Incentivising mastery in primary maths

In my last post, I explained how KS2 maths SATs can encourage students who struggle with maths to chase marks in periphery topics, rather than improve arithmetic understanding and fluency which is necessary for the study of secondary mathematics.

In this post, I’m going to reflect on how we might manipulate accountability to do the reverse. Since I’m not a primary teacher or maths expert (I only ever taught maths to ‘fill up my timetable’), I am not going to think about exactly what we want to teach students. Of course, that discussion needs to happen elsewhere before we look closely at choices around policy reform. I am simply going to look at three broad policy choices we have.

Adding extra accountability devices

If our current accountability tool isn’t getting the incentives quite right, why not just add another one (or two or three)? This has been the approach of this government by loading up primary education with extra simple, narrow tools to manipulate teaching – the phonics test, the multiplication check. I quite like these as short-term devices, put into place for a few years to steer the ship in a new direction. However, they are blunt tools that inevitably create new problems since they don’t reflect the richness and complexity of the knowledge we want to develop in students. We quickly find ourselves wanting to add extra tests to incentivise the things the first test neglected: number bonds, written arithmetic methods, mental maths… Before we know it, we find ourselves writing a set of tests that covers the entire curriculum again! (And there are other issues – no incentives to teach students who clearly won’t pass the check etc…)

Manipulating the Key Stage 2 test paper

We have a lot of choices for how we can use the test paper sat at the end of Year 6 to send stronger signals about the focus of teaching for those who are nowhere near mastering the curriculum. We could, of course, just give less weight to certain topics and more weight to arithmetic, for all students. Alternatively, we could pre-announce that student answers to certain parts of the curriculum will only be included in their final mark if they manage to reach a certain standard in the core numeracy skills. Think of this as like a Part A and Part B, where Part B is only considered once the student scores over (say) 70% in Part A. This might feel reminiscent of the old paper for Level 6. The trouble is that by creating a cliff-edge, it introduces difficult incentives for teachers to make early judgements as to whether a student is likely to be marked in Part B. And it is quite extreme to fully partition the maths curriculum in this way. Ultimately, we need to be clearer on our goal first – is our plan that some students who are struggling will (a) never study Roman numerals, (b) study it but be discouraged from investing time revising it, or (c) the status quo of both studying and incentivising revision?

In an age of computer assessments, we have many better opportunities to devise adaptive tests where all students can answer questions of increasing difficulty for (say) 45 minutes, where the difficulty increases in proportion to accuracy and where we pre-announce to teachers that certain topics will only start getting thrown into the question pool once a particular level of difficulty is reached. It means every student sits an assessment that is unique to them, there is no cliff edge, and maths/policy experts get to agree on how and when different types of topics appear in the assessment. (And their decision must be pre-announced since the aim is to manipulate teaching focus.)

Reducing the size of the curriculum

I think there is still a very strong case for reducing the size of the primary maths curriculum, despite options around test manipulation. Teachers generally need to teach whole classes at once. The problem with keeping a large curriculum in place, knowing some students will never do well enough to be judged on it, is that it stacks the interests of students against each other. Should the teacher teach a particular periphery topic to meet the needs of the higher attainers or should they work on improving understanding of a core topic where half the class are not yet secure? Often we don’t like to be upfront about these very real trade-offs we face in many subjects.

OK, I’m going to leave it here with three vague choices we have because it is New Year’s Eve and I’m typing this on an iPad in someone else’s house! For what’s it’s worth, I vote for a lot of option 3 mixed with a bit of option 2.

To read more about curriculum reduction in primary schools, I’d urge you to go and read Solomon Kingsnorth’s amazing blogs. I’ve never seen a good case made against his arguments yet, except for the miracle solutions that appear to exist in one school but cannot be scaled to 100 schools. Let’s hope for a miracle in 2022 – that 20,000 schools can stay safe and open. Once we’ve achieved that, perhaps we can start talking about policy reform again.

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