How I Wish I’d Taught Maths  34658

Lessons Learned from Research, Conversations with Experts, and 12 Years of Mistakes

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