How I Wish I'd Taught Maths: Lessons learned from research, conversations with experts and 12 years of mistakes

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How I Wish I'd Taught Maths: Lessons learned from research, conversations with experts and 12 years of mistakes

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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.



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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.


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

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, he 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.

Craig is the creator of two of the country’s most popular maths websites:, which provides free resources to teachers and students all around the world; and, 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 identify, understand and resolve key misconceptions.

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. Craig has been fortunate enough to give talks, run workshops and work with teachers and students all over the world, from Bangkok to Basingstoke, and is the author of three (non-maths) novels. Fingers crossed he is also still married to Kate when you are reading this.


''How I wish I’d taught maths' is an extraordinary and important book. Part guide to research, part memoir, part survival handbook, it’s a wonderfully accessible guide to the latest research on teaching mathematics, presented in a disarmingly honest and readable way. I know of no other book that presents as much usable research evidence on the dos and don’ts of mathematics teaching in such a clear and practical way. No matter how long you have been doing it, if you teach mathematics—from primary school to university—this book is for you.' Dylan Wiliam, Emeritus Professor of Educational Assessment, UCL

'How I wish I had taught maths' is a rare and wonderful book, one that could only have been written by someone with Craig’s devotion to teaching and willingness to become immersed in the research literature on how people learn.  In clear, concrete, and compelling terms Craig illustrates evidence-based ways to upgrade mathematics instruction, ways that are often unintuitive and/or at odds with prevailing educational practices.  It makes us wish that young people the world over might have the good fortune to find themselves in classes that incorporate Craig’s insights.  In fact, whereas Craig writes, “I’ll be honest—this book has been created for maths teachers,” we think that Craig’s “lessons learned” can, with some creativity, enhance any teaching.' Robert A. Bjork and Elizabeth L. Bjork, Department of Psychology, University of California, Los Angeles

'It’s rare that we change our habits and beliefs once they are established - cognitive bias is strong in us. And that is what makes this book so exceptional.  Craig describes not only what he’s learned from a methodical study of cognitive science but how he’s changed over time despite his initial success. There’s a joyful relentlessness to Craig’s study of teaching methods.  He starts out telling us he wants to “know every detail,” and what makes the book so exceptional is just that- the way the story of how something he learned about teaching played out in a specific problem or lesson, was refined and improved.  It’s an incredibly useful book for maths teachers especially but really for anyone who teaches and cares about getting it right.' Doug Lemov, former teacher and author of Teach like a Champion, @Doug_Lemov

'This is a really thoughtful and thought-provoking discussion of a series of important and practical questions about the best way to teach.' Daisy Christodoulou, author of 7 Myths about Education and Director of Education at No More Marking, @daisychristo

'History will look back on "How I wish I'd taught maths" as a seminal book leading mainstream teachers into the new world. And who else would you want to narrate us into the unknown than Craig Barton, the leading maths educator in the UK? A role model for excellence in professional development, Craig's enthusiasm, intellect and critical skills navigate readers through vitally important and complex concepts with ease. Pulling on contemporary research from hundreds of papers and books, "How I wish I'd taught maths" concisely summarises all that we know about high-impact teaching and gives specific examples of what it looks like in the classroom. This book will quickly become a classic.' William Emeny, Teacher, Researcher, Author of Great Maths Teaching Ideas, Creator of Numeracy Ninjas, Twitter: @Maths_Master

'This book has the potential to have a huge impact on the way maths is taught. It is so refreshing to see a maths teacher honestly critiquing their own practice and suggesting alternative approaches based on sound research and analysis. Craig's warm and relatable style of writing is a pleasure to read. His book is brought to life by hilarious anecdotes and humble reflections. Craig summarises the key points of the relevant research succinctly and his advice to teachers is perfectly pitched and instantly transferable to any maths classroom. For the sake of our current and future students, I certainly hope that this book becomes essential reading for maths teachers.' Jo Morgan, maths teacher and creator of, Twitter: @mathsjem

'How I wish I’d taught maths' is an honest and insightful reflection of Craig's years as a maths teacher. Through experience, podcasting others and reading broadly, Craig carefully considers every assumption he used to make when teaching maths - assumptions we all make or made. In each chapter he forensically analyses a theme from Explicit Instruction to, my favourite, Choice of Examples, expounding his old approach and backing up his new approach with rich examples and scholarly references. Written in the way he speaks - upbeat, humble and littered with "flippin' 'ecks" - Craig brings together so many aspects of maths teaching and so many shared assumptions that there's something in here for anyone involved in maths education, including teacher trainers, early career teachers and those with many years at the chalkface. Having read How I wish I’d taught maths I'll now be a considerably stronger practitioner. No doubt this will become the defining book on maths pedagogy for generations of maths teachers.' Bruno Reddy, Former Head of Maths at King Solomon Academy and creator of Times Tables Rockstars, Twitter: @MrReddyMaths

'This is one of the most useful books on maths instruction that I have read. Craig’s humility and honesty about his previous reasoning, and responses to received wisdom (and his own biases), invites the reader to examine their own preconceptions and blind spots. The volume of research behind his conclusions – and the down-to-earth summaries of its implications – make it accessible for anyone interested in maths teaching. His stories ring horribly true, encapsulating predictable errors made early (and late!) in a maths teacher’s career. I wish it had existed when I trained; I might have avoided making so many mistakes, and for so long! As the debate about ‘teacher standards’ gathers pace, this book is a timely contribution in answer to the question “What should we expect all teachers, as professionals, to know about the craft of teaching maths to children?” . I would not be surprised if this became compulsory reading for a range of PGCE courses and teacher inductions. Craig’s conclusions about how to help pupils learn interrogate the most fundamental aspects of how we think about teaching, regardless of curriculum area.' Dani Quinn, Head of Maths at Michaela Community School, Twitter: @danicquinn

'Evidence-fueled, down-to-earth, and hugely practical. The book we maths teachers have all been waiting for.' Peps Mccrea, Associate Dean at the Institute for Teaching, Twitter: @pepsmccrea


Additional Information

Author Craig Barton
ISBN 9781911382492
No of pages 302
Format Paperback
Publication Date 16 Nov 2017

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