Reflect, Expect, Check, Explain: Sequences and behaviour to enable mathematical thinking in the classroom
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Description
Contents
Reviews
Language
English
ISBN
9781915361936
Title page
Copyright
Contents
Dedication
Foreword
Glossary
Introduction
Warm up
1: Intelligent Practice
1.1. What I used to do
1.2. What I do now
1.3. A shared vocabulary
1.4. What do I mean by ‘Intelligent Practice’?
1.5. The three elements needed to support mathematical thinking
1.6. What does this look like in the classroom?
1.7. Model the First Relationship
Take a Break #1: Subtracting decimals
1.8. The Self-Explanation Effect
1.9. Student prompt cards
1.10. Writing it down
1.11. Silent Practice
1.12. Paired Discussion
1.13. The 4-2 approach
1.14. What I do whilst my students are working on the sequence of questions
1.15. Relationships
1.16. Discuss Relationships
1.17. Prompts for Delving Deeper
1.18. Differentiation revisited
1.19. Is structured practice even needed?
Take a Break #2: Rounding to 1 decimal place
2: Where does Intelligent Practice fit in?
2.1. How I Wish I’d Taught Maths: Two years on
2.2. A Learning Episode
2.3. What do I mean by ‘method’?
2.4. Introduction
2.5. Atomisation
2.6. Example-Problem Pair
2.7. Example-Problem Pair: Questions and concerns
2.8. Fluency Practice
2.9. Intelligent Practice
2.10. The Example-Problem-Pair-Practice Cycle
2.11. Method Selection
Take a Break #3: Reading scales – decimals
2.12. The ‘why’
2.13. The Four Ingredients of Problem Solving
2.14. The Four Ingredients of Retrieval
2.15. Formative Assessment
2.16. Other elements in the Learning Episode
2.17. Want to know more?
3: Different features of Intelligent Practice sequences
3.1. Confronting the ‘unusual’
3.2. Confronting the ‘obvious’
3.3. Interleaving high-value concepts
3.4. Atomisation
3.5. Providing a purpose
3.6. Fill in the Gaps
3.7. Student-generated sequences
Take a Break #4: Carrying out rotations
4: Intelligent Practice FAQs
4.1. FAQs: Student behaviour
Take a Break #5: Sharing in a ratio
4.2. FAQs: Teacher behaviour
4.3. FAQs: General concerns
Take a Break #6: Equation of a tangent to a circle
5: Rule
5.1. What I used to do
5.2. What I do now
5.3. What are Rule sequences?
5.4. Where do Rule sequences fit in?
5.5. Assessing understanding
5.6. Rule: Frequently asked questions
6: Different uses of Rule
6.1. Definitions
6.2. Decisions
6.3. Depth
6.4. Recap
6.5. How before why
Take a Break #7: Averages and range from a list of data: Increase, decrease, same?
7: Pattern
7.1. What I used to do
7.2. ‘With the grain’ versus ‘across the grain’
7.3. What I do now
7.4. What are Pattern sequences?
7.5. Where do Pattern sequences fit in?
7.6. Patterns and Structured Variation Grids
7.7. Pattern type 1: To establish new ideas
7.8. Pattern type 2: To consider Boundary Examples
7.9. A potential Pattern problem
Take a Break #8: Constructions
8: Demonstration
8.1. What I used to do
8.2. What I do now
8.3. Straight line graphs
8.4. Angle at the centre
8.5. Area of a triangle
8.6. What are Demonstration sequences?
8.7. Where do Demonstration sequences fit in?
8.8. Whole class versus individual
9: Summary table
10: Teachers writing their own sequences of questions and examples
10.1. Why reinvent the wheel?
10.2. Why write sequences of questions and examples?
10.3. A structure for collaboration?
10.4. Tips for making this process work
10.5. Tips for writing sequences of questions and examples
10.6. Sharing is caring
11: Making this work
Conclusion
The warm-down
1. ‘This is not Variation Theory’
2. ‘Where are the rich tasks?’
3. ‘Where is the inquiry?’
A final thought
Acknowledgements
References
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