Primary Mathematics Curriculum Guide

Harvey Blair, Pat Hughes

• Publisher: David Fulton Publishers
• Year: 2014
• eBook ISBN: 9781134138975
• Topic: Education
• Subtopic: Education General

This is a curriculum guide that gives trainee teachers the opportunity to follow a tried and tested primary mathematics curriculum course. The text is easy to follow, up-to-date with good current practice and utilizes materials produced by the DfEE for teachers. It includes interactive tasks to enhance understanding, tasks to consolidate learning at the reader's own level and pace, a full bibliography for further reading, common misconceptions which the reader will find in children's work, and a detailed look at the National Numeracy Strategy (NNS) and the mathematics National Curriculum. The text will provide a firm foundation for teaching mathematics to primary school children and give the reader genuine confidence in their teaching. The text has been piloted by students following a distance learning primary PGCE and revised in line with their comments. The intention of the book is to provide secure subject knowledge for mathematics alongside an understanding of the ways in which children learn mathematics.

Chapter 1

Introducting the book’s objectives

By the end of this chapter you will have:

• gained an understanding of how to proceed through this curriculum guide;

• discovered how to respond to and reflect on set tasks and activities, including making reference to your school’s mathematics policy documents, statements and practice;

• made some progress in identifying and articulating your beliefs about mathematics;

• been introduced to some issues in the teaching and learning of mathematics;

• learned to appreciate some of the many resources available for teaching and learning maths;

• been introduced to key texts for undertaking the government Skills Test in Numeracy.

Using the book

In any distance-learning course, predominantly based on the printed word, it is not possible to emulate precisely the cut-and-thrust of the classroom debate of a traditional PGCE course. Therefore this book is structured around a range of tasks. You may be required to work with a prescribed text and the instruction ‘Read’ should be viewed as shorthand for ‘read, make notes and carry out suggested activities’ or to carry out an activity with children, adults (usually teachers) or on yourself.

Your interaction will take a variety of forms but will generally involve you in making some written response about the outcomes. You will then be expected to compare your thoughts with the commentary provided (as well as with your mentor and other students as you begin to set up support networks). Some commentary usually follows each task and may encourage you to make further, more detailed notes. You therefore need to create a file in which to collect your responses.

One final point – although you are expected, as far as possible, to tackle every task, you may have to modify a few individual tasks to fit your circumstances.

The chapters

Each chapter begins with a list of objectives (see above). These are to help you to:

• focus your learning;

• assess the extent to which you have achieved these through the work in the sections, and decide whether further work is necessary.

Begin by working through the first three chapters. These will give you an overview of the aims of the book, the implications of the maths National Curriculum itself, and an understanding of the National Numeracy Framework (NNF).

The National Numeracy Strategy

The first draft of this maths guide was developed at the same time as The National Numeracy Strategy: Framework for teaching mathematics from Reception to Year 6 (NNS or NNF) (DfEE 1999a) was sent into all schools. Chapter 3 looks at this in more detail and it is assumed that all students will have their own copy of the Framework and be familiar with its content. Additional DfEE materials are available in schools from the subject coordinator.

The role of any curriculum mathematics course is to explore the nature of mathematics and its teaching and learning in much greater detail. Trainee teachers are at the start of learning to be teachers. The NNF has been written for experienced teachers.

Teaching maths

The following text and tasks aim to help you identify your own perception of what mathematics and the teaching of it mean to you. This chapter also touches briefly on issues such as numeracy, multicultural maths, calculators and commercial maths schemes. These should raise and heighten your awareness and help you to locate and develop your own ideas. Each of these issues and more will be developed in later chapters.

1 Your own opinion on maths

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You will already have a wealth of experience of maths teaching and learning, both as a pupil yourself and also through the perceptions of others, perhaps family members and the media. You may also have spent some recent classroom time as a teacher’s aide. Whatever your experience you will have formed impressions, even opinions, about what constitutes good and effective maths teaching.

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Task 1

Begin your file with a mathematical ‘autobiography’ by noting initial thoughts about your own learning of mathematics. You should add to these as you progress through the book whenever further memories occur to you. It is worth dating each entry and leaving space to add other appropriate thoughts and ideas that come to you.

What are your beliefs about teaching mathematics and where do they come from? Reflect on, and make an initial note of, your own experiences of learning mathematics, especially as a child. Were these positive or negative? Do your recollections generate powerful emotional responses? What reasons can you give for this?

You are likely, as this book is intended for primary PGCE students, to have considered your own primary experience and whether you identified yourself or were identified as being successful or otherwise in maths.

Reasons you may have given for liking or disliking maths might include:

• finding the subject easy or difficult;

• relationships with teachers, parents or peers;

• the teaching style and classroom organisation;

• connotations (especially social) with images of maths;

• the language used to communicate the subject.

Task 2

If you haven’t already done so, compare and contrast your primary school maths experience with that of your secondary school years. How did they differ and how do you account for these differences?

By the end of the primary years, many children will have formed attitudes to maths which, especially if negative, may be difficult to change. For some, their success at primary school, which was based on their ability to perform standard written calculations, may be tempered or even negated as they meet the more abstract aspects of the subject. Conversely, some adults report that ‘things began to fall into place’, perhaps as the result of some inspirational or sympathetic teaching.

2 What is maths?

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In a very powerful sense ‘maths is all around us’. It is used in everyday life – in the home, at work, during leisure activities, as well as in other school subjects. People are often surprised when this ‘hidden’ aspect of maths is pointed out to them, sometimes so much so that they will say it isn’t ‘real’ like the maths they learned in school. For example, studies of 10- to 12-year-old Brazilian street children have shown that while they could mentally calculate and recalculate with large numbers (and simultaneously monitor an inflation rate of about 250% at the time) they were unable to perform accurately the standard, simple written arithmetic taught in school. Similarly, a clerk in this country had been shown how to calculate the VAT at 17.5% on VAT-inclusive prices by simply multiplying the price by 0.851 and rounding to the nearest penny, using a calculator of course! This was performed confidently and successfully time and again. When asked, the clerk had no idea why the process worked and commented that ‘We didn’t do this when I was at school’.

This anecdote shows clearly that for many people maths is only about what you do at school, quite often alone and in silence, usually with pencil and paper, applying well-defined sets of procedures and rules, and having little relevance to themselves apart from a basic arithmetic function. (A child who was asked what she did at school that day replied that: ‘I learned a poem in English, found out about the Romans building walls in Britain, measured how much my plant had grown in science, and did pages 14 and 15 in maths’!)

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(Note: pp. 60 and 61 in The National Curriculum 2000 (DfEE/QCA 1999) make useful reading.)

3 Ways of calculating

There is often an inability to link maths to everyday life. To combat this and to help children use methods of calculation which are most appropriate to a given context and to their own level of confidence, the National Numeracy Strategy makes overt, and legitimises by government policy, the use of ad hoc and infrequently-taught mental methods of calculation. In daily one-hour sessions children’s own methods are to be valued, mad...

Table of contents

• Cover
• Title Page
• Copyright Page
• Table of Contents
• Preface
• Acknowledgements
• Chapter 1: Introducing the book’s objectives
• Chapter 2: The National Curriculum for mathematics
• Chapter 3: The National Numeracy Framework
• Chapter 4: Ma2: Number and algebra
• Chapter 5: Ma3: Shape, space and measures
• Chapter 6: Ma4: Handling data
• Chapter 7: Using and applying mathematics
• Chapter 8: Planning, assessing, recording and reporting
• Chapter 9: ICT and mathematics
• Chapter 10: References and further reading
• Useful websites
• Index