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Reflect, Expect, Check, Explain: Sequences and behaviour to enable mathematical thinking in the classroom

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Reflect, Expect, Check, Explain: Sequences and behaviour to enable mathematical thinking in the classroom

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Craig Barton, maths teacher and best-selling author of 'How I wish I'd taught maths', offers an approach to help all our students think mathematically. It requires the careful sequencing of questions and examples, the role of the teacher, and the mathematical behaviour of our students. It has transformed his teaching.

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Some students think mathematically. They have the curiosity to notice relationships, the confidence to ask why, and the knowledge to understand the answer.

They are the lucky ones.

Many others just 'do' maths. They look at a question, think about how to answer it, answer it, and then move on.

Craig Barton, maths teacher and best-selling author of 'How I wish I'd taught maths', offers an approach to help all our students think mathematically. It requires the careful sequencing of questions and examples, the role of the teacher, and the mathematical behaviour of our students. It has transformed his teaching.

Drawing upon research into the Self-Explanation Effect, the Hypercorrection Effect and Variation Theory, together with two years of developing this approach with teachers and students around the world, Craig describes exactly what this looks like in the classroom.

But be warned: not everyone agrees. Indeed, it is this very approach that led to Craig being labelled as 'the most dangerous and clueless man in maths education'. If that is not a recommendation to keep reading, I don't know what is.

Contents
Foreword by Jo Morgan
Introduction
Chapter 1: Intelligent Practice
Chapter 2: Where does Intelligent Practice fit in?
Chapter 3: Different features of Intelligent Practice sequences
Chapter 4: Intelligent Practice FAQs
Chapter 5: Rule
Chapter 6: Different uses of Rule
Chapter 7: Pattern
Chapter 8: Demonstration
Chapter 9: Summary table
Chapter 10: Teachers writing their own sequences of questions and examples
Conclusion: A recipe for change?

About the author

Craig Barton has been teaching maths since 2004, predominantly in two comprehensive schools in the sunny North West of England, Range High School in Formby and Thornleigh Salesian College in Bolton. Four years into his career, Craig was appointed an Advanced Skills Teacher (AST) giving him the opportunity to work with and learn from many teachers and students in a wide variety of schools.

Since 2009, Craig has been the Secondary Mathematics adviser for the Times Educational Supplement (TES), the largest professional network of teachers in the world, reviewing, creating and sharing resources with hundreds of thousands of teachers.

He is the creator of the popular mrbartonmaths.com website and blog, which provides free resources to teachers and students all around the world, with the aim of making maths more fun and exciting for everyone.

Craig is the host of the Mr Barton Maths Podcast, interviewing leading figures from the world of education, such as Dylan Wiliam, Doug Lemov, Daisy Christodoulou and Dan Meyer.

He is the co-creator of Diagnostic Questions, a formative assessment website hosting the world's largest collection of high-quality maths diagnostic multiple choice questions, which aims to help students and teachers from all around the world to identify, understand and resolve key misconceptions, and currently has over 20 million answers and explanations.

More recently he has created the websites variationtheory.com, ssddproblems.com and mathsvenns.com, with millions of teachers from across the globe sharing high-quality resources based on ideas from Craig's book.

Craig has been fortunate enough to give talks, run workshops and work with teachers and students all over the world, from Bangkok to Basingstoke.

He is the author of the best-selling book, How I wish I'd taught maths: Lessons learned from research, conversations with experts, and 12 years of mistakes, and the author of 3 (non-maths!) novels. Fingers crossed he is also still married to Kate when you are reading this.

Additional Information

Author Craig Barton
ISBN 9781912906345
No of pages 350
Format Paperback
Publication Date 28 Feb 2020

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    These are just my views and I hope .it is not a misrepresentation
    The ideas and strategies are well explained and supported by research. It is not presented as a cure-all but I have begun to try some of the ideas in the classroom and the impact on both levels of attention and thinking has been obvious. I don't feel qualified to provide a full academic review as I am better with letters when they are written amongst numbers but I found this book to be readable and immediately useful. The diagrams and examples are superb. Much of the well-researched approach simply rang true. I was concerned about confirmation bias but my students have definitely benefited from 'atomisation' (why have I not been doing this?) and they have asked when I am next going to try the 'different way' to introduce a new concept as it made more sense and they found it easier to concentrate fully during the explanation! I look forward to continuing to build in more elements of this approach and I am confident that the changes I am making to my teaching are not part of a trend but that it will form a significant part of the way that I will continue to teach.