37 37

1. 1. 6. MODERN MA THEMA TICS PROGRAMMES AND IN-SERVICE IN-SERVICE EDUCATION

]. ]. B. Vanniasingham

became independent after World War Two. However ， Introduction Introduction prior to that ， under a colonial administration at best our It It is a great νrivileg 巴 to be invited to this Con- experiences and values had been borne out in ful 五lling ference ference to present a paper at this session. 1 am deeply to the best of our ability ，directives and instructions. indebted indebted to the Organisers for the great honour that There were no opportunities to ask why ，what for and they they have given me to read a paper on “Modern how_ The thinking on most issues was left to the Mathematics Programmes and In-service Education_" colonial government who exacted implicit subservience Though the topic in its widest sense is far-reaching ， for the implementation of their directives_ In this 1 think it would be profitable for me to make my situation ， being regarded merely as passive recepients references references to the experiences borne in South East of order and direction ， there was little or no opportu- Asia ， in particular ， . nity to develop and expound the synthesis of a multi- tude tude of issues and experiences for our society ，and The Need for Change consequently ， with the stamping in of .. do as told ，" Practising Practising Mathematics teachers ，Heads of schools ， the expectations of our society and the future genera- parents ， pupils and the public at large have shown tion had somewhat been thwarted. concern concern in recent times over reform in Mathematics_ However ， with the emergence of Independence for Their Their concern is conceived in terms of the Mathe- the countries in the region ，governments ruled by a matics matics taught them in their days and quite justifiably Democratic system expect of society to be enlightened their their immediate question is: “What is wrong with in its attitudes ， in its thinking and in its way of life ， the the old? Are there defects in the old?" To try and and so ， with the settling effect of independence ，ques- be be able to answer such questions ，it would seem desir- tions on how to develop the future generation in able able to discuss the reasons for change_ What is the terms of the goals and aspirations of society became rationale rationale for effecting change? Or more pertinently ， the focal attention of the day. If it is agreed that a what is the philosophy of teaching Modern Mathe- philosophy entrenched in a curriculum 児島cts the as- matics matics in this part of the world? pirations and hopes of a society ， then certainly there .. .. A philosophy may be regarded as an explanation must be elements within the curriculum continually which attempts to make some kind of sense out of developing the ideas contained in the philosophy. th 巴 natural disorder of a set of experiences ______(It) The present-day philosophy of Mathematics hopes to amounts to a process of reforming and ordering ex- ful 五1 the basic notion of a creative progressive society ， periences periences and values _..… In particular a philosophy able to argue ，accommodate and adjust to the needs of of Mathematics essentially amounts to an attempted of a changing society ，a change brought about by the reconstruction reconstruction in which the chaotic mass of knowledge impact of scientific and technological era ，making over over the years is given a certain sense of orde r. A demands on our present day pupils to be aware of philosophy philosophy is clearly a function of time ，and a par- the rate at which knowledge is advancing ， to be aware ticular ticular philosophy may become outdated or have to be of certain attitudes and trends ， to be aware of the altered altered in the light of additional experiences."ll We importance of readiness and challenge to meet the see see then that a philosophy seeks to explain in a future_ ‘ Curriculum development considered in its systematic systematic and rational way the wealth of knowledge widest sense has been recognised as the main generat- accumulated accumulated over a passage of time_ This wealth is ing force not only for quality in education ， but also reflected reflected in the experiences and values realized by fostering the ability to assimilate changes ， especially Man over the years. If these experiences and values those due to the rapid scienti 五c and technological change ， then it is only proper that the philosophy of evolution now in progress. "2) Mathematics must change also. A further compelling force for change is the Generally ， nearly all countrices of Southeast Asia evidence of recent findings on the nature of the child ， 38 38 and the way in which learning may be registered and is i l1 ustrated by the caSe of the child who learns through through modes of approach compatible to the pupils' that counting a set of objects leads to the same ways of thinking. Reform ， in the midst of the many result ， whether he counts from front to back ， back prevalent prevalent and varied problems of education ， most to front or whatever the configuration in which the certainly certainly adds a further dimension to the complexity objects are arranged. Similarly ， the logico ・mathe- of of educational development. It is seen as fostering matical experience underlying the physical act of the the ability to assimilate changes ，and hence as an grouping and classifying is what we now know as agency of change ， reform integrates the process of the algebra of sets." お We see then that the emphasis development development to reflect the needs of a dynamic and on methodology does not merely indicate how well progressive progressive society for the future. content has been imparted. It lays the foundations for for further mathematical development. Nature of the Changes-Primary Lcvel A third dimension in the change at the Primary The present practices and planned development in school is the re-arrangement of Mathematics topics Mathematics Mathematics education in the region would seem to expressing the ideas repeatedly ， each time at a suggest suggest that reform of mathematics teaching places higher leve l. The transition between the algebra emphasis emphasis on content and methodology. Emphasis is a of numbers and Arithmetic ， for example ， is gradual matter matter of degree rather than of kind ， depending on with mobility existing between the two throughout the the level taught. Thus ， at the primary level ，em- the course. The re-arrangement of topics also takes phasis phasis has been placed on methodology using mainly into account the extent of treatment of the structure the the familiar traditional topics as the core content of of subject matter in terms of the child. What has to the the course. It is obvious that under a centralised be learnt by the child is to be placed into a broader system system of education ，any change on content proper framework in order to enable him to see the structure at at the primary level would have to be fulfilled at the within which the learnt facts are important. operational operational level throughout the schools in the While we make our stand independently within the country. country. region in terms of our own systems of education ， in The legacy of the past has created a situation in terms of our own cultures ，traditions and values ，we which there st i1l exists presently a fair proportion nevertheless consider reform at the Primary level an

of of teachers in the region whose academic and pro 司 essential ingredient for the fulfilment of our national fessional fessional background do not substantiate the case for aspirations. In this sense a start has been made. improvement of new content knowledge as a priority for for reform in Mathematics at the primary leve l. How- Nature of the Changes-Seeondary LeveI ever ， the content of the primary course in Mathe- During the last decade or so changes had taken matics matics is treated from an entirely different point of place in the School Mathematics Curriculum through- view. view. A mathematics education of the kind envisaged out the world. In the Southeast Asian region ， for depends depends not so much on the syllabus as on the attitude the past five or six years ， reform in Mathematics has of of the teacher and the teaching method he employs. been seen at the secondary level both in Content and To the teacher the pupil is more important than the Methodology. The so-called new content is far from subject. subject. Hence the meaning given to the tradition- new ， but it is new in the sense that it has only re- ally ally biased teaching syllabus in re-interpreting the cently been introduced in the school syllabus. The topics topics conducive to the learning situation constitutes elementary treatment of the theory of sets ，vectors ， a major change at the Primary leve l. This change matrices ， linear programming and the like all find is is evidenced by a greater stress on creating class- their way through the secondary course. Besides the room situations in which pupils are provided the change in curriculum content ，much reform has also opportunity opportunity to enquire ， to investigate and draw been taking place on the manner by which mathe- tenable tenable conclusions for themselves. In other words ， matics should be taught. the the change is seen in terms of training the pupil to The present courses in Secondary Mathematics are mathematize mathematize a given concrete situation. In terms of essentially an adaptation of existing courses from mathematical mathematical development and learning ， the nature of the other parts of the world and though the adapta. experience experience provided to the child is most relevant. tion has been in operation as a trial for only a short For ，it is noted that experience besides being physical period ， there appears ， currently a school of thought in in nature through actions and operations by which in Southeast Asia for indigenous curriculum reform. the the pupil organises his environment ， also possesses The thinking is only in its early formative stage. another another fundamental quality. ・. The actions and .. In view of the vast differences in educational operations operations …… have their own properties. This is philosophy ， national goals and identity ， social and called called the logico ・mathematical aspect of experience cultural values and heritage ， the probability of an 39 39 undesirable undesirable mismatch between the .. needs" and the guiding students and evaluating new developments; .. .. wants" of a country become inevitable. In as much towards mastering of the sources of knowledge and as as it is possible for people to ‘want something they methods of enquiry rather than of knowledge itsel f. "7) don't don't need ，it is equally conceivable that they might Reform and so in-service work seeks to change the need need something they don't want. "'4) It must be re- attitude of the teacher .. towards a fuller recognition alized ，however ， that research in the region has been of the importance of understanding the processes of initiated initiated to ascertain the extent to which indigeneous child development ， the social background of children ， curriculum curriculum reform can become a practical reality. and of the impact which teachers' attitudes and Initial Initial steps at Pilot Projects have recently been under- expectations have on the child's performance and taken taken by the Regional Centre for Education in Science development ，…… towards accepting a diminution of and Mathematics (RECSAM) under the auspices of traditional authority in relation to children-partic- the the Southeast Asian Ministers of Education Organisa- ula r1 y to older children and their parents. "7) tion. tion. (SEAMEO) The SEAMEO countries are Indo- In a way then the roles of inservice education in- nesia ，Khmer Republic ， ，Malaysia ， ， volve the various bodies-from the classroom teacher ， ， ， and the Associate to the r巴search worker in th 巴 process of curriculum Member countries are France ， ，and New development in Mathematics. Not only is the need Zealand. ・. An important outcome of this activity is for inservice education recognised. The importance the the launching of the Centre's two vital pilot projects ， if it is c1 ea r1 y seen. Priority to inservice education namely ，The Southeast Asian Science and Mathe- has been stressed elsewhere. .. There seems to be matics matics Experiment (referred to as SEASAME) for international unanimity on the crucial part that should Primary Schools and the pilot study on ‘ Science and be played in continuous inservice education ， for teach- Mathematics Concept Learning for Southeast Asian ers ， for teachers of teachers ，and for others involved Children'. Children'. Thes 巴 two are regional co-operative ven- in administration in the education system. Continuity tures tures and arrangements w i11 be made with SEAMEO and comprehensiveness are the key terms ， continuity Ministries Ministries of Education to co-operat 巴 in carrying out to ensure that there was awareness of ，and involve- trials trials of appropriate units or field studies in these two ment in ， new developments; comprehensiveness to projects projects by participants concerned in their own coun- ensure that all those responsible for the education of tries. tries. If found suitable ， they could be utilised for the young were working together as partners. "7) building building up their national science and mathematics (B) Inservice Education and International Cooper- curricula. curricula. "5) atwn What are the alternatives in Inservice Education in Strategies Strategies for Elfecting Changes Mathematics that can possibly cope with the con- (A) General Considerations tinuity and comprehensiveness referred to above? We can say today that the need for in-service work From our Asian standpoint ， it is our belief that for has has been internationally recognised. By policy and developing countrics a major source for improvement practice practice there is ，however ，some divergence of view and encouragement in Mathematics curricula is through on the nature of such work. A teacher exposed to International Cooperation. Such cooperation can be in-service in-service training reinforces his initial training in met in several ways-through aid-programmes ， the order order to adapt himself to prescribed ends. His role availability of consultants from within the countries would then be of a teacher-employee to be told what and from elsewhere ， but pcrhaps an effective means to to do and how to do it. 6) On the other hand ， with of cooperation is involvement of those already ac- in-service in-service education ，more so with continuous teacher quainted with and those who wish to be acquainted education ， the professional task of the teacher is sup- with development in Mathematics. In fact ，1 think ported ported by a critical appraisal of means and ends ， of it is a tribute to UNESCO in collaboration with educational educational processes and practice ， of self-directed ac- the National Institute for Educational Research in tivity tivity and critical analysis. Japan to have initiated and organised two workshops In In the c1 assroom situation ， the mathematics teacher on Mathematics at the elementary level in 1968 and should should need to see a radical revision of authority 1969 for the Asian Zone. The wealth of experience models models in schools undergoing reform in Mathe- and the interchange of ideas at these sessions have matics. matics. Learning and teaching are regarded as com- contributed towards ascertaining our own respective plementary plementary with a shift in emphasis from merely standing in mathematical education in our countries. imparting imparting knowledge to facilitating learning to take (c) Inservice Education and Regional Co-operation place. place. The teacher sees himself in a changing role If we narrow the field of international activity to a in in his technique “ towards a greater familiarity with regional one ，we see ， as an example of inservice a wide 五eld of knowledge ， not for exposition ， but for education ， the work that has been carried out by 4O 4O

RECSAM referred to ， earlier in my paper as the been given inservice education in the various facets Regional Regional Centre for Education in Science and Mathe. of curriculum development ， the experience of RECSAM matics ，incorporating the countries lndonesia ，Khmer over its first 五ve year cycle would seem to suggest Republic ，Laos ，Malaysia ，Philippines ，Singapore ， Thai. the need for formulating new regional strategies for land land and Vietnam. RECSAM is one of the seven ac ・ inservice education. For the 五rst 五ve.year period cer. tivities tivities serving these countries under the auspices of tain specific areas of the model proposed by Guba and Southeast Southeast Asia Ministers of Education Organisation. Clark had ，however ， been emphasised in RECSAM. The objectives of the regional centre as outlined ln Guba and Clarks' model of Research ，Development ， in in 1967 were “ to help the participating countries in Di 妊usion and Adoption ，it is perhaps in the di 任usion improving improving the teaching of Science and Mathematics stage where awareness of an “ invention" has been in in the region in order that technically and scientifi. stressed by RECSAM. “ lnvention" has been inter. cally cally trained manpower requirements of the region will preted as a re.examination of existing modern cur. be be adequately met."8) An initial start had been made ricula with modifications for possible adaptation. The at at the elementary and secondary levels in four func. adaptation makes the idea available and usable for tional tional areas for purposes of identifying specific pro. dissemination. As the adaptation has in fact been jects. jects. the of result the work of participants themselves at “L Training in the content and methodology of the inservice courses ， there is evidence that it might science science and mathematics. be workable in the respective countries. 2. 2. Research ， development aπd evaluation of new With regard to Research under the model ，Sim 10 ) prototype prototype syllabi ，instructional materials ， teach. says: “ ln developing countries when research is seri. ing ing aids and other equipment. ously lagging behind practice ， not only quantitatively 3. 3. Special Services to the region as required. but qualitatively for technical aspects of reliability and

4. 4. Info 円 nation Centre and regional clearing house validity are often not attended to adequately ，any insist. for for relevant data on Science and Mathematics."8) ence that research should be a necessary first step is Besides Besides the transmission of new knowledge and certainly unwarranted." The Adoption activity of the techniques techniques and the inculcation of right attitudes for mo :l el must necessarily require freedom to try ， to instal the the practising teacher ， inservice education in Mathe. and to institutionalise an idea within the overall system matics matics in Southeast Asia include activities aimed at of education within the region. However ， since the sys ・ providing providing specific training to key educators ， develop. tems are centralised ， decision.making on educational ment activities aimed at developing products usable issues is a central concern and hence adoption in terms in in SEAMEO countries and research activities aimed of operationalising and institutionalising an idea within at at investigating relevant questions in science and the school system is non.existent or marginaLI0 】 mathematics mathematics education in SEAMEO countries.ωAbout ln the midst of problems that differ both in char. fifty fifty training and research projects have been carried acter and in relative magnitude both within and be. by RECSAM over its first five years of activity at tween countries in the region ，Dasbach w suggests the the elementary and secondary levels in Mathematics; RECSAM's opcrational approach be considered in at at any one session there were about 25 key personne l. terms of the project approach. The projects can be The duration of each course is three months giving problem.based and product.oriented in which tangible roughly roughly 300 class hours of instruction ，discussion and products arising out of active experience provide an observations. observations. As the initial stage RECSAM's main atmosphere open to experimentation and try out. The concern concern had been in bringing about an awareness of idea of a project "seems mere open to solving cur. Modern Mathematics to its participants and develop ricular problems by the method of successive ap. practical practical ideas for implementing "new" mathematics proximation. " in in schools of participating countries. Being key edu. The main form of inservice education for the region cators ， they were expected to play leadership roles in for the period 1975-1980 ，was discussed initially at curriculum curriculum improvement programmes in their respec. the national level in each country and agreed upon tive tive countries. In service work on administrative at a regional workshop in April 1974 by all the techniques techniques for project implementation constituted part co of of RECSAM's ac 41 41

Nature Nature of Activity

Course Course (C) Workshop (W) Project (P) (a (a long-term e妊ort seg- (prescribed (prescribed sequence (product-oriented of of studies for self- mented over two or e任。 rt) more RECSAM betterment) betterment) activities)

Orientation Orientation of Training (T) TC TW TP

Research Research (Rat) l RC RW RP RECSAM Activity (investigation) De(vperolodpumcte.nt De(vperolodpumcte.nt (Dnt) Ed) DC DW DP one

The frequency of each entry in the table would national level through the use of prepared guide books depend depend on the needs common to all countries with the for each ot the years ， Grades 1 to V I. Centres are proviso proviso that an entry w il1 be conducted at least once established throughout the country where teachers in during during the second five year plan. neighbouring schools regularly meet during week-ends_ (D) (D) Inservice education at the National level Workshop discussions are held at these sessions by solution-centred solution-centred at ρ roach the key personnel on techniques of teaching topics All All countries in the region are actively involved at contained in the syllabus. Improvised apparatus using some stage or other in Mathematics curriculum re- local materials and how to make the best use of them form. form. The transition from a traditionally biased cur- for maximising learning situations form part of inservice riculum riculum to a modern programme consequently involves help for teachers. The dissemination of new ideas in inservice inservice education and since the education system is this way has a wide coverage. The running of courses centralised ，inservice education to effect changes is na- at centres ， the training of key personnel to run courses tional tional in outlook. In ，Malaysia ， for instance ，inservice at centers and other forms of expenditure are all borne courses courses are provided at the national level for a corps by the central authority. Key personnel hitherto ，at ・ of of teachers selected from secondary schools all over tached to their own schools ， are now fulltime person- the the country. These courses are conducted at each year nel visiting schools in their neighbourhood providing level level of Forms 1， II and II I. Selected personnel from assistance to teachers in classrooms. The first cycle amongst these teachers are given further intensive of this programme of inservice work hopes to reach courses courses on content and methodology to enable them the vast majority of teachers in the country. It would to to conduct courses at various state levels. In this appear that the nature of inservice education is essen- way ， the multiplying e妊ect accelerates the growth tially a solution-centred approach where the solution to rate rate of 'absorption of schools into the modern mathe- the problem is to e妊ect change in methodology among matics matics programme. 12l All inservice work at the upper the practising teachers. It is inevitable that in this secondary secondary level is conducted at the national leve 1. form of inservice work the change is initiated and in- It It should be mentioned that the approach to in- novated “from above" and it is likely that this kind service service work of this nature is essentially a "solution- of paternalism may be regarded as "a tendency to centred centred approach." The assumption is made that stifle initiative and re-inforce over-dependence_" there there is a solution to be found in reforming school Seen in its true perspective ， developing countries mathematics mathematics curricula. This solution would seem to being aware of the limitations existing at the school fit fit the vast number of teachers exposed to the new level have had to consider ， in the first instance ，what programme_ Though teachers may have somewhat can be done to improve the lot of teachers ， rather the the same academic background ， their experience and than expect such improvement to be initiated from the the environmental setting from where they come may the teachers themselves. vary vary considerably. Their problems therefore may (E) Inservice education at the district level: prob ・ not not really have been resolved by the inservice work ， lem-centred approach though though knowledge of the content of modern Mathe- It is only after initiative had been taken from above matics matics and Methodology ，may have been successfully under centralised authority to effect inservice measures imparted. imparted. at the base-level can practising teachers be expected At the primary level where emphasis is largely on to play their leading role in improving themselves the the re-interpretation of traditionally based content ， professionally through continuous inservice education. inservice inservice education calls for the application of the Within this context ， the nature of inservice work multiplier multiplier e百ect. Key personnel are trained at the evolves around a problem-centred approach in a par ・ 42 42 ticular ticular area or district. "In the problem.centred ap. to group schools and the tnspectorate In providing proach proach the emphasis of inservice education is on di. advice ， undertook non-directive roles. The project is agnosing agnosing and studying problems ，and the solution has currently being evaluated by an external body. to to be found by the teacher himself". 6) The signiι cance cance of the distinction between inservice education Evaluation of In.Service Education for for teachers and inservice education by teachers ap. Evaluation of inservice education in the region at pears pears to be the key to life.long education in the RECSAM usually took the form of the questionnaire teaching teaching profession. method. This proved useful to the extent of improv- As an example of the problem.centred approach to ing the process of inservice work for future partici- inservice inservice education ，a project at the primary level had pants at RECSAM. At the national levels too ，ques- been been carried out in Malaysia in a district in 1970. tionnaire proformas were pr 巴pared for those who had This project lasted for 五ve years. Teachers had attended in-service courses. While these served their earlier earlier been exposed to inservice work by national purpose in improving inservice work ， there still re- key personne l. It was the view of the Heads of mained the problem of establishing e妊ectiveness of schools schools and the teachers that the problems inherent inservice courses. In a case study by Sim 13 ) an at- in in their schools had to be satisfactorily resolved to tempt was made to evaluate an inservice course for make inservice work that they had been following sixth form science and mathematics teachers. “A effective. effective. Accordingly ， a district inservice model was ・disguised' technique was employed to test the tea- envisaged envisaged along the following lines: chers' knowledge and perceptions on a pretestjpost- test test basis through a questionnaire which interalia attempted attempted to ascertain if teachers were able to identify crucial crucial principles pertaining to a given topic when an iIl ustrative example was supplied." It It was observed that only about 42% of participants responded responded to both the pretest and post-test. The high high rate of dropouts is an indication of teachers' sensitivity sensitivity to being evaluated. The above questionnaire method was applied in the case case of the inservice education at the district level

ー-~ N~n.directivc rOle rOle in Malaysia. The dropout rate was negligible ，which is is an indication that teachers are con 五dent of their own outcome if they are fully involved in problem- (an (an adaptation of Michael Erau t' s Model)6) identi 五cation and problem-solution.

Study groups had been formed with elected leaders Future Trends in In.Service Education through through the assistance of the District Education The use of educational mass media is generating Department. Department. It was the responsibility of leaders to interest in developing countries. Publications ranging convene convene meetings of their groups and discuss modules from textbooks to teacher guides and pamphlets for prepared prepared by the Inspectorate. These modules were wide circulation have gained momentum in the region. designed designed in a form that seeks the answers to speci 五c OECD through its Centre of Educational Research questions questions pertaining to problems experienced by tea. and Innovation has embarked on a project related to chers chers within the c1 assroom situation. Consultancy the international transfer of micro-teaching materials. workshops of Group leaders were held regularly to Perlberg is of the view that micro-teaching techniques discuss ， inter alia ， the modules and problems pertain- could have a greater impact on the quality of educa- mg group seSS lQ ns. tion in developing countries. “Being an accelerated The facilitation of professional unstructured discus- training technique ，it could speed the process of im- sion sion among participants at the study group sessions proving education in these countries". 14> There is as as the main constituent inservice work had brought scope for a c 泡reful study of micro-teaching for in- about about a total involveme 担 t of participants. This in- service education in the region. volvement volvement not only exploited the expertise and re- sources sources available within the locality. It was the pro- Conclusion motion motion of interaction between people of equal status What do teachers expect at inservice education? that that could possibly allow for adoption at the dass- Are their expectations patterned along seeking inform- room leve l. Outside agents such as the Education ation rather than consultancy? Do they expect to Department for administrative convenience in helping hear or to be heard? To be passive or to be active? 43 43

Do they expect to be le!t in isolation or to be in- 6) ERAUT ，MtCHAEL: Inservice education for in- volved? volved? To implement ， rather than to identify ， seek novation ， Occasional Paper 4. National Council a solution and then implement? for Educ. Technology Much of the future of inservice education will ηOECD EDUCATION COMMITTEE ANNUAL REPORT ， 1972: The Changing Role of the depend ， to a large extent ，on teacher-involvement in teacher teacher and its implications. UNESCO the the process of curriculum reform-from research to 8) REPORT of the Southeast Asian Ministers of development ，diffusion and adoption-from problem- Education Secretariat (SEAMES) Regional Semi- awareness awareness to its solution at the operational leve l. nar on Science and Mathematics PS/SCMS/9. In In this task ，inservice education becomes a life-long RECSAM activity_ activity_ 1 should like to take the opportunity to 9) REPORT on Regional Workshop on Proposals rea 伍rm the closing remarks in D r. A.G. Howson's for RECSAM's second 五ve-year plan 1975-1980 ， Vo l. 11. 1974 ，RECSAM paper paper in which he said "The teacher's status as a 10) 10) SIM WONG KOOI and LAU KAM CHEONG: professional professional must be observed and it is a mark of a The How of lndigenous Curriculum Reform. professional professional that he is prepared to make decisions Paper presented at RECSAM Regional Workshop ， and to accept responsibility for them." 15-19 ， April 1974. RECSAM 11) 11) DASBACH ，). M.: Assignment for Senior Science REFERENCES and Mathematics Education Personnel to Recsam 1) 1) EVES and NEWSON: An lntroduction to the for Pilot Projects. Abstract of paper at the Semi- foundations foundations and fundamental concepts of Mathe- nar on Review of Recsam's Progress and Pro- matics_ matics_ Holt ，N.Y. grammes for 1975-1980. 1973 ，RECSAM 2) 2) SEVAIS ，W. and VARGA ， T.: Teaching School 12) VANNIASINGHAM ， ]. B.: Modern Mathematics Mathematics Mathematics (Source Book). UNESCO in Lower Secondary Schools ー its philosophy ，con- 3) 3) PEEL ， E. A.: Psychological and Educational cept ，rationale; development and implementation Research Research Bearing on Mathematics Teaching; ex- in Malaysian schools. Paper presented at Semi- tracted tracted from Teaching School Mathematics. nar for lecturers of Training Colleges ， Peninsula UNESCO Malaysia. 1973 ， Training College ， . 4) 4) KHOO PHON SAI and YEOH OON CHYE: 13) SIM WONG KOOI: Evaluation of lnservice “ lndigenous Curriculum-Why." Paper presented training. A case study. Seminar extract on non- at at the Regional Workshop on Proposals of Pro- formal education convened by SEAMES with the grammes for RECSAM's SECOND FIVE-YEAR cooperation the Southeast Asia Development Ad- PLAN ('75-'80). 1974 ，RECSAM Penang ，Malay- visory Group (SEADAG) and the Government of Malaysia. Malaysia. RECSAM 5) 5) ANNUAL REPORT ， 1973: Regional Centre for 14) PERLBERG ， A.: “ Micro-teaching" _ Interna- Education Education in Science and Mathematics ，RECSAM tional Review of Educ. XVIII/1972/4