A review into maths teaching in England’s schools has today been published by schools inspectorate Ofsted.

A “core theme” of the review is how to prevent struggling pupils from falling further behind their peers.

Ofsted’s 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.

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“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.

“We hope this review is useful to school leaders and teachers as they continue to design and develop their maths curriculum.”

The review document identifies “factors that can contribute to high-quality school maths curriculums, assessment, pedagogy and systems”, as well as some common features of successful, high-quality curriculum approaches.

These include the following key points:

1. Proficiency, not ‘collective moments of understanding’ should be the aim

The review finds pupils are more likely to develop motivation and confidence in the subject where they attain proficiency.

It states: “The ideal aim is for pupils to attain proficiency, not just collective moments of understanding, familiarity or experience. This will help pupils to develop motivation in the subject.”

2. Rehearse, rehearse, rehearse

Pupils need regular opportunities to rehearse and apply the important mathematical facts, concepts, methods and strategies they have learned, the document says.

3. Timed practice is important

The review says assessment is most useful when it focuses on the component knowledge that pupils have learned.

This aids pupils’ confidence and makes it easier to analyse and respond to gaps in learning.

It adds: “In mathematics, pupils benefit from timed practice of knowledge that should be easily recalled, such as maths facts. The timing element gives assurance that pupils are not reliant on derivation.”

4. Value written work

Teachers can support pupils’ progression by ensuring written work is of a high quality.

This is important, Ofsted finds, because when pupils’ calculations are systematic and orderly, they are better able to see the connections of number and to spot errors.

5. Teachers need opportunities to learn from each other

School leaders can develop teachers’ subject and pedagogic knowledge through opportunities to work with and learn from each other.

This “helps new teachers to see and adopt useful ways of explaining core concepts, methods and strategies to the pupils they teach”.

6. Focus on maths facts, vocabulary and symbols

Pupils need to know the core concepts, formulae and rules to draw on in topics such as algebra, geometry, statistics and calculus, the review finds.

For example, a younger pupil’s knowledge of the concept of “balance” and the way this concept is connected to the equals sign will help them when they encounter linear equations in key stage 3.

The report states: “Teachers engineer the best possible start for all pupils by closing the school entry gap in knowledge of basic mathematical facts, concepts, vocabulary and symbols.”

7. Novices need more instruction, not less

“Novice learners” of new mathematics content need systematic instructional approaches similar to those used to teach early reading and writing, finds Ofsted.

It quotes research showing that, in order to develop more comprehensive and abstract thinking about mathematics, children “often need more than their natural, spontaneous learning”.

Throughout sequences of learning, pupils benefit from teaching that is systematic and clear, Ofsted notes.

Attainment-gap warning

The report says that English pupils, on average, gain higher attainment in maths than pupils in many other countries, and that maths continues to be the most popular subject to study at A level.

However, the attainment gap between the lowest and highest achievers is wider than the Organisation for Economic Co-operation and Development average.

Likewise, disadvantaged pupils in England are much less likely to achieve a grade 4 at GCSE, or to meet the expected standards at the end of the early years foundation stage, or at key stages 1 and 2.

This is the third in a series of reviews into different subjects across the curriculum by Ofsted.