Bold plans for the future of maths teaching which envisage a new "maths for the citizen" course, may be over-ambitious, one of the the subject's associations has warned.
The Mathematical Association is concerned that the government inquiry into the future of the subject, which put forward the move, is taking too little account of whether schools have the staff to make its proposals work.
The association's reservations are outlined in its official response to the paper by Professor Adrian Smith, the inquiry chairman.
The association wants most pupils to sit two GCSE-level exams in maths, as happens with science and English. One of them could be pitched at a lower level than the other and not all pupils would be required to take both.
However, Professor Smith's paper appears to go further. A series of courses, or learning "pathways" would be offered to youngsters, covering both vocational aspects of the subject, or "maths for the citizen" and more academic work for 14 to 16-year-olds.
Post-16, students would be offered a choice of specialist maths courses, tailored for those either planning to go into the world of work, on to maths-orientated degrees or to read social sciences or humanities at university.
Both ideas are poised to be key planks in former chief inspector Mike Tomlinson's plans for a baccalaureate-style diploma, covering all subjects, for England's secondary schools.
The Mathematical Association is concerned about forcing choices on pupils at 14. It worries that schools and colleges could find it difficult to cope with sixth-formers arriving having done several different courses.
And it argues that schools may not have the staff to offer specialist courses in the post-16 phase. How pupils are taught the subject is a bigger issue than what they are taught, the association argues, with the shortage of qualified maths staff the biggest problem.
Its submission criticises Professor Smith's paper for failing to call on the Government to raise morale in the profession, which, it argues, would stop teachers leaving.
The inquiry is due to produce its final report for ministers by the end of the month.