Ofsted’s advice on high-quality teaching and learning approaches for mathematics education risks being undermined by continuing recruitment difficulties, school leaders have said.
On Tuesday (May 25), England’s schools inspectorate published a research review into the “factors that influence the quality of mathematics education”, which included a focus on curriculum, assessment and pedagogy.
The review is particularly concerned with the attainment gap in mathematics, which is wider than OECD averages, with disadvantaged pupils “much less likely to achieve a grade 4 at GCSE or to meet the expected standards at the end of … key stages 1 and 2”.
While it recognises that there is “no singular way of achieving high-quality education in the subject”, the review highlights a number of common features of effective mathematics education.
These include providing regular opportunities to apply mathematical facts, high-quality written work and clearly sequenced learning (see summary below).
The review emphasises the idea of “engineering pupils’ success in maths”. It concludes that variation in the quality of mathematics education is likely to be the result of the “absence of systems and systems thinking, as well as possible gaps in content, instruction, rehearsal, assessment and the plans for their evolution over time”.
Chief inspector Amanda Spielman said: “For too many children and young people, maths is mysterious and difficult, and this has implications not just for their future attainment, but also for their self-esteem. Our Education Inspection Framework is clear that schools should ensure the maths curriculum is designed to help pupils to gain increasing mathematical proficiency and build confidence in their ability.”
Undermined by recruitment challenges?
The review’s recommendations were welcomed by the Association of School and College Leaders (ASCL) as “helpful”. However, it is also concerned that systemic issues are not being addressed, not least the “persistent difficulty in recruiting maths teachers”.
General secretary Geoff Barton said that while the government trainee teacher recruitment targets have been achieved for the first time in several years – thanks in main to the pandemic causing an economic downturn – mathematics recruitment is still “well below target”.
The latest ITT recruitment figures, for 2021/22, published in December (DfE, 2020), show that while 106 per cent of the secondary recruitment target was met, only 84 per cent of the mathematics target has been recruited – a total of 2,792 trainees. Recruitment for primary phase trainee teachers stood at 130 per cent.
Furthermore, research from the Education Policy Institute in March found that the recruitment challenges in shortage subjects such as maths and science has led to teachers who do not have relevant subject qualifications taking these lessons (Sibieta, 2020)
For maths, the research finds that outside of London, only 51 per cent of key stage 4 maths hours are taught by teachers with a relevant degree. This drops to 37 per cent in the most disadvantaged schools. In London, the figures are 55 and 44 per cent respectively.
Overall, the EPI research finds that about 54 per cent of teachers in shortage subjects have a relevant degree. This compares to 68 per cent in subjects such as English, history and geography.
Mr Barton said: “This deficit in maths teachers is most likely to be felt in schools in challenging areas where recruitment can be particularly difficult, and this means that these children are consequently less likely to have a specialist teacher on a consistent basis.
“The government must take more action to recruit and retain teachers – and its intention to freeze their pay in September is obviously not going to help.”
So, what does Ofsted’s review conclude?
Recommendations taken directly from the report
Curriculum progression: The planned and purposeful journey to expertise
- Successful curriculum progression is planned from the beginning of a pupil’s education through focusing on core content to develop pupils’ motivation and to allow more breadth and depth later.
- The planned curriculum details the core facts, concepts, methods and strategies that give pupils the best chance of developing proficiency.
- The teaching of linked facts and methods is sequenced to take advantage of the way that knowing facts helps pupils to learn methods and vice-versa.
- Sequences of learning allow pupils to access their familiarity with the facts and methods they need in order to learn strategies for solving problem types.
Curriculum sequencing: Declarative knowledge (facts and formulae)
- Teachers engineer the best possible start for pupils by closing the school-entry gap in knowledge of the early mathematical code: facts, concepts, vocabulary and symbols.
- Pupils are taught core facts, formulae and concepts that are useful now and in the next stage of education.
- Teachers help pupils develop their automatic recall of core declarative knowledge, rather than rely on derivation, guesswork or casting around for clues.
Curriculum sequencing: Procedural knowledge (methods)
- Teachers teach younger pupils non-distracting and accurate mathematical methods that encourage them to use recall over derivation.
- Teachers plan to teach older pupils efficient, systematic and accurate mathematical methods that they can use for more complex calculations and in their next stage of learning.
- Teachers help pupils to use these methods to see new connections of number, geometry and time.
- Teachers encourage pupils to use core mathematical methods rather than resort to guesswork, cast around for clues or use unstructured trial and error.
Curriculum sequencing: Conditional knowledge (strategies)
- Teachers teach useful, topic-specific strategies to pupils, as well as how to match them to types of problem.
- Pupils are confident using linked facts and methods that are the building blocks of strategies, before strategies are taught.
- Teachers encourage pupils to use core, systematic strategies rather than resorting to guesswork or unstructured trial and error.
Curriculum sequencing: Meeting pupils’ needs
- New content draws on and makes links with the content that pupils have previously acquired.
- Curriculum progression is by intelligent design rather than by choice or chance.
- Rehearsal sequences align with curriculum sequences.
- Pupils who are more likely to struggle or who are at risk of falling behind are given more time to complete tasks, rather than different tasks or curriculums, so that they can commit core facts and methods to long-term memory.
Pedagogy: New learning
- Teachers remember that it is not possible for pupils to develop proficiency by emulating expertise, but by emulating the journey to expertise.
- Systematic instructional approaches to engineer success in learning are incorporated into all stages and phases.
- Teachers aim to impart core content in alignment with the detail and sequence of the planned curriculum.
- Teachers help pupils to avoid relying on guesswork or unstructured trial and error.
Pedagogy: consolidation of learning
- Educators plan to give pupils opportunities to consolidate learning that:
- Goes beyond immediately answering questions correctly.
- Involves overlearning.
- Aligns with the detail and sequence of the curriculum.
- Is free of distraction and disruption.
- Avoids creating a reliance on outsourced memory aids or physical resources.
- Helps pupils to avoid relying on guesswork, casting around for clues or the use of unstructured trial and error
Assessment
- Pupils are well prepared for assessments through having learned all the facts, methods and strategies that are likely to be tested.
- Teachers plan frequent, low-stakes testing to help pupils to remember content.
- Lessons incorporate timed testing to help pupils learn maths facts to automaticity.
Systems at the school level
- School-wide approaches to calculation and presentation in pupils’ books.
- School-wide approaches to providing time and resources for teachers to develop subject knowledge and to learn valuable ways of teaching from each other.
Further information & resources
- DfE: Academic Year 2020/21: Initial Teacher Training Census, December 2020: https://bit.ly/3ccQu8T
- Ofsted: Research and analysis: Research review series: mathematics, May 25, 2021: www.gov.uk/government/publications/research-review-series-mathematics
- Sibieta: Teacher shortages in England: analysis and pay options, EPI, March 2020: https://bit.ly/3bUeugx