*RAINDROP*

TEACHING OF MATHEMATICS
PROGRAM FOR UPGRADING MATHEMATICS SCHOOL TEACHERS

IMPA, although being a world-renowned institution of high mathematical research, has a strong interest in the teaching of high school Mathematics. Since 1991 the Institute has held regular short courses for teachers, not only in Rio but also in other states. Starting in the year 2002, a new development was possible when the program became part of the Millennium Institute Global and Integrated Advancement of Brazilian Mathematics, IM-AGIMB, from there on the program was carried out with the participation of IMPA, the cooperation of RNP (the National Research Web), the Rio de Janeiro State Agency for the Advancement of Science (FAPERJ) and the Agency for Financing Studies and Projects (FINEP). Through the INTERNET the program was spread to an increasing number of other Brazilian states, reaching a much larger number of teachers, over 22.900 in the period 2002-2008, as can be seen in the picture below.

This Program now begins to be part of the Project Instituto Nacional de Ciência e Tecnologia em Matemática – Avanço Global e Integrado da Matemática Brasileira, INCT-AGIMB.

In this way, we are contributing to diminish two very serious gaps that exist today in the teaching of mathematics in Brazil at secondary school level. The first is between the levels of high school and college teaching of Mathematics. The second is due to the large territorial extension of our country: schools in different regions have very diverse standards, most of them far below acceptable level.

We have written a series of textbooks oriented towards teacher training. They have been used in our activities and remain in possession of the participants for further consultation. They are widely praised by the participants.

Our partners in the project have been, so far, 25 federal (and one state) universities, whose Math departments, throughout the country are eager collaborators in our work.

The activities take place twice a year, one week in July and one week in January, during school vacations. They consist of classes in the morning, given at IMPA by the four members of the teaching staff. The lectures are transmitted via INTERNET to the 26 local points, where the audience (from 70 to 150 teachers) attend them. The student-teachers meet again in the afternoon when, divided into groups of about 10 each, they work on problems assigned each day by the central staff at IMPA. The problem-solving sessions occupy one half of the afternoon. The afternoon ends with all 70 to 150 together in the lecture hall, where the solutions to the problems are presented and lively discussed by all, during two or more hours. This is a very important part of the program and its quality depends heavily on the local staff, which has been carefully chosen by the IMPA group. The weekly work ends on Friday, when the four main instructors sit at IMPA to provide live answers to questions that come by e-mail from all over the country. The classes, as well as the Friday sessions, are recorded in the IMPA site (www.impa.br) and can be downloaded at no cost.

NATIONAL PROJECT OF MATHEMATICS OLYMPIADS
BRAZILIAN MATHEMATICS OLYMPIADS 1979-2008

Mathematics Olympiads are under way in more than 100 countries and they occur on national, regional and international scales. If properly structured Olympiads may serve as major instruments for promoting sciences to young students. They are vehicles for improvement of science teacher’s skills, and they are excellent to detect young scientific talents. To achieve these three goals, the Olympiads should be large-scale events in each country, at several grade levels and in three different stages at each level. The first test is very friendly to students and their teachers, with many winners and simple prizes. The second stage involves those who performed well in the first stage. Finally, a third stage determines the best talents, who then compete internationally and are awarded fellowships for further science training. This is precisely the structure of the Brazilian National Mathematical Olympiads promoted by the Brazilian Mathematical Society and the National Council for Scientific and Technological Development – CNPq.

The Millennium Institute - Global and Integrated Advancement of Brazilian Mathematics has been a new partner in this important activity with two goals: to promote regional or state Olympiads within Brazil and to expand the Brazilian participation in international competitions, now specially the International Mathematics Competition for University Students, which is quite new. IM-AGIMG´s contribution leads to a participation of more than 250.000 students in the Regional Olympiads in different States of Brazil and about 300.000 students in the Brazilian Mathematical Olympiads. It’s to be noted the excellent performances by Brazilians at the International Mathematics Competition for University Students, including being awarded in 2006 an especial golden medal, the Grand First Prize.

This Program now begins to be part of the Project Instituto Nacional de Ciência e Tecnologia em Matemática – Avanço Global e Integrado da Matemática Brasileira, INCT-AGIMB, that follows IM-AGIMB, keeping its association with the Brazilian Mathematical Society and the National Council for Scientific and Technological Development- CNPq.

Performance at the International Olympiads
The participation of Brazil at the International Mathematics Olympiads has grown exponentially, including the International Olympiad, the Ibero-American Olympiad, Cone-Sul, Ibero-American in Mathematics, the International Mathematical Olympiads for University Students.

May Olympiads
This competition organized for young students is held in two levels: Level 1 for students up to 13 years old and Level 2 for students up to 15 years old, from Latin America countries, Spain and Portugal. In Brazil, this Olympiad is only for those students that have been awarded in the Brazilian Mathematics Olympiads (golden, silver and bronze medals and honor citations). The tests of the selected students are sent to the Organizing Committee in Argentina, where the final classification is processed.

Brazilian’s Classification: Brazil has consistently being a leader in such Olympiads obtaining always the first place in the classification with maximal awarded: 1 gold medal, 2 silvers medals, 4 bronze medals and 3 honor citations.

South Cone Mathematics Olympiads
It is an international competition in which countries from the South America South Cone take part, represented by 4 students teams that are not yet 16 years old until December 31st. of the year before the celebration of the Olympiad.
Participants: Argentina, Bolívia, Brasil, Chile, Paraguai, Peru and Uruguai

Brazilian’s Classification: Brazil takes part in this competition since 1988 and has been the leader of it, winning so far 69 medals, 18 golden, 26 silver and 25 bronze.

Ibero-American Mathematics Olympiads - OIM
It is an international competition in which the countries of Latin American, Spain and Portugal participate, represented by teams of at most 4 students under the age of 18 years until December 31st of the previous Olympiad.

Brazilian’s Classification: In 2004 and 2005, Brazil won for the first time among all countries 4 gold medals. Again, Brazil is the leader of such a competition and has won since 1985 42 golden medals, 25 silver and 10 bronze.

The 23rd Ibero-American Olympiads will take place in Salvador, Bahia, in the period 18-28th September, 2008. On the occasion, an International Symposium on Teaching of Mathematics will be held involving teachers and students of mathematics at all levels.

There is also an Ibero-American Mathematics Olympiads of Universities - that is an international competition where the participants should not possess a University and should be registered at a University as an undergraduate student. Brazil organizes this competition since 2002. Again, Brazil has been consistently been the leader of the group.

International Mathematics Olympiads - IMO
Organized since 1959, it is the most important international competition. More than 100 countries participate in this competition, represented by teams of up to 6 secondary school students or that have not yet entered at the University or equivalent, at the date of the celebration of the Olympiad. In 2008 Brazil’s performance was above that of Germany, Canada, Italy, India, Israel, France and United Kingdom and it has the best one among the countries of Ibero-America. Brazil takes part in this most global Olympiads since 1979 having obtained so far 7 golden medals, 18 silver and 56 bronze.

International Mathematics Competition for University Students - IMC In 2003 Brazil took part for the first time of the International Mathematical Competition for University Students with a team formed by 8 students from Brazilian universities (3 students of ITA, 1 student of UFRJ, 1 student of UNICAMP, 2 students of IME and 1 student of UFSC). In this competition main universities in the world participate such as, for example, Cambridge, École Polytechnique, Institute Max Plank, Technion Institute, Massachusetts Institute of Tecnology (MIT), Oxford University, Universidade Complutense of Madri and University of Moscow.

Brazilian’s Classification: In six years the Brazilian participants were awarded 41 medals, 1 especial golden medal, a Grand First Prize, besides another 8 golden, 13 silver and 19 bronze medals.