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?

Craig Barton is one of the UK's most respected teachers of mathematics. In his remarkable new book, he explains how he has delved into the world of academic research and emerged with a range of simple, practical, effective strategies that anyone can employ to save time and energy and have a positive impact on the long-term learning and enjoyment of students