The book is developed around the following chapters:
Chapter 1: The changing face of school mathematics
Mathematics education and society
Teaching mathematics in modern society
Mathematics classrooms
New models of teaching mathematics
Content and pedagogy
What is mathematics?
Where does mathematics come from?
The mathematics curriculum
Integrating curriculum
Integrating mathematics with other curriculum areas
Numeracy
Review Questions
Further reading
References
Chapter 2: Theories of learning mathematics
Why study theories of learning mathematics?
Cognitive theories
Sociocultural theories: The influence of Vygotsky
Socially critical theories
Modern society
Theory into practice
Review questions
Further reading
References
Chapter 3: Language and mathematics
The language of mathematics
Word problems
Language error analysis
Mathematical literacies
Making pedagogy explicit
Review questions
Further reading
References
Chapter 4: Diversity and equity
Equity and equality
Cognitive models of difference
Social models of difference
Teachers' beliefs
Home–school differences
Knowledge and world-views
Implications for school mathematics
Review questions
Further reading
References
Chapter 5: Planning for teaching
Planning
Why plan?
Planning: What do I want to teach?
Teaching: How will I teach?
Evaluating teaching: How will I know whether it has been a success?
Planning the learning environment
Planning for substantive learning
Review questions
Further reading
References
Chapter 6: Assessment
Why assess?
Models of assessment
What to assess
Planning assessment
Assessment tools
Student writing
Tests
Rubrics
Opening up assessment
Communicating results
Review questions
Further reading
References
Chapter 7: Working mathematically
Working and thinking mathematically
Problem-solving
Problem-posing
Technology for thinking mathematically
Making connections
Communicating mathematically
Review questions
Further reading
References
Chapter 8: Early number
Number sense
Pre-number
Subitising: Group recognition
Counting
Conservation of number
Number benchmarks
Types of numbers
Numeration and place value
Addition and subtraction
Multiplication and division
Review questions
Further reading
References
Chapter 9: Basic facts and mental computation
Working flexibly with number
Basic facts of addition
Basic facts of subtraction
Addition and subtraction: Mental computation
Basic facts of multiplication
Basic facts of division
Mental computation and estimation
Promoting mental computation in the middle years
Review questions
Further reading
References
Chapter 10: Written algorithms
The value of concrete materials
Principles for using concrete materials
The addition algorithm
The subtraction algorithm
The multiplication algorithm
The division algorithm
Teaching written algorithms in the middle years
Summary
Review questions
Further reading
References
Chapter 11: Rational number
Common and decimal fractions
Whole number and rational number connections
Fractions
Decimals
Ratio and proportion
Promoting language and mental images of ratio and proportion
Rate
Per cent
Teaching rational number in the middle years
Summary
Review questions
Further reading
References
Chapter 12: Patterns and algebra
Patterning
Number, arithmetic and algebra
The importance of algebra in the primary school
Teaching algebra in the middle years
Review questions
Further reading
References
Chapter 13: Measurement
What is measurement?
Teaching measurement
Length
Area
Volume and capacity
Mass
Time
Temperature
Money
Making connections between sub-strands
Teaching measurement in the middle years
Review questions
Further reading
References
Chapter 14: Chance and data
What are chance and data?
Teaching chance
Data collection, representation and interpretation
Measures of central tendency
Statistical literacy: Interpretation of data representations
Teaching notes for graphing
Teaching chance and data in the middle years
Review questions
Further reading
References
Chapter 15: Space
Topics in the space strand
Visualisation
The van Hiele levels of geometric thinking
Teaching notes
Spatial concepts: Early activities
Shape and structure
Transformation and symmetry
Location and arrangement
Teaching space in the middle years
Review questions
Further reading
References
Index
