Ofsted have launched its consultation on proposals for changes to the Education Inspection Framework (EIF). This EIF sets out a framework for how Ofsted inspects schools, and also considers early years settings and further education and skills providers. This new framework will take effect from September 2019.

The proposed new framework has been welcomed in part – it aims to focus on quality of education, looking more closely at the curriculum and curriculum coordination.

Inspections will concentrate on what children learn through a broader curriculum that equips learners for the next stage in education, employment or training. However, there are concerns Ofsted still needs to address when thinking about mathematics-specific education.

Current mathematics teaching and learning

Recent PISA (Programme for International Student Assessment) research for mathematics highlighted that, of all the OECD countries:

  • The UK has the highest use of memorisation, rehearsal, exercises, practices and repetition in lessons.
  • The UK is lowest in lessons involving elaboration, reasoning, deep learning, critical thinking and non-routine problems.
  • UK students are third highest in using ‘learning by heart’ as a strategy.
  • UK students use elaboration strategies least.

Why are current features of mathematics teaching and learning a problem?

Proposals within the new Ofsted inspection framework:

  • No set approach to curriculum teaching – Ofsted highlight that different approaches to teaching can be effective and dependent on the aims of a lesson or activity. Despite this, any approach used has features that must (they say) be present to ensure effective delivery.
  • Inspectors will not rely solely on data – Ofsted have suggested that inspectors will connect lesson observations to other evidence: discussions with curriculum leaders, teachers and pupils, and work scrutiny.
  • Work scrutiny will be pivotal in showing whether pupils have learned appropriate knowledge and skills, and whether the knowledge and skills are well sequenced and have been developed incrementally.

In practice, non-specialist inspectors are likely to depend heavily on the mathematics-specific guidance provided by Ofsted in order to assess the points above. This guidance seems to place a focus on developing memorised skills and knowledge through accumulating small steps lesson by lesson.

So, why is this a concern?

Well, reverting back to the first point, PISA suggests that UK mathematics lessons are often based around the use of memorisation, rehearsal, exercises, practices and repetition. But this does not mean that the use of elaboration, reasoning, deep learning, critical thinking and non-routine problems in mathematics lessons is not also effective. Ofsted have suggested that there is no set approach to curriculum teaching within the new framework, but the subject guidance for mathematics might suggest to non-specialist inspectors that the former kind of lesson is preferable to the latter!

Therefore, whilst a specialist inspector may interpret lessons that focus on ‘elaboration’ (that has been shown to be less prevalent in the UK) as contributing to a ‘knowledge-rich’ curriculum in which skills and factual knowledge are the by-products of mathematics structure and the development of mathematical behaviour, there is a worry over how a non-specialist inspector might use the guidance to understand the value of such lessons.

Ofsted have confirmed inspectors will be given training needed to develop the skills to be able to inspect schools within the remits of the new framework, but we would be naïve to think that every inspector will have the relevant mathematics-specific knowledge needed to assess these lessons.

I therefore leave you with the following question:

Is it going to be safe to teach lessons using an ‘elaboration’ approach while being observed by non-specialist inspectors?

Further clarification is needed!


Below are just a few statements provided within the mathematics-specific guidance which need further clarification from Ofsted:

2.1. pupils understand and remember the mathematical knowledge, concepts and procedures, including knowledge of efficient algorithms, appropriate for their starting points, and which ensure readiness for the next stage, whether that is the next lesson, unit of work, year or key stage, and including post- 16 mathematics

Why is this a concern? – a non-specialist could interpret this to mean that a ‘next task’ has to be based on prior knowledge and skills from the previous lesson(s), but it could instead draw on knowledge from longer ago as part of a spiral curriculum approach – meeting old knowledge in new and unexpected ways.

2.3. the curriculum divides new material into manageable steps lesson by lesson

Why is this a concern? – This could be interpreted by a non-specialist to mean that every lesson is based on some manageable step in an accumulation of elements of knowledge and skill, rather than being an investigation of a new idea or immersion in a problematising approach.

2.4. pupils have sufficient understanding of and unconscious competence in prerequisite mathematical knowledge, concepts and procedures that are necessary to succeed in the specific tasks set.

Why is this a concern? – This could be interpreted by a non-specialist to mean all students ought to be fluent already in particular skills and knowledge that seem to be used in the task, whereas the task itself may involve experiences that work towards stronger conceptual fluency.

2.8.  teaching models new procedures and uses resources and approaches that enable pupils to understand the mathematics they are learning

Why is this a concern? – This could be interpreted by a non-specialist to mean that new procedures and resource use should always be ‘shown’ by teachers, whereas a new procedure might also emerge from learners’ insights during an unfamiliar task.