Too much teaching to the test and an over-emphasis on the routine learning of rules and facts is turning children off maths and leaving them with little understanding of how to apply the subject to the real world, school inspectors have concluded.

A damning report on the teaching of maths in primary and secondary schools in England, concludes that strategies to improve maths examination scores, including booster lessons, revision classes with a heavy emphasis on practising past papers, helped pupils gain qualifications.

But it did not instill in them a proper mathematical understanding that would enable them to apply maths to new situations, solve problems and communicate solutions.

“Too often, pupils are expected to remember methods, rules and facts without grasping the underpinning concepts, making connections with earlier learning and other topics, and making sense of the mathematics so that they can use it independently,” inspectors said.

Pupils were rarely encouraged to investigate open-ended problems which might offer them opportunities to choose which approach to adopt or to reason and generalise, they said.

“Pupils wanted to do well in mathematics. They knew it was important, but were rarely excited by it, were generally not confident when faced with unusual or new problems and struggled to express their reasoning.

“Their recall of knowledge and techniques was stronger than their understanding,” the report concludes.

Too few teachers moved around the class to check for pupils who were stuck, had made slips or who found the work easy.

Teachers also failed to encourage pupils to talk about mathematics, leaving them struggling to express and develop their thinking.

The findings, which follow inspectors visits to 84 primary and 108 secondary schools, suggest that there has been a steady improvement in maths test and examination results in recent years but concluded that teaching of the subject was good in only half of schools.

The greatest weakness were found in secondary schools.

Christine Gilbert, the head of the schools’ inspectorate Ofsted, said that too many schools were letting their pupils down when it came to maths.

“The way mathematics is taught can make a huge difference to the level of enthusiasm and interest for the subject. As well as developing fluent numeracy skills to deal with everyday mathematics, children and young people need to be able to think mathematically, model, analyse and reason," she said.

Marcus du Sautoy, Professor of Mathematics at the University of Oxford, said that the key ages at which children got turned off maths was between 11 and 14.

“Pupils do need to understand the scales and arpeggios that make up the music of maths - things like the multiplication tables. But maths is so much more than that. It’s about a way of thinking, not about applying rules.

“In history we present children with big philosophical ideas, but we don’t do that in maths. Why not? It is as if we are too afraid of challenging children with things they may not understand. But if we did, I think we would find that most would step up to the challenge,” he said.

He added that children who were less enthusiastic about the technical side of the subject could be by learning about the history of maths and the lives of great mathematicians.

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