**II. The Instruction of Mathematical Subjects**

- A. The teaching of mathematics at tertiary level.
- B. The teaching of mathematics at secondary level.

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**A. THE TEACHING OF MATHEMATICS AT TERTIARY LEVEL**

The teaching of Mathematics and Applied Mathematics has always been treated with earnest by SAMS. In the editorial,

*Notices*9/1 of 1977, Niko Sauer took up the matter of the training (or the lack of training) of applied mathematicians in South Africa ([8; 9/1, 1977], [8; 9/2, 1977]), while in the editorial,

*Notices*9/2, Wesley Kotzé held the view “I am of the conviction that there is no such discipline as ‘Applied Mathematics.’ There is only one discipline, namely ‘Mathematics’….By all means, teach the applications of Mathematics, but of good Mathematics, thoroughly prepared for by ‘pure’ courses.” [8; 9/3, 1977].

In a letter to

*Notices*, Prof G Geldenhuys expressed the view that the Annual Congresses of SAMS offer excellent opportunities for members to illustrate through their lectures and discussions how their work could be applied to reduce the polarisation between the two camps [8; 9/3, 1977]. A feature of the 1973-Annual Congress was a Symposium on the Teaching of Applied Mathematics, with the invited speakers Profs HJ Schutte, SRF Göldner and HSP Grässer [9]. At the 1976-Annual Congress two sessions were devoted to a symposium on the same topic. A Conference on the Teaching of Applied Mathematics, sponsored by SAMS, was held at Potchefstroom on 25 and 26 October 1976. Some of the main findings of the conference may be summarised as follows:

*Applied Mathematical students must be taught how to formulate mathematical models of practical problems, solve such models analytically or numerically, and apply the results to the practical problems. On the one hand there was reason for concern about job opportunities outside the teaching profession for graduates in the mathematical sciences. On the other hand it was not clear whether employers were fully aware of the newest directions in the teaching of Applied Mathematics, and of the potential benefits that the correct application of Mathematics could have for their organisations. Teaching staff in Applied Mathematics have the formidable task of convincing, by means of research and/or consulting work, potential clients of the value of their subject. It is clear that this task will demand great sacrifices and dedication.*[14(e)].

The editorials in [8; 10/1, 1978] and [8; 10/2, 1978] (written by Profs GJ Hauptfleisch and PJ Gräbe, respectively) dealt with the teaching and examining of Mathematics at university level. Two articles on the undergraduate curriculum in Mathematics appeared in [8; 12/1, 1980], and in his Chairman’s Report of 1979, Hauptfleisch dealt with relevancy in the teaching of Mathematics. In [8; 12/2, 1980], there were three articles on the teaching of undergraduate students, the teaching of service courses, and the danger of using an abstract approach too soon. In the same issue, Prof HJ Schutte wrote: “The student should be introduced, at a relatively slow pace, to fundamental concepts (‘mathematical vocabulary’) which are to be used in the later development of the courses, without having recourse to excessive abstraction. Geometrical interpretations of functions and relations (‘curve sketching and a rapid review of analytic geometry’) are important for the further understanding of Mathematics. Geometric models in many cases provide a firm intuitive basis for Mathematics.”

The debate continued in [8; 12/3, 1980], with articles on the subject matter in first, second and third year Mathematics courses (RI Becker and B de la Rosa) and the teaching of Statistics at university level. More articles on different topics appeared: the teaching and intellectual content of Computer Science came under the magnifying glass in [8; 13/2, 1981]; an article on Operations Research and Mathematics in [8; 14/1, 1982]; an article on computer-aided teaching in [8; 15/2, 1983], at a time when that technique of teaching was still treated with suspicion; two articles on undergraduate teaching in [8; 18/1, 1986]: one dealt with the Mathematics needed to support undergraduate courses in Computer Science (WA Labuschagne), and the other one with the Mathematics needed in undergraduate teaching in Statistics (HS Steyn).

Not only articles on undergraduate teaching had appeared in the Notices, but also articles on interesting mathematicians like Weyl and Mordell, and also WH Ruckle’s article “The soft side of Mathematics”, that dealt with applications of Mathematics in the so-called soft sciences like Economics, Sociology, Ethics, and so on [8; 17/3, 1985]. Johann Engelbrecht and Michael Sears were jointly responsible for organising the South African Calculus Reform Workshop in July 1994 at the University of the Witwatersrand, coinciding with the AMESA Conference [8; 26/2, 1994]. Special sessions at the 1994 and 1995 SAMS Annual Congresses were devoted to Calculus Reform Workshops. On 24 October 1995, one day before the SAMS Annual Congress at the University of Durban-Westville (UDW, now part of the campus of the University of KwaZulu-Natal), the second follow-up meeting of the South African Calculus Reform Workshop took place there [14(b)]. There was a special session in the form of a panel discussion on tertiary education at the Annual Congress of 1989 [8; 21/2, 1989]. In 1989, Prof Johann Engelbrecht was the Council member co-opted to take charge of the Education portfolio [14(b)]. Dr A Harding resigned as Council member for that portfolio in September 2002, and Maritz Snyders was co-opted in that portfolio, until he resigned in September of 2006, and was then succeeded by Carol Bohlmann.

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**B. THE TEACHING OF MATHEMATICS AT SECONDARY LEVEL**

According to the 1957-Constitution, one of the two objectives of the South African Mathematical Association (SAMA) was to ‘promote the instruction of Mathematics at all levels.’ The Association regarded its involvement in the teaching of Mathematics at Secondary School in a serious matter. At that time some local branches of SAMA still existed. The Transvaal branch, for example, was quite successful in organising rather large meetings of school teachers, at which the revision of the matriculation syllabus was usually the main point on the agenda. In other parts of the country teachers also displayed interest in the Association. One of the first actions in this direction was when the Council of the Association decided to arrange a symposium for Saturday, 24 May 1958 in the AE du Toit Auditorium of the University of Pretoria on the subject ‘The Critical Condition of Mathematics Instruction in High Schools.’ The speakers on that occasion were Prof DJ van Rooy (Potchefstroom University), Dr TF Gevers and Mr CM Moll. (See Part I.A) Before this symposium, the Secretary of SAMA had sent out a circular, dated 2 May 1958, to principals of High Schools in which (i) the objectives of the Association were set out, and (ii) the teachers were cordially invited to attend the symposium [13(n)]. It was the intention of the Association to devote at least one meeting per year exclusively to problems pertaining to the teaching of Mathematics, and the Association was therefore eager to enrol interested teachers as members. “In this way we hope to achieve cooperation between Schools and Universities and to eliminate the tendency to find fault and to reproach. Only by such cooperation will we ever be able to meet South Africa’s demand for mathematicians of high standard”, according to the last paragraph of the circular. It was mentioned in Part I.A that during the initial years of the Association, it was the custom to notify the heads of universities, university colleges and the different departments of education of the four provinces and South West Africa (now Namibia) of the Annual Congresses, and to invite official representatives of such institutions to attend the congresses. Each department of education in the country used to send at least one representative, which served as a good contact between the Association and the departments.

On 4 September 1959, the Secretary of the SAMA wrote to Dr PM Robbertse, the Director of the National Bureau of Educational and Social Research (NBESR) (predecessor of the Human Sciences Research Council (HSRC, established in 1968)), requesting, on behalf of the Council of SAMA, a thorough survey of the teaching of Mathematics in the secondary schools, and informed him that his Council was prepared to be involved and to be of assistance in this proposed survey. On 15 June 1961 the Department of Education, Arts and Science invited SAMA to appoint at least one representative to serve on an Advisory Committee of the NBESR to investigate the following aspects of the teaching of Mathematics in South African schools: curricula, textbooks, training of Mathematics teachers, methodology of school Mathematics, and possible creation of opportunities for the advancement of the teaching of Mathematics. The Council of SAMA appointed Prof JH van der Merwe and Dr J van der Mark as their representatives on the Advisory Committee, and Prof GL Isaacs as an observer. On 22 October 1963, Dr AJ van Rooy of the NBESR delivered a report on the activities of this Advisory Committee at die SAMA Annual Congress. He mentioned that the following aspects were investigated: (i) the educational value of Mathematics; (ii) the possibilities of uniform departmental curricula; (iii) textbooks; (iv) the training in the methodology of the teaching of Mathematics; (v) personal initiatives of learners. The Council of SAMA was requested to appoint committees to take the lead in the reconsideration of curricula, textbooks, publications and in reforming the training of teachers. It was expected that these committees would serve as sub-committees of the National Advisory Board for Education, but that later turned out to be impossible, as the procedure for establishing its committees was prescribed by law. On the 1964-Annual Congress of SAMA in Grahamstown, there were two lectures on the teaching of Mathematics at secondary level: Dr AJ van Rooy delivered a lecture, ‘Die Onderwys van Wiskunde aan die Suid-Afrikaanse Hoërskole’ (The Teaching of Mathematics at South African High Schools), and Prof SE Cruise (Rhodes University) on ‘Some new ideas in Mathematics Teaching’ [13(f); 13/04/1964]. (Professor Cruise died on 7 March 1965 at the age of 48. He matriculated at the age of 13, the youngest matriculant in England of that year [13(i); 1964].) On 16 May 1962, the Secretary of SAMA informed the Joint Matriculation Board (JMB) that, according to the findings of the Advisory Committee, they (the JMB) should rather pay serious attention to the methodology of the teaching of Mathematics by the teachers, and not that much to the Mathematics curricula. The general view was that a good curriculum alone does not offer the teacher enough guidance to direct his teaching. The JMB replied (5 July 1962) that they were considering a guide for the teaching of Mathematics. On 30 May 1963, the Chairman of SAMA wrote to the Chairman of the National Advisory Board for Education about:

(i) the desirability of the centralisation of curricula — then universities need not have to build on the lowest standard offered by the various departments of education, and it would be advantageous for learners moving from one province to another;

(ii) the improvement of the promotion system for well-qualified teachers — then teachers of the best quality could be recruited and retained. The Executive Committee of the National Advisory Board for Education convened a conference regarding greater uniformity and efficiency with respect to curricula for 22 August 1963. A delegation of SAMA attended the Conference together with ten other institutions, all with the common interest of improving the teaching of Mathematics and science in high schools. At that stage, there were eleven different authorities working on curricula for high school Mathematics, with no proper coordination between them. The Secretary of SAMA wrote on 8 November 1965 to the Chairman of the National Advisory Board for Education with the request that SAMA should play a permanent role in the planning and teaching of school Mathematics. The National Advisory Board for Education referred this request to the JMB on 29 November 1965.

**(i) The Mathematical Association of South Africa**

A rather simple incident in 1965 brought about a turning-point in the involvement of SAMA in Secondary Mathematics. Mr d’Arcy C Alletson, a well-known Mathematics teacher from Kearsney College, Botha’s Hill, Natal, resigned from the Association, which, according to his letter of resignation, did not have anything to offer to the ordinary teacher [8; 13/3, 1981], [13(f); 03/07/1965]. Whereas, initially there were quite a number of school teachers who became members of the Association, their numbers decreased as the Association gradually began to concentrate its activities on those of the ‘professional mathematician’. The Council of SAMA saw this writing on the wall, and in 1966 a sub-committee was set up to approach teachers’ associations and provincial Education Departments to determine what measure of response could be expected.

At the AGM of October 1966 at Stellenbosch, the convenor of the Committee re Programmes for Schoolteachers (Prof Grässer) proposed:

(i) that the need has arisen for the creation of an association to cater explicitly for teachers of Mathematics;

(ii) that a committee be appointed to enlist the support of teachers of Mathematics both at school and undergraduate university level, for the purpose of bringing such an association into being;

(iii) that the closest possible contact be maintained between such a newly formed Association and the present South African Mathematical Association;

(iv) that ‘The South African Mathematical Association/Die Suid-Afrikaanse Wiskundige Genootskap’ would be a suitable name for such a newly formed body, provided that the name of the present South African Mathematical Association be changed to ‘The South African Mathematical Society’. This name change involved an amendment of the Constitution [13(g); 25/10/1966]. The Secretary arranged a postal ballot and the name changed in March 1967 [13(a); 22/02/1967]. The Council of the newly constituted SAMS received an invitation to send a delegate to the meeting of the Federation of South African Societies of Science Teachers that was held in Durban from 10 to 14 June 1967. Prof FJ Schuddeboom represented Council at that meeting [13(i); 1967]. Council met with representatives of the various teachers’ associations in Pretoria on 6 July 1968 to discuss the formation of a South African Mathematical Association whose primary object would be to provide a forum in which school teachers of Mathematics and university lecturers could meet to discuss matters of common concern [131].

The founding meeting of ‘The Mathematical Association of South Africa’ (MASA) (In Afrikaans: Die Wiskundegenootskap van Suid-Afrika (WGSA)) was eventually held on 28 June 1969 at the UNISA, Pretoria, and a Constitution was adopted. Most of the teachers’ associations were presented at the meeting. Prof KO Househam acted as Chairman and Prof HSP Grässer as Secretary at that meeting. A large part of the initiative for the founding of MASA came from the Society, and Profs JH van der Merwe and HSP Grässer represented the SAMS for many years on the Council of MASA. In addition, SAMS donated some funds to MASA in order to get its administration off the ground. Since its inception, membership of MASA was restricted to White persons. The membership issue was discussed on the founding meeting, and the following decision was taken: “Realising the realities in South Africa, the meeting resolves that the membership shall be restricted to White persons. This meeting furthermore expresses the hope that the MASA would give its support to the formation of a similar Association with non-White members” [13(l)]. From the start, MASA proved to be viable, and it already had 158 members at the time of the first Annual General Meeting. In October 1972, MASA already had 400 members, divided into six branches, and 570 members a year later [8; 13/3, 1981]. [13(f); 22/10/1973].

Two invited lectures were presented at the 1966-Annual Congress of SAMS at Stellenbosch in the category ‘On the Problems of Mathematics Teachers’: Mr d’Arcy C. Alletson lectured on ‘The Crisis in School Mathematics’, and Mr C de Jager, Rondebosch Boys’ High School, lectured on ‘How can we improve the teaching of school Mathematics in this country?’ The Alletson-lecture is still applicable to the present situation in South Africa. He mentioned that the crisis which arises in school Mathematics is that schools are failing abysmally to produce a sufficient number of mathematicians: there are not enough students who wish to take up careers in Science. He attributed the situation to two causes, namely the school syllabus and the teaching in the schools. He mentioned that South Africa must be one of the few countries where school-leaving examinations are controlled so largely by University Boards. In most other countries the boards of examining bodies are composed very largely of practising school teachers who are able to assess the requirements and potential of children and to set examinations which are suited to them. Mr Alletson appealed to SAMA to consider the experimental syllabi drawn up by a group of teachers from private schools, and if approved, to press for its adoption by the Joint Matriculation Board (JMB). The second feature of the crisis in school work he mentioned was the teacher problem: teachers teaching Mathematics but not qualified as teachers of Mathematics at all, shortage of teachers, the remuneration of teachers. A high percentage of teachers are working right up to the boundaries of their knowledge and were quite unable to illuminate their work. Alletson’s second appeal to SAMA is to help with the teachers: to organise refreshers classes or conventions or local discussion groups led by university lecturers. These meetings should not be designed to tell teachers how to teach but to widen their experience of the subject, without going to such academic depth as to frighten them [13(i); 1966]. In 1967, the JMB requested the SAMS to consider the experimental syllabi drawn up by the teachers from the private schools, and to come up with a recommendation. The SAMS Committee recommended to the JMB not to accept the experimental syllabi. In 1968, the Secretary of SAMS wrote to all Provincial Education Departments and to the Department of Higher Education offering the cooperation of SAMS in matters concerning syllabi and terminology. Most of the Departments reacted positively [13(f); 15/07/1968].

KO Househam (Courtesy of his son Craig)

During August 1969, the first International Congress on the Education of Mathematics was held in Lyon, France. The South African delegates returned home filled with enthusiasm. Under their inspiration and with the cooperation of the Foundation for Education, Science and Technology (FEST), MASA and SAMS, they planned ‘The South African Mathematics Project’ (SAMP). The organisers planned the SAMP to be a free association of teachers of Mathematics (at all levels) who have a common interest in improving the teaching of Mathematics by investigating and developing classroom materials and supplementary guides. Although the Project would operate more or less independently of government and official bodies, the work of the SAMP must, however, be seen as supplementary to that of the Department of Education, and the approval of the latter will be sought.

The following aspects would receive attention: the writing of short dissertations by eminent mathematicians to emphasise suitable mathematical material, the guidance of parents and teachers, the cooperation between school and university concerning the teaching of Mathematics, and, eventually, the establishment of committees of teachers and university lectures to write on a full-time basis books and guides intended to supplement and enhance the ones in common use. Shell South Africa agreed to sponsor the Project, and the Foundation for Education, Science and Technology (FEST), (which published the journals Spectrum and Archimedes), would provide the secretariat and administer the Project [8; 2/1, 1970]. The SAMP was formally launched during a conference from 1 to 3 April 1970, with Dr Bryan Thwaites, Director of the ‘School Mathematics Project’ in the UK as guest speaker. In 1969, the Education Committee of The Associated Scientific and Technical Societies of South Africa offered SAMS the opportunity of participating in a project according to which career guidance brochures on various fields and professions were to be published in Archimedes.

An article ‘Careers for Mathematicians’ was eventually drawn up by Mrs A Noble (Rhodes University) and NCH Ferrandi (University of the Witwatersrand), and it was published in close collaboration with MASA, and under the auspices of FEST, as part of the SAMP in Archimedes XIII, no. 3, Aug 1971, 49–53 (in Afrikaans) and in Archimedes XIII no. 4, October 1971, 45–50 (in English) [13(m)]. One of the most important products which the Project had led was the work done by various study groups or workshops under the leadership of Mr Ralph L Nero. Some of the publications which originated from these gatherings were memoranda on ‘Syllabus Proposals’, teacher’s guides on ‘The Teaching of Geometry in Standards 5, 6, and 7’, ‘The Teaching of Geometry and Mensuration in Standards 1–4’, and ‘The role of functions in Standards 5–7’, while a national journal, PYTHAGORAS, had been started in 1980. A ‘Draft Policy Document on Mathematical Education in South African Schools’ was compiled and an ‘Action Plan for Mathematics Teaching in the RSA’ was drawn up. The Project, however, also had its hand in various other publications such as ‘Notes on Groups and Fields’ by D Allison and ‘Wiskundige probleme vir die fynproewer’ (Mathematical problems for the connoisseur) by AP Malan. Without the contribution by Shell all these activities would have been impossible. During the years 1976–77, MASA organised a Syllabus Workshop as part of the SAMP. At each of the previously mentioned working sessions led by Mr RL Nero (the ‘Mbona Workshops’ since they always took place at Mr Nero’s ‘Mbona Mountain Estate’ in the Natal Midlands), SAMS had been represented by the invitation of the Association [13(f); 28/10/1981].

A further fruitful consequence of the cooperation with FEST had been that, since 1972, the Annual Congress of MASA was incorporated in the bi-annual National Convention for Teachers of Mathematics and Science which had been regularly organised by the Foundation in collaboration with the Federation of Science and Mathematics Teachers’ Association of South Africa. At each of these Conventions there were overseas participants. These Conventions, as well as the Annual Congresses held in the years between the Conventions, normally lasted four or five days, and were usually well attended. As far as the administrative side was concerned, SAMS was represented officially on the Council of the Association by two of its members. The participation in Cape Town in the 1981-Convention by Professor Peter J Hilton would not have been possible if the SAMS had not invited him to visit South Africa as its Distinguished Guest for 1981.

Through its representatives on the Council of the Association, the Society was involved in the compilation of the programmes and the selection of speakers for the Annual Congresses, but fewer and fewer members of the Society were chosen. There was, for instance, no speaker of the Society at the 1981 Convention, although quite a number of its members attended. The main reason seemed to be that the teachers at that stage felt that they need mainly lectures which were more or less directly relevant to classroom situations. Two such very good talks at the 1981-Convention were given by CJ (Tiekie) de Jager (‘Apparatus for Mathematics’) and Professor PJ Human (‘Variation of possibilities in Geometry teaching’). Despite this understandable need of the teachers for more ‘practical’ talks and workshops, the SAMS representatives on the MASA Council felt that the members of the Society could and should have played a more active role in the Association, especially as far as the MASA Annual Congresses were concerned [8; 13/3, 1981].

On the 1974 Annual Congress of SAMS, the following motion was accepted: ‘That the Joint Matriculation Board and the respective departments of education are requested to consult with SAMS when Mathematics syllabi are being revised.’ This proposal was later supported by MASA [8; 8/1, 1976]. The JMB and the respective departments of education pointed out to SAMS that their request should be directed to the Committee of Educational Heads (CEH). In August 1975, MASA (with about 1000 members) appointed a permanent Syllabus Committee of five members from their ranks, and they requested SAMS to appoint two SAMS members on that Committee. Prof JH van der Merwe and Dr JH Webb were appointed in this capacity [8; 8/1, 1976].

On 1 June 1976, the Society and the Association made joint representations to the Joint Matriculation Board and the Committee of Educational Heads concerning the establishment of a Permanent Syllabus Working Group, in the place of the Joint Committee which normally only met once approximately every five years. The JMB had decided to support this idea and referred the matter to the CEH for consideration [8; 9/1, 1977]. The CEH reacted on 11 July 1977 and pointed out that they had previously rejected permanent syllabus committees and that education departments review syllabi among them [13(f); 24/10/1977]. It was mentioned in Part II.A that, during the years 1977–86, a number of editorials, letters and articles on the teaching of Mathematics (also, Applied Mathematics), Statistics and Computer Science at university level had appeared in the Notices. Those lively discussions on educational matters had the effect that, in 1981, the Council of SAMS had co-opted Dr DP Laurie as member responsible for educational affairs. In November 1981, Laurie was appointed as SAMS representative on the AS & TS Education and Training Committee. In April 1982, the Council of SAMS decided to form an Education Committee to coordinate SAMS policy on all matters concerned with mathematical education. The first Committee consisted of Profs TP Dreyer, JH Swart, JH van der Merwe, JH Webb, and Dr DP Laurie as convener. In 1983, SAMS made representations through one of its members, Dr TG Alant (MP for Pretoria East), to the Minister of National Education (Prof G v N Viljoen), about the possible inputs of SAMS in school Mathematics syllabi. In a letter dated 30 June 1983, Prof Viljoen informed Dr Alant that not all subject societies could be represented in syllabus committees, that the education departments have their own research committees giving them advice where necessary, and that these research committees occasionally consult with experts from outside.

In his capacity as convenor of the SAMS Education Committee in 1983, DP Laurie wrote ([8; 15/2, 1983]) that in his view, SAMS could advise and make recommendations to a research committee, but that SAMS should not

In 1997, Prof Jan Persens was nominated to represent SAMS on the Learning Area Committee for Mathematical Literacy, Mathematics and Mathematical Sciences of the Western Cape Education Department, while Prof Johann Engelbrecht represented SAMS on the National Learning Area Committee for Numeracy and Mathematics [14(b)]. The South African Mathematics Education Reform Network came into being in February 1996 as an informal grouping of people interested in new developments in Mathematics Teaching. In 1996 and 1997 they held workshops in Cape Town and in Pretoria, and also a session at the 1997 SAMS-AMS-SAMSA Conference in Pretoria. At the 2006-AGM, Congress expressed its concern that Geometry had become an optional topic at secondary level Mathematics and that the new Mathematical Literacy topic offered at secondary level was inadequate for acceptance into mainstream Mathematics at tertiary level. It was strongly recommended that universities and other tertiary institutions adopt a more pro-active role in adopting bridging programmes [8; 37/3, 2006].

At the AGM of 2007, it was suggested that an increased collaboration and cooperation between SAMS, SAMF, the DoE and the DST suggests a greater willingness on the part of the Government to take seriously the concerns of mathematicians regarding the country’s Mathematics Education Policy. At a joint meeting in July 2007, in which the above-mentioned bodies were involved, SAMS undertook to play an advocacy role with respect to the mathematical content of teacher education programmes. At that AGM, SAMS resolved to request the DoE to: (i) stipulate two years of undergraduate Mathematics as the minimum requirement for teacher education programmes, and (ii) involve SAMS in education policy planning [8; 38/3, 2007].

A symposium at the National Convention on Mathematics, Natural Science and Biology Education in July 1991 resolved to work towards a unified structure for Mathematics education associations. Exploratory discussions in Cape Town led to several groups working together at regional level negotiating the aims and objectives and constitution of a new organisation. A unity meeting was held in Stellenbosch in May 1992, where eleven previously divided Mathematics education organisations, including MASA and SAMS, were present. The meeting resolved to form a new national unitary Association with object ‘Mathematics Education’, which is independent, open to all, and will focus on the needs of the wider South African community. An interim National Council, consisting of one representative from each of nine associations and one representative from each of eight regions, was convened in Bloemfontein at the launch of the Association for Mathematics Education of South Africa (AMESA) on 8 July 1993. The first Annual General Meeting of the Association was held at the first National Congress of the Association (with theme: ‘Redress, Access and Success’) in July 1994. The Constitution was formally adopted at this AGM. The aims of AMESA are, in general, to promote Mathematics education and, in particular, to enhance the quality of the teaching and learning of Mathematics in South Africa [8; 32/1, 2001]. Because AMESA was the successor to MASA, the Council of SAMS approached the AMESA Executive with a view towards establishing a good working relationship. This has led towards the formation of a Joint Coordinating Committee. The major area of collaboration between SAMS and AMESA is the South African Mathematics Foundation (SAMF), which is a joint project of SAMS and AMESA, sponsored by Harmony Gold, see Part III.C of this paper. In 2004, it was agreed that each Society would nominate someone to speak at the Annual Congress of the other society. The exchange has started with Prof Jill Adler (Wits), Vice-President of the ICMI, who was the AMESA speaker on Mathematics Education at the 2004-Annual Congress of SAMS at Potchefstroom. Mr Aarnout Brombacher was the AMESA speaker at the 2005-Annual Congress of SAMS, and for the first time, SAMS nominated someone, namely the SAMS President, to present a plenary lecture at the 2005-AMESA Conference in Kimberley. Kerstin Jordaan presented a plenary lecture at the 2006-AMESA Conference. Hayley Barnes of the University of Pretoria was the invited speaker on educational matters at the SAMS Congress in November 2006, while Chris Breen of UCT was the invited AMESA speaker at the SAMS Congress in November 2007 at UCT. Marcia Moremedi was the SAMS speaker at the AMESA Congress in July 2007. Professor Maritz Snyders (SAMS) delivered an invited talk at the Annual AMESA Congress in July 2008, while Dr Busisiwe Goba of AMESA was a plenary speaker at the 2008-SAMS Congress in November 2008 [8; 39/3, 2008].

During August 1969, the first International Congress on the Education of Mathematics was held in Lyon, France. The South African delegates returned home filled with enthusiasm. Under their inspiration and with the cooperation of the Foundation for Education, Science and Technology (FEST), MASA and SAMS, they planned ‘The South African Mathematics Project’ (SAMP). The organisers planned the SAMP to be a free association of teachers of Mathematics (at all levels) who have a common interest in improving the teaching of Mathematics by investigating and developing classroom materials and supplementary guides. Although the Project would operate more or less independently of government and official bodies, the work of the SAMP must, however, be seen as supplementary to that of the Department of Education, and the approval of the latter will be sought.

The following aspects would receive attention: the writing of short dissertations by eminent mathematicians to emphasise suitable mathematical material, the guidance of parents and teachers, the cooperation between school and university concerning the teaching of Mathematics, and, eventually, the establishment of committees of teachers and university lectures to write on a full-time basis books and guides intended to supplement and enhance the ones in common use. Shell South Africa agreed to sponsor the Project, and the Foundation for Education, Science and Technology (FEST), (which published the journals Spectrum and Archimedes), would provide the secretariat and administer the Project [8; 2/1, 1970]. The SAMP was formally launched during a conference from 1 to 3 April 1970, with Dr Bryan Thwaites, Director of the ‘School Mathematics Project’ in the UK as guest speaker. In 1969, the Education Committee of The Associated Scientific and Technical Societies of South Africa offered SAMS the opportunity of participating in a project according to which career guidance brochures on various fields and professions were to be published in Archimedes.

An article ‘Careers for Mathematicians’ was eventually drawn up by Mrs A Noble (Rhodes University) and NCH Ferrandi (University of the Witwatersrand), and it was published in close collaboration with MASA, and under the auspices of FEST, as part of the SAMP in Archimedes XIII, no. 3, Aug 1971, 49–53 (in Afrikaans) and in Archimedes XIII no. 4, October 1971, 45–50 (in English) [13(m)]. One of the most important products which the Project had led was the work done by various study groups or workshops under the leadership of Mr Ralph L Nero. Some of the publications which originated from these gatherings were memoranda on ‘Syllabus Proposals’, teacher’s guides on ‘The Teaching of Geometry in Standards 5, 6, and 7’, ‘The Teaching of Geometry and Mensuration in Standards 1–4’, and ‘The role of functions in Standards 5–7’, while a national journal, PYTHAGORAS, had been started in 1980. A ‘Draft Policy Document on Mathematical Education in South African Schools’ was compiled and an ‘Action Plan for Mathematics Teaching in the RSA’ was drawn up. The Project, however, also had its hand in various other publications such as ‘Notes on Groups and Fields’ by D Allison and ‘Wiskundige probleme vir die fynproewer’ (Mathematical problems for the connoisseur) by AP Malan. Without the contribution by Shell all these activities would have been impossible. During the years 1976–77, MASA organised a Syllabus Workshop as part of the SAMP. At each of the previously mentioned working sessions led by Mr RL Nero (the ‘Mbona Workshops’ since they always took place at Mr Nero’s ‘Mbona Mountain Estate’ in the Natal Midlands), SAMS had been represented by the invitation of the Association [13(f); 28/10/1981].

A further fruitful consequence of the cooperation with FEST had been that, since 1972, the Annual Congress of MASA was incorporated in the bi-annual National Convention for Teachers of Mathematics and Science which had been regularly organised by the Foundation in collaboration with the Federation of Science and Mathematics Teachers’ Association of South Africa. At each of these Conventions there were overseas participants. These Conventions, as well as the Annual Congresses held in the years between the Conventions, normally lasted four or five days, and were usually well attended. As far as the administrative side was concerned, SAMS was represented officially on the Council of the Association by two of its members. The participation in Cape Town in the 1981-Convention by Professor Peter J Hilton would not have been possible if the SAMS had not invited him to visit South Africa as its Distinguished Guest for 1981.

Through its representatives on the Council of the Association, the Society was involved in the compilation of the programmes and the selection of speakers for the Annual Congresses, but fewer and fewer members of the Society were chosen. There was, for instance, no speaker of the Society at the 1981 Convention, although quite a number of its members attended. The main reason seemed to be that the teachers at that stage felt that they need mainly lectures which were more or less directly relevant to classroom situations. Two such very good talks at the 1981-Convention were given by CJ (Tiekie) de Jager (‘Apparatus for Mathematics’) and Professor PJ Human (‘Variation of possibilities in Geometry teaching’). Despite this understandable need of the teachers for more ‘practical’ talks and workshops, the SAMS representatives on the MASA Council felt that the members of the Society could and should have played a more active role in the Association, especially as far as the MASA Annual Congresses were concerned [8; 13/3, 1981].

On the 1974 Annual Congress of SAMS, the following motion was accepted: ‘That the Joint Matriculation Board and the respective departments of education are requested to consult with SAMS when Mathematics syllabi are being revised.’ This proposal was later supported by MASA [8; 8/1, 1976]. The JMB and the respective departments of education pointed out to SAMS that their request should be directed to the Committee of Educational Heads (CEH). In August 1975, MASA (with about 1000 members) appointed a permanent Syllabus Committee of five members from their ranks, and they requested SAMS to appoint two SAMS members on that Committee. Prof JH van der Merwe and Dr JH Webb were appointed in this capacity [8; 8/1, 1976].

On 1 June 1976, the Society and the Association made joint representations to the Joint Matriculation Board and the Committee of Educational Heads concerning the establishment of a Permanent Syllabus Working Group, in the place of the Joint Committee which normally only met once approximately every five years. The JMB had decided to support this idea and referred the matter to the CEH for consideration [8; 9/1, 1977]. The CEH reacted on 11 July 1977 and pointed out that they had previously rejected permanent syllabus committees and that education departments review syllabi among them [13(f); 24/10/1977]. It was mentioned in Part II.A that, during the years 1977–86, a number of editorials, letters and articles on the teaching of Mathematics (also, Applied Mathematics), Statistics and Computer Science at university level had appeared in the Notices. Those lively discussions on educational matters had the effect that, in 1981, the Council of SAMS had co-opted Dr DP Laurie as member responsible for educational affairs. In November 1981, Laurie was appointed as SAMS representative on the AS & TS Education and Training Committee. In April 1982, the Council of SAMS decided to form an Education Committee to coordinate SAMS policy on all matters concerned with mathematical education. The first Committee consisted of Profs TP Dreyer, JH Swart, JH van der Merwe, JH Webb, and Dr DP Laurie as convener. In 1983, SAMS made representations through one of its members, Dr TG Alant (MP for Pretoria East), to the Minister of National Education (Prof G v N Viljoen), about the possible inputs of SAMS in school Mathematics syllabi. In a letter dated 30 June 1983, Prof Viljoen informed Dr Alant that not all subject societies could be represented in syllabus committees, that the education departments have their own research committees giving them advice where necessary, and that these research committees occasionally consult with experts from outside.

In his capacity as convenor of the SAMS Education Committee in 1983, DP Laurie wrote ([8; 15/2, 1983]) that in his view, SAMS could advise and make recommendations to a research committee, but that SAMS should not

- decide when learners ought to be ready to grasp certain concepts
- plan how concepts could be made accessible for learners
- write textbooks
- prescribe methods of examining

In 1997, Prof Jan Persens was nominated to represent SAMS on the Learning Area Committee for Mathematical Literacy, Mathematics and Mathematical Sciences of the Western Cape Education Department, while Prof Johann Engelbrecht represented SAMS on the National Learning Area Committee for Numeracy and Mathematics [14(b)]. The South African Mathematics Education Reform Network came into being in February 1996 as an informal grouping of people interested in new developments in Mathematics Teaching. In 1996 and 1997 they held workshops in Cape Town and in Pretoria, and also a session at the 1997 SAMS-AMS-SAMSA Conference in Pretoria. At the 2006-AGM, Congress expressed its concern that Geometry had become an optional topic at secondary level Mathematics and that the new Mathematical Literacy topic offered at secondary level was inadequate for acceptance into mainstream Mathematics at tertiary level. It was strongly recommended that universities and other tertiary institutions adopt a more pro-active role in adopting bridging programmes [8; 37/3, 2006].

At the AGM of 2007, it was suggested that an increased collaboration and cooperation between SAMS, SAMF, the DoE and the DST suggests a greater willingness on the part of the Government to take seriously the concerns of mathematicians regarding the country’s Mathematics Education Policy. At a joint meeting in July 2007, in which the above-mentioned bodies were involved, SAMS undertook to play an advocacy role with respect to the mathematical content of teacher education programmes. At that AGM, SAMS resolved to request the DoE to: (i) stipulate two years of undergraduate Mathematics as the minimum requirement for teacher education programmes, and (ii) involve SAMS in education policy planning [8; 38/3, 2007].

**(ii) Association for Mathematics Education of South Africa**A symposium at the National Convention on Mathematics, Natural Science and Biology Education in July 1991 resolved to work towards a unified structure for Mathematics education associations. Exploratory discussions in Cape Town led to several groups working together at regional level negotiating the aims and objectives and constitution of a new organisation. A unity meeting was held in Stellenbosch in May 1992, where eleven previously divided Mathematics education organisations, including MASA and SAMS, were present. The meeting resolved to form a new national unitary Association with object ‘Mathematics Education’, which is independent, open to all, and will focus on the needs of the wider South African community. An interim National Council, consisting of one representative from each of nine associations and one representative from each of eight regions, was convened in Bloemfontein at the launch of the Association for Mathematics Education of South Africa (AMESA) on 8 July 1993. The first Annual General Meeting of the Association was held at the first National Congress of the Association (with theme: ‘Redress, Access and Success’) in July 1994. The Constitution was formally adopted at this AGM. The aims of AMESA are, in general, to promote Mathematics education and, in particular, to enhance the quality of the teaching and learning of Mathematics in South Africa [8; 32/1, 2001]. Because AMESA was the successor to MASA, the Council of SAMS approached the AMESA Executive with a view towards establishing a good working relationship. This has led towards the formation of a Joint Coordinating Committee. The major area of collaboration between SAMS and AMESA is the South African Mathematics Foundation (SAMF), which is a joint project of SAMS and AMESA, sponsored by Harmony Gold, see Part III.C of this paper. In 2004, it was agreed that each Society would nominate someone to speak at the Annual Congress of the other society. The exchange has started with Prof Jill Adler (Wits), Vice-President of the ICMI, who was the AMESA speaker on Mathematics Education at the 2004-Annual Congress of SAMS at Potchefstroom. Mr Aarnout Brombacher was the AMESA speaker at the 2005-Annual Congress of SAMS, and for the first time, SAMS nominated someone, namely the SAMS President, to present a plenary lecture at the 2005-AMESA Conference in Kimberley. Kerstin Jordaan presented a plenary lecture at the 2006-AMESA Conference. Hayley Barnes of the University of Pretoria was the invited speaker on educational matters at the SAMS Congress in November 2006, while Chris Breen of UCT was the invited AMESA speaker at the SAMS Congress in November 2007 at UCT. Marcia Moremedi was the SAMS speaker at the AMESA Congress in July 2007. Professor Maritz Snyders (SAMS) delivered an invited talk at the Annual AMESA Congress in July 2008, while Dr Busisiwe Goba of AMESA was a plenary speaker at the 2008-SAMS Congress in November 2008 [8; 39/3, 2008].