Helping Children Learn Mathematics

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 being 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 students’ learning and dispositions
	4.4 Keeping records and communicating about 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 and 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 school 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