Part 1 – Setting the scene
Introduction
Powerful learning
Why was this book written?
Collaborative practice
Chapter 1: The big picture
Leading in learning
Improving Learning in Mathematics
Thinking mathematically
Improving students’ attainment
Chapter 2: How to use the book
Part One: Setting the scene
Part Two: Strategies and exemplars
Part Three: Thinking Skills and mathematics teaching and learning
Strategies and exemplars
The CD
Chapter 3: The strategies
Part 2 – Strategies and exemplars
Strategy 1 – Odd One Out
Exemplar 1 Sometimes or always? (Algebra)
Exemplar 2 Transformations (Shape and space)
Exemplar 3 Fractions, percentages and decimals (Number)
Exemplar 4 Shapes and angles (Shape and space)
Strategy 2 – Collective Memory
Exemplar 1 Formulae sheet (Algebra)
Exemplar 2 Simple transformations (Shape and space)
Strategy 3 – Classification
Exemplar 1 Angle properties of triangles (Shape and space)
Exemplar 2 Identifying compound shapes (Shape and space)
Exemplar 3 Three-dimensional shapes (Shape and space)
Exemplar 4 Linear and quadratic graphs (Graph work)
Exemplar 5 Number sequences (Number)
Strategy 4 – Living Graphs and Fortune Lines
Exemplar 1 The house swap (Graph work)
Exemplar 2 Football share prices (Graph work)
Strategy 5 – Mysteries
Exemplar 1 The garden (Shape and space)
Exemplar 2 Where should the Hunter family go on holiday? (Number)
Strategy 6 – Relational Diagrams
Exemplar 1 Geometrical reasoning (Shape and space)
Exemplar 2 Number properties (Number)
Strategy 7 – Taboo
Exemplar 1 Various words and topics
Strategy 8 – Sequencing
Exemplar 1 The zin obelisk (Number)
Exemplar 2 Triangle theorems (Shape and space)
Exemplar 3 Creating and solving equations (Algebra)
Part 3 – Thinking Skills and mathematics teaching and learning
Chapter 4: What do Thinking Skills lessons look like?
Principles of teaching thinking
Key episodes in Thinking Skills lessons
Characteristics of Thinking Skills lessons
Chapter 5: The roles of the teacher in the Thinking Skills classroom
Implications for the roles of the teacher
Mediation
Exploratory talk
Mediation and exploratory talk and key episodes of Thinking Skills lessons
What can you do to promote and develop students’ metacognition
Implications for the roles of learners
Chapter 6: Practical advice and suggestions for getting started
Five rules of thumb for teaching thinking to support mathematical learning
What support is needed to maximise students’ learning?
Working in groups
What is your role?
Chapter 7: How Thinking Skills lessons can develop mathematical habits of mind
Habits of mind
Mathematical Thinking Skills
Mathematical problem solving
Visualisation
Chapter 8: Stages of professional engagement
What support is there for teachers’ learning?
Bibliography