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
- 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
- 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
All of the above activities have a positive effect, direct or indirect, on
the teaching and learning of mathematics and in attracting students to the study
of mathematics. In particular the WFNMC highlights the following characteristics.
- 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.
- 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
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.
- 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.
- 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.
- 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.
- 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.
- 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
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.
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
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