No-frills maths

This is a reply to Solomon’s excellent post on a proposal to strip out some of the frills in the KS2 mathematics curriculum in order to address the issue of children not really being fluent enough in the basics such that they would be able to cut the mustard in KS3 and beyond.

Solomon argues that:

  • There are too many objectives on the KS2 maths curriculum and it takes ages to assess it all as well
  • The current standard of expected ‘achievement’ at KS2 is still quite low
  • Far too many children leave primary school without even achieving this quite low benchmark
  • Research in cognitive psychology behoves us to make space for practice to automaticity, spaced retrieval practice and we can’t do that effectively because the curriculum is too bloated
  • Far too many activities happening outside of the usual school timetable that also prevent a focus on mastery
  • Let’s strip the KS2 curriculum back and focus on fluency

I pretty much agree with everything that Solomon says, except for the last bullet point, sort of. I’m not sure where he works, but I also used to think the same about the KS2 curriculum until I moved from KS2 to KS1 and EYFS. It worries me that so much of the focus is at KS2 when logic dictates that we should look to where the the problems begin. I would hypothesise that the reason KS2 receives so much focus is because:

  • There are more secondary teachers and leaders within the twittersphere and the wider world of education debate and it’s natural look to the key stage preceding secondary school and perhaps think ‘Well if only that bit got sorted, then everything would be sorted’
  • It seems most primary school leaders are based in or have spent most of their time in KS2 (for example, via deputy headship combined with year 6 responsibility), therefore may not see the bigger picture that includes the foundations
  • A possible view held by the wider public that KS1 and EYFS shouldn’t be as rigorous as structured as KS2 and that a focus on fluency combined with very high expectations can wait until they’re older
  • An interpretation of the theory of ‘biologically primary knowledge’ which is used as a lever to raise the status of explicit teaching of reading, writing etc at the expense of degrading the what and how of acquisition of early and important knowledge in the formative years of a child’s life, relegating it to ‘nature’. I can’t really say more because I do need to spend much more time diving into the nitty-gritty of all this, but essentially I believe that what we know about memory also applies to everyone at all stages of life

What I like to do is think about a time when pretty much everyone seemed to be really good at arithmetic – my grandparents’ generation. How and what did they learn at primary school? The comparison with modern primary mathematics education (including KS1 and EYFS  reception year) is really interesting. Also, I like to think of a child’s journey through life being like a droplet of water that eventually joins a river: they start out on a leaf, rolling off to form, with other water droplets, a tiny little stream finding its way down a valley, gathering strength along the way as many streams join it. Many look at the river and think that it is going in the direction of disaster, choosing to wade half way up while thinking ‘If only we put all our resources into designing a bit of clever engineering here and then we can divert its course towards that pleasant landscape over there’ whereas I feel like many of us could do with trudging to the highest point where the little droplets are formed and where changing their course could be as simple as angling a leaf in a different direction. Simplistic, yes, but helpful to me.

droplets

Therefore, I think that a no-frills approach that focuses on fluency should be the approach from the very beginning. What tends to happen though is that the narrative of planning for mathematics education focuses on ‘variety’ and ‘activities’ such that each and every maths lesson is about what they are doing rather than what they are thinking at any one time, as well as the relegation of simple, routine practice to the scrapheap (with all the textbooks). The upshot is that children in the younger years spend a smaller proportion of their time in maths lessons just doing maths. If you compare maths workbooks by year group you will see that the number of calculations increases as the years go by. If a child in KS1 is practising using his number bonds to add one digit numbers such that he ends up knowing his number bonds off by heart, you’d think he would need to do roughly the same number of calculations as a child in year 4 who is practising using his 8 times tables knowledge until he learns said 8 times tables off by heart, but you will see he has only done about 5 calculations while also being distracted by pictures, having to choose manipulatives, amidst general noise before being moved on to the next ‘activity’, whereas his friend in year 4 has done a good solid 15 minutes of just maths (hopefully) in silence.

So, when I look at the mix of mathematicians in year 1, I can see who is probably going to progress to the joys of calculus one day, and who is going to be lucky to scrape a 4 at GCSE; it’s like I’m standing at the top of the valley seeing in all directions where these little streams of water will end up. To illustrate the difference and to get you to understand what I see, I once did an experiment in a year 1 Friday lesson where we usually do lots of practice under test conditions which absolutely everyone in the school loves – I simply provided an unlimited supply of calculation practice. My top mathematicians who were able to screen out distraction and who had their number bonds down pat did around 100 questions, egging each other on and pushing themselves to make headway into the hundreds. My struggling mathematicians did about 10 questions and even then it was like flogging a dead horse. My observations were that the rhetoric of ‘waiting’ and ‘following’ and ‘choosing’ in EYFS needs to change because some children have the habit of avoidance entrenched, as well as a stark realisation that a key factor in mathematics prowess wasn’t so much intelligence as concentration (particularly the ability to screen out distractions all around) and this is why I now believe that rules, habits and routines are as important as curriculum content in primary schools, even for the youngest children.

My beliefs are reinforced when I scan the horizon and see how the GCSE results at Charter academy have massively improved and how much of this has been down to installing rules, habits and routines such that all the children are now concentrating in their lessons for a greater proportion of lesson time. It’s not rocket science really, but can you imagine what our youngest generation could achieve if a similar approach to rules, habits and routines were learned to automacity all the way back in year 1?

So, back to my grandparents’ generation. Their maths lessons were no frills, right from the beginning. This is partly because there wasn’t the technology or finance to buy lots and lots of resources to add the kind of variety to maths lessons we see in primary schools today: you had pen, paper, an abacus perhaps, the teacher, the blackboard, your own brain and NO teaching assistant to do your thinking for you. Later, a textbook and a geometry set. Back then, perhaps they also knew that lessons needed to be plainer: a set routine of teach, chant, practise (lots, in silence) and then test. It was a winning formula that also induced a bit of resilience, focus and work ethic in children, so why deviate from it? It was only as you got older, more mature and had the habit of hard work and concentration that you were allowed a bit of freedom and independence to discover, noodle around with your maths so to speak – some had to wait for university for this. Somewhere along the line we, in our infinite wisdom, reversed this process such that the earliest years are now all about freedom and then much later those rules, routines and habits are foisted upon children we wonder why they resist and protest, particularly in year 6! It’s all back to front.

So, to conclude, I kind of agree with Solomon that we need to focus on fluency. Perhaps we need to get back to a no-frills approach and strip out some superfluous objectives, but I would extend this back to the beginning of a child’s academic life and I would also extend this no-frills approach to how lessons proceed, as well as the content of what is taught and practised (which is what Solomon concentrates on). Instead of making each maths lesson different and spending so much time explaining each activity, why not cut out all that bumph and just have a maths lesson where the majority of the teacher talk is about imparting knowledge and then through a set routine everyone gets on with the business of doing maths? If we could have all children concentrating and working hard from the start, then I believe there wouldn’t be such a stark contrast between those lucky few who can happily do 100 questions at 5 years old (because they received number bond knowledge as well as experiencing concentration-inducing rules, habits and routines at home), and those who can only do 10 under duress because they have the habit of messing about. That way, those droplets of water will end up in the right river at KS3 and beyond.

Who’s with me?

Post-script October 2018: we’re now using CMC maths! Looking forwarded to reporting back to you all on that.

 

 

 

 

 

 

 

 

 

 

 

 

 

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5 thoughts on “No-frills maths

  1. I think the problem is not frippery but with training. There is too much for Primary teachers to master and in Scotland we now have 40 pages of parental engagement outlined in the latest tome. This comes on the trail of the overly hyped UN rights for the kids and how to cope with xyz2017 etc etc

    It is hard to teach Maths, in particular and looming over the horizon is coding, not to mention IT mark4.0. The edutwitter-sphere has added to the angst and confusion with people writing hundreds and even thousands of words which are often unread (so I will stop there)

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  2. Wonderful stuff. A key point I’ve tried to make in Ofsted’s consultation on secondary maths is that schools should test their Yr 7 intakes to see just how far back they need to go in order to build on fluent foundations. Certainly the testing we’ve done indicates that a sizeable percentage–quite likely more than half–need to go right back to KS1 material.
    Needless to say, teachers, especially those in community schools where there is a legal obligation to teach the National Curriculum, are concerned about failing to cover everything. This leads us to the surreal conclusion that secondary teachers are obliged to teach the bottom sets–pupils who are still shaky on adding and subtracting–how to “make and test conjectures about the generalisations that underlie patterns and relationships; look for proofs or counter-examples; begin to use algebra to support and construct arguments and proofs”.
    There is, of course, an out: schools can deviate from the NC “with good reason”. Now only a lunatic would propose that there is no good reason to teach the bottom sets a little multiplication instead of the above, but sadly, I think Ofsted really do need to be very explicit on this point. Even though I can’t imagine any secondary maths teachers daft enough to teach the bottom sets material that even the top sets can’t handle, they still would feel uncomfortable teaching them basic arithmetic, let alone number bonds.
    It’s hard to say how much the primary maths framework will change. Here, we don’t even have the influence of teachers who have maths degrees to counter the weight of the international maths education community. It is well to consider that synthetic phonics is still fighting an uphill battle against the Michael Rosens of this world, and that 12 years after the Rose Review, the dreaded ‘searchlights’ are still burning bright in most infant schools. It’s a lot easier to get teachers to do something new than it is to get them to abandon what they’ve been trained to do.

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  3. I liked this “What tends to happen though is that everyone worships at the alter of ‘variety’ such that each and every maths lesson for the little ones is about ‘activities’ rather than simple, routine practice.” Think it applies to more subjects than just maths.

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