Instead pupils should have "a deep, rigorous and challenging" school maths experience, says the Advisory Committee on Mathematics Education (Acme).
The report says that England is "significantly underachieving in terms of developing able mathematicians".
Professor Steve Sparks, of Acme, urged "deep learning over rapid progress".
On Tuesday, a study put England in the global top 10 for maths at both primary and secondary level - but the Acme report draws on separate statistics which examine the performance of 15-year-olds in mathematics, science and reading.
The data, from the 2009 PISA tests run by the Organisation for Economic Cooperation and Development (OECD) suggested that just 1.7% of England's 15-year-olds reached the highest levels in maths, compared with an OECD average of 3.1%.
The report says that schools' success is too often measured on their ability to accelerate pupils through the curriculum, both at primary and secondary level.
Talented 11-year-olds in primary school are being entered for maths tests with concepts from the secondary curriculum and able secondary pupils are being entered early for GCSE, the report found.
It warns that this can lead to shaky foundations and hinder progression to A-level.
"Just because a pupil can charge through the curriculum at top speed through procedural learning, does not mean that he or she has developed a clear grasp of the subject matter or could apply the fundamental principles more broadly", said Professor Sparks.
"The 'acceleration' approach is driven by league tables, and puts us at odds with many of the world's highest performers in terms of mathematics education. It is inconsistent with the government's stated aim to encourage more students to study maths to 19."
The report calls the issue both "serious and urgent" and urges the government to use the ongoing curriculum reform to produce an "extended" version for students with the potential to study the subject at A-level.
The report calls for an enriched curriculum to be available in all mainstream schools and suggests that around 30% of pupils would find it "a challenging but satisfying experience".
The government said it had already instigated top-to-bottom overhaul of maths in schools, extending from primary school to A-level.
A spokesman for the Department for Education said: "ACME is right. Learning maths, indeed any subject, must not be a treadmill of revision and exams. Young people must gain a deep understanding. This is what will produce the mathematicians of the future."
Sue Pope of the Association of Teachers of Mathematics, said some schools were doing an excellent job but too much teaching to the test meant that not enough young people were getting "the opportunity to experience the excitement, fascination, joy and beauty of maths".
"It is a vitally important subject in a wide range of contexts but it can be creative and exciting in its own right."
Ms Pope cautioned against limiting the enriched curriculum to the ablest pupils: "There is quite a lot of evidence that no matter who your learners are, they all need challenges. All children will be more engaged if they manage to complete a task they didn't think they were capable of."
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