20 January 2018

How I Wish I'd Taught Maths

Craig Barton's new book 'How I Wish I'd Taught Maths' is a game changer... in a game that very much needs changing. It's absolutely superb. I genuinely think it might have a huge impact on the way maths is taught. Or at least, I hope it does.

Craig's teaching has transformed significantly in recent years. Through a charming and witty narrative, Craig explains how he used to teach - back when he was a highly successful 'Ofsted outstanding' advanced skills teacher - and why he teaches totally differently now that he has properly engaged with education research. He jokes about how ineffective his previous approaches were, and this may make uncomfortable (but worthwhile) reading for maths teachers who still teach in this way.

Teachers are trained pretty quickly in this country, particularly those on school based schemes. New teachers are often thrown into classrooms with no knowledge of cognitive science whatsoever. As Craig writes, "a teacher not considering how their students think and learn is kind of like a doctor not being overly concerned about the workings of the body, or a baker taking only a casual interest in the best conditions for bread to rise". Thankfully Craig's book gives both new and experienced teachers the opportunity to remedy this.

Craig's anecdote about 'The Swiss Roll Incident' (in which his students remembered swiss rolls instead of maths after a messy jam-filled lesson) perfectly illustrates the notion that "students remember what they think about". Throughout the book Craig's anecdotes and reflections beautifully exemplify some of the common mistakes that teachers make. Each anecdote comes with a description of Craig's key takeaways from the relevant research and an explanation of what he now does differently. This provides a clear way forward for maths teachers looking to improve the effectiveness of their practice.
In his chapter on deliberate practice, Craig writes about identifying sub-processes and isolating skills. He shares examples of short activities which allow him to pick up on specific misconceptions and address them before they get wrapped up in more complex processes. The example below is part of a series of short activities for teaching students how to add fractions.
I'm not sure that this kind of activity is currently common practice, but like many approaches featured in Craig's book, I think it may become recognised as a highly effective approach over the coming years. It's great that Craig has shared so many specific examples of activities, resources and explanations. These are incredibly helpful to teachers. 

In summary, I love this book! Not only has Craig put all the relevant education research in one place, which is perfect for overworked and exhausted teachers like me, he has also interpreted broad education research specifically in the context of maths teaching. Most of the research isn't new, but Craig adds so much value by describing how it relates his own practice that even teachers who keep up to date with the latest research will benefit from reading Craig's interpretations. His advice is easy to understand and instantly transferable to the classroom.

Craig's book is a real pleasure to read and had me giggling throughout ("keep this quiet, but I flipping hate 3D trigonometry!"). It has the potential to have a huge impact on the way maths is taught. It's delightfully controversial at times and I'm certain that it will spark lots of interesting discussions in maths departments all over the country. Once you've read it, do let me know what you think.


  1. Will be ordering this! I find it so comforting that Craig is not a lover of 'flipping 3D trigonometry'. Me too! (Have ordered (another) set of 'the ultimate' (hopefully...) perspex 3D shapes. Hopefully Craig's book will help me... Plus all the other suggestions in it, many of which I may rebel against initially but, having had a chance to mull, will I'm sure improve my tutoring. Thanks again, Jo.

  2. Can't wait to get this. It's actually on order already.

  3. All trainee Maths teachers should own a copy

  4. Thanks for the informative review, Jo.

    It is a pity that the Swiss Roll incident sort of backfired, as described, because the idea of using the real thing in the classroom is very attractive. I wonder whether a deliberate shift in emphasis would have saved the day e.g. "Now, children, although Swiss rolls are very tasty, we must not forget what we set out to do. The solution of the problem is what really interests us..." for want of a better way of putting it.

    I favour this policy of preemptive isolation of misconceptions, provided that some effort is put into conveying the reason why the isolation is being done. For example, in the situation that you describe with finding the common denominator, perhaps we can make children see that this process achieves some notion of "compatibility" between fractions. 1/5 and 1/4 have a different denominator and we cannot add the two just like that. If we transform them into 4/20 and 5/20 respectively, then they are both "on the same level", "on equal footing", "on common ground"... "the first one is a number of 20ths and so is the second one, so off we go to find their total, which is simply 4 + 5 or 9/20..."

    Thanks again.

  5. Only 10 pages in and loving it. Already 2 'flippin's

    Craig is great and I think his warmth as a person, podcaster and writer has helped me access some material I would have otherwise not read due to it's 'dryness'.