A shortage of good teachers, particularly in maths and science, is at the root of South Africa's underperforming education system, a new study has found.

"The poor performance of many teachers is a major reason for the dismal results achieved by large sections of the schooling system," according to a report released on Wednesday by the Centre for Development and Enterprise (CDE).

The study it commissioned concluded that South Africa's maths and science results were "at or near the bottom of the world class" at the moment.

The 2011 Annual National Assessment results released in June this year showed the national average performance in mathematics in grade six was 30%.

Maths and science were essential for skilled jobs and economic growth and development, and producing good teachers in these subjects was central to this.

Good teachers should not become scapegoats, but many were poorly managed and not teaching effectively.

The CDE said many teachers had been badly trained, and "possibly most" were underperforming.

"For example, there is a shortage of maths teachers, yet many qualified maths teachers are not teaching maths – despite being willing to do so," said CDE executive director Ann Bernstein.

Of the 16 581 teachers in the Eastern Cape who were qualified to teach mathematics, only 7 090 were actually teaching the subject. Only 5 032 of these had a mathematics qualification.

The country needed about 15 000 more teachers to keep up with the annual demand for 25 000 new teachers.

Two-thirds of the current teachers were over 40. This age profile suggested a looming shortage, and a growing need for more younger teachers. Many existing teachers in maths and science were not doing well and also poorly managed.

A recent assessment of 73 physical science teachers at the Dinaledi schools, which provided extra help with maths and science, found only 60% of those given problem-solving tests could solve them.

Thousands of new bursaries a year were needed for trainee teachers willing to study and teach scarce subjects.

The CDE found that at least a quarter of all newly-trained teachers did not take up teaching posts in South Africa's schools.

They were being deterred largely by low salaries and the poor image of the profession. They either emigrated or took up other professions.

Some posts were being filled by immigrant teachers, but some policy makers and planners did not like this approach, so the "importation" of teachers was not properly planned.

The CDE suggested incentives to get teachers to teach in the "scarce" subjects, but was not suggesting all teachers deserved greater rewards.

Teachers in scarce subjects who were performing should be selectively rewarded, and prospective teachers in subjects most needed for economic growth and national development, should be better paid.

While their formal qualifications had improved, existing teachers spent too little time in the classroom, and many taught badly.

The biggest future demand would be for teachers in languages, maths (and mathematical literacy), commerce, life sciences and physical sciences.

The projected expansion of Further Education and Training colleges would also require more good teachers in technical subjects.

Private companies should be allowed to compete for public funds to produce more and better quality teaching training programmes.

The country was spending enough on education, but the money could be better utilised, the CDE said.

"South Africa cannot continue to rely solely on current systems to train more and better teachers," Bernstein said.

"The public sector alone cannot address this vital national need with sufficient scale, quality and speed."