Craig Barton’s “How I Wish I’d Taught Maths” – my takeaways


I have just finished Craig Barton’s (@mrbartonmaths) book, “how I wish I’d Taught Maths”.


Wow! It’s the best thing I’ve read since @Doug_Lemov‘s Teach like a champion.


Here are my top 10 Takeaways


  1. Silent teacher worked examples:

This has been a game-changer for me. Silent teacher was around when I was training and whilst I was an NQT around 2012-13 but it seemed like such a fad at the time and was lumped together with a whole load of other ‘engagement’ strategies. It was presented as a novel way to start a lesson just to spice up lessons a little to keep otherwise bored students engaged. The problem was that behaviour in the school (and in my lessons) was RI at best and terrible a lot of the time. Trying to engage students with silent teacher when running up and down telling dirty jokes was a viable alternative activity was never going to happen. (It is worth noting here that that particular school has since sorted out behaviour using much of the techniques found in @Doug_Lemov‘s Teach Like a Champion, @PivotalEd and @TouchBase_UK).

While I am on the topic of terrible advice given to me whilst an NQT, another one was the ‘hook’. I was required, for a short time, to have a slide in every presentation which linked the maths to the real world which would engage the students and get them to be more interested in the lesson. I would spend more time thinking about this one slide during planning than the whole rest of the lesson. I would spend up to 1 minute on it and the best outcome was that the students didn’t end up more confused than they might have been anyway. Usually my attempt to segue some tenuously related real-life situation into the lesson would just baffle the students rather than making it more relevant. It was a bit like playing a game called “guess why this random picture has anything to do with this topic of maths which I haven’t taught you yet!”.

Anyway, back to Silent Teacher. It is interesting to me now that although I was being persuaded to try this new gimmicky approach it was only ever suggested as an engaging starter activity and none of the other benefits which Craig describes were mentioned: “It turns out that the Silent Teacher approach has significant merit in terms of Cognitive Load Theory” (p177).

Another benefit I have found is that it is empowering for students. By not talking and explaining the process during the silent worked example I am implicitly giving the message that I believe they can follow this themselves. They don’t need my explanation, they can read and figure it out by themselves. And because of the reduction on cognitive load, I have found that they are much more able to follow and understand the process. This is such a win-win. I have reduced their cognitive load, I have shown that I believe in their own reasoning powers and they have proven to themselves that can get it and the success they feel motivates them for the next part of the lesson and builds their self-esteem.

  1. Diagnostic Questions:

I have known about Craig’s diagnostic questions for a long time but never used them. Partly due to my slight aversion to technology, partly because I didn’t want to have to sign my students up to another online platform where they would lose their passwords etc but mainly because I didn’t appreciate the power of their use for teasing out misconceptions and I also didn’t see how I might use them in the classroom.

Well, all that has changed. Diagnostic questions is a go-to website during planning for me now and I am embedding them in all my lessons. And when I do not find the questions I want on the website I make my own (which I will send in when I get the chance!). I make workpacks for my lessons à la Bruno Reddy (@MrReddyMaths) so it has taken me a while to get my head around how to use them in this format, but I am beginning to get there. I also have not trained all my classes to respond to the diagnostic questions yet, but I will have by the end of this term.

Diagnostic questions are definitely a development focus for me moving forward.

  1. Minimally different questions and intelligent variation:

This is another area that I need to focus on developing. After the diagnostic questioning and the silent worked examples I need to consider the order and sequencing of the questions that I give students in order for them to practice. Too often I have just given them 10 random questions on pythag or whatever and not considered how best to vary them. from @FortyNineCubed is a great place to start as is from @taylorda01.

Update: Since I first published this blog post Craig has been busy and has released a brand new website called with a new set of growing resources in 4 different formats:

a: Example-Problem Pair + Intelligently varied practice

b: Rules – Examples and non-examples of a concept to demonstrate and practice

c: Patterns – Carefully chosen examples presented in order to draw pupils’ attentions to certain key features of a concept + practice questions.

d: Demonstrations – using software to demonstrate key concepts. Craig makes the point that he always has two versions of the diagram on the screen and changes on so that the pupils can see what is the same and what is different.

This website is a new go-to for me when planning, cheers Craig!

  1. SSDDs:

These are so great they now feature towards the back of every workpack I make. A great way to interleave (interweave?) previously learnt topics with the current topic. Visit to find out more. And what I love about Craig’s style is that he is keen for teachers to collaborate so you can send in your own questions for the diagnostic questions, the SSDDs and the Maths Venns (see below). I had a go with some of my students and got them to come up with some SSDDs of their own which is a great activity. And Craig even published them on the site which pleased the kids no end.

  1. Maths Venns:

These are awesome. It didn’t occur to me initially that they have such a great ‘in’ for students as any example they think of will fit somewhere in the Venn diagram. I will make this explicit in the future. These are another great question type featuring now towards the back of my workpacks and are an example of purposeful practice, see below. Visit to find out more.

  1. Purposeful practice:

This is something that I definitely need to spend more time thinking about and researching. There are some great websites that Craig recommends like Colin Fosters’s Mathematical etudes (, NRICH (, Don Stewards Median Maths ( and each of which I need to explore more. I do feel however that none of these sites presents exactly what I want in a super easy to access format, not because they are not full of excellent questions and activities (they are) but because not all the activities on them are ‘purposeful practice’. I may just need to make myself more familiar with them but I do think there is a gap in the market for a purposeful practice website where these tasks can be collated in a one-stop-shop, much like the SSDD website. Anyone interested?!

7: Always supplying the answers.

This is not something I do very often. Usually because I am creating my own questions and I can’t be bothered. I usually use show-call (from @Doug_Lemov’s Teach like a Champion 2.0) to reveal the answers and highlight misconceptions as well.

Next year I will be teaching mixed ability year 10. I am slightly bricking it about this, but I think that if I supply the answers then it will encourage my students to be a bit more independent in their learning. This will be important as I don’t think I will be able to keep all students working on the same thing at the same time. Sometimes it will be necessary to do a few example-problem pairs for one set of students while another set get on with some minimally different questions, increasingly difficult questions, some purposeful practice or maybe a low-stakes quiz (see below).

8: The spacing effect:

I tweeted earlier ( about how this is the only section of the book that I have nailed down already:

– Teachers should dedicate part of each lesson to reviewing concepts learned several weeks earlier.

Well, I already do this. And in my tweet I gave credit to the amazing John Corbett (@Corbettmaths) for his phenomenal 5-a-day. I can expand a little here on what I do day to day.

I actually rarely use John’s 5-a-day except in emergency or with yr 11 for revision now. Instead I have taken the 5-a-day format and I create my own. Every term my pupils sit a cumulative assessment testing everything they have learned since they met me. I QLA this and pick the 15 skills which the class did worst on. These 15 skills go into my Do Nows (@TeachLikeAChamp) and get rotated all term at the start of every lesson.

The first week back after half term there is always a little abrasiveness from the children as the Do Now is hard and takes a long time to go through. I explain why am doing it this way and what is great is that by even the second week the pupil’s confidence has grown considerably on these topics. As an aside, we had our MALT ( @HodderSchools ‏) test results back and all classes under this system at my new school have made significant progress.

– Homework assignments should be used to re-expose students to important information they have learned previously

I do this through the amazing @hegartymaths online homework platform. I set the homeworks bespoke for each pupil according to the QLA from the recent assessment.

– Teachers should give exams and quizzes that are cumulative.

Done! Thanks to the fact that within maths at my school I am my own boss and I report directly to the head teacher who gives me almost free reign, I can design my assessments as I see fit. They are not perfect and are very much a work in progress but they are at least cumulative.

9 – The testing effect.

Using the assessments as a tool for learning is high on my agenda. As there is a low accountability culture in my school the assessments that I make my pupils sit are only seen by me, the data is only seen by me (sometimes by the head). We have completely mixed ability so no set changes or other outcomes as a result of the tests. They are low stakes formative assessments. They sit a test every half term and review it the next lesson. They have a front sheet with all the skills per question like a QLA, with the Hegarty video numbers next to the questions and they RAG each question and then are encouraged to look the red topics up on Hegarty.

Improvement I need to make: I need to make a more user friendly pledge sheet for the students to take home to use with Hegarty where they write down 5 videos and quizzes they will complete off the back of the assessment.

10: Low-stakes quizzes:

I want to make my 5-a-day-style Do Nows slightly more quiz-like. I am going to print out a sheet for each pupil which has each of the 15 topics which will be coming up every week and each day they can record how many of the topics they got right so week by week through the term they should be able to see their progress.

One thing I have noticed this year is that although the students are doing better, some of them don’t know they are doing better. I need ways to show that they are making progress without making a big deal of the assessments. Quizifying the Do Now in this way is one method of achieving this. After all success begets motivation.


So there you have it. 10 things I learnt from Craig Barton’s amazing book “How I Wish I’d Taught Maths”. There are so many more things I could mention, but you might as well just go and buy his book! The main other thing I am taking away is the importance of research. I am just starting my journey in this regard but can’t wait. I have never enjoyed my job more than since I started reading about maths, maths teaching and learning in general.

A massive thanks to Craig for opening my eyes to so many aspects of teaching and memory that I didn’t know about before.

And if you haven’t already I thoroughly recommend subscribing to Craig’s podcast ( which is a gold mine of info and has in-depth interviews with many of the people discussed in the book.


  1. Thanks Brendan I’m still working through Craig Barton’s book and you have challenged me to keep going and to focus on one or two areas to work on at a time in my own practice.

    Liked by 1 person

    • Cheers Alistair, I definitely think one should ficus on just one or two things a term, otherwise it is overwhelming!

      I have been practicing example problem pairs and experimenting with SSDDs and maths Venns for the last 6 weeks or so and feel about ready to embed these as permanent features of my lessons.

      From September I will be focusing on making my retrieval practice more quiz-like and finding more purposeful practice activities.

      Good luck!


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