SUMMING UP: Joseph Khorommbi, a maths teacher in the grade 11 class at Mbilwi Secondary School in Sibasa, Limpopo. Paper 3, not a prerequisite for any university course, deals with geometry that engineers require. Picture: SYDNEY SESHIBEDI

THE new school mathematics curriculum does not give pupils a grounding good enough for post-matric study in mathematics-dominant university courses such as engineering and pure mathematics, experts say.

SA's economic prosperity depends on the availability of sufficient highly educated and trained people in science, mathematics and technology, and suffers from a shortage of people trained in these fields, particularly those from disadvantaged backgrounds. The gaps left by the school mathematics curriculum have forced universities to adapt their mathematics-dominant undergraduate courses, from extending the years of study from three or four, to four or five, to setting extramural study tasks.

"It is really a matter of, if you are teaching and you see your students do not have the required background, you have to go back and teach it to them," says Stellenbosch University's vice- dean of engineering, Prof Peter Dunaiski.

This year's first-year students were different to those from previous years because last year's matriculants were the first to write the new curriculum, called the National Curriculum Statement, which changed the mathematics curriculum.

Many of the mathematics topics this year's first-year students were missing at the start of the year are in the optional school-level Advanced Mathematics Programme, commonly called Maths paper 3, which many schools do not have the capacity to teach, even if they want to.

"It is very, very clear that mathematics papers 1-3 make a coherent whole, but paper 3 involves the more difficult bits that the system couldn't do, or was not doing well," says Prof Nan Yeld, dean of the University of Cape Town's (UCT's) Centre for Higher Education Development. "Now the compulsory part of the mathematics curriculum (tested in papers 1 and 2) is not a coherent whole, and that's a double bind for universities ... (many of) the schools say the universities are not putting their weight behind mathematics paper 3 (by making it a prerequisite for certain fields of study), so they won't teach it."

Yeld is principal investigator in Higher Education SA's National Benchmarking Test (NBT) Project. Many of the universities test the knowledge of prospective students so that teaching programmes can be adapted and augmented.

The problem, for universities, is that they cannot demand that prospective students write paper 3 when the majority of schools do not have the capacity to teach the subject, says UCT's dean of engineering and the built environment, Prof Francis Petersen. "We can make it an incentive, but we need to structure that carefully. The discrimination in paper 3 is much more pronounced than that between higher and standard grade, but you must not disadvantage your ordinary matriculant," says Petersen, who is to raise the issue at a coming engineering deans' meeting.

"We need to emphasise the message (that paper 3 is critical). We have good Model C schools that can offer paper 3, but aren't," he says.

The problem for schools, says Joanna Holliday, head of Pretoria Boys High School's mathematics department, is that it is very difficult to motivate 18-year-olds to study something that does not count towards their final mark, and is not a prerequisite for any university course.

The biggest problem for universities, say several experts, is in the field of geometry, which the compulsory mathematics curriculum largely ignores in the final three years of school. This means those who do not study towards writing paper 3 in matric are completely unfamiliar with complex geometry when they get to university. Almost half of paper 3 is Euclidean geometry.

"Euclidean geometry is a means and an end. It is an end in that the geometric topics are important for the understanding of shapes in space and for later, when they (the students) are doing integration (an important concept in mathematics which, with differentiation, is one of the two main operations in calculus).

"They struggle if they have never had to grapple with the way shapes change in space as the parameters change. This limits their ability to perform integration. It is also a means, a vehicle for developing deductive reasoning," says Dr Carol Bohlmann, who works in Yeld's centre and leads the NBT mathematics team.

While the universities are adapting their curricula in various ways to cope with the gaps in first-year students' mathematical knowledge, this just means that the students now have more with which to grapple in their first year because the experts say that nothing can be removed from the mathematics required in the various degree programmes.

"If we want to turn out competent engineers then the students need the spatial skills ... these are standard requirements. We can't take them out of the curriculum, they are essential. Maths majors become physicists, nuclear physicists.

"They have to know proper maths," says Dr Belinda Huntley, principal tutor of mathematics at the University of the Witwatersrand.