Guest blog by Jane Jones HMI, Ofsted

Charlie Stripp’s recent blog on mastery and differentiation has raised the question, voiced widely by maths teachers around the country, of the implications - if the mastery principle is followed rigorously - for Ofsted inspectors’ evaluation of maths teaching in a school (Inspectors no longer judge teaching in individual lessons).

To address that very question, Jane Jones, Ofsted’s National Lead for Mathematics, has contributed this Guest Blog

You might not expect to see the three words, mastery, Ofsted and synergy in the same sentence or blog, but they are exactly what I’m going to use in thinking about the direction of travel in mathematics teaching following the implementation of the new national curriculum in September 2014. Following the publication of Charlie Stripp’s blog, a number of thoughtful and constructive comments have been posted on the page. In one of them, JL Pearson posed the question: The Mastery Approach is clearly going to make an impact, but has anyone spoken to Ofsted about this? Well, the short answer to that question is ‘yes’ – at policy and leadership levels, and through initial training for inspectors on the new national curriculum. Ofsted does not have fixed expectations of what the curriculum in practice will look like, including how teachers differentiate to meet pupils’ learning needs. It’s also worth saying here that Ofsted inspectors no longer give judgements on the quality of teaching in individual lessons.

The aims of the mathematics national curriculum, fluency (that blend of conceptual understanding and procedural flexibility), mathematical reasoning and problem solving, capture the best in mathematics education that we would surely want for any pupil. The word mastery is not used in the programmes of study, but the principles cited by Charlie are at one with them. Likewise, the messages from Ofsted’s report, Mathematics: made to measure, emphasise the importance of developing conceptual understanding (not just procedural proficiency on its own) and giving all pupils the chance to solve problems and reason about their work. So, there’s synergy in what we are all aiming for.

The national curriculum makes it clear that the majority of pupils are expected to move through the programmes of study at broadly the same pace. In all key stages, pupils who grasp concepts rapidly should be challenged through rich and sophisticated problems before any acceleration through new content and those who are less secure should consolidate their understanding before moving on. Ofsted is considering whether a footnote referring to this in our school inspection handbook would be helpful.

Differentiation should therefore be about how the teacher helps all pupils in the class to understand new concepts and techniques. The blend of practical apparatus, images and representations (like the Singaporean model of concrete-pictorial-abstract) may be different for different groups of pupils, or pupils might move from one to the next with more or less speed than their classmates. Skilful questioning is key, as is creating an environment in which pupils are unafraid to grapple with the mathematics. Challenge comes through more complex problem solving, not a rush to new mathematical content. Good consolidation revisits underpinning ideas and/or structures through carefully selected exercises or activities. Mastery calls this ‘intelligent practice’.

The notion that headteachers might encourage their staff to retain previous ways of working because they fear criticism from an Ofsted inspector is a concern but one that everyone can play a part to dispel. While the curriculum is new, leaders whose schools are being inspected may want to take the opportunity to explain to inspectors how mathematics is organised in the school, what an inspector might typically see in a mathematics lesson or a support/challenge session including how differentiation works, and how pupils’ attainment and progress are assessed.

[In addition to reading the above blog post, you may like to refer to the paragraph relating to mathematics in the Ofsted School Inspection Handbook from September 2015 See paragraph 160, which starts on page 47 of the handbook]