Title Page
Copyright Page
Contents
About the authors
Preface
CHAPTER 1 School mathematics in achanging world
Introduction
1.1 What is mathematics?
1.2 What determines the mathematics beingย taught?
1.3 Where can you turn?
CHAPTER 2 Helping children learn mathematics with understanding
Introduction
2.1 How can we support the diverse learners in our classrooms?
2.2 Meaningful connections between procedural and conceptual knowledge
2.3 How do children learn mathematics?
2.4 How can we help children make senseof mathematics?
CHAPTER 3 Planning and teaching
Introduction
3.1 Effective planning and preparation for teaching: using strategic questions to inform teaching practice
3.2 Planning for effective teaching
3.3 Levels of planning
3.4 Planning different types of lessons
3.5 Meeting the needs of all students
3.6 Assessment and analysis in planning
CHAPTER 4 Enhancing learning and teaching through assessment and feedback
Introduction
4.1 Enhancing learning and teaching
4.2 Gathering information on student learning
4.3 Ways to assess studentsโ learning and dispositions
4.4 Keeping records and communicating aboutย assessments
CHAPTER 5 Processes of doing mathematics
Introduction
5.1 Problem solving
5.2 Reasoning and proof
5.3 Communication
5.4 Connections
5.5 Representations
CHAPTER 6 Helping children with problem solving
Introduction
6.1 What is a problem and what is problem solving?
6.2 Teaching mathematics through problem solving
6.3 Strategies for problem solving
6.4 The importance of looking back
6.5 Helping all students with problem solving
CHAPTER 7 Counting and number sense in early childhood and primary years
Introduction
7.1 Developing number sense
7.2 Counting principles
7.3 Counting strategies
7.4 Cardinal, ordinal and nominal numbers
7.5 Writing numerals
CHAPTER 8 Extending number sense: place value
Introduction
8.1 Our numeration system
8.2 Nature of place value
8.3 Beginning place value
8.4 Consolidating place value
8.5 Extending place value
8.6 Reading and writing numbers
8.7 Rounding
CHAPTER 9 Operations: meanings and basic facts
Introduction
9.1 Helping children develop number sense and computational fluency
9.2 Developing meanings for the operations
9.3 Mathematical properties
9.4 Overview of learning the basic facts
9.5 Thinking strategies for basic facts
CHAPTER 10 Mental computation, calculators and estimation
Introduction
10.1 Calculators
10.2 Mental computation
10.3 Estimation
CHAPTER 11 Solving problems with written strategies
Introduction
11.1 Learning strategies that lead to understanding
11.2 Addition
11.3 Subtraction
11.4 Multiplication
11.5 Division
11.6 Finding the balance between practice andย proficiency
CHAPTER 12 Fractions and decimals: meanings and operations
Introduction
12.1 Conceptual development of fractions
12.2 Operations with fractions
12.3 Conceptual development of decimals
12.4 Operations with decimals
CHAPTER 13 Ratio, proportion and percentages: meanings and applications
Introduction
13.1 Ratios
13.2 Proportions
13.3 Percentages
CHAPTER 14 Extending students with number theory
Introduction
14.1 Number theory in primary school mathematics
14.2 Number theory topics for primary schoolย students
14.3 Other number theory topics
CHAPTER 15 Algebraic thinking
Introduction
15.1 Problems, patterns and relations
15.2 Language and symbols of algebra
15.3 Modelling, generalising and justifying
CHAPTER 16 Geometry
Introduction
16.1 The geometry of 2-dimensional shapes and 3-dimensional objects
16.2 Locations and spatial relationships
16.3 Transformations
16.4 Visualisation and spatial reasoning
CHAPTER 17 Measurement
Introduction
17.1 The measurement process
17.2 Identifying attributes and comparing
17.3 Measurement concepts for all units
17.4 Measuring with informal units
17.5 Measuring with formal units
17.6 Applications including formulae
17.7 Comparing and converting measurements
17.8 Estimating measurements
17.9 Connecting attributes
CHAPTER 18 Data analysis, statistics and probability
Introduction
18.1 Formulating questions and collecting data
18.2 Organising and representing data
18.3 Analysing data: descriptive statistics
18.4 Interpreting results
18.5 Probability
Appendix A
Appendix B
Appendix C
EULA