Thinking Through Mathematics is a resource for maths teachers at secondary level to create challenging maths lessons built on maths thinking skills. Teaching maths using thinking skills activities will develop transferable learning skills through interaction and independent learning.
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The activities included in Thinking Through Mathematics will help you to:
Encourage students to discuss and share their mathematical understanding with each other, and with you
Vary the diet of teaching and learning for you and your students
Develop students’ reasoning and thinking skills so that they are able to take a more active role in lessons
Enable students to realise that mathematics is not always about getting one right answer
Make maths a more enjoyable experience for all.
Summary of contents
Thinking Through Mathematics provides teachers of maths with 21 thinking skills activities which develop both generic thinking strategies and more specialised mathematical thinking.
Thinking Through Mathematics is divided into three parts:
Part One provides you with a general introduction to the book. It takes you through the principles that underpin thinking skills, the benefits of teaching thinking in the mathematics classroom, the structure of the book and information about the exemplars included.
Part Two contains 21 exemplars, grouped under eight thinking skills strategies. Each of the strategies is demonstrated with at least one activity which was developed for use in the mathematics classroom and trialled with different age and attainment groups.
Part Three elaborates and expands on points made in the exemplars, drawing attention to why the teachers did things in a particular way, and to how you might adapt them to your own teaching and learning contexts.
Part 1 – Setting the scene
Why was this book written?
Chapter 1: The big picture
Leading in learning
Improving Learning in Mathematics
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
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 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
Chapter 8: Stages of professional engagement
What support is there for teachers’ learning?