Thread by @EmathsUK

@ashtonC94 @blatherwick_sam @mathsteacher09 Not really sure how much (if any) help I can be, but I'll try...

I think the first thing to do (and this is fundamental) is, as teachers, to change our view of mathematics.

You mention KS2 maths. But this doesn't exist.

There is no primary maths or secondary maths...

@ashtonC94 @blatherwick_sam @mathsteacher09 ...these are false dichotomies that hold the profession and pupils back.

There is just maths.

And there are no kids who have gripped KS2 (of whatever), there are just kids. They have gripped some maths and not gripped some other maths.

So, first of all, we need to try...

@ashtonC94 @blatherwick_sam @mathsteacher09 ...to work out, for every pupil, where they are at in their journey of learning mathematics.

This cannot be pinpointed. And it won't be linear (they go backwards as well as forwards). But have a broad idea of their mathematical repertoire allows us to choose starting points...

@ashtonC94 @blatherwick_sam @mathsteacher09 ...for individuals or groups of pupils in similar positions.

Now we can start to build their expertise.

All children (yes, all) can learn mathematics well.

But only if we take this really seriously and do the hard graft required.

First, we need to appreciate that in order...

@ashtonC94 @blatherwick_sam @mathsteacher09 ...to think about, well, anything, we need to have mental representations of the thing we wish to think about.

So, target your instruction to developing mental representations.

Then, we must appreciate that almost all of what is considered 'practice' in classrooms is not.

...

@ashtonC94 @blatherwick_sam @mathsteacher09 ...rather, what tends to happen in classrooms is surface level. We have moved away from what has always been known; the correct type of practice makes perfect.

Schools have largely stopped doing this because national bodies have promoted automaticity and fluency as the aim...

@ashtonC94 @blatherwick_sam @mathsteacher09 ...these are simply not sufficient and do not help pupils to gain expertise in mathematics.

They are steps towards practice, but they are not practice.

So, once you have worked hard to ensure mental representations are forming, it is crucial that meaningful practice follows...

@ashtonC94 @blatherwick_sam @mathsteacher09 ...all pupils need these 'phases' of practice:

- repetition
- doing
- automaticity
- fluency
- purposeful practice
- deliberate practice

(these are all very different things and well defined)...

@ashtonC94 @blatherwick_sam @mathsteacher09 ...all pupils have potential to become experts in maths. But only if they undertake these steps.

This proposes a challenge because there is absolutely nothing enjoyable about deliberate practice!

So, we need to continually demonstrate to pupils to benefits of determination...

@ashtonC94 @blatherwick_sam @mathsteacher09 ...getting deliberate practice right in mathematics requires us to know the technical details of the mathematics at hand and to know the tried and tested techniques for best honing these - in other words, the teacher needs to know how to coach pupils in very specific ways...

@ashtonC94 @blatherwick_sam @mathsteacher09 ...by following such an approach all pupils can learn well and at pace.

Now, to your question, which is perhaps one about qualifications?

If so...

Suppose a pupil arrives in year 7 having gripped no maths at all (highly unlikely, but let's use the extreme example)...

@ashtonC94 @blatherwick_sam @mathsteacher09 ...if you wish that pupil to get a Grade 4 at GCSE (I think that was the suggestion?), then all is well: it is absolutely possible and, actually, not particularly difficult if taken seriously.

So, we start afresh with them and build maths from the beginning.

...

@ashtonC94 @blatherwick_sam @mathsteacher09 ...you have 5 - 7 years with the pupil in order to hit the Grade 4.

That is perfectly doable. Take, for example, the 'KS2' you referred to (although there is no such thing really) and review the expectations. Compare to a foundation paper. You'll see that...

@ashtonC94 @blatherwick_sam @mathsteacher09 ...someone who has gripped those stated areas of maths can comfortably complete a full foundation paper (you might have to throw in a bit of mean, median, mode and range, but not much else).

Getting from no maths to that maths in 5 years is more than achievable 👍

@ashtonC94 @blatherwick_sam @mathsteacher09 ...the key to establishing, revising, strengthening and expanding mental representations is deliberate practice. And deliberate practice absolutely depends on consistently working as the very boundary of one's comfort zone.

This is why it is crucial to ignore KS2 or 3 etc...

@ashtonC94 @blatherwick_sam @mathsteacher09 ...instead treat mathematics as a full domain and every pupil as an individual with some specific level of knowledge. Always target their learning at a 'just right' level of challenge to keep them in that zone.

This is why a goal of automaticity is harmful rather than helfpul...

@ashtonC94 @blatherwick_sam @mathsteacher09 ...the teacher who is happy about the pupil who completes 30 questions correctly is the teacher who wonders why they can't do the same skill 12 months later.

30 ticks means they are completely in their comfort zone. No learning is happening. No long term memory is at play...

@ashtonC94 @blatherwick_sam @mathsteacher09 ...In sum, for the pupils you are referring to:

- Know that they can all learn well. They have identical potential
- Work hard on mental representations
- Ensure practice really is practice and not regurgitation
- Keep them at the bounds of comfort zone

In 5 years, they'll fly!