Studying towards a BSc degree at universities in South Africa requires at least one course in mathematics. A course in mathematics also is a
prerequisite if a candidate wants to register as a professional scientist with the South African Council for Natural Scientific Professions.
^{1} Programmes in actuarial science, engineering and mathematics itself require more than one year of university
mathematics, whereas
other BSc programmes typically require mathematics in the firstyear curriculum only. Entrance to study a BSc at South African universities is based on a prospective student’s level of performance in the final school leaving
– Senior Certificate (SC) or National Senior Certificate (NSC) – examination. At the University of the Free State (UFS), the
mathematics entrance requirement for the BSc in Actuarial Science and the pure mathematics and applied mathematics programmes is a highergrade B
(HG B) symbol in SC school mathematics or a level 6 for mathematics in the final NSC examination. Other BSc programmes require a minimum of a standardgrade C (SG C) in SC school mathematics or a level 4 for mathematics in the final NSC examination. In 2008, the first cohort of matriculants completed the new NSC curriculum. An analysis of the mathematics examination results indicates that
the number of learners that obtained a mark of 80% and higher in school mathematics increased significantly.^{2} A
disproportionate number
of students achieved high mathematics symbols, and consequently significantly more students achieved the minimum entrance requirements and were
accepted into engineering and science faculties nationwide in 2009.^{3} For example, 30% more students entered the
Faculty of Engineering
and the Built Environment, and 8% more entered the Faculty of Science at the University of Cape Town
in 2009.^{3,4} During February 2009, the 2009 cohort entering the UFS undertook a battery of Alternative Admissions Research Project
(AARP) tests.^{5}
Students entering the Faculty of Natural and Agricultural Sciences wrote a mathematics comprehension test and a mathematics achievement test. In
the mathematics comprehension test the students achieved an overall average score of 44%. The students performed well in the basic mathematics
cluster with an average of 83%, but achieved low average scores in the analysis cluster (34%) and the synthesis cluster (2%). In the mathematics
achievement test, the students achieved an overall average score of 37%. The average in all clusters of this test was below 40%. According to the
AARP Centre, this result is an indication that the majority of these students would find it difficult to pass mathematics at university level
without additional support. The National Benchmark Test Project (NBT), piloted in February 2009 with the 2009 cohort of higher education entrants at selected institutions,
was implemented in August 2009 for the 2010 entrants. The results of the tests are divided into four proficiency
levels^{6}: proficient
(62% – 100%), upper intermediate (49% – 61%), lower intermediate (34% – 48%) and basic (0% – 33%). The results of the pilot
study indicated that of the students who wrote the NBT mathematics, 6% achieved the proficient level, 73% achieved an intermediate level and 21%
achieved the basic level.^{7,8} The 2010 NBT report^{6} indicates that
8% of the cohort achieved the proficient level, 21% achieved
the upper intermediate level, 36% the lower intermediate level and 35% the basic level. These results indicate that 92% of the students who applied
for entry into universities in 2010 would need some form of mathematics support^{6}; these findings are similar to
those of the AARP project
mentioned above. Several media reports have expressed the view that learners had been poorly prepared at school level.
Serrau^{9 }suggested that weakness
in the 2008 school mathematics was directly responsible for the poor performance of firstyear students in firstyear university mathematics
courses. Blaine^{10} has claimed that the new school mathematics curriculum does not give learners enough grounding
for programmes such as
engineering and mathematics itself. The performance in 2009 of firstyear engineering students, who moved directly from school to university,
showed a marked decline in firstyear mathematics compared to the 2008 cohort. At the UFS we use a precalculus test for firsttime entrants into firstyear mathematics to establish their competency in mathematics, primarily
to offer curriculum advice. The precalculus test has been taken by all students entering the Faculty of Natural and Agricultural Sciences since
2004. Table 1 shows a comparison of the symbols of firsttime entrants from the old SC final examinations (between 2004 and 2008), their
performance in the precalculus test, and their final results in the mathematics modules WTW 114 (major module) or WTW 134 (service module). When
universities calculate an Mscore for entrance purposes to universities, it is generally accepted that a SG A symbol is equivalent to a HG C symbol.
However, our observations in terms of the precalculus test clearly show a significantly larger difference in student proficiency between these
two
symbols, namely that the SG A symbol instead corresponds to a HG E symbol.
TABLE 1:
Performance in the precalculus test and in firstyear mathematics modules WTW 134 and WTW 114 compared to Senior Certificate mathematics symbols
of
students in the 2004–2008 firstyear cohorts in the Faculty of Natural and Agricultural Sciences at the University of the Free State.

The main aim in applying the precalculus test since 2004 has been the benchmarking of the SC mathematics symbol against the NSC performance
level. Table 1 shows that SC learners with a HG A symbol obtained an average of 84% in the precalculus test. According to Table 2, NSC learners
with a performance level 8 (90% – 100%) obtained an average of 82% in the precalculus test. From this we conclude that a level 8 symbol
corresponds well to a HG A for school mathematics. Similarly, we can argue that performance level 7 (80% – 89%) and level 6 (70% – 79%)
correspond to HG C (60% – 69%) and HG D (50% – 59%) symbols, respectively. Table 2 also shows that performance level 5 (60% –
69%) and level 4 (50% – 59%) correspond to SG B and SG C symbols, respectively, which indicates a difference of approximately 20%. Our results
confirm the finding that NSC mathematics may be inflated by 20% in the lower ranges.^{11}
TABLE 2:
Performance in the National Benchmark Test (2010 cohort only), the precalculus test, and firstyear mathematics modules WTW 134 and WTW 114
compared to
National Senior Certificate mathematics level of students in the 2009 and 2010 cohorts in the Faculty of Natural and Agricultural Sciences at the
University of the Free State. 
The only NBT results available are those of the 2010 cohort. Table 2 shows the NBT results and their corresponding precalculus results. Students
in the proficient level (≥62%) in the NBT, obtained a higher mark in the precalculus test, while students in the intermediate and basic levels
of the NBT, obtained a similar mark in the precalculus test.An important factor to consider is, however, the entrance requirement with respect to mathematics for study at a higher education institution and,
with that, the success rate in mathematics in the first year of study. At the UFS, two mathematics modules are presented in the first semester of
the first year: WTW 114 and WTW 134. WTW 114 is the module which leads to majoring in mathematics and actuarial science and in some programmes in
physics and chemistry. This module is also the one which other universities recognise for engineering study. WTW 134 is a ‘service’
module, which is mainly for biological, earth and agricultural science programmes where mathematics is required only in the first year of the
programme. At the UFS, until 2008, the entrance requirement for WTW 114, the higher level mathematics, was a HG D symbol in the SC mathematics final
examination. Since 2009, the requirement has been set as a level 6 in NSC mathematics. The data in Tables 1 and 2 clearly indicate that a HG D
and a level 6 school mathematics proficiency is not sufficient to achieve success in the WTW 114 mathematics module. The entrance requirement for
WTW 134, the ‘service’ module, was a SG C and a level 4 school mathematics proficiency. This entrance requirement leads to a success
rate in this module considerably below 50%. We therefore conclude that standardgrade mathematics in the SC and a level 4 performance in NSC
mathematics are not sufficient for success in our WTW 134 mathematics module. One of the objectives of the NBT project is to assess the relationship between highereducation entrylevel requirements and schoollevel exit
outcomes.^{7} The NBT reports show a dismal picture regarding the mathematics proficiency of the pilot
cohort^{7} in 2009 as
well as that of the 2010 cohort.^{6} Table 3 and Figure 1 indicate the success rates in the two
firstsemester mathematics modules, WTW
114 and WTW 134, at the UFS compared to the NBT scores. Our data reveal a more positive picture than the NBT reports for success in firstyear
mathematics. That is, to be successful in WTW 114, a student should score at the proficient level in mathematics in the NBT, but a basic level
for mathematics in the NBT is sufficient to be successful in the WTW 134 module.
TABLE 3:
Performance in the precalculus test and in firstyear mathematics modules WTW 134 and WTW 114 compared to National Benchmark Test results of the
students in the 2010 cohort in the Faculty of Natural and Agricultural Sciences at the University of the Free State.


FIGURE 1:
Performance of the 2009 and 2010 cohorts of the Faculty of
Natural and Agricultural Sciences at the University of the Free State in the
National Benchmark Test (NBT), the precalculus test (PreCalc) and firstyear
mathematics modules (WTW 134 and WTW 114) compared to their final
matriculation mathematics level (L3–L8).


The claim of the 2010 NBT report^{6} that 92% of students with NSC mathematics entering higher education would
need some form of
mathematics support is only partly correct, at least at the UFS. Here, the claim is valid in terms of the mathematics required for programmes
in actuarial science and mathematics itself, but not for programmes in the biological, earth and agricultural sciences, where NSC mathematics
does adequately prepare students to pass the mathematics courses required.A new school curriculum dictated by the ’Curriculum and Assessment Policy Statements (CAPS)’^{12} has
been implemented
from 2012. The grade 12 learners of 2014 will be the first cohort to complete this curriculum. However, no major changes have been made to the
mathematics content. The performance reporting (proficiency levels 1 to 7) will be similar to that of the current curriculum. Consequently,
changes in mathematics entrance requirements at universities are unlikely to apply to the 2014 grade 12 cohort.
1. SACNASP Information Brochure [document on the Internet]. No date [cited2010 Nov 16]. Available from:
http://www.Sacnasp.org.za/documents/information_brochure_2010_2011.pdf
2. Department of Education. Abridged Report: 2008 National Senior Certificate Examination Results [document on the Internet]. c2008
[cited 2010 Oct 03]. Available from:
http://edulibpretoria.files.wordpress.com/2009/01/abridgedreport2008nscexams.pdf 3. Wolmarans N, Smit R, CollierReed B, Leather H. Addressing concerns with the NSC: An analysis of firstyear student performance in mathematics
and physics. Paper presented at: 18th Annual Conference of the Southern African Association for Research in Mathematics, Science and Technology
Education; 2010 January 18–21; Durban, South Africa. 4. CollierReed BI, Wolmarans N, Smit R. The impact of NSC mathematics on student performance in mathematics in firstyear engineering programmes:
Where does the gap lie? Paper presented at: Academy of Science of South Africa’s Mind the Gap forum; 2010 Oct 21–22; Cape Town,
South Africa. Available from:
http://www.uct.academia.edu/brandoncollierreed/papers/362566/The_impact_of_nsc_mathematics_on_student_performance_in_mathematics_in_firstyear_engineering_programmes
5. WilsonStrydom M. Results of the Alternative Admissions Research Project (AARP) tests written February 2009. Report for the Centre for Higher
Education Studies and Development, University of the Free State, May 2010. 6. Prince R. The National Benchmark Test Project: 2010 intake report. Pretoria: HESA consultative Forum, Higher Education South Africa; 2010. 7. The National Benchmark Tests Project. Report on the February 2009 pilot tests, University of Cape Town. Pretoria: Higher Education South
Africa; 2009. 8. MacGregor K. South Africa: Shocking results from university tests [homepage on the Internet]. c2009 [cited 2010 Oct 24]. Available from:
http://www.universityworldnews.com/article.php?story=20090816082047397&mode=print
9. Serrao A. Last year’s matric maths results a big headache. The Star 2009 June 26. 10. Blaine S. New maths curriculum does not add up. Business Day 2009 Nov 19. Available from:
http://www.businessday.co.za/articles/content.aspx?id=87514
11. Hunt K. Comparability of NSC mathematics scores and former SC HG scores: How consistent is the signal across time? [document on the Internet].
No date [cited 2010 Nov 09]. Available from:
http://www.assaf.org.za/wpcontent/uploads/2010/11/KarinHunt.ppt 12. Department of Basic Education. Curriculum and Assessment Policy Statement (CAPS). Pretoria: Department of Basic Education; 2011.
