The International Commission on Mathematical Instruction
Bulletin No. 47 
December 1999


A Brief Report on the

Tenth Inter-American Conference on Mathematics Education

10th IACME

(Décima Conferencia Inter-Americana de

Educación Matemática, X CIAEM)

Carlos E. Vasco


With the help of the District Council and other authorities of the District of Maldonado, Uruguay, and under the leadership of Alicia Villar, a group of enthusiastic mathematics educators from Uruguay organized the 10th IACME - Tenth Inter-American Conference on Mathematics Education (X CIAEM - Décima Conferencia Inter-Americana de Educación Matemática) from the 8th to the 13th of August, 1999.

The local organizing committee was composed of Alicia Villar, José Luis Muñiz, María del Carmen Sartori, Víctor Martínez and Héctor Deambrosi, president of the Uruguayan Society for Mathematics Education (SEMUR).  They also received help from Juan Machado, Marta Martínez, Elizabeth Gandolfo, Antonio Velásquez and Alicia Fort, and especially from a group of students of the teachers' college "Instituto de Profesores Artigas" (IPA) of Montevideo, who were the ubiquitous guardian angels of the meeting.

With this tenth conference, the Inter-American meetings on mathematics education reached one more cycle since their inception in Bogotá, Colombia, in 1961, which have continued against all odds and obstacles during almost 40 years.

This time the odds and obstacles were formidable, especially because of the difficulties in electronic communications in Montevideo and Maldonado, and of the financial depression all Latin-American countries are currently undergoing, felt especially in Uruguay since its large northern neighbor, Brazil, drastically devalued its currency early in the year 1999.  This situation combined negatively with the lack of funds in institutions like UNESCO and OAS, which in other more prosperous times had supported other CIAEM-IACME meetings.

Even though the day before the beginning of the conference only 260 early registrations had been paid, the flood of last-moment participants surpassed all expectations, quickly going beyond 600, a number that caused understandable snags and confusion during the first day; but these difficulties were promptly overcome by the organizers who were able to carry out a very successful meeting from day two on.

The inauguration
On the evening of August 8, the authorities of the District of Maldonado, the delegate of the Minister of Education and Culture of Uruguay, and the District's secretary of education formally welcomed the participants.

Because of a sudden illness of the president of CIAEM-IACME, Dr. Fidel Oteiza (Chile), the vice-president, Dr. Carlos E. Vasco (Colombia), formally opened the meeting with an address in which he pointed to three phases of the Inter-American Conferences of the last 40 years.

The first phase, inaugurated by Marshall Stone in Bogotá in 1961, was led by many university professors of the Americas with the explicit intention of fostering in all countries from Canada and the U.S., to Chile and Argentina, the "New Math" reform movement.

The second phase, from the mid-seventies to the late eighties, centered around fostering the exchange of the growing experiences in research on mathematics education in Mexico, the U.S. and Canada with the then very incipient initiatives of researchers in mathematics education in the rest of the Latin-American countries.  This second phase was more restricted to college teachers, university professors and members of research institutes.

The third phase, from the late eighties to our days, has seen the expanding participation of school teachers, and the presentation of many forms of research with qualitative and quantitative methods, action-research and systematizing of practices by teams of primary, secondary and tertiary level teachers.

The scientific program
The second day started with the invited address of Dr. Ubiratan D'Ambrosio (Brazil), former president of CIAEM-IACME and permanent supporter of all its initiatives, who expressed a grounded fear of many mathematicians and mathematics educators aroused by the growing pressure from politicians, parents, and businessmen to decrease the number of hours dedicated to mathematics in primary and secondary education, and the decline in the public image and esteem of mathematics, especially among the young.  To counteract such tendencies, he suggested to link school mathematics much more closely with the needs of technology and the workplace through integrated project-based learning, to increase the connectedness between curricular areas and everyday life, and to bring traditional mathematics curricula much closer to the local cultures through ethno-mathematics.

From 10:30 a.m. to 12:15 p.m., simultaneous topic-group meetings were held on ethno-mathematics, history of mathematics, teacher training, technology and mathematics education, and mathematical competitions.  These topic-groups met once again on Thursday, August 12.

In the afternoon, four simultaneous lectures and two hours of short communications were held.  The two-hour session on short communications was also held on Tuesday and Thursday from 5 to 7 p.m. Tuesday, August 10, started with an invited lecture by Luis Balbuena, from Tenerife, Spain, on the teaching of mathematics through inter-disciplinary projects.  He presented the experience held in Tenerife with Project "Nereida", on navigation from the year 1400 to the year 1700, with the co-operation of high schools from Spain, Portugal, and Italy.  He explained the many difficulties arising in the planning and executing stages of inter-disciplinary projects, and some strategies to overcome those difficulties.  More information on this project can be obtained at the following web site:


In the morning of Tuesday, simultaneous topic-group meetings were held on the following areas: mathematics in the early grades, problem solving, the teaching of geometry K-12, and the teaching of mathematics at the tertiary level.  These topic groups also met on Friday, August 13.

In the afternoons of Tuesday, Thursday, and Friday, four simultaneous lectures and four workshop sessions took place.

A welcome break
Wednesday was a free day, in which the organizers invited the participants to bus tours of the summer resorts.  Unfortunately, August is a winter month in the Southern hemisphere; but the tours of La Barra, Punta del Este, Maldonado, Punta Ballena, and Piriápolis with their beach resorts, luxury hotels and mansions made it clear to the participants why during the summer months this region of Uruguay becomes a world meeting point for tourists, artists and celebrities.

Back to work
Thursday, August 12, started with an invited lecture by Dr. Antonio Pérez Jiménez (Spain), on the relation of traditional mathematics and modern functional programming, with examples taken from the treatment of classical problems, like the splitting of wagers as proposed by Méray, and interpreted differently by Pascal and Fermat, both through traditional algebra and through functional languages like SCHEME, a dialect of LISP, HASKELL, or ML.  The lecture ended with a concise presentation of top-down methods in functional programming.

After the topic groups, lectures and workshops of Thursday, August 12, two key meetings convened.  The first one assembled all representatives of societies or associations of mathematics educators in Spain and the Americas which had members present in the conference, with the purpose of discussing a first draft of by-laws to configure an Ibero-American federation of societies and associations related to mathematics education.  This meeting was chaired by the president of CIAEM-IACME, Dr. Fidel Oteiza (Chile), who recovered from his illness just in time to attend the last two days of the conference.  The minutes of the meeting were taken by Dr. Luis Balbuena (Spain), who is in charge of collecting the observations to the draft, rewriting the by-laws, and getting the new federation started before the end of the year 2000.

Many suggestions to the draft were formulated, and it was agreed to fix the date of January 31, 2000, as the final deadline for observations on the wording of the by-laws, forms of affiliation, admission criteria, and payment of dues.  Copies of the current draft can be obtained by sending an e-mail message to Dr. Luis Balbuena at


The international meeting to formally start the new federation should be held not later than October 31, 2000.

It was proposed that the new federation should take charge of the organization of the Ibero-American Conferences in Mathematics Education (CIBEM), three of which have already been held in Spain, Brazil, and Venezuela.  It was also proposed that CIAEM-IACME would co-sponsor the CIBEM meetings, and vice-versa, and that their dates should be set in such a way that the Fourth CIBEM could be held in the year 2001, and the Eleventh CIAEM-IACME in the year 2003, alternating every other year from there on.

The representative of the Bolivian Society for Mathematics Education, Begoña Grigoriu, ratified the offer made last year in Caracas to hold the Fourth CIBEM in Cochabamba, Bolivia, which could be moved back to the year 2001 as suggested before.  This proposal was supported by all societies and associations present in the meeting, and will be discussed by Dr. Balbuena with the Spanish and Portuguese federations of societies for mathematics education.  More details on the future CIBEM meeting can be obtained from Ms. Grigoriu at


CIAEM-IACME 1999-2003
The second meeting was the official assembly of CIAEM-IACME, chaired by the president, Dr. Fidel Oteiza (Chile), with the presence of one of the vice-presidents, Dr. Carlos E. Vasco (Colombia), and the secretary, Dr. Patricio Montero (Chile).  Some members-at-large and former members of the Executive Committee of CIAEM-IACME were also present, as well as many representatives of societies and associations for mathematics education.

Dr. Maria Salett Biembengut, and Dr. Nelson Heine, both from the Regional University of Blumenau in Brazil, formally submitted a bid to hold the Eleventh CIAEM-IACME in the city of Blumenau, Brazil, in the year 2003.  They brought an official letter of support from the President of their University, and showed a video of the campus.

Given the positive experience of the Second CIBEM, which was held in Blumenau, and the support of the University, the bid was unanimously approved.  More details of the meeting can be obtained from Drs. Biembengut and Heine at   or

A specific e-mail address for the Eleventh CIAEM-IACME will be active soon at

and a web page for that meeting will be maintained by the Regional University of Blumenau starting at the end of the year 1999.

The next item on the agenda was the composition of the Inter-American Committee on Mathematics Education for the next four-year period, 1999-2003.  The following officials were elected to the Executive Committee:
        President: Dr. Carlos E. Vasco (Colombia).
        Vice-presidents: Dr. Alicia Villar (Uruguay), and Dr. Maria Salett Biembengut (Brazil).
        Secretary: Dr. Eduardo Mancera (Mexico).
        Members ex-officio of the Executive Committee of CIAEM-IACME are to be the last three former presidents: Ubiratan
        D'Ambrosio (Brazil), Eduardo Luna (Dominican Republic and the U.S.), and Fidel Oteiza (Chile).

The discussion centered afterwards in the need to amplify the international presence and representativity of the Committee by increasing the number of members-at-large (in Spanish "Vocales") from different countries.  It was decided to set the number of members-at-large at twelve, and several names were suggested.  The former and future presidents and secretaries were commissioned to draft the final list of members-at-large.  The official list of members-at-large for the period 1999-2003 appears in this Bulletin just after the present report.

The final day
The work of the last day of the meeting, Friday, August 13, started with the invited lecture by Dr. Carlos E. Vasco (Colombia), who addressed the ways of approaching school mathematics for the first decade of the new millennium, emphasizing the development of mathematical thinking in all its forms, and the incorporation of different forms of research in the practice of teachers of all grades.  He proposed to distinguish five specific types of mathematical thinking: numerical, geometric, metric, stochastic and variational.  There are specific types of systems related to each one of these types of thinking, which he explained with the language and examples used in the guidelines for curriculum development in mathematics proposed by the Colombian Ministry of Education.  He concluded by suggesting that mathematical curricular units and mathematical components of inter-disciplinary units would be very appropriately centered around the modelization of real-life situations and processes by means of models taken from the mentioned five types of mathematical systems.

After the topic groups, simultaneous lectures and final workshops, the closing session of the meeting was started with a lecture by the president of CIAEM-IACME, Dr. Fidel Oteiza (Chile), on the national project under his responsibility, oriented to a large-scale transformation of mathematics teaching in Chile.  He presented the three project components of curricular and pedagogical reflection, teacher training, and technological support, and invited mathematics educators of all countries of CIAEM-IACME to contribute to and learn from this Chilean experience.

Then, he made public to all present the composition of the new Committee for the next four-year period, and the approval of the bid for the Eleventh CIAEM-IACME to the Regional University of Blumenau in Brazil for the year 2003.

After a brief recess, the organizer of the Eleventh Conference, Dr. Alicia Villar (Uruguay), thanked the participants and the support persons and organizations; Dr. Oteiza thanked her and her immediate co-workers, especially the teacher students form the "Instituto de Profesores Artigas", and formally handed over the presidency of CIAEM-IACME to Dr. Carlos E. Vasco.  The new president declared the event formally closed, inviting all present, and now all readers of this chronicle, to the Eleventh CIAEM-IACME in Blumenau, Brazil, in the year 2003.

Carlos E. Vasco  (Colombia)
President of CIAEM-IACME (1999-2003)
Harvard G. S. E. - Project Zero
Cambridge, MA 02138, USA