Now in its third edition, Mathematics in the Primary School has been updated to reflect recent mathematics curriculum documentation and revised standards for QTS.
Key areas include:
Providing a coherent set of principles for teaching primary mathematics across the main topics in the curriculum, the authors explore children’s understanding of key areas of mathematics, at reception, infant and junior levels. Important principles and teaching approaches are identified, including the use of calculators and computers, and there is an emphasis on mental mathematics and problem solving supporting key issues raised by the Williams review (2008). Case studies are used throughout to illustrate how different teaching approaches are put into practice and how children respond to them, and there is advice on planning, organisation and assessment of mathematical learning in the classroom.
Emphasising the importance of teachers’ own mathematical knowledge and offering clear guidance and practical advice, this book is essential reading for students, NQTs and practising teachers with a focus on primary mathematics.
Contents
Acknowledgements viii
Preface to the third edition ix
Section 1: Using and applying mathematics 1
Mathematical thinking 1
1.1 Why do children learn mathematics in school? 1
Key questions 3
Case studies
How can we develop reasoning at Key Stage 1? 4
How can we develop reasoning at Key Stage 2? 5
Glossary 8
Section 2: Number 10
2.1 Introduction – the teaching of number 10
2.2 Number in the early years 10
Learning to count 11
What activities help children to count and learn about numbers and numerals? 13
Case studies
A nursery shopping game 14
Revised version of the game 17
Extensions 17
Starting to calculate 17
Some activities 19
Board games 23
2.3 Developing a feel for number 23
Understanding place value 24
Mental mathematics 26
Multiplication and division 27
Common misconceptions 29
Case study
Circle game 31
A range of methods for calculating 34
Fractions, decimals, percentages and division 42
Estimation 46
2.4 Extending the number system 46
Really large numbers 46
Glossary 48
Introducing negative numbers 49
Glossary 49
Fractions, decimals and percentages, ratio and proportion 50
Properties of numbers 55
Glossary 57
2.5 Ideas leading to algebra 58
Early generalisations: the search for pattern 58
Developing pattern and generalisation 58
Case study
Growing shapes 58
Seeing the link with algebra 60
Other activities leading to algebra 61
2.6 Solving numerical problems 62
Practical tasks 62
Real life problems 62
Problems within mathematics itself 63
Case study
How many ways can you make ... 48? 66
Assessment 67
Glossary 68
Solving equations 68
Section 3: Shape, space and measure 69
3.1 Shape and space: introduction 69
Teaching points 70
Case study
Visualising: an initial assessment activity 71
Visualising activities 72
3.2 Shape and space activities 72
Glossary 88
3.3 Measurement: general principles 91
Introduction 91
Standard and non-standard measures 92
Use and interpretation of measuring tools 95
Estimating 95
Assessing for starting points 96
3.4 Aspects of measurement 97
Length 97
Capacity and volume 98
Area 99
Perimeter 100
Weight and mass 100
Measuring time 102
Case study
Food technology 103
Organising the classroom and children appropriately 111
Solving problems involving measure 111
Glossary 112
Section 4: Handling data 113
4.1 Introduction 113
Handling data in the classroom 113
The data handling process 114
The teacher’s role in the process 115
4.2 Case studies
Case study at the Foundation Stage 123
Case study at Key Stage 2 126
4.3 Mathematical thinking and data handling 131
Solving problems 131
Mathematical communication 132
Reasoning mathematically 132
The use of computer databases 132
Key points to remember when children are using the computer 137
Activities 137
Examples for Foundation Stage/Key Stage 1 138
Examples for Key Stage 2 139
4.4 Probability 139
Probability in society 139
Activities 140
Glossary 142
Section 5: Planning, assessment and classroom organisation 148
5.1 Planning and assessment 148
Early years settings 148
Planning and assessment 149
Identify the learning objectives 150
Recording assessments 152
Reporting 154
5.2 Classroom organisation 154
Atmosphere and ethos 154
Starting an activity in stimulating ways 155
Encouraging and facilitating talk about mathematics 158
Groupings 162
Selecting and organising resources 164
Early years settings 164
Key Stages 1 and 2 165
5.3 Children with specific mathematics learning difficulties 167
Case studies
Two children with mathematical learning difficulties: Ben and Amanda 170
Conclusion 171
Resources 172
References 174
Index 176
