Investigating access to Mathematics in the FET:A quantitative case study
By Dr VG Govender (ACM: Advisory Committeefor Mathematics)
Introduction
Mathematics is regarded as a difficult subject to learn and to teach in South Africa and other countries. Much of this difficulty stems from the Mathematics content which has to be taught in the various grades (Tambychika,T &Meerahb,T.S.M, 2010). At democracy in 1994, Mathematics was a compulsory school subject until grade 9 (formerly standard 7). In grade 10, learners selected a minimum of 6 subjects, which may have included Mathematics as a subject. There was further separation within Mathematics, where learners could do Mathematics at either the standard or higher grade. This situation continued until 2007, when the last group of learners wrote Mathematicsat either the higher or standard grade at Grade 12.
Curriculum changes in South Africa since 1994
Since democracy was achieved in 1994, there have been a number of revisions or changes to the South African school curriculum and these have had an impact on the teaching and learning of Mathematics and other subjects in South African schools.
In this regard, it is important to examine how various curriculum changes in the years from 1994 till 2014 affected or influenced Mathematics teaching and learning. Those teaching Mathematics in South African schools in this period would have no problem in identifying the effects listed:
“Teachers at the schools did not have the required capacity to teach paper 3 topics such as Probability and Euclidean Geometry; learners did not take up Mathematics P3 because of its optional status and added workload; learners did not want to spend time on content they thought would have no benefit to them”.
It took complaints from a number of universities and other stakeholders to change this situation. They complained about learners leaving school without having done Euclidean Geometry and its negative impact on their studies in Engineering, Architecture and other technical fields (Serrao, 2010). As aresult, this optional paper was done away with the introduction of the CAPS curriculum and its components such as Euclidean Geometry, Probability and Statistics were reassigned to the other two Mathematics papers(DBE, 2011b).
One of the key decisions in South Africa in the past decade has been the introduction of Mathematical Literacy as an alternative to Mathematics in the FET phase. This was a major breakthrough for learners in South Africa as, prior to 2008, a large number of learners (up to 80% in some schools) left school at the end of grade 12 without having done any form of Mathematics. This clearly put these learners at a disadvantage when accessing careers where some basic mathematical skills were needed. However, the introduction of Mathematical Literacyhas resulted in some other unintended consequences which will be dealt with later in this report.
While it is educationally sound for school curricula not to be static and that changes should occur to get a better curriculum for the citizens of a country, there have been too many changes to the South African curriculumin a short space of time. The introduction of Technical Mathematics and Technical Science in technical high schools in grade10 from 2016 show that the process of curriculum change in South Africa is far from over.
Literature survey
A lot has been written about access and redress in South African Education since 1994 with various initiatives promoted and conducted by both governmental and nongovernmental organisations. Mathematics is compulsory up to grade9, meaning that all learners have access to Mathematics until this grade. However, there seems to be issues with regard to this access.Campbell (2014) states that several international studies and the Annual National Assessment (ANA) results in South Africa indicate that problems associated with learner performance in Mathematics has its roots in primary school, where many learners fail to gain basic mathematical skills. The 2013 ANA results saw only 39% of grade six learners and 2% of grade nine learners scoring more than 50% in Mathematics. In 2014, the average grade 9 ANA mark was 10,8%.(DBE, 2014a).
Brodie (2015) refers to analyses compiled by Mark Chetty (Chief Education Specialist at the Department of BasicEducation) which reveal that learners difficulties are with algebra, higher order spatial relationships and that learners have weak problem solving skills and show weak logical reasoning. This means that learners leave the GET with serious learning deficits in Mathematics. If these deficits are not addressed at the beginning of grade10, there is a likelihood of learners performing poorly in FET Mathematics and dropping the subject (in favourof Mathematical Literacy) or leaving school altogether.
Campbell (2014) asserts that the dramatic drop in performance in grade 9 is a “direct consequence of compounding back logs and in creasingly inventive ways learners use to beat the system and dodge detection, with dire consequences for individual learners and the system”. Brodie(2015) locates the problem with the teaching and learning of Mathematics when she states that “one reason pupils are not learning more complex mathematical thinking could be that they are either not being taught this kind of thinking, or are struggling to learn it”. A study by Govender (2013) on the 2012 ANA results found that teachers’ qualifications in Mathematics tend to impact on learner performance. Teachers who are unqualified or underqualified in Mathematics (or have old“outdated”qualifications) have difficulties with teaching Mathematics in ways in which children can understand.
Despite challenges with regard to learner performance in Mathematics in the GET,there has been a noticeable change with regard to access to Mathematics at FET level.The change of curriculum to the NCS in 2006 and CAPS in 2012 was to increase the numbers of learners doing Mathematics. This was evidently successful as the numbers of learners doing Mathematics in South Africa has increased.In table1 below, the numbers of learners who wrote grade 12 Mathematics in the years 2011 to 2014 are given.
Table 1 Number of learners doing Mathematics in South Africa (2011– 2014)
Year 
Number who wrote Mathematics 
2011 
224635 
2012 
225874 
2013 
241509 
2014 
225456 
NSC diagnostic report (2014)
The numbers have been fairly consistent with only 2013 showing a spike in numbers. Columns have been added to table1 to show the numbers (and percentage) of learners passing Mathematics at the 30% and 40% level. This is shown in table 2 below.
Table 2 Mathematics numbers and performance (2011– 2014)
Year 
Number who wrote Mathematics 
Number achieved at 30% or above 
Percentage achieved at 30% or above 
Number achieved at 40% or above 
Percentage achieved at 40% or above 
2011 
224635 
104033 
46,3% 
61592 
30.1% 
2012 
225874 
121970 
54,0% 
80716 
35,7% 
2013 
241509 
142666 
59,1% 
97790 
40,5% 
2014 
225456 
120523 
53,5% 
79050 
31,5% 
NSC diagnostic report (2014)
The grade 12 Mathematics performances show that, prior to the writing of the first examination under the CAPS in 2014, there was a steady increase in learner performance at both the 30% level and 40% level. 2014 showed a decline in the results. This is possibly due to the changes in the assessment of grade12 Mathematics. One major change was the inclusion of Geometry as a compulsory part of the examinations for the first time since 2007. However, one should not find fault with the 2014 Mathematics results as these results were still far better than the 2011 results and marginally less than the 2013 results.
It would appear that the number of learners writing the Grade12 Mathematics papers in South Africahas stabilised over the years (2011–2015). But this represents a drop in the numbers when compared to the year 2009 when 290400 learners sat for the grade12 Mathematics examinations.This drop is significant and one may ask whether the situation in 2009 was once off and that the trends in the years 2011 to 2015 give at true reflection ofthe numbers of learners writing grade12 Mathematics examinations in South Africa.
Problem statement
It would appear that access and redress, in terms of Mathematics in theFET, as the numbers in table 2 suggest, has been successful at a national level. But what has been the case in individual schools? This report examines the trends with respect to numbers at selected schools in a diverse district in one of the South African provinces by comparing number of learners who completed grade9 Mathematics (in 2011) with those who complete grade12 Mathematics three years later (2014). It,further,compares the 2014 numbers with those of 2004.
Research questionand subquestion
The following research question was devised to shed some light on problem statement above:
“What are some of the contextual factors which impact on the numbers of learners writing Grade12 Mathematics examinations?”
The following sub questions were formulated in an attempt to answer the research question.
Research strategy
This report involved the collection of quantitative data which was provided by the district in question, with the proviso that both the district and the names of schools be anonymous. Other quantitative data was gleaned from the literature, government and newspaper reports. There were 19 high schools in this study.
The schools in this study were divided into three groups.
Group A: This group consisted of only exmodel C schools, located in the more affluent areas of the district. These schools are largely nonracial and all are feepaying. The majority o fthe staff and learner populations at these schools would be classified “white”. In many instances, learners travel daily from other areas to these schools.There were 6 group A schools in this study.For purposes of identification in this research, group A schools are assigned the codes A1; A2; …
Group B: This group consisted of schools which reflect a nonracial profile. The majority of the staff and learners in all the schools, bar one, belong to the “coloured”population group. Most schools in this group are“nonfeepaying” schools. Only schools B5 and B6 are fee paying (see later). There is a diverse range of neighbourhoods in areas serviced by group B schools with some being affluent and others being less affluent. Learners from th emore affluent areas are more likely to attend exmodel C schools, in other parts of the school district. Some of the less affluent neighbourhoods in group Bare plagued by poverty, unemployment and in some cases,by gangsters. There has been a steady increase of learners from the “black” townships to some of these schools. There were 7 group B schools in this study and areassigned the codes B1; B2;B3; …
Group C: Schools in this group are located in the “black” African townships. For purposes of description, these schools are exclusively “black”. The majority of staff at these schools would be classified as “black”. However, there are teachers from other South African population groups who also teach at these schools. Group C schools are from diverse neighbourhoods, including learners from informal settlements. There were 6 group C schools in this study. Group C schools are given the codes C1; C2; C3;…
Conceptual framework
This study is located within the “access and redress” framework in education, with special focus on Mathematics. Issues of access and redress have featured in all of the curricula in democratic South Africa, including the latest curriculum, the Curriculumand Assessment Policy Statement (CAPS).This has been reflected in the purpose and principles of this curriculum. While these purposes and principles are applicable to all subjects, its relevance to this research cannot be overstated.
Two of the purposes of this curriculum are:
“Equipping learners, irrespectiveof their socioeconomic background, race, gender, physical ability or intellectual ability, with knowledge, skills and values necessary for selffulfilment, and meaningful participationin society as citizens of a free country”
and
“Providing access to higher education” (DBE, 2011:4)
Further, this curriculum is based on seven of principles, one of which is:
“Social transformation:ensuring that the educational imbalances of the past are redressed, and that equal educational opportunities are provided for all sections of the population” (DBE, 2011:4)
One of the specific aims of Mathematics (in CAPS) focuses on access. This aim is stated as:
“To promote accessibility of Mathematical content to all learners. It could be achieved by catering for learners with different needs.” (DBE, 2011:8)
One may summarise the above purposes and principles of CAPS and the specific aim of Mathematics (in terms of access) as follows:
All learners should be equipped with the knowledge, skills and values to make them better citizens and to participate meaningfully in society. This is important in a subject such as Mathematics as it will give learners access to some of the important higher education programmes in Science and Engineering. This should be provided to all learners, irrespective of socioeconomic status, race, gender, physical or intellectual ability. This means that equal educational opportunities should be provided for all learners,with teachers also ensuring that the Mathematical content is accessible.
Case study
The schools in this research have been classified into groups using mainly the criteria of geographical location. This geographical location has “Apartheid” connotations as all schools in this research were built before 1994. Prior to 1994, each of the three groups of schools served communities of a specific racial classification. Since democracy in 1994, most of the grou pA and B schools (described earlier) have become nonracial, while group C schools have remained largely the same. While there are similarities within each group of schools, there are differences when schools across the different group classifications are compared.
As a result of the similarities within each group of schools, each group of schools could be regarded as a case study.Case study research allows the researcher to explore individuals or organizations, simply through complex interventions, relationships, communities, or programmes (Yin, 2003) and supports the deconstruction and the subsequent reconstruction of various phenomena.
Since this research only involved working with numbers of learners in the different groups of schools, the research could be classified as quantitative case study research.
The data
The district in question gave permission for the data to be used in this research. It provided details (from its EMIS section) of the numbers of learners from a school group who did Mathematics in grade 9 in 2011 and the numbers (from the same school group)who did Mathematics and Mathematical Literacy (ML) in grade 12 three years later. The total number of Mathematics and Mathematical Literacy learners gives the total number of learners in grade 12 at each school. Included in the table is the possible percentage of learners of the 2011 grade 9 classes who ended up doing Mathematics in grade12 in 2014 as well as numbers of learners who did not make it to grade 12 at the particular school.
The details for each school group are shown in the next three tables. Please note the following in respect of tables 3, 4 and 5:
Table 3:Group A schools
School 
2011 Grade 9 Maths 
2014 Grade 12 Maths 
(as a percentage) 
2014 Grade 12 ML 
2014 Total Maths and ML 
Number of grade learners in 2011 who did not complete grade12 at the school 
A1 
223 
108 
48,4% 
99 
197 
25 
A2 
146 
95 
65,0% 
45 
140 
6 
A3 
200 
94 
47,0% 
98 
192 
8 
A4 
166 
120 
72,3% 
40 
160 
6 
A5 
157 
124 
79,0% 
45 
169 
12 
A6 
222 
85 
38,3% 
134 
219 
3 
TOTAL 
1114 
626 
56,2% 
461 
1087 
27 
Table 4:Group B schools
School 
2011 Grade 9 Maths 
2014 Grade 12 Maths 
(as a percentage) 
2014 Grade 12 ML 
2014 Total Maths and ML 
Number of grade learners in 2011 who did not complete grade 12 at the school 
B1 
315 
3 
1,0% 
95 
98 
217 
B2 
305 
8 
2,6% 
65 
73 
232 
B3 
236 
3 
1,3% 
79 
82 
154 
B4 
303 
5 
1,7% 
53 
58 
250 
B5 
208 
12 
5,8% 
97 
109 
111 
B6 
235 
19 
8,0 
141 
160 
75 
B7 
308 
43 
13,9% 
169 
212 
139 
TOTAL 
1910 
93 
4,9% 
699 
792 
1118 
Table 5: Group C schools
School 
2011 Grade 9 Maths 
2014 Grade 12 Maths 
(as a percentage) 
2014 Grade 12 ML 
2014 Total Maths and ML 
Number of grade learners in 2011 who did not complete grade 12 at the school 
C1 
275 
35 
12,7% 
99 
134 
141 
C2 
315 
80 
25,4% 
130 
210 
105 
C3 
228 
56 
24,6% 
92 
148 
80 
C4 
309 
58 
18,8% 
101 
159 
150 
C5 
308 
51 
16,6% 
99 
150 
158 
C6 
170 
27 
15,9% 
100 
127 
43 
TOTAL 
1605 
307 
19,1% 
621 
928 
677 
The data in the preceding three tables have been included in the next table (table 6) to show the percentage of learners who wrote Mathematics and Mathematical Literacy in the grade 12 examinations of 2014.
Table 6: Mathematics and Mathematical Literacy:GroupA, B and C schools
Groups ofschools 
Grade 12 Mathematics 
Grade12 ML 
Group A 
58,6% 
41,4% 
Group B 
10,5% 
89,5% 
Group C 
24,9% 
75,1% 
Trends emerging from tables 3 6
To put the above trends into perspective, it may be necessary to compare the numbers of learners who did Mathematics at these schools in 2014 with the numbers who did Mathematics in the same schools in 2004 (10 yearsearlier). These records were also available from the district. In 2004 Mathematics was offered at both the higher grade (HG) and standard grade (SG). For purposes of comparison an assumption is made in the calculations that all learners who did HG Mathematics and 40% of those who did SG Mathematics (in 2004) would have been able to do the new NCS/CAPSMathematics.Thus, the choice of 40% is arbitrary.
Table 7:Group A Schools (2004 to2014 comparison)
School 
2004 Maths HG 
2004 Maths SG 
Weighted 2004 Maths HG+ 0.4 × SG 
2014 Grade 12 Maths 
A1 
99 
58 
122 
108 
A2 
56 
43 
73 
95 
A3 
39 
91 
75 
94 
A4 
54 
79 
86 
120 
A5 
27 
43 
44 
124 
A6 
35 
98 
64 
85 
TOTAL 
310 
412 
464 
626 
Table 8 GroupB Schools (2004 to 2014 comparison)
School 
2004 Maths HG 
2004 Maths SG 
Weighted 2004 Maths HG+ 0.4 ×SG 
2014 Grade 12 Maths 
B1 

55 
22 
3 
B2 
1 
18 
8 
8 
B3 

32 
13 
3 
B4 
1 
45 
19 
5 
B5 

29 
12 
12 
B6 
5 
41 
21 
19 
B7 
7 
48 
26 
43 
TOTAL 
14 
268 
121 
93 
Table 9 Group C Schools (2004 to 2014 comparison)
School 
2004 Maths HG 
2004 Maths SG 
Weighted 2004 Maths HG+ 0.4 × SG 
2014 Grade 12 Maths 
C1 

28 
11 
35 
C2 
12 
47 
31 
80 
C3 
1 
154 
63 
56 
C4 

130 
52 
58 
C5 
28 
121 
76 
51 
C6 
6 
35 
20 
27 
TOTAL 
47 
515 
253 
307 
Trends emerging from the 2004 to 2014 comparison (tables 7 – 9)
Findings
The findings of this research are given in the context of the research questions.
In the light of the findings, one may ask the question:Who should be responsible for ensuring that schools prepare their learners well for FET Mathematics and that these learners take the subject up to grade12? Surely, it is the school and parent community that should take the lead in this process. The Department of Education should also play its role by monitoring, supporting and intervening.
Discussion
It is now important to discuss the findings from the previous section further in an effort to highlight challenges faced by some schools in ensuring that learners have access to Mathematics in the FET.
Conclusion
Although this research was confined to one school district, it has highlighted the need to interrogate the teaching and learning of Mathematics at all schools in our country. Of crucial importance is the work done in Mathematics in the Senior Phase, especially in grades 8 and 9. This research has shown that within one school district that there are major differences between schools when it comes to access to Mathematics in the FET. Access to Mathematics in the FET is crucial, but once learners are doing FET Mathematics, there should be measures in place to ensure that the majority of these learners should remain in Mathematics until Grade12. Only in exceptional cases should learners be allowed to change to Mathematical Literacy.
Despite all that has been achieved in South Africa since democracy, there are still some sections of society that languish behind in terms of access to Mathematics in the FET. There has to be a concerted effort from all stakeholders to address this issue as a matter of national priority.
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