The “easy” questions in the 2008 national senior certificate maths exam could have been easier; while the difficult questions could have been more difficult. Had this occurred, fewer learners would have achieved “A” symbol passes.
This is a finding of a ministerial panel established to review the grade 12 national senior certificate maths exam. Last year was the first time learners wrote national exams in most subjects, but there was no higher or standard grade distinction. Learners had to either study maths literacy or core mathematics, which had two compulsory exams and an optional paper which included Euclidean geometry.
The maths results was cause for alarm because 63 035 learners attained a more than 50% pass mark. There was criticism from the Concerned Mathematics Educators, who claimed that the maths results were “watered down” and that the standard of the exam had dropped to an unacceptable level. They also believed that learners who achieved 50% passes were not prepared to cope with maths-related courses at university, such as engineering, architecture and business science.
Some academics and analysts were concerned that too many learners passed maths at 50% compared with the 28 156 learners who passed higher grade maths at 40% in 2006; and 28 263 who passed it in 2007. They questioned whether the 2008 results at this level were comparable with higher grade passes in previous years.
In response Education Minister Naledi Pandor set up a committee to assess the levels of complexity of the maths question papers to determine the standard set for the subject last year and to compare this with questions set in previous exams. The panel was asked to advise whether those students who scored at or above the 50% level would historically, and in the opinion of the panel, have passed maths at the higher grade level.
According to private maths consultant Aarnout Brombacher, who chaired the panel: “There weren’t enough straightforward questions and there weren’t enough difficult questions. This made passing harder, but getting an A or B symbol possibly easier.”
He said the education department had structured the exam along levels of difficulty: 25% of marks should have focused on knowledge (easy questions); 30% for routine procedures; 30% complex procedures; and 15% to solving problems. However, an analysis by the Association of Maths Educators of SA (Western Cape) and the matric exam quality assurance body, Umasli, found that this was not adhered to.
Based on these two studies, Brombacher said: “The papers did not differentiate enough between people who got As and Bs. Some who got Bs might have gotten Cs.”
However, he said the panel believes those who got 50% or more in the 2008 core maths exam would historically have passed higher grade at 40%.”
Brombacher said that one should be sympathetic to the exam panel as it had to create a new exam and deal with a bigger cohort of learners. “They did not have a historic percedent. It’s very hard to measure the level of difficulty of questions.”
He said in future the panel needs to ensure that there are more difficult papers at the top end and that the bottom-end questions are a little more accessible.
According to Aslam Mukadam of the Concerned Mathematics Educators: “It is practically impossible to satisfy the two extreme groups, namely the top learner and the below-average learner in the same mathematics examination.
“In the 2008 mathematics examination the top learner found the paper to be less of a challenge because about 70% of the paper could be done without much cognitive demand. On the other hand, the below-average learner started the paper off with a handicap of about 30% due to questions outside this learner’s cognitive range.”
He said it is crucially important “that we raise the standard of mathematics education in South Africa if we are to produce engineering and science graduates of substance in the future”.
“The CME recommends that the maths paper three be made compulsory for learners wishing to attend university. Papers one and two will test only basic knowledge and routine procedures and a small percentage of complex procedures and paper three will contain all the higher-level questions of papers one and two. In reporting we propose to continue to show the results from papers one and two separately from that of paper three. This will naturally cater for the need to distinguish between those learners wishing to enter university and those wishing to enter universities of technology.”
Mukadam said his organisation is confident that it’s proposed modification in the assessment system will provide a solution for preparing learners more adequately for tertiary studies, as well as attract more learners into the maths stream instead of losing them to maths literacy.
However, Brombacher said the reason for Euclidean geometry being put into the optional paper three was that in many schools teachers who were not in a position to teach the content could have forced learners to take maths literacy. “We can’t make paper three compulsory until the teachers can teach the content.”
Some univeristy acdemics are concerned that first-year students lack basic mathematical concepts that are required for economics. “Students are struggling with basic equations. Sometimes lecturers have to go through equations three times to explain simple mathematical procudures. Students’ maths backgrounds are weak,” said one academic.