First Prize (a team from Romania): USD 1.000, their teacher USD 750,

Second Prize (a team from Iraq) USD 750, their teacher USD 600,

Third Prize (a team from Turkey) USD 600, their teacher USD 500.

ICMI

Bulletin No. 44

June 1998

This is report on a

As a preliminary remark, I would like to mention that back in the 70's we dreamed, together with Tamas Varga, father of the new-maths wave in Hungary, that a real continuation of hands-on, discovery, etc. approaches to young (up to 10-12 years old) childrens' maths education should be based, or at least should involve, the *complete* solution of real life problems. There were single examples all over the world of such kind of attempts (e.g. in Italy by L. Grugnetti) but they never became general practice. This kind of *project* work attracted the attention of Anne Hawkins (Hawkins, 1986) who started a project competition *in statistics* in England, which is still running successfully and has been copied by others. This type of extra-curricular activity was not exercised within mathematics, however (to the best of my knowledge; if you know of some activities going on in this direction, please inform me).

I have kept advocating this idea within different forums, like the conferences on the teaching of mathematical applications and modelling, but without much success. Recently, during my two years' stay at the Middle East Technical University (METU), Ankara (Turkey), I offered (conducted) a "Project Course in Mathematics for Students Teachers" which was extremly well received by my students. This is reflected in the fact that one of them, Ilyas Karakaya, was able to convince officials to sponsor an international competition with 16 participating countries, formally organized by the Kocaeli Private Erkul Secondary School, Izmit, Kocaeli, Turkey, 23-28 Jul, 1997. I was invited to take part in the work of the jury and I very much enjoyed this work. There were plans to make a tradition out of this competition, and it would have been nice to conclude this report by announcing the date of the next one. Unfortunatelly, the organizers seem to have financial difficulties in proceeding with their plans. I am convinced that a continuation is needed and that this topic would be worth deeper considerations.

Originally the Competition was considered for Turkey only. As the idea spread amongst former METU students, it turned out that those practising in foreign private schools also wanted an opportunity to include their students in the competition. Therefore, the Announcement was formulated as a call for an international event. It was issued by Mehmet Ertekin, Director (Chief Organizer) and Ilyas Karakaya, General Coordinator, on behalf of the Kocaeli Private Erkul College, Izmit, Kocaeli, Turkey.

The organizers invited contestants aged 13-19 years old, from any country, who were not yet registered at any university. Participating teams were expected to report on their own project work done in their own schools, with the help of their own teachers and possiblysupported by some academic advisors. Submissions had to be original and should be collective works of the students. They further had to reflect scientific work. A guide to submissions specified their required structure: Title, followed by the stating the goal of the project; then a formal introduction; methods applied in the project; conclusions and finally discussion. References and resources were also to be mentioned. The projects were to be assessed by an international jury "according to scientific existence, economic existence, actuality, practicability, preservance, conductibility, productivity, free imagination in exhibiting the project, understandability in the report, etc." Policy on partiipation costs was also announced and carried out as follows.

The organizers were generous about the participation costs. They had invited 2 representatives of all teams with full coverage of local costs. Travelling of foreign participants from Istanbul to Izmit was covered by the organizers. Awards were presented to winners in a well organized ceremony with the highest ranking officials from the province, and with coverage by several TV channels. Suffice it to announce the prizes of the winners:

The upper 10 percent of the participants were presented with Gold Medals, the second 20 percent with Silver Medals, and the following 30 percent with Bronze Medals. Excursions and socialt events were also provided free of charge.

The topics of the submissions may be divided into the following main categories with their numbers in brackets:

Algebra, general (10), Analysis, general (13), Computers (6), Covering and Packings (4), Didactics (6), Discrete Mathematics (7), Geometry (12), Inter-Science (3), Mean values (6), Number Theory (12), Practice and Applications (8), Recreation (4), Non-classified (8).

The quality of the submissions varied a lot. A few (and luckily just a few) of them did not meet the formal requirements: Participants had copied or re-written published articles, or listed and solved common school exercises. The majority of the submissions, however, dealt with topics far beyond compulsory school mathematics.

Interestingly, many projects aimed at improving the level of maths instruction. These listed nice collections of illustrations, examples of cross-topics applications within maths and between different subjects. There was even an essay about the methods of proofs at school level. Several projects within pure maths were initiated by problems posed at national/international maths olympiads, showing that the contestants are regular readers of the periodical QUANT. Favorite topics were the general inequalities between different mean values, packing-and-covering themes and the Fibonacci numbers. /

As it may have been guessed, predominant areas were Combinatorics, Number Theory,Geometry and Algebra. Just a few topics came from more sophisticated fields, e.g. Game Theory.

Information on the conference was (and is) available at the web site

- This work was partially supported by Grant No. T-17427 of the National Scientific Research Foundation (OTKA).

Ersoy, Y., Nemetz. T., 1995: 'Mathematics Project Course in Teacher Training: constructing nice puzzles', in *Advances and Perspectivces in the Teaching of Mathematical Modelling and Applications*, (C. Sloyer et al. eds.), Water Street Mathematics, Yorklyn, Delaware

Hawkins, A., 1986: 'Students' Project Work and the UK Applied Statistics Competition', *Proc. of ICOTS-3*, (1986), 209-213