development work in 520 primary schools from 14 LEAs.

Such was the enthusiasm for the early results coming from the Numeracy Project that this formed the basis of the National Numeracy Strategy: Framework for Teaching Mathematics (DfEE 1999a). This framework was highly influential and dramatically changed practices in schools in England within a very short time. A pilot programme to extend the work of the NNS into Year 7 was started in 2000 and, without waiting for the results, the DfEE demanded that all schools use the new framework in KS3 from September 2001.

Prior to the changes set in motion by the NNP and the NNS, Reynolds (1998a: 19) claimed that primary school teachers ‘usually deploy only a narrow range of teaching strategies’ and that they ‘rely too heavily on published schemes, which pupils work through individually’ with pupils left to teach themselves’. Our own observations lead us to believe that this was probably the case in some of the least successful primary schools.

The RSN Project

Our own research at that time was focused on the most successful schools rather than the least successful. The Raising Standards in Numeracy (RSN) Project was a collaborative project involving five Welsh local education authorities (LEAs) and was funded by the National Assembly for Wales during 1998/9. (For further details see Tanner et al. 1999.) The project utilised earlier work by the Vale of Glamorgan LEA involving the development of value-added analyses linking National Curriculum data to prior attainment scores based on pupil-level data.

As part of the project we used value-added analyses to identify schools where pupils obtained significantly higher than expected scores in statutory tests. We then identified two primary and two secondary schools in each LEA whose results were far higher than would have been expected for their intake. On visits to these schools we interviewed head teachers, subject leaders and teachers and asked them to describe the factors to which they attributed their success. Lessons were then observed to examine these classroom processes in practice.

Subject leaders from the schools met as a teacher inquiry group (TIG) during the course of the year to discuss their approaches and our observations in order to identify key features, under the control of the school and the teacher, which represent good practice in the teaching of numeracy.

We were privileged to work with many highly skilled, enthusiastic teachers during the project. Much of the material to be found in this book is based on our observations of their lessons and our discussions with them afterwards when they reflected critically on their own practice.

In the chapters which follow it is not our intention to act as propagandists for the changes demanded by government strategies and frameworks. Rather it is our intention to explore the nature of numeracy and to consider some of the schemes which might be employed by reflective, professional teachers to improve teaching in secondary schools.

Objectives

By the end of this chapter you should be aware of:

• the wide range of abilities associated with numeracy;

• the most influential definitions of numeracy in use today;

• the different knowledge and skills required according to these definitions;

• the extent to which calculators can be used or misused in the development of numeracy;

• some of the implications for teaching and learning, providing a suitable background for the chapters which follow.

What is numeracy?

Numeracy is a theme for our times. However, it is not clearly defined as a concept and seems to have expanded its scope of late to encompass most of the mathematics curriculum at least up to the end of Key Stage 3. Numeracy seems to take on a wide range of meanings according to the aims of the speaker, with politicians enjoying its utilitarian or basic common-sense tone and teachers, such as ourselves, emphasising its further-reaching mathematical characteristics.

Its common usage in Britain began as a mathematical equivalent to literacy – as the ‘mathematical literacy’ suggested by the Crowther report (1959). Common usage today tends to emphasise the dimension of arithmetical calculation (e.g. Reynolds 1998b). However, just as one would expect a literate person to be able to do much more than read lists of words it is clear that the numerate person must be able to do far more than perform arithmetical calculations to order. This was recognised in the influential Cockcroft report (1982) in which numeracy was defined as an ability to cope with the mathematical demands of everyday life and to develop an ‘at homeness’ with number.

This is far more than a knowledge of number bonds and multiplication tables, although many would argue that such skills form the basis of numeracy. Although the instantaneous recall of certain simple number facts can be helpful in many circumstances, they do not by themselves ensure that children will feel ‘at home’ with number or be able to apply their knowledge in real life. In fact the literature is full of evidence of children failing to apply school-taught methods to real-life problems (e.g. Lave 1988; Nunes et al. 1993; Schliemann 1994).

During the 1970s some teachers regarded the automatic recall of arithmetical facts as reduced in importance through the common usage of calculators. One of Her Majesty’s Inspectorate even went so far as to define numeracy as the ‘sensible use of a four-function calculator’ (Girling 1977). This view is now well out of kilter with the spirit of the times, but the use of calculators in the development of numeracy remains a contentious issue and we will return to it later.

Task 1.1: What is numeracy?

Try to write your own definition of numeracy. Numeracy is …

We hope that your definition of numeracy included far more than swift recall of arithmetical facts. At a recent meeting of a teacher inquiry group we asked a group of primary and secondary teachers to describe what they thought numeracy implied. Some of their answers are listed below and encompass a far wider set of knowledge and processes than simply a facility with a few basic number bonds. Numeracy is:

A knowing enough mathematical structure to be able to use what you know to be able to work out what you don’t know;

B being fluent with number, being at ease with it, so that you can play around with it to get what you need;

C knowing the language, grammar and symbolism of mathematics;

D being able to solve problems with number and language and knowing when your answer is reasonable;

E coping with the demands of everyday life and knowing how to choose an efficient process in any situation which will lead to a reliable answer;

F knowing when it is appropriate to use a calculator.

(Tanner and Jones 2000b: 145)

The following definition is offered by the National Strategy for KS3:

Numeracy is a proficiency which is developed mainly in mathematics but also in other subjects. It is more than an ability to do basic arithmetic. It involves developing confidence and competence with numbers and measures. It requires understanding of the number system, a repertoire of mathematical techniques, and an inclination and ability to solve quantitative or spatial problems in a range of contexts. Numeracy also demands understanding of the ways in which data are gathered by counting and measuring, and presented in graphs, diagrams, charts and tables.

(DfEE 2001a: 1.9)

You may be surprised to find that the definition is so broad, encompassing algebra, shape and space and data handling. You may be wondering what the distinction is between numeracy and mathematics. We like a suggestion we heard Anita Straker make in a presentation to the annual Mathematical Association Conference: ‘Numeracy is what you develop when you learn mathematics well.’

We think that numeracy is about using mathematics, both theoretically and practically. We prefer to focus on the ability to use and apply mathematical knowledge in problem solving rather than on specific items of mathematical knowledge. We suggest that, at one level, numerate people have ‘the ability to solve simple everyday problems involving number, by using effectively the knowledge and skills that they possess’, and that this should include being able to choose and to devise their own appropriate strategies (Mathematical Association 1992: 71). However, on another level, we think that numerate people should be able to use the mathematics they know to solve problems in mathematics itself, in other subjects and in real life. The difficulty of the problems we expect numerate peopl...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Table of Contents
• Acknowledgements
• Preface
• Section 1 Issues in numeracy and mathematics teaching and learning
• Section 2 Numeracy in practice: lesson ideas from the classroom
• Section 3 Plenary: developing numeracy across your own school
• Bibliography
• Index