I have found that a very useful frame of reference for exploring teaching and learning is to think about the things students find difficult to do and then to work backwards analysing the reasons why. Even if you are a great teacher, not all your students ace the test or produce exemplary work. Why is this? What is it exactly that they don’t know? What can’t they do? Or, more subtly, what don’t they know well enough and what can’t they do well enough yet?

My observations tell me that, very commonly, teachers are making assumptions about what students should know and should be able to do – and this is the platform they build their lessons around. If questioning and other forms of formative assessment are weak, then a teacher can be fooled into thinking that a few students’ knowledge is representative when, actually, all kinds of gaps are lurking unseen in students’ schema. Crucially, for those students who struggle the most, there can be quite a large gap between the teachers’ assumptions and the reality – the truth of what they actually know and can do.

What teachers can do very usefully is to track back through a learning sequence to work out very precisely where a student might be stuck and to focus more intensively on moving them forward from that point.

**Is it a conceptual or mental model issue?** How can we make abstract ideas more concrete for them? Usually by using more examples of concrete applications of the abstract idea, working harder to make connections to what students already know.

How can fractions be made more concrete? If students don’t have a secure schema for the link between the numbers and symbols and concrete representations then they’re never going to be able to add fractions confidently beyond learning shaky surface methods. I often joke in CPD that, for some students ‘LCM’ or ‘lowest common multiple’ might as well be called Dibble Dobble Dabble because the words themselves don’t have meaning for them. They are ‘timesing 3 and 4’ not finding the lowest common multiple of 3 and 4. If you can’t see that 3/12 and 1/4 are equivalent, there’s work to do before we start adding them to something else

**Is it a recall or fluency issue?** Perhaps they need more intensive, focused retrieval practice on a set of knowledge or a skill. You can’t cut corners on practice and very often the answer is to identify the thing they need to practise more and get them to do a lot more of it. A LOT more.

How well can your students explain the water cycle? Do they understand the concepts, the sequence and the terminology? Can they mentally track water in its various states at a particle level? Can they use the word ‘precipitation’ or ‘condensation’ in context, un-prompted? If not, then it’s likely that more intensive practice with the words and concepts is needed – linking diagrams and models to words generatively (from memory) practising saying the words; using various quiz formats; rehearsing telling the whole story; explaining more scenarios where the water cycle comes into play. (This is where the variation in schema-building comes in as per my last post: Schema-building: A blend of experiences and retrieval modes make for deep learning.)

**Is it a quality issue?** Are students knowingly pitching towards a high standard with real intent and purpose or is it that they just don’t really know what to aim for? The use of exemplars and models of varying quality alongside extensive discussion of success criteria and checking for understanding about the features of those exemplars might be needed, followed by practice on just a few elements at a time.

Part of the problem I see quite often is that students are being asked to practise too much at once. You might make an analogy with running: they’re not fit enough to run the distance they’ve been asked to run. Or with dance: they don’t know each of the steps well enough yet for it to be worth trying out the whole routine. In practice, this is real enough:

- Writing: they struggle to write a sophisticated paragraph because they still can’t write a sophisticated sentence. They can’t do this because they don’t have a vocab toolkit that they know sufficiently fluently to explore and deploy.
- Art: they feel that ‘can’t draw’ because they’re not practising a precise enough element of the drawing process to get better at it.
- Brick-laying: the chimney stack isn’t 100% plumb in every plane because, after the second course, the precision is already off or the first course placement isn’t 100% square. Knowing how to keep a wall plumb and square starts at the bottom.

This thought process is useful for anyone. It is also certainly a defence-buster. If you ever meet someone who has their defences up about improving their teaching (perhaps with good reason), focusing on the reasons that not every student can do it all yet can be a more productive conversation than ideas about teacher performance. Personally I also find that this helps make the link to effectiveness research and cognitive science. Lots of the issues here are addressed by engineering more intense practice, focused on a particular knowledge set in varying conditions – something that lies at the heart of evidence-informed teaching and good curriculum planning.

The main challenge teachers find with this is feeling they have capacity to go all the way back to where students are stuck. It can feel like going back years. And how do we manage that if there’s a curriculum to cover? There’s no simple general answer to that but, as Mark McCourt has said, teaching is essentially about finding out what students don’t know and then teaching them that. If they don’t know it… you can’t just brush that aside. If a back-to-basics approach is needed to reconnect students to what they know, then you have no choice. Solve learning problems at the source: start back with what they know and build.

Great description of the difference between discovering a problem and diagnosing one. Thanks for this post! There’s a new book out with some related themes: The Subtle Side of Teaching Definitely worth a look.

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though provoking,

Thank you

Lisab

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I tutor special needs students. One of our Y10 students was known to be low level. One day a co-tutor came back from working from this student saying “He doesn’t know how to multiply, we need to teach him.” I worked with this student more often and had been trying to identify their problem with maths. I had identified that the student couldn’t count out a number of objects accurately or understand what that number meant – he could gabble out the numbers by rote to about 15, but if asked to count out 5 pencils, or even 2, had no idea what that meant. I spent the next six months teaching him one to one correspondence for the numbers 1-5, then 1-10 before I even considered addition (although we were beginning to use the language for addition), let alone multiplication. I had only got him accurately counting out up to 8 before I stopped working with him.

If students are that low level it takes a lot of repetition to teach anything – I had in my head 50 times as a way of keeping myself sane. (So when this student had not retained something, we hadn’t done it 50 times yet.) It also takes a lot of work to vary the task to stop it becoming meaningless rote and change it about for those all repetitions.

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