Mastery of mathematics myth-busting: pupil progress

Pupil progress shouldn’t be confused with curriculum pace: good progress in mathematics is not about moving on quickly

Primary schools are still responding to significant changes to assessment and accountability put in place by the government over recent years. This started with the removal of National Curriculum levels and was followed by new key stage assessments and school accountability measures. Amongst this is the new headline measure of pupil progress. It averages the progress each pupil makes from KS1 to KS2 in English reading and writing and mathematics, and is designed, as the Department for Education (DfE) says: ‘to allow better recognition of schools doing well with a challenging intake, and to challenge those that are not doing enough with a high attaining intake.’ [1]

The new measure focuses the attention of school leaders, not simply because it’s new: pupil progress has a central place in inspection, and the performance measure features both in the floor standard and coasting schools definition. I warrant that primary head teachers are looking long and hard at progress pupils make between key stages, and at how to provide evidence of this.

The government’s recently published consultation on primary assessment means that further changes may be afoot. If agreed, proposals to make KS1 assessment non-statutory and to establish a reception rather than KS1 progress baseline will be important. But whatever the case, the focus on progress, and on its tracking and management is here to stay.

As pupil progress has gone up the agenda, something important may have gone unnoticed by some: underpinning the curriculum is a new assumption about what constitutes good progress. Schools could become unstuck if they focus their attention wrongly.

What is this new assumption?

The idea is simple: progress is about mastering a subject well rather than passing through a curriculum. The ‘mastery’ principle is explicit in published curriculum programmes of study for mathematics, which state that ‘pupils who grasp concepts rapidly should be challenged through being offered rich and sophisticated problems before any acceleration through new content’. The more that pupils consolidate and deepen their understanding, particularly at earlier stages of the curriculum, the better their later progress will be. Accelerating pupils through curriculum topics may be tempting, particularly if they grasp these quickly, but it doesn’t help them master a rich and complex subject.

I worry that the need to evidence progress may send some schools down a wrong track. There may be a tendency, for example, to see the year-by-year curriculum as a kind of ‘route map’ for progress in the subject, or there could be a temptation to adopt curriculum levels in a new guise. In either case, while there is every chance that pupils can be tracked and monitored, there is very little assurance that their knowledge and understanding is fluent, or secure – that they are mastering the subject well.

Ofsted understands the shift to mastery and has used advice from the National Centre for Excellence in the Teaching of Mathematics (NCETM) in its training for inspectors.[2] Inspectors now know to look for able pupils being challenged, and learning deepened, through more complex problem solving rather than acceleration through new material. And Ofsted’s inspection handbook says, of judgements of pupil progress that: ‘pupils, including the most able, do work that deepens their knowledge, understanding and skills, rather than simply undertaking more work of the same difficulty or going on to study different content.’ (paragraph 176).[3]

How to demonstrate progress?

While the new assumption of progress may be well understood, schools still face the challenge of how best to evidence it. If good progress in mathematics is not the same as racing through a curriculum, what should schools do to demonstrate the distance traveled from a pupil’s starting point? Specifically, how can schools show that a pupil with strong earlier performance (KS1 as things stand) are progressing sufficiently in the subject?

The NCETM has been thinking about this challenge and has looked closely at the need for evidence of ‘mastery with greater depth’ for pupils who grasp concepts quickly. Working with Oxford University Press, they have published a suite of resources for mathematics teaching in years 1 to 6.[4] It includes examples of tasks and questions to provide greater challenge and depth in central areas of mathematics: same topic, greater demand. The NCETM’s introduction to the materials says: ‘just being able to get the correct answer is not necessarily evidence of sufficient understanding; teachers will need to probe more deeply… many of the questions in the materials are designed to identify deeper understanding.’ They also make the important point that ‘evidencing progress using questions has been shown to produce more reliable information than a tick-box list of criteria.’

Stepping back, it’s worth reflecting on the rationale behind 2014 National Curriculum changes. International and other studies consistently identified a stubborn ‘tail’ of underperformance in mathematics, which was reinforced by low expectations of some pupils. And, while others may have been on faster tracks, our 16-24-year-olds still performed amongst the lowest in mathematics in the OECD because their mathematics was not secure – they did not have sufficient depth. Mastery is not a fad or just another scheme – it’s a necessary and fundamental change to how we teach mathematics, and the only way to ensure that all pupils progress well.



Vanessa Pittard was Assistant Director for Curriculum and Standards at the DfE in 2011–2017, where she held responsibility for mathematics education and worked on STEM and literacy policy. Vanessa was central to the development of the Maths Hub programme and worked closely with the NCETM on the introduction of mastery teaching of mathematics in schools. Prior to that, Vanessa led the evidence and research function at Becta, the UK agency for technology in education, and was a subject leader and head of department at Sheffield Hallam University. She now works as an independent consultant.

[1]  Primary School Accountability: techincal guidance. January 2017.

[2] Mastery and Mathematics. January 2015.

[3] School Inspection Handbook. September 2015.

[4] National Curriculum: assessment materials. September 2016.

 

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