The Really Useful Maths Book

A guide to interactive teaching

Tony Brown, Henry Liebling

• Publisher: Routledge
• Year: 2014
• Print ISBN: 9781138138278
• eBook ISBN: 9781317913542
• Edition: 2
• Topic: Education
• Subtopic: Education Curricula

The Really Useful Maths Book is for all those who want children to enjoy the challenge of learning mathematics. With suggestions about the best ways to use resources and equipment to support learning, it describes in detail how to make learning the easy option for children. An easy-to-follow, comprehensive guide packed with ideas and activities, it is the perfect tool to help teachers who wish to develop their teaching strategies.

The second edition has been fully updated in light of the latest research, as well as in response to the new mathematics curriculum. It includes many more practical activities for each mathematical topic and explores exciting new areas. Key topics covered include:

• Numbers and the number system
• Operations and calculations
• Shape and space
• Measures, statistics and data handling
• Cross-curricular approaches
• Resources and planning for teaching and learning
• Contexts for making sense of mathematics
• Bridges, strategies and personal qualities
• Dialogue and interactive teaching
• International perspectives on teaching and learning
• Psychology and neuroscience to maximize learning.

The Really Useful Maths Book makes mathematics meaningful, challenging and interesting. It will be invaluable to practicing primary teachers, subject specialists, maths co-ordinators, student teachers, mentors, tutors, home educators and others interested in mathematics education programmes.

Tony Brown was formerly the Director of ESCalate, the UK Centre for Education in HE at the Graduate School of Education, University of Bristol, UK.

Henry Liebling formerly led Primary Mathematics Education at University College Plymouth, Marjon, UK.

Part I

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PART I

MATHEMATICAL ACTIVITIES AND TEACHING STRATEGIES

Introduction

N NUMBERS AND THE NUMBER SYSTEM

1 Counting and counting out

2 Saying and making numbers

3 Arabic and other number systems

4 Working with grids

5 Working with target boards

6 Working with sets

7 Working with square numbers

8 Exploring algebra

9 Taking ideas from ‘floor to head’

O OPERATIONS AND CALCULATIONS

1 Number lines

2 The story of 24

3 Arithmetic operations

4 Arithmogons and other puzzles

5 Teaching multiplication tables

6 Divisibility rules

S SHAPE AND SPACE

1 Visualisation techniques and activities

2 Activities and investigations

3 Working with cloths

4 Unusual and unfamiliar

5 Changing shapes

M MEASURES, STATISTICS AND DATA HANDLING

1 Measures and measurement

2 Data handling and using the media

3 Statistics and probability

4 Using personal measurement

5 Investigating measurement

X CROSS-CURRICULAR APPROACHES

1 Cross-curricular approaches

2 Playing with the language of mathematics

3 Maths in music, dance and knitting

4 Maths, sustainability and the global dimension

5 Reasoning, logic, proof and programming

Part I: Introduction

WHAT IF NOT!–TURNING A SINGLE ACTIVITY INTO MANY

Part I of this book provides a rich set of activities from across the whole of the primary maths curriculum, including ideas for teaching and using maths in cross-curricular activities. Maths needs to be introduced into other curriculum areas, for example by applying statistical ideas to raw data found in geography, science or English. Maths also needs to be exemplified in activities by drawing on other curriculum areas. Music and some poetry for example have a mathematical basis.

Give a person a fish and they will eat for a day.

Teach a person to fish and they will eat for a lifetime.

Teachers who believe they have to fish for a new activity every time they teach a maths lesson are like those who only have sufficient fish to eat for a single day: enough to stay alive but not enough to sustain themselves. The pedagogical equivalent of learning how to fish is to learn to adapt, change, modify and re-use mathematical activities, making many activities from a single starting point. One book can only provide a small set of activities but the teacher who takes a single good idea can generate innumerable activities. We hope to provide enough exciting starting points for teachers to create an infinite variety of interesting mathematical activities. When trying to generate plenty from one, the teacher will need to adapt, change and expand the activities in Part 1 of this book. We describe below various ways to do this.

Starting points for planning

When planning, include activities based on students’visual, auditory or kinaesthetic learning preferences. Have a different focus for different lessons. Plan some lessons to have a range of tasks; others can have a range of resources, people, or team work.

Some variables to think about when planning

No need to write comments in every box. Just focus on different variables for differentlessons: today might include grouping students differently; tomorrow might be teaching different forms of representation using the same activity but with different resources.

Deciding how much direction to give

Investigate the number line between 0 and 1

There comes a point when children are aware that the counting numbers 1, 2, 3, 4, etc. are not the only numbers in mathematics. One activity requires each student to write a number on a sticky note and place it on a number line segment drawn on a wall, in what they think is the appropriate part of the number line. How much direction might you give and when? Do you tell the pupils what to do, what to expect? Do you leave them to say what they know about the number, savouring each word and exploring what the investigation might entail? If they get stuck, then what is the least you can do to move thinking on?

This is useful as a seemingly simple investigation. It is good for pupils to try to define what might “live” between 0 and 1 on a number line or ruler. Expect fractions and decimals, notions of smaller and smaller divisions, more and more decimal places; likely to show up the depth of their knowledge and understanding. Imagine magnifying the small space between 0 and 1cm on a ruler, or use a metre ruler, or a 1 metre garden cane with no other markings than 0 and 1. Use a 0 to 1 probability scale. What happens if 1 is one apple, 1 Kg, 1 litre, one life time, one millennium?

Changing the order

Plan for pupils to select the order in which they use the resources provided. For example, instead of reading the instructions first, try to make or use a new piece of kit and then look at the instructions afterwards. Start a problem or investigation with free play using an open-ended exploration of a box of bits. Provide some objects that don’t obviously go together, such as Blutack, string, plastic bottles and coffee jar lids. Begin with a brief brainstorming session and follow this with a terse instruction such as, ‘Make a timing device.’ And follow this with some clues or hints if needed. Alternatively, give a formal introduction and demonstration of types of timing device, then encourage children to make their own. These two approaches are likely to feel different to the students and can lead to very different outcomes.

Try other changes. Try shuffling or even randomising the order of resources, the order of teaching sessions or the order of instructions. Is your current order good for you, your students, or both of you, or perha...

Table of contents

• Cover Page
• Half Title Page
• Series Page
• Title Page
• Copyright Page
• Contents
• List of resource pages
• Acknowledgements
• Why another book about primary school mathematics?
• Using The Really Useful Maths Book
• Part I Mathematical Activities And Teaching Strategies
• Part II Developing Interactive Teaching Strategies
• Part III Additional Material