New numbers in mathematics in South Africa

This article was downloaded by: [University of California, Berkeley]On: 21 October 2014, At: 20:26Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954 Registeredoffice: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK

International Journal of MathematicalEducation in Science and TechnologyPublication details, including instructions for authors andsubscription information:http://www.tandfonline.com/loi/tmes20

New numbers in mathematics in SouthAfricaJohann Engelbrecht a & Ansie Harding aa Department of Mathematics and Applied Mathematics ,University of Pretoria , Pretoria, South AfricaPublished online: 16 Feb 2009.

To cite this article: Johann Engelbrecht & Ansie Harding (2009) New numbers in mathematics inSouth Africa, International Journal of Mathematical Education in Science and Technology, 40:1,73-86, DOI: 10.1080/00207390802597738

To link to this article: http://dx.doi.org/10.1080/00207390802597738

PLEASE SCROLL DOWN FOR ARTICLE

Taylor & Francis makes every effort to ensure the accuracy of all the information (the“Content”) contained in the publications on our platform. However, Taylor & Francis,our agents, and our licensors make no representations or warranties whatsoever as tothe accuracy, completeness, or suitability for any purpose of the Content. Any opinionsand views expressed in this publication are the opinions and views of the authors,and are not the views of or endorsed by Taylor & Francis. The accuracy of the Contentshould not be relied upon and should be independently verified with primary sourcesof information. Taylor and Francis shall not be liable for any losses, actions, claims,proceedings, demands, costs, expenses, damages, and other liabilities whatsoever orhowsoever caused arising directly or indirectly in connection with, in relation to or arisingout of the use of the Content.

This article may be used for research, teaching, and private study purposes. Anysubstantial or systematic reproduction, redistribution, reselling, loan, sub-licensing,systematic supply, or distribution in any form to anyone is expressly forbidden. Terms &Conditions of access and use can be found at http://www.tandfonline.com/page/terms-and-conditions

http://www.tandfonline.com/loi/tmes20

http://www.tandfonline.com/action/showCitFormats?doi=10.1080/00207390802597738

http://dx.doi.org/10.1080/00207390802597738

http://www.tandfonline.com/page/terms-and-conditions

http://www.tandfonline.com/page/terms-and-conditions

International Journal of Mathematical Education inScience and Technology, Vol. 40, No. 1, 15 January 2009, 73–86

New numbers in mathematics in South Africa

Johann Engelbrecht* and Ansie Harding

Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria,South Africa

(Received 1 October 2008)

This article is a follow-up of a study conducted in 2000 by the same authors ontrends in numbers of mathematics majors at South African universities. Datafrom 12 universities for the 2000–2007 period is investigated. The previouslyobserved trend of general and dramatic decrease in numbers of mathematicsmajors appears to have been reversed and an increase of numbers is observed atall but one of the universities. Diversification into applied fields such as financialmathematics has aided in increasing numbers of mathematics majors and hasbeen largely successful at universities that have ventured this way. Universitieswhere mathematics teacher training is situated within mathematics departmentsalso show a noteworthy increase in numbers. Of concern is the decrease innumbers of mathematics majors over the last 2 years.

Keywords: mathematics majors; student numbers; trends in mathematics studentnumbers

1. Introduction

South African universities have been subjected to many changes in the almost decade anda half since the 1994 change of government, following the demise of the apartheid era. At theturn of the century, in 2000, the authors took stock of what the trends were in mathematicsdepartments at South African universities. Results were published in [1] (subsequentlyreferred to as the 2000 study) and showed a disturbing decline in the number of students thatmajor in mathematics, not only locally but also internationally. At the time cleardemarcations still existed in South Africa between, for example, universities using differentlanguages as teaching medium and historically disadvantaged (mainly black) universitiesand others. Since then the situation in higher education has undergone substantial changes.There have been mergers of universities and colleges and/or technikons (the term formerlyused in South Africa for tertiary institutions in technology) in order to reduce the number oftertiary institutions and former technikons have become universities of technology.

Jansen [2] is of the opinion that the transition from an apartheid state to a post-apartheid society created the conditions for fundamental changes to all levels of education,including higher education. He describes the landscape of South African higher educationat the time of political changes as ‘a wide range of institutions spread thinly and unevenlyover urban and rural areas with considerable variation in their capacities for teaching,research and development’. The plethora of tertiary institutions included 21 universities,15 technikons, 120 colleges of education and 150 technical colleges, as well as a growing

*Corresponding author. Email: [email protected]

ISSN 0020–739X print/ISSN 1464–5211 online

� 2009 Taylor & Francis

DOI: 10.1080/00207390802597738

http://www.informaworld.com

Dow

nloa

ded

by [

Uni

vers

ity o

f C

alif

orni

a, B

erke

ley]

at 2

0:26

21

Oct

ober

201

4

private higher education system. Significant mergers and other changes only took effectafter 2000 and did not come without criticism. Jansen [2] argues that ‘the merger process inSouth Africa has to date been marked (by) behaviour and action that has been bothirrational and incoherent as well as not necessarily in the interests of the highereducational process’.

Although mergers between universities themselves and with technikons took place inorder to reduce the number of universities, the remaining former technikons, on the otherhand, were transformed to become universities of technology, and therefore, in turnincreased the number of universities. The total number of universities in South Africa standsat 23 at present. These universities comprise 11 traditional universities, 6 comprehensiveuniversities and 6 universities of technology. Traditional universities are just that:full-spectrum universities with faculties of science, engineering, law, arts/humanities andso on, engaging in pure, as well as applied research and teaching. The comprehensiveuniversities were created by the merger of universities with technikons, and offer sometraditional university programmes as well as career-orientated programmes of the typefound in the former technikons. The universities of technology are basically renamedtechnikons (which were themselves originally designated technical colleges). At universitiesof technology (as was with technikons) the emphasis is on training engineers.

Such radical changes complicate a potential follow-up of the 2000 study. Yet it remainsof utmost importance to monitor the situation in the rapidly changing tertiary educationenvironment of South Africa.

2. Trends investigated

For the 2000 study on trends in numbers of mathematics majors, 15 participatinguniversities were considered and for the present study we use the data of 12 universities.The current and previous studies have an overlap of six universities but these universitiescorrespond with respect to their official names only and not necessarily with respect todemographical dispensation.

Requests for data on the numbers of mathematics majors, third-year students inapplied fields and numbers of first-year students were sent to 16 academic universities.Universities of technology were not surveyed. Responses were received from 12 of theseuniversities. One major university, University of South Africa (a distance university) didnot see their way clear to supply the required information. The other three universities thatdid not respond are the University of Fort Hare, University of Zululand and RhodesUniversity. These universities are fairly small and we do not think that their data wouldsignificantly change the conclusions of this study.

The main concerns regarding the number of mathematics majors at South Africanuniversities as raised by the authors in the 2000 study are as follows:

(1) There was a general decline in numbers of students majoring in mathematics atSouth African universities. This finding was in line with international trends.The decline in numbers of mathematics majors was in contrast to the increasingnumbers of first-year students.

(2) A breakdown of the numbers into various categories showed that traditionallyAfrikaans universities displayed a steeper decline than traditionally Englishuniversities and rural universities showed a greater decline than urban universities.Furthermore, historically disadvantaged institutions contributed more to thedecline in numbers than did other universities.

74 J. Engelbrecht and A. Harding

Dow

nloa

ded

by [

Uni

vers

ity o

f C

alif

orni

a, B

erke

ley]

at 2

0:26

21

Oct

ober

201

4

(3) Recoveries were taking place at certain institutions where new, more pragmatic

mathematics courses had been introduced.

Because of the changed dispensation it is only the first and last of these findings that have

a bearing on the present study. The 2000 study cautioned that undergraduate mathematics

needs to attract and retain sufficient numbers of students in order to supply the highly

mathematically qualified people needed for the workforce of the future and the

mathematics teachers that are so badly needed in this country. The article also alerted

to the fact that the observed and dramatic decline seemed to be tapering off at some

universities. New diversifications into applied fields such as financial and biological

mathematics, for example, may come to the rescue in reversing the trend of decline.The questions of concern in the current study are:

. whether the trend of decline in numbers of mathematics majors has been halted or

even reversed in the recent period of 8 years;. whether the trend in South Africa is in line with international trends;. what the impact and evolution have been of diversifications into applied fields in

mathematics departments.

3. International trends

In 1998, International Commission on Mathematics Instruction (ICMI) organized a study

conference on the teaching and learning of mathematics at university level. This conference

resulted in a publication [3] reporting on a large number of countries. The international

programme committee of this study also conducted a survey in order to obtain data from

mathematics departments at universities worldwide. The survey included 70 universities

from 10 countries [4].General observations include:

. Although in most countries more students registered for beginner courses in 1997

than in 1987, the number of mathematics graduates decreased from 1987 to 1997.

The number of first-year students who eventually become mathematics graduates

form a very small percentage of the first-year enrolment.. Courses in applied fields, such as discrete mathematics, financial mathematics and

stochastic modelling have been introduced in many countries. The trend is also to

include less abstract analysis in undergraduate programmes. There is increased

emphasis on applications, especially in economics. Programmes had to be

reconstructed to serve a more diverse student body.

In the United States, three (fairly) recent reports contain important data on undergraduate

mathematics majors. The first is the Conference Board of the Mathematical Sciences [5]

report published by the American Mathematical Society, the second is part three of

the Annual Survey of the Mathematical Sciences Joint Data Committee annual report [6,7]

and the third is the National Science Foundation [8] report named Science

and Engineering Indicators. These reports show that there has been a decline in the

baccalaureates awarded in mathematics. Interesting, however, is the fact that

the percentage of undergraduates receiving mathematics degrees remains higher than the

percentage of freshmen intending to major in mathematics [9].Garfunkel and Young [10,11] have expressed their concern about the situation in the

United States more than once.

International Journal of Mathematical Education in Science and Technology 75

Dow

nloa

ded

by [

Uni

vers

ity o

f C

alif

orni

a, B

erke

ley]

at 2

0:26

21

Oct

ober

201

4

The reason for writing this piece is our belief that our profession is in desperate trouble –immediate and present danger. The absolute numbers and the trends are clear. If something isnot done soon, we will see mathematics department faculties decimated and an already dismaljob market completely collapse. Simply put, we are losing our students. [11, p. 256].

In 2005, 15 prominent business organizations in the United States joined together toexpress their concern about the United States’ ability to sustain its scientific andtechnological superiority through this decade and beyond [12]. Their goal is to double thenumber of science, technology, and engineering and mathematics graduates withbachelor’s degrees by 2015.

Their alarm is based on domestic concerns, such as that in 2005 the number ofengineering degrees awarded in the United States was down 20% from the peak year of1985 and international concerns such as fierce competition. It is estimated that by 2010,if current trends continue, more than 90% of all scientists and engineers in the world willbe living in Asia.

Davis [13] was concerned with the high unemployment rate of new PhDs in the UnitedStates. This rate rose from 2.5% in 1990 to a peak of 13.2% in 1994. This situationhas improved, however, over recent years. The 2007 unemployment rate for the 1028new doctoral recipients whose employment status is known was 4%, down from 4.4% for2006 [14]. In contrast, Reys [15] raises serious concerns about the shortage of doctorates inmathematics education.

In a report in 2000 on the future of mathematical sciences in Australia [16], Thomascomes to the conclusion that mathematical sciences are in a crisis. Thomas reportsa decline in Australia in the number of year 12 students studying advanced mathematicalcourses, a consistent trend since 1990. Furthermore, few mathematics graduates arechoosing teaching as a career at a time when many experienced and well-qualified teachersare retiring.

Mathematics departments at Australian universities have also experienced a notabledecline in staff since 1995, a brain drain of both experienced and new researchers,marginalized or restructured departments, fewer applications for research grants, few ifany new appointments and difficulties in making appointments in key areas such asfinancial mathematics and statistics. Some universities no longer offer a 3-year degreemajoring in mathematics or statistics.

In a review of mathematical sciences research in Australia, published by the NationalCommittee for the Mathematical Sciences of the Australian Academy of Science [17],serious concern is expressed about the situation of the mathematical sciences in Australia.Nationally, the percentage of year 12 students taking advanced and intermediatemathematics fell from 41% in 1995 to 34% in 2004.

Australia will be unable to produce the next generation of students with an understandingof fundamental mathematical concepts, problem-solving abilities and training in moderndevelopments to meet projected needs and remain globally competitive (p. 5).

The reviewers also expressed concern about the transfer of mathematics and statisticsservice teaching to departments other than mathematics and statistics departments.

4. Mathematics majors

For the 2000 study of trends in numbers of mathematics majors in South Africa theworking definition for mathematics major was taken as a student who enrols for anabstract mathematical course such as analysis on third-year level, because such a course


Dow

nloa

ded

by [

Uni

vers

ity o

f C

alif

orni

a, B

erke

ley]

at 2

0:26

21

Oct

ober

201

4

serves as prerequisite for any continued study on graduate level in pure as well as in

applied mathematics. For the current study the definition was expanded slightly.A mathematics major is defined as a third-year student that takes a pure mathematics

course such as real analysis on third-year level without which (s)he will not be able to

continue with postgraduate studies in mathematics. This number includes students in

applied fields such as financial or industrial mathematics but not engineering students.

Students in applied fields would be students doing a mathematics course but with main

emphasis in some applied field such as statistics, financial mathematics, physics, chemistry

or economics. For the purposes of this study this number was considered to be a subset of

the mathematics majors.For some of the data reporting we also used the term pure mathematics students. By this

terminology we mean the mathematics majors that are not studying in applied fields. This

means that the mathematics majors, in our terminology, would be the sum of the pure

mathematics students and the students in applied fields.A first-year mathematics student is defined as any student who takes a first-year course

in mathematics that will lead to second-year study in mathematics. This number includes

students in applied fields such as financial or industrial mathematics but not engineering

students. It also excludes students taking a course in mathematics as part of a study

programme in life science.The adjusted definitions as well as the changed demographic situation regarding all

universities make continuation of the graphs in the 2000 study impracticable. Where

applicable graphs of the 2000 study will be given in addition to new graphs.

5. Data from individual South African universities

We commence by listing the number of mathematics majors at the 12 participating

universities for the period 2000–2007. These numbers are given in Table 1 and represented

in Figure 1.In the 2000 study, we observed that 11 out of the 15 participating universities showed

a trend of decline in mathematics major numbers over the 1990–2000 period. Three of the

other four universities showed marginal increases whereas UNISA, the only

Table 1. Number of mathematics majors at participating universities 2000–2007.

University 2000 2001 2002 2003 2004 2005 2006 2007

NMMU 23 15 23 13 18 27 21 23NWU 12 13 32 40 53 48UCT 38 35 45 33 31 53 30 33UFS 26 16 21 22 21 41 32 33UJ 23 29 38 57 50 48 56 38UKZN 29 27 25 26 26 50 38 38UL 88 89 66 70 77 116 95 90UP 100 79 81 146 142 151 122 118US 11 17 16 12 28 32 32 19UV 39 33 30 48 47 70UWC 33 28 22 21 33 49 32 39WITS 90 92 130 160 148 138 165 106

Note: Gaps indicate missing data.


Dow

nloa

ded

by [

Uni

vers

ity o

f C

alif

orni

a, B

erke

ley]

at 2

0:26

21

Oct

ober

201

4

correspondence university to take part in the study, was the only one to show a substantialincrease of almost 25%. From Figure 1 and Table 1, it appears that 11 out of the 12participating universities show an increase over the 2000–2007 period. This data displaysdefinite signs that the previous downward trend has not only been halted but could indeedhave been reversed. Although some of these increases could be subscribed to mergersshortly after 2000, it is satisfying to observe recent and rapid increases in numbers ofmathematics majors at the Universities of the Northwest, Stellenbosch and Venda. Theonly university to show a decrease over this period is the University of Cape Town (UCT).Recent decreases in 2006 and 2007, which could perhaps be attributed to naturalfluctuation in numbers are observed at the Universities of Limpopo, Pretoria, Stellenboschand the Witwatersrand.

To honour the extent of the general trend of increase it has to be noted that in the 2000study, drops in the number of mathematic majors of ranging between 52 and 88% werereported at 7 of the 15 participating universities for the period 1990–2000, a phenomenonthat is certainly refuted in the current study.

In the 2000 study, the general downward trend for the total number of mathematicsmajors was quantified as a decrease of 32% over the 10-year period 1990–2000 and raisedalarm. Figures for the 2000–2007 period show the reversal of the previously observeddownward trend (Figure 2) and a marked overall increase of 28% is evident (missing datawas extrapolated in a few instances).

Nelson Mandela

0

10

20

30

40

00 01 02 03 04 05 06 07

North West

0

1020

3040

50

00 01 02 03 04 05 06 07

Cape Town

0

1020

30

40

50

00 01 02 03 04 05 06 07

Free State

0

10

20

30

40

50

00 01 02 03 04 05 06 07

Limpopo

0

25

50

75

100

00 01 02 03 04 05 06 07

Johannesburg

0

20

40

60

00 01 02 03 04 05 06 07

Kwazulu-Natal

0102030405060

00 01 02 03 04 05 06 07

Pretoria

0

50

100

150

00 01 02 03 04 05 06 07

Stellenbosch

0

10

20

30

40

00 01 02 03 04 05 06 07

Venda

0

20

40

60

80

00 01 02 03 04 05 06 07

Western Cape

0

10

20

30

40

50

00 01 02 03 04 05 06 07

Math majors

Applied fields

WITS

0

50

100

150

200

00 01 02 03 04 05 06 07

Figure 1. Number of mathematics majors and students in applied fields at participating universities2000–2007.


Dow

nloa

ded

by [

Uni

vers

ity o

f C

alif

orni

a, B

erke

ley]

at 2

0:26

21

Oct

ober

201

4

The steady increase for 2000–2005 has been followed by a recent decrease for 2006

and 2007. Time will tell whether there is reason for concern but speculatively one could

link the recent decrease to recent harsh economic conditions and more stringent

enrolment requirements. We report on this observation subsequently as more data is

presented.The observed decline from 2005 to 2007 is mirrored by the intake of first-year

mathematics students as shown in Figure 3 and adds more substance to the speculative

reasons of harsh economic conditions and more stringent enrolment requirements.

Figure 3 represents the mathematics major numbers as percentages of the 2000 numbers

(missing data for early years in was extrapolated two cases). A gratifying observation is the

general trend of increase that is also observed for the first-year numbers. The first-year

numbers are up by 20% over the 2000–2007 period. The surprising and pleasurable

observation is that the growth in the number of mathematics majors has surpassed the

growth in the first-year numbers; 28% for mathematics majors as compared to 20% for

first years. In 2005, the growth in mathematics majors peaked at an increase of 55% over

the 2000 numbers compared to 26% for first-year numbers.

6. Natural science student numbers

Data on the number of students studying in the natural sciences that are nationally enroled

at all South African universities obtained from the website of the national department of

education [18] shows a pattern of increase similar to that of the mathematics majors.

Yet this data also puts a slight damper on the elation with which the observations of

80

100

120

140

160

00 01 02 03 04 05 06 07

Math majorsFirst years

Figure 3. Percentage growth in first year and mathematics major numbers 2000–2007.

0100200300400500600700800

0100200300400500600700800

00 01 02 03 04 05 06 0790 91 92 93 94 95 96 97 98 99 00

Figure 2. Total number of mathematics majors at the participating universities 1990–2000 (left) and2000–2007 (right).


Dow

nloa

ded

by [

Uni

vers

ity o

f C

alif

orni

a, B

erke

ley]

at 2

0:26

21

Oct

ober

201

4

increase in mathematics majors have been reported on so far. Percentage-wise science

student numbers have consistently outperformed mathematics major numbers. A positive

trend, however, is that mathematics majors have been increasing at the same rate over the

last 5 years. An interesting observation is that science student numbers do not display the

recent downwards trend that was observed for mathematics majors, an observation of

concern.

7. The impact of diversifying into applied fields

The 2000 study reported on recoveries of dwindling mathematics major numbers taking

place at certain institutions where new, more pragmatic mathematics courses had been

introduced. One such field was financial mathematics, a field that proved to be

attractive to many students, probably because of the excellent career options. The

disappointing trend, observed in Figure 4, is that although the applied fields promised

to boost numbers and take off in an impressive manner, this promise was not delivered

in full. For the period from 2002 to 2005 numbers in applied fields thrived but

subsequently failed to keep up the pace. Numbers in the pure field also experienced

a short-lived growth spurt from 2004 to 2005. Unfortunately numbers in both pure and

applied fields have shown recent decreases. This may be because student output

numbers have caught up with the market demand in South Africa and that

employment opportunities are not that abundant any longer.Data for only 10 universities were used for creating Figure 5 as numbers in applied

fields for Nelson Mandela Metropolitan University (NMMU) and UJ were not available.Actual numbers of mathematics majors in pure and applied fields are given in Table 2.From Figure 5 and Table 2, diversification into applied fields does not, at first glance,

appear to have been as successful as was anticipated. For a closer investigation into this

matter we turn to a few individual universities in order to address general issues.

8. Individual universities

Table 3 represents the increases/decreases percentage-wise of mathematics majors over the

2000–2007 period. We select the University of Venda, the University of Northwest and the

80

100

120

140

160

180

00 01 02 03 04 05 06

Mathematics majors

Science students (national)

Figure 4. Percentage growth in science students (nationally) and mathematics majors 2000–2006.


Dow

nloa

ded

by [

Uni

vers

ity o

f C

alif

orni

a, B

erke

ley]

at 2

0:26

21

Oct

ober

201

4

NMMU for closer inspection. The first two Universities were selected because of their high

percentages of increase and the third university was selected because it showed no increase

or decrease.

9. University of Venda

The University of Venda has shown an increase in mathematics majors of almost 80%

over the 2002–2007 period. Table 4 shows that between 2002 and 2004 the number of

first-year students fluctuated somewhat without showing any clear pattern, after which

a clear upward trend emanated. The explanation for the upward trend lies in the fact that

80

100

120

140

160

00 01 02 03 04 05 06 07

Math majors (Pure)Math majors (Applied)

Figure 5. Percentage growth of mathematics majors in pure and applied fields.

Table 4. Mathematics student numbers at the University of Venda.

2002 2003 2004 2005 2006 2007

First years 110 115 102 156 213 243Math majors 39 33 30 48 47 70Applied math majors 18 18 17 17 6 6

Table 2. Numbers of mathematics majors in pure and applied fields.

2000 2001 2002 2003 2004 2005 2006 2007

Pure 173 187 153 163 149 253 217 217Applied 291 245 304 373 419 465 429 377

Table 3. Percentages increase/decrease of mathematics majors from 2000 to 2007.

NMMU NWU UCT UFS UJ UKZN UL UP US UV UWC Wits Total

0% " # " " " " " " " " " "

380% 13% 27% 65% 31% 2% 18% 72% 79% 18% 18% 26%


Dow

nloa

ded

by [

Uni

vers

ity o

f C

alif

orni

a, B

erke

ley]

at 2

0:26

21

Oct

ober

201

4

the year 2005 saw the ministry allocate funding to support school teachers who wanted to

enrol for degree programmes. This support led to a steady increase in numbers of first-year

students as more and more teachers became aware of the sponsorship.Unfortunately there also appears to be a large attrition rate. For example, 102 students

registered for first-year in 2004 whereas only 47 registered for a third-year analysis course

in 2006, meaning that more than half the students decided not to continue with

mathematics. The reason for the large attrition rate could lie in the fact that teachers

do not need more than second-year level mathematics for teaching mathematics up toGrade 12 level. Rather than lament the loss of half the students it is commendable that

many students do pursue mathematics at third-year level resulting in a clear boost for the

numbers.Diversification into applied fields is clearly not strong at the University of Venda and

numbers have dwindled steadily over the past 8 years. The explanation offered by staff isthat teaching applied mathematics requires skilled manpower and it takes time to acquire

the necessary expertise.The successful general increase in numbers at the University of Venda is attributed

to more teachers enroling for a degree, a commendable action. Traditionally, many

mathematicians were originally teachers who decided to further pursue a love and talentfor mathematics after many years of teaching. Unfortunately, mathematics teacher

training at most universities happens in the education faculty and courses presented at

mathematics departments are not required. Table 5 shows that only half of participating

mathematics departments provide trainee teachers with mathematics courses.

At the University of Western Cape the BSc Education degree has been replaced by a

B Education degree, presented by the education faculty that no longer require students to

do mathematics as a major subject. Most students now only do a semester of second-year

mathematics. This is in accordance with the new requirements for teacher training by the

national department of education.

10. University of Northwest

The University of Northwest shows a trend of increase in first-year numbers with numbers

more than doubling over the last 5 years (Table 6). In addition, and probably as a result of

Table 6. Mathematics student numbers at the University of the Northwest.

2000 2001 2002 2003 2004 2005 2006 2007

First years 89 92 137 262 258 208Math majors 10 10 12 13 32 40 53 48Applied math majors 3 1 11 28 34 36

Note: Blank cells are due to missing data.

Table 5. Training of mathematics teachers.

NMMU NWU UCT UFS UJ UKZN UL UP US UV UWC WITS

Math dept X X X X X XEducation X X X X X X


Dow

nloa

ded

by [

Uni

vers

ity o

f C

alif

orni

a, B

erke

ley]

at 2

0:26

21

Oct

ober

201

4

the increasing first-year numbers, the numbers of mathematics majors are also increasing

and have grown almost fivefold. A closer look at these numbers reveal that the increase in

mathematics majors can almost exclusively be attributed to the increase in applied

mathematics majors. The university maintains that the growth in numbers is due to

a successful programme in financial mathematics and risk analysis that attracts students

with excellent ability from school level. They say that in South Africa this programme is

supported by a large commercial bank and students coming to university can find

employment with a qualification in mathematics, other than in education. They view this

applied field as a window of opportunity that opened for mathematically gifted students.Another university that presents a successful programme in financial mathematics is

the University of Pretoria. For the past 6 years the applied mathematics students (mainly

financial and actuarial mathematics students) have provided 80% or more of the total of

the mathematics majors. Universities where little diversification into applied fields took

place, such as at the UCT, one of the strongest traditional universities, numbers have not

increased. UCT is, in fact, the only university to show a decrease in numbers of

mathematics majors.At universities where financial mathematics is presented, it has certainly proved to be

a lifeline. The overall numbers for applied fields do not do justice to pockets of excellence

such as pinpointed here.The applied field of mathematical epidemiology is considered as the field of the future

and is of particular importance in a country such as South Africa. Yet again expertise in

this field is not easy to come by and this aspect certainly could be a drawback to

universities that would consider this option of diversification.

11. The NMMU

The NMMU is a result of the merger process of the new millennium. Two former

universities and a technikon merged to form a new comprehensive university. The

merger took place at the beginning of 2005, claiming (on their website NMMU [19] to

bring together the best traditions of technikon and university education. Although

a generally thriving institution, mathematics does not seem to attract increasing

numbers (Table 7). The mathematics major numbers have been more or less stable over

the 2000–2007 period but first-year numbers show a decrease, despite overall numbers

increasing at NMMU. Mathematics staff complain about the calibre of student that

they attract and the perceived increase in under preparedness of students entering the

university.These problems experienced by the NMMU are representative of a larger national

dilemma. The former school system has over the last few years been replaced by an

outcomes-based approach that has received a fair amount of criticism and has undergone

many changes during the implementation. In 2007 and 2008, students who had been

partially subjected to the new schooling system entered university and in 2009 students

Table 7. The Nelson Mandela Metropolitan University (NMMU).

2000 2001 2002 2003 2004 2005 2006 2007

Math majors 23 15 23 13 18 27 21 23


Dow

nloa

ded

by [

Uni

vers

ity o

f C

alif

orni

a, B

erke

ley]

at 2

0:26

21

Oct

ober

201

4

who have only been subjected to the new schooling system will be entering the university.A number of universities have raised the entrance requirements for enroling intoa mathematics degree based on experiences of students not being able to cope with thedemands of university mathematics.

There is a high failure rate on third-year level at NMMU as reported by staff. Puremathematics is not considered as an attractive option, according to staff, and students aremore inclined to venture into career oriented study programmes because of morefavourable job opportunities and promotion prospects.

The data from NMMU does not bode well for the future of mathematics as anacademic discipline. This fledgling comprehensive university is trying to establish itself butmathematics-wise is struggling to succeed.

12. Conclusions

The bleak picture regarding the numbers of mathematics students, painted in 2000, isconsiderably brighter at present. There is a definite upward turn in the total number ofmathematics majors for the 2000–2007 period. The diversification into applied fields hashad a positive effect but has not been the overwhelming success story that was anticipated.The past 2 years has also witnessed a general downward trend in numbers that one shouldbe alerted to. Mathematics does not seem totally out of dire straits yet. The concernsvoiced over the world still prevail in South Africa as well.

Universities that have actively pursued diversification into applied fields arecertainly reaping the benefits of substantial increases in numbers of mathematicsmajors. Our study has shown that universities should not necessarily set their sights onskills-demanding fields such as financial mathematics for advancing numbers ofmathematics majors. Location of teacher training in mathematics departments has thepotential of positively impacting on the numbers and standard of mathematics inSouth Africa.

Concern regarding the mathematical calibre of school-leaving students has been raisedat a number of universities. A solid grounding at school level is paramount for success atuniversity level. A developing country such as South Africa cannot afford a school systemthat leaves students under prepared for university studies.

South Africa is still in a state of transition and change. The change of governmenta decade and a half ago has been followed by a restructuring and merger of universities aswell as a completely revised schooling system. Amidst all the turmoil mathematicsdepartments are experiencing pressure to increase numbers for survival and to deliverthinking and skilled students to enter the job market. This article serves as a report of thecurrent state of affairs regarding mathematics majors but can by no means report ona stable, settled situation. However, the situation has improved over recent years and thereare many positive aspects to build on. It will remain important to keep a finger on thepulse of mathematics in South Africa.

13. Recommendations

In spite of the improvement in the numbers of students getting degrees in mathematicssince 2000, the mathematics situation in South Africa is still critical. Performance ininternational arenas, such as TIMSS, shows that we need many more people gettinginvolved in mathematics. To sustain international competitiveness in science and


Dow

nloa

ded

by [

Uni

vers

ity o

f C

alif

orni

a, B

erke

ley]

at 2

0:26

21

Oct

ober

201

4

engineering, we need a focussed, long-term, comprehensive initiative by the public and

private sectors to:

. Build public support for making improvement in mathematics performance

a national priority.. Devise and use a variety of incentives to motivate South African students and

adults to study and enter mathematics careers.. Attract and retain good mathematics students from around the world to study for

advanced degrees and stay to work in the country.

Perhaps the most serious problem is the shortage of well-trained teachers at primary and

secondary schools. The teacher talent pool is further depleted by the private sector.

University graduates who major in mathematics and science can earn far more as private

sector employees than as teachers. Higher-aptitude students also find performance-based

compensation in the private sector more appealing than the traditional teacher salary

schedule based on years of experience and degrees.Secondary school teachers, giving advice to learners on future careers are in many

instances ignorant about possible employment opportunities in mathematics. High school

and university students need better information about the wide range of opportunities that

mathematics degrees open up to them.Universities should be encouraged and funded for pursuing study programmes in

applied fields. Such programmes seem to be more attractive to potential students but lack

the necessary impetus, probably as a result of a lack of skills and infrastructure.

References

[1] J. Engelbrecht and A. Harding, Is mathematics running out of numbers? S. Afr. J. Sci. 99 (2003),

pp. 17–20.[2] J. Jansen, Mergers in South African higher education: Theorising change in transitional contexts,

Politikon: S. Afr. J. Polit. Stud. 30 (2003), pp. 27–51.[3] D. Holton, (ed.), The Teaching and Learning of Mathematics at University Level (An ICMI

Study), Kluwer, Dordrecht, 2001.[4] J.C. Engelbrecht, What has happened to undergraduate mathematics teaching over the past ten

years? An international survey of undergraduate mathematics courses, presentation given at the

ICMI Study Conference on the Teaching and Learning of Mathematics at University Level,

Singapore, December 1998.[5] D. Lutzer, J. Maxwell, and S. Rodi, CBMS 2000: Statistical Abstract of Undergraduate

Programs in the Mathematical Sciences in the United States, American Mathematical Society,

Providence, RI, 2002.[6] D. Loftsgaarden, J. Maxwell, and K.R. Priestly, 2000 Annual survey of the mathematical sciences

(third report), Notices Am. Math. Soc. 48 (2001), pp. 819–828.[7] D. Loftsgaarden, J. Maxwell, and K.R. Priestly, 2001 Annual survey of the mathematical sciences

(third report), Notices Am. Math. Soc. 49 (2002), pp. 928–938.[8] National Science Board, Science and Engineering Indicators 2002 (NSB-02-1), National Science

Foundation, Arlington, VA, 2002.[9] D.J. Lutzer, Mathematics majors 2002, Notices Am. Math. Soc. 50 (2003), pp. 235–237.[10] S.A. Garfunkel and G.S. Young, Mathematics outside of mathematics departments, Notices Am.

Math. Soc. 37 (1990), pp. 408–411.[11] S.A. Garfunkel and G.S. Young, The sky is falling, Notices Am. Math. Soc. 45 (1998),

pp. 256–257.


Dow

nloa

ded

by [

Uni

vers

ity o

f C

alif

orni

a, B

erke

ley]

at 2

0:26

21

Oct

ober

201

4

[12] Business Roundtable, Tapping America’s potential: The Education for Innovation Initiative,

Business Roundtable, Washington, 2005.

[13] G. Davis, Mathematicians and the market. Notices Am. Math. Soc. 44 (1997), pp. 1307–1315.[14] P. Phipps, J.W. Maxwell, and C. Rose, 2007 Annual survey of the mathematical sciences, First

report: Preliminary report on the 2006–2007 new doctoral recipients, Notices Am. Math. Soc. 54

(2008), pp. 253–263.

[15] R.E. Reys, Doctorates in mathematics education – an acute shortage, Notices Am. Math. Soc. 47

(2000), pp. 1267–1270.

[16] J. Thomas, Mathematical sciences in Australia: Looking for a future. FASTS Occasional Paper

Series 3, FASTS, Deacon West, Australia, 2000.

[17] National Committee for the Mathematical Sciences of the Australian Academy of Science,

Mathematics and statistics: Critical skills for Australia’s future. The national strategic review

of mathematical sciences research in Australia, Australian Academy of Science, Canberra,

Australia, 2006.[18] Department of Education. Education statistics in South Africa at a glance 2000–2006. (Retrieved

15 September 2006) (2000–2006). Available at http://www.education.gov.za/emis/emisweb/

statistics.htm

[19] NMMU (Current). Official website. Available at http://www.nmmu.ac.za/


Dow

nloa

ded

by [

Uni

vers

ity o

f C

alif

orni

a, B

erke

ley]

at 2

0:26

21

Oct

ober

201

4

Documents

New numbers in mathematics in South Africa