Grammar schools and setting by subject deprive disadvatanged children of the chance to learn about core mathematical concepts that are vital to academic success, a new analysis of Programme for International Student Assessment (Pisa) data suggests.

The link between the content covered in maths lessons and the socio-economic background of students and schools is greatest in countries that set and stream pupils, have selective schools and transfer less able pupils between schools, according to the report based on the latest data from the influential Pisa study.

Pupils from poorer backgrounds are more likely to be exposed to simple applied mathematical problems while those from richer backgrounds are taught to “think like a mathematician”, Andreas Schleicher, director of education at the Organisation for Economic Co-operation and Development (OECD), writes in the study of 64 schools systems from across the globe.

The report says: “On average, across OECD countries, the higher the percentage of students enrolled in selective schools in a country, the less equity in opportunity to learn mathematics in that country”.

It also reveals that, on average, fewer than 30 per cent of students across OECD countries (18.6 per cent in the UK) understand the concept of an arithmetic mean, while fewer than 50 per cent of students can work with the concept of a polygon.

Politicians should develop “more ambitious and coherent mathematics standards that cover core mathematical ideas in depth”, Mr Schleicher says, and teachers should replace “routine tasks” with “challenging open problems”.

Although mixed-ability teaching is preferable, according to the report ”Equations and Inequalities - Making Mathematics Accessible to All”, it also says teachers need support to make it work.

The report shows that in the UK, 5 per cent of the variation in familiarity with maths concepts is explained by students’ background and by the concentration of disadvantaged students in certain schools. This is below the OECD average of 9 per cent.

But in England only around 5 per cent of state secondaries are academically selective grammar schools.

Maths ‘helps social mobility’

The report comes after the UK government has stressed that its back-to-basics approach to maths in English schools - including forcing all primary pupils to learn their times tables up to 12 - will be a key driver of social mobility.

Debate is also raging around whether to allow grammar schools to expand by building annexes ​- sometimes miles away from their original sites.

The report says: “Across OECD countries, socio-economic differences among students and schools account for around 9 per cent - and in some countries, as much as 20 per cent - of the variation in familiarity with mathematics concepts.

“Certain system-level policies, such as between-school tracking, academic selectivity or transferring students from one school to another because of low achievement or poor behaviour, are also associated with more unequal access to mathematics content.”

Mr Schleicher adds: “While disadvantaged students tend to learn simple facts and figures and are exposed to simple applied mathematics problems, their privileged counterparts experience mathematics instruction that helps them think like a mathematician, and develop deep conceptual understanding and advanced mathematical reasoning skills.

“These differences matter, because greater exposure to pure mathematics tasks and concepts has a strong relationship with higher performance in Pisa, and the data suggest that exposing all students to challenging problems and conceptual knowledge in mathematics classes can have a large impact on performance.”

The report’s findings were welcomed by the maths charity National Numeracy. Chief executive Mike Ellicock said: “Young people need both to master the essentials of numeracy and to know how to apply these to challenging practical problems. And it’s clear from the data for adult numeracy in the UK that too often this is not happening - that young people are finishing their formal education without real understanding of basic maths concepts and so are unable to do the maths they need at work and in life.”

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