Elton 1986_Aspects of Mathematics Education in Third World Universities

8/3/2019 Elton 1986_Aspects of Mathematics Education in Third World Universities

1/28

Aspects of Mathematics Education in Some Third World UniversitiesAuthor(s): M. E. A. EltomSource: Educational Studies in Mathematics, Vol. 17, No. 2 (May, 1986), pp. 165-191Published by: SpringerStable URL: http://www.jstor.org/stable/3482534 .

Accessed: 01/09/2011 10:27

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of

content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms

of scholarship. For more information about JSTOR, please contact [email protected].

Springeris collaborating with JSTOR to digitize, preserve and extend access toEducational Studies in

Mathematics.

http://www.jstor.org
http://www.jstor.org/action/showPublisher?publisherCode=springerhttp://www.jstor.org/stable/3482534?origin=JSTOR-pdfhttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/stable/3482534?origin=JSTOR-pdfhttp://www.jstor.org/action/showPublisher?publisherCode=springer


2/28

M. E. A. EL TOM

ASPECTS OF MATHEMATICS EDUCATION IN SOMETHIRD WORLD UNIVERSITIES*

ABSTRACT. Information on principal aspects of the present state of mathematics education in18 third world universities is presented. The principal tool used in collecting the informationwas a questionnaire which was widely distributed. Analysis of the information revealsimportant variations and similarities in the programs and structures of responding institutions.Some weaknesses are identified.

1. INTRODUCTIONConcern with the problem of developing mathematics in third worldcountries (TWCs) and awareness of the leading role of these countries'university mathematics departments in tackling the problem leads one toreflect on the goals of teaching mathematics at university level. It isgenerally agreed that one of these goals is to serve the societies whichsupport the institutions in question, and in the case of TWCs, I have arguedelsewhere (El Tom, 1980, 1984) that university mathematics departments inmost countries of the region should adopt the utilitarian goal as theprincipal one for teaching mathematics.

Acceptance of this position means that mathematicians and mathematicsdepartments must be seen, at least by elites, to be contributing effectivelytothe solution of major societal problems. A proper assessment of the extentto which they are performing this role requires, in the first place, adequateknowledge of the actual mathematics teaching-learning situation in uni-versities. It also requires a knowledge of the nature of links that are forgedbetween a particular mathematics department and other (scientific, in-dustrial, educational, commercial, etc.) institutions in society at large. Somedetailed information on several aspects of both requirements is presented inthe paper.

The analysis of the presented information (identification of similaritiesand differences and dominant factors which seem to shape activities) runsinto certain methodological difficulties. An obvious first difficulty is thewide political, economic, social and cultural differencesbetween the variouscountries. A standard way of handling this difficulty is to categorizecountries according to a specific indicator (e.g., cultural). Even then thedifficulty is not satisfactorily resolved. For, if one considers the specific*This is an extended version of a paper presented to the Symposium on the State of Physicsand Mathematics in Africa, held at ICTP, Trieste, Italy, 8-13 October, 1984.Educational Studies in Mathematics 17 (1986) 165-191.Q 1986 by D. Reidel Publishing Company.


3/28

166 M.E.A. EL TOM

example of two Latin American countries such as Brazil and Peru then,given the great differences between their higher educational systems, it isapparent that one is unlikely to gain much insight into the type of issuesconsidered here by placing them in one category. Another difficulty has todo with countries having a large number of universities. For, unless one isprepared to sift through enormous amounts of data, it would not be feasibleto make meaningful comparisons between such countries, on the one hand,and others with a few universities, on the other.

In order to avoid such difficulties, two groups of countries have beenexcluded from the present study. First, those countries possessing a ratherextensive higher educational system such as Brazil and India. Secondly,countries whose higher educational systems are at present relatively in-sufficiently developed such as Guinea Bissau and Oman.

The information presented in the paper was obtained using a question-naire which was designed and despatched in April 1984 to at least onemathematics department in 70 TWCs. Only 18 responses were received.This obviously sets an important limitation on the scope of the study.Nonetheless, I believe that the nature of the responding departments is suchthat it would be reasonable to consider them representative of a muchlarger group of departments.

Some general features of the questionnaire and the responding in-stitutions are given in the next section. In Section 3, information on variousfacets of the curriculum is presented. Information on postgraduate studiesand employment opportunities for mathematics graduates is given inSection 4 and 5, respectively. Partial data on academic staff and informationon services performed by departments to local institutions is presented inSection 6. Section 7 summarises the main findings.

2. GENERAL FEATURES OF THE QUESTIONNAIREAND RESPONDING INSTITUTIONS

The questionnaire consisted of ten sections comprising a total of 34questions. Below are given the headings of the sections and the number ofquestions in each. (Those interested in further details may obtain a copy ofthe questionnaire by writing to the author.)A. General information (4)

B. Curricula and degree structures (6)C. Staff (4)D. Undergraduate students (3)E. Postgraduate students (9)


4/28

MATH EDUCATION IN THIRD WORLD UNIVERSITIES 167

F. Resources (1)G. Links with society (3)H. International links (4)I. Comments/Remarks.

Responses to the questionnaire were received from only 18 mathematicsinstitutions. Some general information on respondents is given in Tables I,II, and III. Certain interesting features may be deduced from these Tables.

First, however, let us note that there are important differences in theeducational systems of the responding institutions' countries. For economic,political and/or historical reasons they are all influenced to a more or less

TABLE IGeneral features of responding institutions (1983/84)

Year of No. of Further remarksestablish- institutionsment in countrywith similarfunctionsMathematics Department,aUniversity of:Abidjan/Ivory Coast 1960 0 Information in the quest-ionnaire is given for boththe dept. of mathematicsand the institute deRecherches Mathematiques.Addis Ababa/Ethiopia 1961 2 This is the oldest, largest,most prestigious department

and the only one which runsa postgraduate program.Ahmadu Bello/Nigeria 1962 n.a.b The largest in Nigeria interms of student enrolment.Assiut/Egypt 1957 13Ateneo de Manila/ 1952 10 One of the most prestigiousPhilippines departments.Bujumbura/Central Africa 1968 0Cairo/Egypt 1925 20 The oldest, largest andmost prestigious department

in Egypt.Costa Rica 1954 1 The oldest, largest andmost prestigious departmentDar es Salaam/Tanzania 1965 0Ghana 1948 3 The oldest department inGhana.Habana/Cuba 1962 3 The oldest, largest andmost prestigious department.Ife/Nigeria 1962 27


5/28

168 M.E.A.ELTOM

TABLE I - (continued)Year of No. of Further remarksestablish- institutionsment in country

with similarfunctions.Mathematics Department,*a

University of:Khartoum/Sudan 1978 1 Prior to 1976, the year inwhich three mathematics unitswere pooled in a 'School of

Mathematical Sciences', theB.Sc. mathematics degree wasawarded by the Faculty ofScience, established in 1947.The other dept, belongs to theUniversity of Cairo, KhartoumBranch, Khartoum.

Malaya/Malaysia 1959 5 The oldest, largest and mostprestigious department.Nairobi/Kenya 1960 2 The oldest, largest and most

prestigious department.Philippines 1910 3 The largest and most prest-igious department.South Pacific/Fiji 1969 0Yaounde/Cameroon 1964 0

a Here and throughout the paper the word 'department' designates an organizational unitresponsible for teaching mathematics to undergraduates and/or postgraduates in a university.b Not available.

degree by corresponding Western systems. For instance, Abidjan,Bujumburaand Yaounde belong to a French tradition; Ahmadu Bello, Dares Salam, Ghana, Ife, Khartoum, Malaya and Nairobi belong to a Britishone; Addis Ababa is known to have been established under Americaninfluence; Ateneo de Manila, Costa Rica and Philippines show importanttraces of the American system; and, finally Assiut and Cairo are difficult toplace within any single Western tradition of higher education. Theseinfluences will become clearer in later sections.Table I shows that some institutions (the Egyptian, Nigerian and Filipinoones) are situated in countries with a relatively larger number of un-iversities, whereas the remaining institutions are either the only ones in thecountry (Abidjan, Bujumbura, Dar es Salam, South Pacific, Yaounde) orelse part of a relatively small system (Addis Ababa, Costa Rica, Ghana,Habana, Khartoum, Nairobi).


6/28

MATH EDUCATION IN THIRD WORLD UNIVERSITIES 169TABLE II

No. of first year students enrolled for a bachelor/licencedegree in the department

1980/81 1981/82 1982/83 1983/84Mathematics Department, University of:Abidjan 100 150 200 280Addis Ababa 136 95 159 140Ahmadu Bello 85 100 90 80Assiut n.a. n.a. n.a. 100Ateneo de Manila 22 24 27 23Bujumbura 8 10 12 14Cairoa 100 100 100 100Costa Rica 130 135 128 135Dar es Salaam 50 50 40 25Ghana 60 60 60 n.a.Habanab 400 400 400 400Ife 25 47 17 25Khartoum' - 25 20 40Malaya 75 118 93 122Nairobi 160 180 160 150Philippinesb 274 222 437 530South Pacific 30 40 40 50Yaounde 100 100 100 100Numbers given include (about 30-50) students who would follow study courses in physics asfrom their second year in university.'Although the questionnaire asks explicitly for the number of first year students admitted toread for an undergraduate degree offered in the department, it is possible that the numbersgiven here include those who take mathematics as a minor or ancillary subject.cFaculty of Science students reading for a combined degree (such as maths-physics) are notincluded.

The same table also shows that they vary in age from 6 (Khartoum) to 74years (Philippines).

Table II shows that the institutions vary in the size of their under-graduate student population.

Finally, in the section on resources, departments were asked to indicateaccording to a 5-point scale (very poor-excellent) the degree of availabilityof undergraduate and postgraduate texts, periodicals, computing facilities,travel and research funds and audio-visual aids. A summary of the re-sponses is given in Table III. In general. however, most departments seemto have a satisfactory situation as regards both undergraduate and post-graduate texts and computing facilities; and, not unexpectedly, to be poorin travel and research funds. This feature is obviously relevant to the issuesconcerning external aid.


7/28

170 M.E.A. EL TOM

TABLE IIIAvailability of Resources/Materials (1983/84)

Unsatis- Satis- Very Remarksfactory factory goodMathematics Department,University of:Abidjan x The department has avery good stock ofundergraduate texts butis poor in periodicals,travel and research

funds.Addis Ababa xAhmadu Bello xAssiut xAteneo de Manila xBujumbura xCairo xCosta Rica xDar es Salaam x Poor in everythingexcept travel and

research funds andpostgraduate texts.Ghana x Very good in computingfacilities.Habana x Poor in everythingexcept undergraduatetexts.Ife xKhartoum x Very poor in audio-visual aids.Malaya x Very good stock of bothunder- and postgraduatetexts.Nairobi x Very good computingfacilities and stock of

undergraduate texts.Philippines x Excellent stock ofundergraduate texts.South Pacific xYaounde x Only department with

a very good stock ofaudio-visual aids.

In closing this section, I would like to point out that the variationsbetween departments noted above cut across each other. Moreover, weshall see later that they furthervary in their functions. For instance, whereasin the university of Ghana there are separate departments for mathematics,


8/28


statistics and computer science, in the university of Khartoum the threedisciplines come under a single administrative unit. Another instance is thatof the responsibility for teaching mathematics to future teachers of mathe-matics and to engineering students (see Section 3 below).

3. ASPECTS OF THE UNDERGRADUATE CURRICULUMIn this section, I shall present and discuss information on degrees offered,syllabi and assessment procedures for undergraduate studies.

3.1. Nature of Degrees OfferedTable IV below shows the subjects in which courses of study leading to abachelor/licence degree may be followed in the departments listed inSection 1 above. Several features of the table are worthy of comment:

(i) Until recently, many universities offered combined degrees in whichthe non-mathematics subject would typically be physics or chemistry. Now;however, more universities are offering combined degrees in which statistics(10) and computer science (9) are typical second subjects.(iil The number of universities offeringa maths with education degree (8)suggests that several universities are responsible for teaching mathematicsto future secondary school mathematics teachers. Indeed, 15 of the re-spondents affirmed, in the questionnaire, that this is the case. The threeexceptions are the universities of Cairo, Habana and Yaounde. In the caseof Cairo university this responsibility is carried out by an independentmathematics department in the Faculty of Education, which is typical of theEgyptian system of higher education.(iii) The only departments in which one-subject specialized degrees inmathematics may be followed are those in Abidjan (2), Bujumbura (2),Costa Rica (l), Philippines (1), Habana (2) and Yaounde (1) universities.Note that the first two and the last one are francophone.

(iv) The universities of Ghana, Dar es Salaam, Malaya and South Pacificare the only ones which allow social sciences subjects to be combined withmathematics. Similarly, only Abidjan, Assiut, Malaya and South Pacificuniversities admit biology as a second subject. The universities ofKhartoum and Philippines are unique in offering a one-subject degree incomputer science.

(v) The number of degrees offered varies from I (Ateneo de Manila) to 10(Abidjan). The information given in Tables II and IV shows that thenumber of students/degree offered in 1983/84 varies from about 177(Philippines) to 2 (Bujumbura).


9/28

172 M.E.A. EL TOM

x 0 8

LU X XX X X X X=00 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 000

_ X X X X X X ~~~~X X II 0,X

()i I (#) ;x x x x x x x x x x -

3 001 2 vx x x x x x x x x 0 -

0)

x 0~~x00~~~~~~~~~~~~~~~~~~~~~~

,::3 Z V,tS

00~~~~~~c0 ~ ~ ~ ~ ~ ~ ~ ~ ~~ ~~~~~~~~~~~~~~~~~~L- x~~~~~~~~~~~~~~~~~~~~C)~~~~ C E X X X XX_

,, 8 E ~~x x x x x x x x x x x x x , e,,0 11) 0 0

A~ 0p m r _ ? E 9 ,5 * CZ

0) ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ Cx x t x 0 0z CL


10/28

MATH EDUCATION IN THIRD WORLD UNIVERSITIES 173As for the duration of undergraduate courses, the degrees offered in the

universities of Abidjan, Ahmadu Bello, Bujumbura,Dar es Salaam, Ghana,Nairobi, South Pacific and Yaounde last for 3 years. Those offered in AddisAbaba, Assiut, Ateneo de Manala, Cairo, Costa Rica, Ife and Philippineslast for 4 years. In Habana the duration is 5 years. In the case of Khartoumuniversity, the duration is 4 years for a general degree and 5 years for anhonours degree. Khartoum and Malaya universities also appear to beunique (even amongst anglophone universities) in using the general/-honours classification of their degrees (a British tradition) to indicatesignificant differences in the content of study courses (see also El Tom(1980), Section 3.1).

3.2. Courses of the UndergraduateProgramThe questionnaire contained a list of 46 topics, and departments were askedto indicate the levels (lst-5th year) during which aspects of the listed topicsare offered as part of their respective undergraduate programs. (Additionsof further topics is allowed for in the questionnaire.) The list of topics isgiven in an Appendix below.

The results are given in Table V below. Numbers 1--46 in columnsindicate the topics as they appear in the Appendix and the n-th row(1 An < 5), for each department, indicates the level (n-th year) at which someaspect of a particular topic is offered. Table V exhibits several interestingfeatures:(i) In most universities, the first two years are largely spent in covering

basic material: calculus, analysis and algebra. Much of this material is, ofcourse, a prerequisite for courses covered in subsequent years. The uni-versity of Costa Rica seems to be an exception.(ii) There are interesting variations in the treatment of geometry (18). Infour departments (Abidjan,Assiut, Bujumbura and Cairo) geometry coursesare offered in both first and second year; in four other cases (Habana, Ife,Khartoum and Nairobi) they are only offered in the first year; in SouthPacific and Yaounde only in the final year; and in five cases (Ahmadu

Bello, Ateneo de Manala, Costa Rica, Dar es Salaam and Ghana) nogeometry courses are offered at all. In Addis Ababa courses are offered inthe first and third years. In Malaya they are offered in the last two years;and in Philippines in the first and final years.(iii) In 13 departments functional analysis (8) is offered in the final yearas a culmination of a calculus-analysis sequence given in earlier years. Thefive exceptions are Addis Ababa, Ateneo de Manila and Costa Rica


11/28

174 M.E.A. EL TOM

I I

O - + + + q !C 8t !b? I ! r ' t ~~~~~~++ + I ! I I I I I I

I I e

I I 4I I NI . iNNNo00)101 I +++lC iCt |tt I I I ICl-rt I

l0 CIN+ ++lIr~~~~~~lr

.:I I tI

CO - 111111' 1 I III I

Q vo oo oo oo oo Cro O0 ooo~~~~~~~~~~~~~~~CAffCOe * F-_I

sI- CJ0 - OC -- - 00 - n r

, ~ ~ ~ ~ ~ ~ ~~ ~ ~ ~ ~ ~ ~ ~ ~ ~~~~ ~~~~~~~~~~~~~~~~~,a

CO I- - I I-S I-n I-[

I ClI o I N0

D) | < ', [ s + + + + q r~~~~~~~~~~~~~~~~~~~~~~~~~~~~n4oon

o~~~~ CZ ~ & l

Cl ClCIClCl q q > q I t ClClClI

S)Cl I lCl I I Ci IC l lCCI Ci I IClC

om Cl Cl ClsA >

Cl ClQ~~~~C o YCl ^ - s Cl -

|~~~0 0C 00 E0O ON 00000 ON 00? E


12/28


0 oal l o 00I

e e ~ ~ ~~~ ~~~~~en e e nn

00 00 -:06000

Q0% 000

0~~~~~~~~~~~~~~~~~~~~~~~~00|~ ~ ~~s so sr- let sor- so se t

I", v "r v-i vo~~v,v

00 00%( Q00 0%D s '-0 o %s

_ ~~ _

E

0 ~~~~~~E0~~~~~~

!.. 0 0I

Q I _ _ _ I~~~~t t t t !~~~


13/28

176 M.E.A. EL TOM

ff 0~~~~~~~~f

41~~~~~e 4Cn44 r-4 4 C44 4 r C4r qc r

ON olI

fr-C r--o r-r--~~~~~~~~cn r-nI--c -- II I)~~~~~cncnc

CZ

cq 0~~~~~~

cn C4 _

00 0. COI -

ci CO~~~~~~~~~

0 ~~~0- I I-~~~~~~~~~~~~~ci?I - 2~~~~~~~~~~jli 0


14/28


universities, where it appears nowhere in the program; and Bujumbura andHabana universities, where it is offered in third year. In the case ofBujumbura no further analysis courses are offered in the final year.(iv) Only eight departments (Assiut, Bujumbura, Cairo, Costa Rica, Ife,Khartoum, Malaya and Nairobi) offer any (traditional) applied mathematicscourses (26-37) in the first year; and only three (Bujumbura, Ghana andNairobi) offer a variety of such courses in the second year. No appliedmathematics courses are offered in the departments at Ateneo de Manila,Philippines, South Pacific and Yaounde. Two other departments which donot appear to emphasize applied mathematics are the ones at Abidjan andHabana. Excepting these last 6 departments, all other departments offerseveral applied mathematics courses in their final year.(v) The strongest sequence on differential equations (24, 25) is offered inthe departments at Ghana, Dar es Salaam, Malaya and Nairobi. 5 depart-ments (at Abidjan, Addis Ababa, Costa Rica, Ife and Yaounde) offer nocourses on partial differential equations (25).

(vi) There is a quasi-uniformity amongst departments in their treatmentof algebra (12--16).For most of them, the typical sequence is: linear algebra-- group theory-- rings and modules-- field theory (12--3-14-15). The onlyexceptions to this are the departments at Ateneo de Manila, Costa Rica,Dar es Salaam, and South Pacific universities.(vii) Important differences also exist between departments in their treat-ment of probability (11) statistics (38) and operations research (39). Exceptfor the departments at Ahmadu Bello, Ghana, Ife, Malaya, Nairobi andSouth Pacific no department introduces any of these topics in the first year.In the case of the departments at Abidjan, Assiut, Ateneo de Manila, Cairoand Yaounde, no statistics courses are offered before the third year. Nooperations research courses are offered in the departments at Addis Ababa,Cairo and Ghana. Moreover, the department at Cairo offers no courses onprobability; and at Addis Ababa, the department introduces probabilitycourses in the third year as an elective. These remarks need to be read inconjunction with the information shown in Table IV above concerning thedegree in Maths with statistics.

(viii) Most departments offer their undergraduate students courses onnumerical analysis (42) and computers (43). However, in three cases(Abidjan, Ateneo de Manila and Yaounde) no numerical analysis coursesare offered (c.f. entry in Table IV against Maths with Computer Science).Moreover, it appears that the strongest offeringsin these topics are given bythe departments at Ahmadu Bello, Bujumbura, Ghana, Habana, Ife,Khartoum, Malaya and South Pacific universities. It is interesting to note


15/28

178 M.E.A. EL TOM

here that none of the departments at Ghana, Ife Malaya or South Pacificuniversities offer a degree in maths with computer science (see Table IVabove). The information in Table V does not of course reveal the extent towhich students actually use a computer. In Section 2 above some infor-mation on availability of computing facilities is given.

(ix) As for mathematical education (46), except for the departments atAddis Ababa and Ife universities, both of which provide a sustainedtreatment of aspects of the discipline, it is either not introduced at all(Ahmadu Bello, Assiut, Ateneo de Manila, Cairo, Costa Rica, Dar esSalaam, Ghana, Habana, Malaya, Nairobi, South Pacific, Yaounde), orappears to be treated incidentally (Abidjan, Bujumbura, Khartoum,Philippines). Again compare the relevant entry in Table IV above.

It is interesting to note at this point that the departments at Bujumburaand Ife universities are unique in offering courses on both the history andphilosophy of mathematics (3 and 4). At Khartoum university a project onhistory of mathematics is offered as an elective for fifth year students.History of mathematics is also offered for final year students at bothHabana and Philippines universities, and for third year students at Malayauniversity.

(x) My final observations concern discrete mathematics (17), mathemati-cal modelling (40) and biomathematics (41). These topics have only recentlybeen included in undergraduate programs on an international scale. Thedepartments at Ahmadu Bello, Habana, Ife and Philippines universitiesoffer courses in all three topics. The departments at Costa Rica offerscourses in both modelling and biomathematics in second year. The pro-grams at both Cairo and Khartoum universities include courses on discretemathematics in the fourth year, and in the latter university students areintroduced to modelling in the fifth year. Also students at Nairobi areintroduced to modelling in their final year. The department at Bujumburauniversity offers courses on modelling in both the third and fourth years.The department at Malaya offers discrete mathematics in the last two years.The remaining eight departments do not introduce their undergraduatestudents to any of the three topics.

3.3. Assessment ProceduresThe following five methods of assessing students' academic achievementwere listed in the questionnaire.

(a) Oral examinations.(b) N-hour written paper at the end of an academic session (or semester).


16/28


(c) Open book examinations.(d) Continuous assessment.(e) Projects and/or essays.Departments were asked to indicate the extent to which they used each of

these methods at the undergraduate level according to the following scale:0. Never used.1. Used with a few courses.2. Used with many courses.3. Used with most courses.4. Used with all courses.

A summary of the responses is presented in Table VI below. The followingconclusions may be drawn from it.

TABLE VIMethods used to assess undergraduate students' academic achievement

Method of assessmentaOral Tradi- Open Continuous Projects(a) tional book assessment and/or(b) (c) (d) essays

(e)Mathematics Department,University of:Abidjan x xAddis Ababa xAhmadu Bello x xAssiut xAteneo de Manila xBujumbura xCairo xCosta Rica x bDar es Salam x xGhana x x bHabana b b x xIfe x xKhartoum x xMalaya xNairobi x xPhilippines xSouth Pacific x x xYaounde x x x

a Used with all courses but only in final year.b Used with many courses.


17/28

180 M.E.A. EL TOM

(i) Most departments make frequent use of continuous assessment. Theexceptions are the departments at the universities of Assiut, Bujumbura,Cairo and Malaya. Moreover, departments at Addis Ababa, Ateneo deManila and Philippines which are known to be influenced by the Americansystem rely almost exclusively on continuous assessment.

(ii) The traditional method of assessment (method b) is frequently usedby most departments. The exceptions in this case are Abidjan, Addis Ababa,Ateneo de Manila and Bujumbura universities.

(iii) Six departments (Ahmadu Bello, Dar es Salaam, Ife, Khartoum andNairobi) appear to rely almost exclusively on a combination of the tradi-tional and continuous assessment methods (b and d).(iv) The only departments which make frequent use of oral examinations(method a) are the francophone ones: Abidjan, Bujumbura and Yaounde.

(v) Methods (c) and (e) are hardly ever used by any department. Theexceptions are the departments at Assiut and Ghana universities, whichmake some use of method (c) and the department at Habana universitywhere the same method is used as a principal tool of assessment.

4. ASPECTS OF POSTGRADUATE STUDIESThe vitality of any academic institution is clearly indicated by the size andquality of its postgraduate program. Some information on the size of theseprograms is given in Table VII below; and in Table VIII information onareas in which work at the doctoral level is being carried out is given.Unfortunately, however, I have no information to present on the qualitativeaspect of these programs.Table VII shows that most departments have a (numerically) weakpostgraduate program and, moreover, most departments are still stronglydependent on institutions in industrialized countries for developing theirstaff. The departments at Assiut and Habana universities have by far the(numerically) strongest program. The table further shows that the diploma,and masters degree by research only, appear to be out of fashion. Regardingthe diploma, the only exceptions are the departments at Khartoum andHabana universities; the figure for Habana is worth noting. Table VIIIindicates that as far as staff development is concerned, seven departments(Abidjan, Ahmadu Bello, Ateneo de Manila, Bujumbura,Cairo, Costa Ricaand Ghana) emphasize pure and applied mathematics. Dar es Salaam,Habana, Khartoum and South Pacific, however, seem to be moving intonon-traditional areas. If the areas of study of locally-registered doctoratestudents in departments with three or more students is examined, Table


18/28

MATH EDUCATION IN THIRD WORLD UNIVERSITIES18

E~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~CE~~~~~~~~~~~~~~~~~

00 ~ ~ ~ ~ ~ ~ ~ ~ ~62~~~~~~~~~~~~~~~~~~~~~0Encz~~~~~~~~~~~~~~~~~~~~

L- Ln- ~ h

E

C) C) C C o 0r- )C)C n r O -

C)0~~~~C~~~~~~~~~0 -~~~~~~~~~~~~~~E E~~~~~~~~~C

C) ~ ~ ~ ~ ~ 0 2 ~ C .- C;C~~~~~~~~~0 C)) - ) c " ' C)~~2 ~0~ . m U


19/28

182 M.E.A. EL TOM

rA(UcoE

7F E r. cnCZ

CZco CZ .- 0.U - E ECZ CZr- rn E.2 Q CZ U.CZ cn En :: cir cnZ 0 &- coCZ E 0 ct 0 co CJ cn -C C E= r CZ ECZ E E EE tuE C-t Q.Z CZ 0. C.S 0 0 71 la3crE v UE E

UrU EU CZ_r_ U C EE cnC cn U--fl w EZ CZ cnC UCZ C)

Ecn CZ CZiE E E CLM to to CZZ C - -p

C/)- z < Z 1cn Lt r Cl CZ

E C :3 CZCZ w cn 7;Z 1.2< < U U a Q = . 4 2 Z


20/28

MATH EDUCATION IN THIRD WORLD UNIVERSITIES 183VIII clearly shows that the emphasis is on pure mathematics. Indeed, theproportions of those students working in areas of pure mathematics,(traditional) applied mathematics and in other areas, are about 582, 62'/and 36?%s,espectively. One might expect such students to become staffmembers of other universities or institutes of higher education uponcompletion of their studies.

Another useful indicator of the vitality of an academic institution is theextent of organized extra-curricular activities such as seminars and con-ferences held there. In Table IX below, information relevant to this in-dicator is given. The table suggests that there is in general little scientificinteraction between departments and the surrounding local environment.On average one local and four foreign speakers gave talks in each depart-ment during 1983/84. The departments at Cairo and Habana seem to be

TABLE IXMagnitude of scientifically advanced extra-curricular activitiesorganized by departments (1983/84)

Seminars/week Visitors invited to give talks ScientificconferencesLocal Foreign during 1979/80visitors visitors 1983/84

Mathematics Department,University of:Abidjan > 1 0 6 3Addis Ababa 1 0 2 0Ahmadu Bello 1 Several 0 lAssiut (1/month) 1 1 0Ateneo de Manila (Bi-weekly) 1 2 3Bujumbura I 0 4 lCairo 1 5 12 4Costa Rica > 1 0 3 5Dar es Salaam (Bi-weekly) 2 1 lGhana (1/month) 0 0 0Habana (Bi-weekly) 5 10 3Ife 1 4 1 OaKhartoum 1 0 4 bMalaya (I/month) 0 7Nairobi 1 2 1Philippines (1/month) 3 8South Pacific (1/month) 0 5 0Yaounde >1 0 2a Two are planned for 1985.bThis was a symposium extending over one year.


21/28

184 M.E.A.ELTOM

more active than others. It is rather surprising to note that the departmentat Assiut, which has one of the two largest postgraduate programs, appearsto be the least active (as defined in the context of Table IX).

5. EMPLOYMENT OPPORTUNITIESIn this section I shall look at employment opportunities for mathematicsgraduates of the 18 respondents to the questionnaire and try to relate thedata to relevant aspects of curricula on the one hand, and to the degree ofpopularity of mathematical sciences, on the other.

In an earlier paper (El Tom (1980), p. 434) I discussed the functionswhich third world mathematicians can usefully perform in their respectivesocieties and concluded that: "Third-world countries need mathematiciansprimarily to teach mathematics; to help in the various stages of social andeconomic planning processes and in the area of computer applications."

This conclusion seems to be largely confirmed by the information inTable X. In the questionnaire, departments were asked to indicate the fivelargest employers of their graduates. Only seven departments were able toindicate more than three distinct employers. It is obvious from the tablethat apart from schools and the civil service there are few employmentopportunities for mathematicians. Given the low level of technological andscientific development in the third world, it is not surprising that industryand research (outside universities) offer practically no jobs formathematicians.

Since a good many mathematicians end up as school teachers, it shouldbe asked whether they are adequately prepared for this job. Table V andremark (ix) in Section 3 above strongly suggest that in the majority of casesundergraduate training is hardly adequate for a teaching job. Of course it ispossible that in certain cases the graduates in question undergo a limitedperiod of pre-service teacher training and in this way the inadequacy oftheir initial training is partly compensated for. Even so, the inadequacy oftheir initial training still stands.

In view of the low status of the teaching profession in most third worldcountries and the limited job market for mathematicians outside teaching,one would expect mathematical studies to be unpopular in these countries.Table XI below gives an indication of the extent to which this is true or not.Departments were asked to indicate whether, for first year students, adegree in a mathematical discipline is a first choice for most, many, a fewstudents or a last resort for may. It appears that outside Cameroon, Egypt,Fiji, Ivory Coast and the Philippines, studies in mathematical sciences arenot popular.


22/28


>0

00

m CZ

0

C :' X _Ic-1I I I r _-I I-_IIII I0

E

X l-_ .

E 3

E~~~~

0

0 U

0 CZS < ,<


23/28

186 M.E.A. EL TOM

TABLE XIThe degree of popularity of studies in mathematical sciences amongst first year students

First choice for Last resortfor manyMost Many A fewMathematics Department,University of:Abidjan - x -Addis Ababa - - xAhmadu Bello - x - -Assiut - x - _Ateneo de ManilaBujumbura - xCairo - xCosta Rica - - x -Dar es Salaam - - x -Ghana - - x -Habana - - x -Ife - - x -Khartoum - - x -Malaya - - x -Nairobi - - x -Philippines x -South Pacific - xYaoundea xa First choice for all.

6. FURTHER ASPECTSIn this section I shall present some information on academic staff and onthe interaction between each department on the one hand and its localenvironment on the other hand.

6.1. Academic StaffA department's establishment of academic posts, the number of qualifiedindigeneous staff and their fields of specialization are obvious importantindicators of the nature of its present and future activities. Some limitedinformation on these indicators is presented in Table XII. (See also El Tom(1980, p. 442).)

In El Tom (1980, p. 439) a 5-stage model describing staff development ofthird world mathematics departments was proposed. The stages indicate, indescending order, the degree of dependence on expatriate staff and foreign


24/28

MATH EDUCATION IN THIRD WORLD UNIVERSI1 IES 187

TABLE XIINo. and specializations of indigenous academic staff

Full-time academic staffTotal Indigenous staff holding a Ph.D.

No. Field of specializationMathematics Department,University of:Addis Ababa 25 5 Analysis (2), Algebra (1), Model theory (1),Probability (1).Ateneo de Manila 8 3 Geometry (1), Combinatorics (1), O.R. (1).Bujumbura n.a. 0Cairo 36 36 Mechanics and theoretical Physics (10),Logic (4), Algebra (5), Analysis (7),Topology (3), Differential geometry (2),

Statistics (3), Numerical analysis (2).Dar es Salaam 16 3 Analysis (1), Fluid mechanics (1),Oceanography (1).Khartoum 23 17 Probability and statistics (4), Fluidmechanics (5), Topology (2), Algebra (2),

Differential equations (1), Numericalanalysis (2), Computer science (1).Nairobi 23 7 Topology (1), Analysis (2), Differentialequations (1), Mathematical statistics (2),Fluid mechanics (1).Philippines 53 7 Algebra (2), Analysis (1), Mathematicalstatistics (1), Topology (1), Numericalanalysis (2).South Pacific 12 0Yaounde 27 6 Analysis (1), Differential equations (1),

Algebra (1), Differential geometry (1),Computer science (2).This information is available for only 10 of the 18 departments of earlier sections.

institutions starting with total dependence. Table XII shows that mostdepartments are in an early stage of their development. Departments atCairo and Khartoum universities are the only two exceptions. The case ofthe department at Philippines university is rather interesting. For althoughit is one of the oldest universities in the third world, only 13% of its largestaff are Filipinos. The dependence of a department on expatriate staff maycause important instabilities (due to their short period of residence) in itsacademic programmes. In particular, for stable postgraduate studies onewould expect a department to emphasize those disciplines in which itsindigenous staff are specialized (compare the relevant entries in TablesVIII and XII).


25/28

188 M.E.A. EL TOM

6.2. Links with SocietySociety's appreciation of and support for the mathematical sciences is verymuch a function of the type and strength of links between universitymathematics experiments and society.

In the questionnaire departments were asked to indicate whether theyhave engaged during the past five years in any of the following activities:

(a) Inservice teacher training.(b) Writing syllabi for schools.(c) Preparing materials for schools.(d) Research/consultancy work for public or private institutions.The responses of the various departments are shown in Table XIII below.The table reveals that all departments, except those at Assiut and

Khartoum universities, have had during the past five years important linkswith their respective ministries of education. In contrast, only seven depart-ments have had, during the same period, productive links with other localinstitutions. These latter links appear to be strongest in the cases ofdepartments at Habana and Malaysia universities. It is possible that themain reason for this weakness is the non-existence in the relevant depart-ments, of critical masses of indigenous specialists in disciplines such asoperations research, modelling and discrete mathematics which are essentialfor the mathematical treatment of real world problems. (Compare remarks(vii) and (x) in Section 3.2 and Table XII).

7. SUMMARYThe information presented in the previous sections gives some ideas aboutthe actual situation of mathematics education in several third world uni-versities. Given the variations, noted in Section 2, in the mathematicsdepartments considered, it is not unreasonable to assume that they arerepresentative of mathematics departments in many third world countries.It is known that mathematics is young in most third world countries.This is confirmed by Table I which shows that most of the departments ofmathematics considered are barely 30 years old. The same table shows that,with two exceptions, such departments are small in number - 1-3 depart-ments in each country. Moreover, each of the departments in the tableenjoys a characteristic (age, prestige, size) which confers upon it a leadingrole in the development of mathematics in its own country. For a discussionof the nature of this role see El Tom (1984).

The information in Tables III and XIII indicates that the resources (bothmaterial and human) available for departments to meet their responsiblities


26/28


>

04 0

5~~~~~~~~c cn W $:,~~~~~ _

1 >2 go0 V>)

~~ xn O s ? GJ0 ?0 a0) C) '0 0

> ~ ~ ~ ~ ~ ~ ~ ~ 0 0C,, z zz0 0 -0

0 o 0 0 -00w~~~~~~~~~~~~~~~CZ ~ 0 -0 0o 0 ) 0 -

CZ~ ~ ~ ~~ ~~~~~~~2 -~~~~~~~~~~~~~10 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 7 r0)0)0V 0con 2 co01 0 ~ ~ ~ ~ )< 0-o 0 C-~~


27/28

190 M.E.A. EL TOM

are not adequate. Thus if one measures the availability of material resourcesby the mean for each department in Table III, then it turns out that 13departments have an unsatisfactory situation (mean less than 2). As forhuman resources, Table XIII shows that most departments are heavilydependent on expatriate staff members.Clearly, this poses problems for thedevelopment and implementation of a coherent programme for the pro-motion of the discipline.

Except for the department at Ateneo de Manila, departments offer severalsingle and combined bachelor degrees. Of the combined degrees, mathe-matics with physics seems to be the most popular one (Table IV). However,students who follow these degree courses are, in the majority of cases, notstrongly motivated (Table XI). Of course, this is related to the social statusof mathematicians and to the limited job market for them (Table X).

Finally, if one looks at the content of undergraduate programmes (TableV), areas of study of Ph.D. students (Table VIII) and fields of specializationsof indigenous staff (Table XII), then it is evident that most departmentsemphasize pure and (traditional) applied mathematics. In particular,modern trendsin applications of mathematicsand mathematical education arenot adequately represented.This is despite the fact that the future careers oftheir graduates (most of whom end up in teaching (Table X) and thepossible contribution of mathematics to the solution of developmentalproblems demand that these areas be adequately emphasized in the trainingof both undergraduate and postgraduate students.

ACKNOWLEDGEMENTI'm glad to acknowledge the cooperation of those colleagues and heads ofdepartments who took the trouble of filling in and returning a ratherlengthy questionnaire.

APPENDIXThe questionnaire contained the following list of topics which may beoffered at various of the undergraduate program:

1. Set Theory2. Logic3. History of Maths4. Philosophy of Maths5. Calculus6. Real Analysis7. Complex Analysis

25. Partial Differential Equations26. Mechanics27. Fluid Mechanics28. Elasticity/Plasticity29. Electromagnetic Theory30. Themodynamics31. Relativity


28/28

MATH EDUCATION IN THIRD WORLD UNIVERSITIES 1918. Functional Analysis9. Approximation Theory10. Measure Theory

11. Probability12. Linear Algebra13. Group Theory14. Rings and Modules15. Field Theory16. Lattice Theory17. Discrete Maths18. Geometry19. General Topology20. Algebraic Topology21. Differential Topology22. Differential Geometry23. Number Theory24. Ordinary Differential Equations

32. Quantum Theory33. Statistical Mechanics34. Space Science35. Mathematical Physics36. Astronomy37. Oceanography38. Statistics39. Systems Analysis/Operations Research40. Mathematical Modelling41. Biomathematics42. Numerical Analysis43. Computer Science44. Control Theory45. Optimization46. Mathematical Education47. Others (Please name them)

REFERENCESD'Ambrosio, U.: 1979, 'Overall goals and objectives for mathematical education', in NewTrends iMMathematics Teaching, Vol. IV, Unesco, Chapter IX, pp. 180-198.El rom, M. E. A. (ed.): 1979, Developing Mathematics in Thirdi Wor-ldCountries, North-Holland.El Tom, M. E. A.: 1980, 'Remarks on structures of university mathematics institutions in thirdworld countries', International Journal of Mathematical and Educational Science andTechnology,11, 433-446.El rom, M. E. A.: 1984, The Role of Third World University Mathematics Institutions in?

Promoting Mathematics, paper presented at the 5th ICME, Adelaide, Australia, 24-30August, 1984.

School of Mathematical Sciences.University, of Khartoum,P.O. Box 321,K1hartoum, udan

Elton 1986_Aspects of Mathematics Education in Third World Universities

Documents