POLICY STATEMENT ON COMPETITIONS AND MATHEMATICS EDUCATION

Definition of Scope of Competition Activities

The scope of activities of interest to the WFNMC, although centred on competitions for students of all levels (primary, secondary and tertiary), is much broader than the competitions themselves. The WFNMC aims to provide a vehicle for educators to exchange information on a number of activities related to mathematics and mathematics learning. These activities include

• Mathematical competitions of various kinds
• Mathematical aspects of problem creation and solution, a dynamic branch of mathematics.
• Research in mathematics education related or pertaining to competitions or the other types of activities listed here.
• Enrichment courses and activities in mathematics.
• Mathematics Clubs or “Circles”.
• Mathematics Days.
• Mathematics Camps, including live-in programs in which students solve open-ended or research-style problems over a period of days.
• Publication of Journals for students and teachers containing problem sections, book reviews, review articles on historic and contemporary issues in mathematics.
• Support for teachers who desire and/or require extra resources in dealing with talented students.
• Support for teachers, schools, regions and countries who desire to develop local, regional and national competitions.

With qualification, WFNMC also facilitates communication through its Journal and Conferences, in the following areas

• Topics in informatics parallel to those in mathematics. This applies particularly in that no equivalent body exists for informatics. It takes into account that the disciplines are closely related, that many journals cover both topics, and that in many countries the organisation of competitions in mathematics and informatics, and mathematics and informatics themselves, are closely related.
• Recreational mathematics, including mathematical puzzles, particularly as they might inspire the creation of mathematics problems.

WFNMC is concerned with activities particularly when they have international significance or are significant within their own country.

EFFECT ON TEACHING AND LEARNING

1. Two classes of competitions

   Competitions generally fall into one of the following two categories, both of which have increased substantially in popularity over the past century, and particularly in the last three decades.

   1. Inclusive Competitions

      These competitions are of a popular nature, designed for students of all standards, and certainly accessible to the student of average or below average standard. Such competitions give each student the opportunity to solve simple though often intriguing problems set in familiar circumstances. These competitions, aimed also at highlighting the importance of the curriculum, will not usually be set according to a published syllabus, but will often be checked by experienced teachers to ensure that the mathematical skills involved are within the scope of virtually all students in the countries or regions where the competitions are held.

      Examples: Multiple choice competitions such as exist in Australia, Europe (Kangaroo and UK Challenges) and North America (Canada and USA). First rounds of National Olympiads as they are held in some countries.

   2. Exclusive Competitions

      These Competitions are aimed at the talented student. Once again the syllabus of the competition is rarely formal, although past papers and other materials are often available as guidelines for new participants and their teachers. Because the subject of mathematics is so broad, there is vast material of a challenging nature which enables students to deepen their knowledge and command of mathematics without the need to accelerate their study. This can aid the talented student to mature intellectually and better equip him or her for later study or careers.

      Examples: National and International Olympiads in Mathematics, ARML. Some of the related activities, such as mathematics camps, are often focused toward the talented student.

2. Independence of Administration

   Often such competitions are promoted independently of normal mathematics curricula and in fact usually outside the framework of the administration of the curriculum. As a result, competitions can be written by students without the pressure normally associated with the assessment process, giving students a means of discovering their talent without risk.

3. Competitions test ability to deal with unexpected situations

   Competitions are usually held over many schools, sometimes in more than one country. As a result they are rarely in a position to test material freshly taught in the classroom, and are therefore likely to be directed toward a broad level of mathematics achievement and an ability to deal with problems or situations beyond usual experience or expectations. As a result competitions not only test direct mathematics knowledge and skill, but also the ability of the students to meet more general challenges in life. Similarly it can be observed that the associated activities of preparing for competitions involve the development of logical reasoning and thus the ability to deal with new situations.

   The creation of problems that address unexpected situations explores profound interrelations among mathematical topics and arguments, or between mathematics and other academic or daily experiences, in effect constructing conceptual maps which underscore and delimit understanding and command of mathematical thinking as opposed to knowledge of topics, an aspect of competitions that makes a unique contribution to research in mathematics teaching and learning.

   Competitions often expose students to types of mathematics not often offered in school, certainly including mathematics that can be exciting, surprising, elegant and beautiful. For many students competitions become a deciding factor in choosing mathematics as their profession. Thus, competitions can allow mathematicians to pass the baton to new generations of mathematicians, a critical element in the preservation of mathematics.

4. Resources for Teachers

   Competitions, especially those of the inclusive type as defined above, provide vast resources for the teacher and the class room.

   Inclusive competitions usually have the items published later. These items are often sorted into mathematical topics and statistics, which give a clear guide to the level of difficulty.

5. Opportunity for Interaction

   Competitions provide a rare opportunity for teachers and academics to work together. They also provide a unique opportunity for academics and teachers to work with talented students.

VOLUNTARY COMMITMENT OF TEACHERS

The WFNMC notes that most competitions are dependent on the voluntary contribution of dedicated teachers and academics who are highly committed to their subjects, and often work long hours, much beyond the call of paid duty, in composing problems, working with students or marking scripts. These people serve professional societies or non-profit organisations which are equally committed to highlighting publicly the importance of mathematics.

The WFNMC supports programs that seek to provide recognition to those who contribute their expertise, time and effort to competitions and associated activities.

SOME FURTHER COMMENTS

• Competitions inspire in many students a further interest in mathematics and increases their desire to learn more mathematics.
• Participation in competitions is often voluntary and can generally be done to a level chosen by the student.

CONCLUSIONS

Through the preparation for competitions and the work with talented students a whole classical branch of mathematics is both preserved and developed. Without these activities this important mathematical heritage and treasure would die out very soon and the society will lose something important.

The work with talented students (preparation for competitions) reveals the frontiers of what could be given to school students, what the students could assimilate and, most importantly, didactical know-how is gathered helping to determine how this special and more difficult material could be transmitted to students. If one day such topics are to become (for one or another reason) a part of the curriculum (not necessarily in the usual schools) knowledge on how to do this will be available. In this respect the role of competitions is similar to the role played by car-races for the development of the car industry.

The preparation for competitions develops the minds of young people. As the physical efforts contribute to bodybuilding, the preparation for competitions serves "mind-building" which is often neglected in the modern society. Taking into account that in some competitions (earlier stages of national Olympiads) hundreds of thousands of students make "brain exercising" one understands that after the competition the human resource potential of the respective country is improved.

Competitions allow young people to compare their abilities and achievements in a very categorical way which is free of subjective opinions. This helps them make decisions about who they want to be professionally and what kind of career to pursue. It is difficult to overestimate the role of the WFNMC in this respect.

Adopted as policy on 10 August 2002