By Gary Eason
BBC News Online education editor
An immediate start should be made on reforming GCSE maths as one way to reverse the subject's decline, the government's maths expert says.
Report calls for more creative use of new technology
And the recent reform of A-levels had been "an utter and complete disaster" for the subject, said Prof Adrian Smith.
From what employers had told him, "nothing or very little" in the present qualifications structure could be relied upon as an indication of what students knew.
Maths teachers should be paid perhaps £5,000 a year more to try to tackle the shortage of specialists, and financial incentives might also be needed to persuade youngsters to study the subject.
These are among some of the key findings of the 171-page report on post-14 maths education, Making Mathematics Count - UK-wide but primarily concerning England - published on Tuesday.
The government said maths was "at the top of the education agenda" and it would consider its response carefully.
society must recognise the importance of maths
make GCSE a two-tier double award
rationalise vocational qualifications
pay maths teachers more
set up a maths tsar and centres of excellence
make better use of information technology
consider financial incentives to study A-levels
Presenting his report, Prof Smith, principal of London University's Queen Mary college, said maths was so central to much of the modern economy it should be treated as special, not on a par with other subjects.
GCSE students felt the single qualification did not reflect the amount of work they had to do - certainly compared with the science double award or the two awards in English.
So making the GCSE a double award would help with its "image problem".
"I would like to see a start on that right now," Prof Smith said.
Also, maths GCSE was a three-tier qualification and the 30% or so entered for the "foundation" tier could achieve no more than a grade D - when in the outside world and in league tables, grade C was "the golden threshold of success".
Grade B featured in two tiers but was "ambiguous" because of the different content of the syllabuses - and the "tactical behaviour" of schools was influenced by a perception that the intermediate version was easier.
CURRENT MATHS GCSE
grade C regarded as minimum acceptable
foundation students feel "failures" before they start
intermediate grade B seen as "easier"
Once it became possible to get a B on the intermediate tier paper, the proportion of entries for the higher paper halved from 30% to 15% of the total and had stayed at that level.
At the other end of the scale the maths GCSE did not stimulate the most able 10% of students - "a very important minority" for whom the current system did not provide sufficient motivation and challenge.
So it should be just two tiers, as in a pilot version being tried by the OCR exam board, with "only one route to each grade".
OCR's MATHS GCSE PILOT
Paper 1: grades E - G
and Paper 2: grades C - D
and Paper 3: grades A* - B
everyone can access grade C
only one route to each grade
Asked about the validity of the grades, Prof Smith said the top concern among the more than 300 responses to his inquiry from organisations was how to interpret them.
Employers did not know what a grade C was supposed to tell them about youngsters' skills.
He also said he had found the welter of vocational qualifications featuring maths "something of a nightmare to understand" and in need of "serious rationalisation".
At A-level, universities said students could not do the basic maths expected of them at the beginning of their courses.
Asked what, in the present structure, employers could rely upon, he said: "If you heard what they told me, nothing or very little."
It was no surprise pass rates were rising because schools were, in effect, teaching to the test.
A complaint was that instead of "teaching the joy of mathematics", teachers always had to have an eye on the next exam module due to the "perverse and negative" effect of league tables.
Prof Smith was scathing in his comments on the Curriculum 2000 changes, splitting A-levels into AS and A2 halves, which he said simply did not work for maths.
This had resulted in 20% fewer A-levels being completed and contributed to the spiral of fewer people doing maths degrees and fewer going on to teach - at a time when competing demand for maths graduates from industry and the City was rising.
The Qualifications and Curriculum Authority (QCA) had made changes as a result - such that some now regarded A-level as not sufficiently challenging for the best students.
It was too early to say what the effect of those changes would be.
But if there was no "significant restoration" of the numbers doing AS and A2 maths within two or three years, the implications were so serious that the UK authorities should consider offering incentives to students.
One of the "upsides" to £3,000 tuition fees was the opportunity to provide financial sweeteners.
So universities might offer financial incentives to include AS or A-level maths as a pre-requisite for their courses.
Or there might be fee waivers or targeted bursaries to those following relevant courses - such as maths, sciences, engineering or even psychology.
As an incentive to people to teach maths, higher pay might be offered in the region of £5,000 a year - adding up to a £125m increased salary bill.
This could be justified if necessary through a greater responsibility on the teachers to keep their skills updated.
But they also needed better support, through the greater use of assistants - perhaps including university students - and information technology.
The report advocates national and regional centres of excellence to lift the quality of maths teaching, and a national champion or "tsar" to raise its profile.
Prof Smith expects his recommendations to fit with the final outcome of Mike Tomlinson's wider inquiry into 14 to 19 education.
"Tomlinson said he was relying on me to tell him what to do [about maths]," he said.