This week I have been putting together some ideas and practical activities to share with teachers on the upcoming training, “Mental Mathematics: the secret to success at Key Stage 1” and it got me thinking...
The framework in mathematics clearly indicates the requirement for pupils to be mentally fluent to a higher level than previous years. Exploring the Essentialmaths planning tool, we have a huge variety of practical ideas and games to share with teachers to take back to the classroom that will make a real difference. I also looked back at the Fluency Project, led by Charlie Harber, Rachel Rayner and Louise Racher, that I took part in as a teacher last year. I knew there were some fantastic ideas in there because I used them with my own Year 2 class and have never seen such a transformation in mental fluency and precise explanation of calculation in such a short time. In refreshing my memory, I came across a training slide from the launch day that explored the memorisation of facts by rote. They mused that the dismissal of rote learning as ‘evil’ had pushed us too far away from the message that key skills and facts require rehearsal and time to develop fluency. Recall of essential facts, or memorisation, is in fact crucial. It reduces the cognitive load for pupils who when later meeting formal written methods spend so long working out the basics, that the learning process is hindered.
So as I mentioned earlier, I had a go myself at the 2017 KS2 Reasoning Paper – Paper 3. The reason for this was that I wanted to explore how pupils are being asked to apply their fluency skills within the reasoning context in KS2, the foundations of which are obviously being developed much earlier. Now before I tell you what happened… let me just add that I had in fact already tackled 2016’s Paper 1, Paper 2 and Paper 3, as well as 2017’s Paper 1 and 2 in quick succession – I wanted to see if the same types of things were being asked of the pupils year on year. And you may be asking why I didn’t just have a look at the question level analysis now available to see where the pupils excelled and struggled but I wanted to see it from a more real perspective. So I timed myself as well. Anyway… enough excuses…
Let me present you with this question:
No scrolling down before you’ve had a go at this yourself.
So, suffering with a little ‘test fatigue’, I read the question, found the 2 shapes with 4 acute angles, re-read the question, saw that it said ‘exactly 4 acute angles’ and counted them again. C and D both have 4 acute angles, I thought to myself. There must be a misprint in the test because it says, ‘the pentagon’ – singular. I don’t even know how many times I have had this exact conversation with children. That one where they insist that there must be a misprint in the test because their answer doesn’t quite fit the question. Well that was me. I moved on to the next question, convinced that I was right and the test was wrong. When I finished, I used the mark scheme to see how I had fared. I had been quite proud of myself up until this point (yes I know this is a test for 10 and 11 year olds but some of it is pretty challenging!) and then I came across the answer to this question:
I am happy that shape C has 4 acute angles. I can see those. But what I am still certain that I see are 4 acute angles in shape D. So I count them again. And again. The mark scheme is wrong too!
So then I took to Google. Turns out that I’m not the first person to conduct a Google search on this particular question. Many others have fallen into the trap!
I finally realised my error in this blog on Third Space Learning – a very interesting read about the demands of the 2017 KS2 maths assessments. As part of the analysis of geometry in the paper, they state that, “Interestingly, on question 13 of paper 3, pupils would only have achieved the mark if they not only remembered what an acute angle was, but also how many sides a pentagon has”.
I flicked back to the question and there it was, clear as day, HIGHLIGHTED IN BOLD…
Circle the pentagon with exactly four acute angles. It’s not that I hadn’t considered pentagon in my thinking but made an assumption about shape D being a pentagon because the 3 shapes previous all were. This got me thinking; thinking about the demands on working memory that these assessments put on our young learners.
Consider the scene Paper 3… taken on the Thursday at the end of a long SATs week. The brain has already had a good old workout but may be a bit jaded and tired by now. Nevertheless, of the 91.5% of children nationally who attempted this question, 70.8% of them got it correct. Hats off to them! I mean, acute angles first appear in the curriculum as non-statutory guidance in Year 3, pentagons in KS1 and counting to 4 is taught in Early Years! Why was it then that just under 30% of our nation’s Year 6 children didn’t achieve this mark? That’s just under 4000 children!
I believe that it comes back to the issue of cognitive load that I mentioned earlier. What we do not know is where the children were caught out here. Was it about too much focus on acute angles like me? Or was it that they identified the pentagons in the group but neglected the acute angles. Regardless, there are two units of knowledge being tested at once here and there are further examples of this throughout the test – many that are far more complex than this one (Question 23 for example). The testing at both KS1 and KS2 demands that children go to these potentially complex depths. Rightly so as mathematics shouldn’t be viewed as a series of compartmentalised learning. It is, as defined by the NCTM, ‘a coherent whole with rich interplay among mathematical topics’. So… we need to give our children daily opportunities to make explicit links between concepts and give them the tools of fluency, strategy and reasoning to reduce their cognitive load when the test (and actually, more importantly, maths in everyday life) purposefully tries to make them wobble.
After all, the essence of mathematics is not to make simple things complicated, but to make complicated things simple (Stan Gudder, University of Denver).
Spaces still available by the way – on the following courses
https://www.nctm.org/uploadedFiles/Standards_and.../PSSM_ExecutiveSumma… (Accessed online on 30.10.17)
Third Space Learning:
https://www.thirdspacelearning.com/blog/ks2-sats-papers-2017-guide-year… (Accessed online 30.10.17)