Explicit Memorisation

Recently I’ve learned a poem by heart for the first time ever. I found it a hugely enjoyable thing to do, and also quite difficult. This now becomes part of my crystallised knowledge.

It is only recently that I’ve become aware that intelligence is thought of in two ways: fluid and crystallised. Nick Rose’s article Are these the 7 Pillars of Classroom Practice? put me on to Schooling Makes you Smarter by Richard E. Nisbett which discusses how IQ actually measures two types of intelligence:

  1. Fluid intelligence: perhaps the ability to solve novel problems using one’s working memory; and
  2. Crystallised intelligence: one’s store of knowledge about the world in the long term memory.

David Didau has (obviously) written about this and his blog is as usual essential reading. The second part of that blog puts forward the idea that although it is very difficult to increase one’s fluid intelligence, crystallised intelligence can be improved. It can be improved by knowing more things. Hence, school can and does increase the IQ of its students by getting them to know more.

This ties in with blogs by Joe Kirby which I have been reading over the last couple of years, advocating students memorising knowledge by using knowledge organisers, in fact his school have students memorising/ learning by heart knowledge for all their subjects every day. It is a knowledge based curriculum.

Back to my memorisation of the poem. Memorising it was hard. Learning things by heart is hard. To ‘rote learn’ as some may have it is not an easy option. Lets look at the detail of how I did it and how it can be done at school. Again, this is basically all from Joe Kirby. What I did was have the poem as the screen saver on my phone and followed these steps:

  • Look
  • Cover
  • Write
  • Check

It took me about a week, and now I can recite it whenever I want to.

I’ve tried getting students to do this at school with some success. They tell me it’s what they did at primary school and what they do to learn vocab in MFL. It makes sense to me that we as teachers should be making explicit strategies for memorisation with our students: explicit memorisation. In fact, in my role as leader of whole school numeracy I am going to be getting every single student to know a huge number of mathematical facts off-by heart. I will be helping to increase their IQ.

So what is the teacher’s role in this? (with apologies to the huge amount of people who have already advocated knowledge organisers)

  1. Make a list of all the knowledge that you want students to know by heart (I’ve seen Dani Quinn say that anything we as teachers know without having to reason it out should go in the knowledge organiser)
  2. Explicitly teach methods of memorising this knowledge, such as look-cover-write-check and the use of Quizlet
  3. Frequently test the students on this knowledge.




I’m free to be whatever I
Whatever I choose
And I’ll sing the blues if I want

–  Whatever by Oasis *

There are many great freedoms in school.

  • Freedom to have an education
  • Freedom to listen to teachers’ explanations
  • Freedom to be in a calm environment trying one’s best
  • Freedom to learn about the greatest that has been thought and said by humankind
  • Freedom to learn good habits towards hard work

And these freedoms give rise to other freedoms

  • The freedom to choose to study at university
  • The freedom to enter the world of work with good qualifications and habits
  • The freedom to enter the great discussions that are part of what makes us human
  • The freedom to build upon the knowledge of what we have learned at school

School is a truly wonderful place.

There is a price to be paid for these freedoms

  • Discipline so that teachers can teach in the way that is best for all students.

A pretty reasonable price I think.


* In my opinion this is one of the greatest live performances of all time, because of the beauty of the song, the simplicity of the arrangement and the strength of Liam’s voice. The fact that his voice deteriorated so rapidly is one of the world’s enduring misfortunes.

Automaticity: Entering the classroom

The teacher-student three-step.

With thanks to Doug Lemov and the excellent Teach Like A Champion 2.0

Three steps for a teacher to minimise wasted time and disruption at the beginning of the lesson:

  1. Meet and greet the students at the door
  2. Supervise the student three-step
  3. Have a ‘do now’ or ‘recap’ for them to do immediately

The three steps for the students is on a handy poster: three step entry

3 step entry

Implementing this will require me to:

  • explain why and how I want students to do this
  • believe 100% that it is the right thing to do
  • persevere through difficulties
  • guide the students through numerous practices of it until it becomes automatic for them.

Maths: Conceptual understanding first, or procedural fluency?

From Kris Boulton, the best thing I’ve read on maths teaching in a long time

...to the real.

Should you teach conceptual understanding first, or focus on raw procedural fluency?

This question drives endless debate in maths education, but its answer is very straightforward: it depends.

I can demonstrate this quickly and easily with a single example, by teaching you how to multiply logadeons (e.g. 5-:-9,) something you’re probably not familiar with already.

Observe the following examples:

8-:-20     *   2-:-5       = 10-:-25

9-:-20     *   2-:-5       = 11-:-25

100-:-50 *   30-:-7     = 130-:-57

19-:-20    *   5-:-5      = 24-:-25

By this point, you can probably multiply logadeons together quite comfortably.  If you’d like to give it a go, try these two (answers at the end.)

30-:-17  * 4-:-3

17-:-0.5 * 9-:-2

But even if you can evaluate those correctly, you’re probably still not comfortable about all this; you probably don’t…

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Useful bits and pieces

Awesome summary and links for pretty much everything of interest to a teacher from Adam Boxer

A Chemical Orthodoxy

Below is a list of things I have read and found interesting and have helped me develop as a teacher. I’ve been collecting them over the last year or so and tried desperately to keep them in order. This is a work in progress and I’m going to try and update it when I can. I’ve marked everything that I think is super important with a * so you can ctrl+f for it. I’ve tried to keep my summaries as short as possible – the individual pieces will speak for themselves. You will note that I have avoided books too. This is because I don’t really find the time to sit and dedicate time to full books, I prefer to read stuff on the go, in the little snippets of time I find for myself here and there.

This is mainly a list for my own benefit. If anyone else…

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Necessary & Sufficient

What does a good education at school look like?

I think it’s essential to look at this question through the paradigm of what is necessary to a good education and what is sufficient.

Briefly, a necessary condition must be met for a good education, and sufficient conditions guarantee that a good education has been had. My argument here is that Education has been too focused on sufficient conditions, and as a result of this many necessary conditions to a good education are not being met. A good education cannot be had without the foundation of necessary conditions.

My view is that we must look to the necessary conditions and only once these are in place should we layer the sufficient conditions on top of these foundations.

So, what are the necessary conditions of a good education and what are the barriers to them being met? My subject is secondary maths, and this is the lens through which I will be answering the question.

1. Behaviour should be respectful and conducive to learning. The responsibility for behaviour lies with the students and the school as a whole. It is not the responsibility of the classroom teacher.

1b. (added 20-2-16) Homework should be easy to set and mark, ideally with a computer system that automatically marks the work and records the areas of strength and weakness of the students. Ideally, a whole school policy that picks up those students who don’t do their homework would be in place. 

2. Explanations. Teachers should carefully and clearly explain the curriculum to the students. The use of a good set of textbooks would help with this.

3. Hard work and practise. There is no royal road to geometry, and there is no easy way to learn. The responsibility for doing well ultimately rests on the shoulders of the students.

4. Teaching should be responsive. I think that all teachers engage in responsive teaching (a phrase coined by Dylan Wiliam) by which I mean they respond to whether students are learning what is being taught or not and change what they’re doing accordingly. It may be possible to find teachers that don’t but I think they’d be extremely rare. Clearly this can be done to variable levels of success but I think that teachers simply being allowed to exercise their professional judgement in their classes is a necessary condition of a good education.

5. Exam preparation. By this I mean the awareness that students are working towards a high stakes GCSE and referencing this in teaching. The use of past papers and mock exams is, I think, necessary to a good education.

There it is, 5 perhaps obvious necessities to a good education. What are the barriers to this happening?

1. The responsibility for good behaviour is often left with the classroom teacher. Teachers are told to plan ‘engaging’ lessons and to try to have good relationships with students who exhibit bad behaviour. This results in teachers planning for ‘engagement’ and pandering to the troublemakers as opposed to planning for learning and teaching to the top.
2. Teachers have been inculcated into the erroneous belief that they should minimise teacher talk and students should learn by doing and realising things for themselves . Teaching by telling has got a bad reputation even though it is probably the best way for students to learn at school.

3. The responsibility for students doing well is not often enough put on the students themselves. Too often, teachers are blamed for what is simply students not being prepared to graft to do well.

4. Teachers are put off making their own judgements about how to respond to their classes by tick box exercises such as confused whole-school AfL diktats that act as a proxy for teacher judgements.

5. ‘Teaching to the test’ is maligned as being a last resort when other teaching hasn’t worked as opposed to being an integral teaching process. Tests are disparaged as being damaging to students as opposed to a useful learning tool.

So there we go. Let’s start with the necessary conditions for a good education.

Starting with Why

I saw this Ted talk yesterday and I think it has illuminating resonance for me as a teacher.

In the talk, Simon Sinek identifies 3 stages of all communication: what, how and why. 

For example, as a teacher who wants my students to do the best they possibly can, what I want to happen is excellent behaviour, concentration and hard work in class and the completion of 100% of homework to the best of their ability. Typically I will start with this what

If not all students get on board with this, and I always find at least one of them in each class, then I move to the how. I will talk about how they should SLANT when I am talking, how they should do their homework as soon as it is set, how the harder they work the more they’ll learn, how much easier it is to concentrate on their work in a silent classroom.

What I rarely articulate is why I want students to do this. And why do I? Well, it could be that my job is on the line and I need them to ‘make 4 levels of progress in a year’. It could be that I construct all children as needing to do their best. It could be that it’s convenient for me to have obedient, hard-working students. I’ve been thinking about the why.

The reason I want students to work hard and have good behaviour is because I care about them doing their best. I’ve thought about it, read about it and argued about it and I’ve come to the conclusion that students will have the best chance of learning in a calm, focused environment where academic excellence and hard work are prized virtues.

That is my why. Sinek observes that the most successful, effective communicators start with the why. If I were to start with the why then my communication with my classes would run something like this:

  • I want you to do your best. More than that, I want all of you to achieve excellence in maths. At the end of the year I want you to be thinking you’ve never worked so hard in your life, that you know more about maths than you ever thought possible. You will be confident going into that end of year exam. You will have developed an excellent work ethic that will stay with you and make it easier for you to work hard in the future. You will know so much more than you do now, and that will make it easier for you to learn more in the future, as the more you know, the easier it is to know more.
  • This is not going to be easy. It is going to be worth it but it will not be easy, it will require hard work and discipline from you. We are going to minimise wasted time as much as possible. And when we’ve minimised it, we are going to get a stopwatch out and try to minimise it even more. You’re going to SLANT every time I ask for it, at the first time of asking. When I ask for silent working you are going to work in complete silence so that everyone in the class and can think clearly without distractions. You are going to do every piece of homework I set on the day I set it, to the best of your ability.
  • What people are going to see when they look in on this class is every single student doing their absolute best.

Of the many great ideas that I have read about from Joe Kirby, the boot camp has always struck me as being one of the most interesting. I think that is him starting with the why, and I think it might well be a good idea for every school and teacher to try this approach at the beginning of the year.

Standing on the shoulders of giants

I took a couple of Philosophy modules in my first year of university. I was frustrated that I couldn’t write essays just based on my opinions. It’s taken me some time to realise that any decent idea I’ve ever had has been thought before, and with more clarity and better arguments.

After being on Twitter and working in an excellent department for some time now, I’ve gleaned enough good ideas to put forward some thoughts for teaching maths from KS3 to KS5.

1. Keep it simple. I think a good set of textbooks, traditional teaching, regular testing and preparing well for exams will lead to good outcomes for any school.

2. The biggest impact on results is out of control of a maths department, it is a strong whole-school behaviour policy.

I am fortunate in that the school I work in is exemplarary in this respect. The school’s systems including behavioural, homework, pastoral, and with interventions probably has a bigger effect than any of us maths teachers on the students’ improvement in maths.

3. Students enjoying maths is predicated on them learning maths. Prior to my Twitter journey, I thought that if I could get the students interested in the subject then they would learn it. I think I was completely wrong.

I like the analogy of learning an instrument, no one would expect to just jump into playing piano concertos, find it exciting and then learn how to play the piano from there. One has to start with practice and hard work on learning scales, it is as a result of this hard work that the joy of the music becomes apparent to the player.

4. Test the students a lot. It helps them learn.

5. Drilling is good. The more parts of maths students are fluent with the easier they will find it to learn more.

6. The more a student knows the easier they find it to learn more. Identify those who have a knowledge deficit as early as possible and intervene to close the gap.

7. Teachers are always pushed for time. Reduce marking to the essential. There is no evidence that a huge amount of time spent marking benefits the students in any way. This is not to say ‘don’t mark’, it is to say ‘consider the way time is used knowing how valuable time is to teachers’. Consider how feedback is different to assessment.

8. A huge amount of secondary school maths is built on the necessity of knowing Number well. Prioritise Number in Years 7 and 8, and use the excellent Times Tables Rockstars and Numeracy Ninjas to help with this.

9. Practise exam papers and past papers are hugely useful for students especially in the years running up to the GCSE and A-Level exams. Worth spending the money on photocopying.

10. Homework is hugely important at all Key Stages. Back to the learning an instrument analogy, no one would dream of turning up to music lessons expecting to learn their instrument only through those lessons, effective practising is key to learning anything.

11. Knowledge Organisers are a great idea.

12. If you want to learn how to be a better teacher, read David Didau and Daisy Cristodoulou for a start.

13. Targeted interventions can be very helpful. Kids seem more alert to listening in these.

14. Knowing your subject well is crucial. This is particularly apparent at KS5. The better I know A-Level maths the better I teach it. I think this is true at every Key Stage.

Department meetings would be usefully spent discussing the actual maths to be taught so all teachers end up knowing all topics inside out.

15. Teachers who are well rested and have a reasonable workload will be better in the classroom than those who are otherwise.

That’s enough for now. Thank you for all the wisdom. Apologies for not referencing and acknowledging.

Marking is not the same as feedback

Great post on the difference between marking and feedback by Toby French


Marking and feedback.Marking is feedback?Marking isn’t feedback.

A little while ago I wrote thisabout marking policies:

It’s the evidencing of new ways to do more of something we’re doing too much of anyway to please someone else which annoys me.

I’d read about a school which outsourced its marking. This annoyed me. The thought behind this plan was well-meaning: take away the pressure of marking so that teachers could focus on planning. But marking is planning, isn’t it? How would I get to know a student’s writing without reading it? How would I plan to help students without knowing how they wrote? It’s all very well the marker giving me feedback but that money could be better spent elsewhere, I thought.
There were lots of questions: Could the marker give feedback to students without knowing them? Was this necessarily a problem, or perhaps even a benefit? How would I…

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