Department of Mathematics at the Faculty of Electrical Engineering of University of Ljubljana

**ABSTRACT**

Slovenia, although a small European country, has a long tradition in organizing competitions in many scientific disciplines. The competitions in logic and in recreational mathematics seem to be peculiarity of the country.

In the paper the general information of the competitions is given: the reasons of starting them, the source of questions, population involved, aims to be achieved, problems with organization, research implications from the competitions, etc.

All of us who are involved in organizing of various mathematical competitions are aware of the influence they have on students future professional careers. The best student on national competitions can expect a university job, the best on International Olympiad are able to achieve research results of a very high standard.

Besides that, to achieve its role mathematics needs a huge number of devoted teachers and applied mathematicians. For many teachers it is true that they haven't reached high scores on competitions and as a consequence many of them don't even mention the existance of such competitions to their students.

The third important group are students that have high scores on junior level competitions but later they get interested in other disciplines, not necessarily connected with mathematics. So they can't compete with students that all their free time devote to solving mathematical problems. Aren't we obliged to take care of deductive abilities of these students? The answer to this question must be "yes" since in such a way we enlarge the mathematical culture in other disciplines.

To achieve this goal the competitions must not involve difficult mathematical formulas but it is better to emphasize the difficulty of deduction. This can be reached by competitions in logic, recreational mathematics and computer programming.

Mathematics is usually the subject where pupils get best opportunity to develop their logical thinking. This is particularly true during axiomatic development of geometry. The weakness of such an approach is meeting simultaniously two subjects, namely logic and mathematics. Because of increasing difficulty of mathematics many children loose their interest for it and in this way the opportunity to learn logic is lost as well.

A better way to exercise thinking is solving logical problems that are independent of particular subject.

In regular curriculum logic is usually represented by a few hours inside mathematics. On the other hand the importance of logic outside of mathematics is growing - in computer science, law, medicine etc.

With the appearance of Smullyan's logical books the opportunity to systematically present logic as a set of problems had occurred. Therefore one of the aims we posed to ourselves was tol translate as many books as possible, the books that adequately introduce children to logic.

To stimulate solving of logical puzzles a competition in logic has been organized.

The first competition took place in 1986 with 123 competitors devided into three age groups (from 13 to 15). The first round of the eighth competition was attended by 7000 competitors devided into 10 groups aged form 12 to 21. The second round was attended by 500 students. For this year a three round competition will be prepared.

Three logical problems were posed and had to be solved in 90 minutes. The result was dependent on quality of explanations.

The problems were taken from foreign literature which was not available to our pupils. Occasionally some original problems were introduced.

The competition is not connected with school curriculum and takes place at the beginning of each school year, with the intention that pupils prepare for it during vacations.

At the last competitions the same problems were posed to two age groups in order to get some information about how much the logical abilities depend on age. We got small diffenrence with older generations and some more differences with younger generations. The interested thing to note was that in the group of first year university students the second and the forth place were achieved by law students.

Further tasks concerning logical competitions and promotion of logic in school curriculum are:

- Each mathematical text book should contain some logical problems.
- With posing same problems to different generations more information on development of logical thinking should be found.
- Development of new logical problems, their classification and problem solving methods.
- To prepare sets of logical problems for different generations.
- To study correlation between success in mathematics and logic.

While for the competition in logic the emphasis is on deductive reasoning we wanted a competiton in which also algorithmic reasoning, space representability and mathematical representability of problem is to be developped but at the level of elementary mathematics.

Mathematical recreation problems are ideal for such a competition. The first national competition was organized in 1990.

To enter the competition a student must solve some problems in our journal Logika & razvedrilna matematika (Logic & Recreational Mathematics). In this way approximately 140 students participated in competition. They were devided into 9 age groups, the last one includes university students.

Four problems are to be solved in two hours: a logical puzzle, an algorithmic problem, a geometrical problem and an arithmetical puzzle (for instance a cross number puzzle).

The problems are taken from foreign books and journals of recreational mathematics.

In these competitions we have an opportunity to present mathematics as a very entertaining subject.

Lessons from computer programming were introduced to our secondary schools (attended by pupils from 15 till 18 years of age) in 1969 with one group of pupils. Next year there were five groups that attended to these lessons in better organized form. The seminars for teachers (mainly mathematicians) were organized and in next few years almost all secondary schools introduced computer programming as optional subject of two hours per week. Of course these optional lessons were not treated as seriously as compulsory subjects. Such a state of affairs lasted almost ten years. Then computer programming became compulsory subject.

At first FORTRAN was used for work on computers, later it was replaced by Pascal.

To encourage the best pupils to deepen their knowledge about computers, and to increase inscription on Department of computer science of our Faculty, which was about 20 students per generation, we organized in 1977 the first national competition in computer programming. It was attended by 47 competitors. In 150 minutes they had to solve four problems.

In present form the competition is attended by 200 pupils which are chosen from school competitions.

The competitors are devided into three groups:

- competitors after one year of computer programming lessons;
- competitors after two years of lessons;
- experienced competitors.

The book with problems from the first twelve competitions was published. The problems are classified as follows:

- simple exercises;
- computational problems;
- recursive functions;
- sorting;
- graphs;
- real time processing;
- other problems.

In 1988 the International Computer Science Olympiad held in Slovenia.

In 1986 the competitions for elementary school pupils started- for children from 7 - 15 years. Pupils are devided into three groups:

- pupils from first to forth class compete in solving exercises in Logo;
- fifth and sixth class solve problems with Basic or Pascal;
- seventh and eighth class solve more advanced problems.

The first round of the competition has about 3500 competitors, the last about 60.

Computer programming is not compulsory subject in elementary schools, but optional circles are very active. Some knowledge of computers children get through so called technical education.

The competitors have shown relatively high knowledge, and that shows there were many good mentors. The main problem is the choice of adequate programming languages.

Now there are too many applicants for studying computer science but the main reason to run competitions in computer programming still remains: to motivate youngsters to work hard in the subject.

Last Update: June 12th, 1997 u. |