- Foreword Kristopher Boulton
- Dedication
- Introduction
- How students think and learn
- A simple model of thinking and learning
- Experts and Novices
- What are they thinking about?
- Expanding working memory capacity
- Methods that last
- Maths anxiety
- If I only remember 3 things
- Motivation
- Models of motivation
- Do students make good decisions?
- Real-life maths
- Teacher influence
- Providing a purpose
- Rewards and sanctions
- Why struggle and failure aren’t always good – Part 1
- Achievement and motivation
- If I only remember 3 things
- Explicit Instruction
- What makes great teaching?
- Are some students natural mathematicians?
- When and why less guidance does not work
- The problem with guided discovery
- Teaching lower-achieving students
- Story structure
- Analogies
- Cognitive conflict
- How before why
- Ending on a high
- If I only remember 3 things
- Focusing Thinking
- Cognitive Load Theory and the Cognitive Theory of Multimedia Learning
- When silly mistakes may not be that silly
- The Modality Effect
- Learning styles
- The Goal-free Effect
- The Split Attention Effect
- The Redundancy Effect
- Silent teacher
- Germane Load
- If I only remember 3 things
- Self-Explanations
- The Self-Explanation Effect
- Making the most of self-explanations
- If I only remember 3 things
- Making the most of Worked Examples
- The Worked Example Effect
- Example-Problem Pairs
- Labels
- Supercharged Worked Examples
- Mistakes in Worked Examples
- Fading
- The Expertise Reversal Effect
- If I only remember 3 things
- Choice of Examples and Practice Questions
- Examples v Definitions
- Examples v Rules
- Boundary examples
- Same Surface, Different Deep Problems
- Ambiguous answers
- Ambiguous questions
- Extension questions
- Minimally different examples and Intelligent Practice
- If I only remember 3 things
- Deliberate Practice
- Breaking it down
- The five stages of deliberate practice
- Practice v final performance
- Three reasons to always give students the answers
- If I only remember 3 things
- Problem-Solving and Independence
- What is a problem?
- Why are some students bad at problem-solving …
- … and what can we do about it?
- Why struggle and failure aren’t always good – Part 2
- Independent learners
- Purposeful Practice
- The most difficult part of teaching
- What is purposeful practice?
- If I only remember 3 things
- Formative Assessment
- What is formative assessment and why is it important?
- Classroom culture
- What is a Diagnostic Question?
- What makes a good question?
- How to ask and respond
- When to ask a diagnostic question
- Seven common criticisms of multiple-choice questions
- Anticipating mistakes and misconceptions
- The benefits of teachers writing questions
- If I only remember 3 things
- Long-term Memory and Desirable Difficulties
- How long-term memory works
- The problem with performance
- The Spacing Effect
- The Interleaving Effect
- The Variation Effect
- The Testing Effect
- The many, many other benefits of tests
- Low-stakes quizzes
- The Pretest Effect
- Delaying and reducing feedback
- If I only remember 3 things
- Conclusions
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