How I Wish I'd Taught Maths: Lessons learned from research, conversations with experts, and 12 years of mistakes: Reflections on research, conversations with experts, and 12 years of mistakes

Cover
Reviews
Contents
Foreword
Dedication
Introduction
1. How Students Think and Learn
	1.1. A simple model of thinking and learning
	1.2. Experts and Novices
	1.3. What are they thinking about?
	1.4. Expanding working memory capacity
	1.5. Methods that last
	1.6. Maths anxiety
	1.7. If I only remember 3 things…
2. Motivation
	2.1. Models of Motivation
	2.2. Do students make good decisions?
	2.3. Real-life Maths
	2.4. Teacher influence
	2.5. Providing a Purpose
	2.6. Rewards and Sanctions
	2.7. Why struggle and failure aren’t always good – Part 1
	2.8. Achievement and Motivation
	2.9. If I only remember 3 things…
3. Explicit Instruction
	3.1. What makes great teaching?
	3.2. Are some students natural mathematicians?
	3.3. When and why less guidance does not work
	3.4. The problem with guided discovery
	3.5. Teaching lower achieving students
	3.6. Story structure
	3.7. Analogies
	3.8. Cognitive conflict
	3.9. How before Why
	3.10. Ending on a high
	3.11. If I only remember 3 things...
4. Focusing Thinking
	4.1. Cognitive Load Theory and the Cognitive Theory of Multimedia Learning
	4.2. When silly mistakes may not be that silly
	4.3. The Modality Effect
	4.4. Learning styles
	4.5. The Goal-free Effect
	4.6. The Split-Attention Effect
	4.7. The Redundancy Effect
	4.8. Silent teacher
	4.9. Germane Load
	4.10. If I only remember 3 things…
5. Self-Explanations
	5.1. The Self-Explanation Effect
	5.2. Making the most of self-explanations
	5.3. If I only remember 3 things…
6. Making the most of Worked Examples
	6.1. The Worked Example Effect
	6.2. Example-Problem Pairs
	6.3. Labels
	6.4. Supercharged Worked Examples
	6.5. Mistakes in Worked Examples
	6.6. Fading
	6.7. The Expertise Reversal Effect
	6.8. If I only remember 3 things…
7. Choice of Examples and Practice Questions
	7.1. Examples v Definitions
	7.2. Examples v Rules
	7.3. Boundary examples
	7.4. Same Surface, Different Deep Problems
	7.5. Ambiguous answers
	7.6. Ambiguous questions
	7.7. Extension questions
	7.8. Minimally different examples and Intelligent Practice
	7.9. If I only remember 3 things…
8. Deliberate Practice
	8.1. Breaking it down
	8.2. The five stages of Deliberate Practice
	8.3. Practice v final performance
	8.4. Three reasons to always give students the answers
	8.5. If I only remember 3 things…
9. Problem-Solving and Independence
	9.1. What is a problem?
	9.2. Why are some students bad at problem-solving…
	9.3. …and what can we do about it?
	9.4. Why struggle and failure aren’t always good – Part 2
	9.5. Independent learners
	9.6. If I only remember 3 things…
10. Purposeful Practice
	10.1. The most difficult part of teaching
	10.2. What is Purposeful Practice?
	10.3. If I only remember 3 things…
11. Formative Assessment and Diagnostic Questions
	11.1. What is formative assessment and why is it important?
	11.2. Classroom Culture
	11.3. What is a Diagnostic Question?
	11.4. What makes a good question
	11.5. How to ask and respond
	11.6. When to ask a diagnostic question
	11.7. Seven common criticisms of multiple-choice questions
	11.8. Anticipating mistakes and misconceptions
	11.9. The benefits of teachers writing questions
	11.10. If I only remember 3 things…
12. Long-term Memory and Desirable Difficulties
	12.1. How long-term memory works
	12.2. The problem with performance
	12.3. The Spacing Effect
	12.4. The Interleaving Effect
	12.5. The Variation Effect
	12.6. The Testing Effect
	12.7. The many, many other benefits of tests
	12.8. Low-stakes quizzes
	12.9. The Pretest Effect
	12.10. Delaying and reducing feedback
	12.11. If I only remember 3 things…
Conclusion
Acknowledgements