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

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'I genuinely believe I have never taught mathematics better, and my students have never learned more. I just wish I had known all of this twelve years ago...' When you speak to the likes of Dylan Wiliam, Doug Lemov, Daisy Christodoulou, Kris Boulton and the Bjorks, you are bound to learn a thing or two. But when he started his Mr Barton Maths Podcast, Craig Barton wasn’t expecting to have his whole outlook on teaching and learning turned upside down. How I Wish I’d Taught Maths is the story of an experienced and successful maths teacher’s journey into the world of research, and what it looks like in the classroom. Along the way we meet practical, easy-to-implement strategies including Supercharged Worked Examples, Silent Teacher, SSDD problems, low-stakes quizzes, diagnostic questions, Purposeful Practice, self-explanations, harnessing the power of the hypercorrection effect, how to (and how not to) teach problem-solving and much more. No matter your experience, teaching style or favourite number, every maths teacher will find something to think about in this book. Chapters 1. How students think and learn 2. Motivation 3. Explicit Instruction 4. Focussing Thinking 5. Self-Explanations 6. Making the most of Worked Examples 7. Choice of Examples and Practice questions 8. Deliberate Practice 9. Problem Solving and Independence 10. Purposeful Practice 11. Formative Assessment and Diagnostic Questions 12. Long-term Memory and Desirable Difficulties 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