Contests around the world
Overview. The AMC/US lags behind other countries’ mathematics contest programs in several ways. First, we have a smaller participation, both among schools and among students. Second, other countries have ongoing programs that support their students throughout the year. Many countries have competitions that are not timed, multiple choice events, and some have contests that require teamwork.
Below is a collection of summaries of email messages from friends in other countries about their national contests
Math Challenge for Young Australians: http://www.amt.canberra.edu.au/mcya.html
The Mathematics Challenge for Young Australians targets the top 10 per cent of primary students in Years 5 and 6, and secondary students in Years 7 to 10. Whereas it is directed at all students in this category it may be particularly useful in schools where teachers may be working in isolation and have a handful of talented students spread out over a number of classes.
The Challenge provides materials so that these teachers may help talented students reach their potential. Teachers in larger schools also find the materials valuable, allowing them to better assist the students in their care.
The aims of the Mathematics Challenge to Young Australians include:
There are three independent stages in the Mathematics Challenge for Young Australians - the Mathematics Challenge Stage, the Mathematics Enrichment Stage and the AMOC Intermediate Contest.
The Mathematics Challenge Stage (held during a 3 week period normally including April, but dates for current year may be found here) comprises four problems for those in the primary schools and six problems for the secondary school versions. All but two of the problems are to attempted individually while the other two problems can be discussed in pairs before individual submission of solutions. There are separate problem sets for Primary (Year 5-6), Junior (Year 7-8) and Intermediate (Year 9-10) students.
The problems for the Challenge stage are designed by the Challenge Problems Committee, a voluntary committee of Australian teachers and academics.
The Mathematics Enrichment Stage is a six-month enrichment program which commences in April. It comprises (2004) six parallel series of comprehensive student and teacher support notes. Each student participates in one series. These programs are designed for students in upper primary and lower to middle secondary (Years 5 to 10).
The materials for all series are designed to be a systematic structured course over the duration of the program. This enables schools to time-table the program to fit their school year.
The Mathematics Enrichment Stage is independent of the earlier Challenge Stage, however they have the common feature of providing challenging mathematics problems for students, as well as accessible support materials for teachers.
This Series comprisies a number of introductory topics in geometry, counting and numbers. It is suitable for students in Years 5 and 6.
This Series contains mathematics concerned with tessellations, patterns, arithmetic in other bases and recurring decimals. It is suitable for students in years 6 or 7.
This Series comprises elementary number theory, geometry, pigeonhole principle, elementary counting techniques and miscellaneous challenge problems, mainly for Year 8 and outstanding Year 7 students.
This Series comprises elementary geometry, similarity, Pythagoras' Theorem, elementary number theory, counting techniques and miscellaneous challenge problems, mainly for Year 9 students and those who have already done the Euler Series.
This Series consists of material on problem solving, algebra and number theory. It is designed for students in the top 5 to 10 per cent of Year 9 who have taken the Gauss series in another year, and are not yet ready for the Polya series.
This Series consists of notes on deductive reasoning (Euclidean geometry) and algebra. It was designed specifically for the top 5 per cent of Year 10 students and outstanding students in lower years. Schools have found that this series gives a sound base for students who wish to specialise in Years 11 and 12 mathematics.
From the Australians about the
It was the model for our own very successful event and I would have thought the format was very suitable for your country and that the paper had very serious respect, not only in your country but also from an external viewpoint. Your competition enriches the teaching of mathematics in your country by providing students the opportunity of showing a talent for handling an unexpected situation rather than been tested on immediate recall. It is an opportunity for really being able to discover a student's talent for mathematical thinking and problem solving.
The only negative comment I would make is the use of calculators being permitted. Our feeling is that a paper like this should be a test of mathematical thinking, and that the use of calculators in such contests leads to expectations by students that they might be useful, in fact disadvantaging them by the distraction caused. There is of course a use for calculators in the class room, but we do not think this is an appropriate occasion.
Our structure differs
significantly from that of the AMC. In essence, our view is that students
need more than just multiple choice or fill in the correct number. We run
the traditional contests in Grade 7/8 and 9-11. These contests are
multiple choice and are written by approximately 90K
students in each of these two divisions. We have introduced contests in
grades 9-11 which are 75 minutes in length and are in essay form. The
idea is to get kids to think about writing solutions to problems and presenting
written solutions. Of course, as you know, we have our grade 12
We are now offering a Grade 5/6 paper which is not really timed (up to the discretion of the teacher) and is done three times per year. There are three sets of problems provided free of charge on the Web that teachers can access and then use in their class. We provide certificates for the kids at both the participation level and at the excellence level. I feel very happy with this approach because it is taking the emphasis out of just competing and is putting the onus on learning. We do not produce National Summaries but provide detailed solutions for teachers so that they can work with the kids.
In addition to timed individual competitions in the form of math exams, we have another nationwide competition. It is called Team Maths Challenge. Materials are offered
to schools to select their teams. The schools then compete in
very many regional and then one national final. Some schools from continental
The format is: two children from each of two consecutive years (I think grades 8 and 9 in American notation) comprise a team and work together against teams from other schools. There is lots of running about and changing seats, and noise.
The problems involve hands on questions (manipulating
geometric shapes, spotting patterns and so on). In the national final there is also a poster competition; the kids are invited in advance to become expert on a particular (often
geometric) topic (e.g. the centres of a triangle). On the day of the final they manufacture a poster which incorporates what they have learned, together with their answers to three questions which we give them on the topic when they arrive. As well as being educationally splendid, this keeps the kids busy and quiet while the administration of the main part of the competition is being organized (e.g. 40 teams, each with a teacher and the teachers have to be trained on the rules and how to administer the event, so the time is invaluable).
The competition director is Jacqui Lewis
Jacqui Lewis <firstname.lastname@example.org>
me outside) still has a monopoly.
Multiple choice first round for large numbers:
Primary (Grades 4-5): new, informal and growing (multiple choice) -
around 100 000 and likely to grow to 250 000
Grades 6-7: around 290 000 from 65% of schools
Grades 8-10: around 260 000 from 60% of schools
Grades 11-12: around 60 000
Grades 4-5: multiple choice for around 1500
Grades 6-7: 2 hour written for around 1500
Grade 8: 2 hour written (6 questions) for around 600
Grade 9: 2 hour written (6 questions) for around 600
Grade 10: 2 hour written (6 questions) for around 600
Grades 11-12: BMO1 3.5 hour written (5 questions) for around 900 BMO2 3.5 hour written (4 questions) for around 100
Bits and pieces for the IMO squad.
One other summer school for Grades 9-10 (and some 11s)
At senior level things are not healthy, since the system is being
dominated by "Birds of Passage" (from PR China). But no one will
Admit this. There is a clear drift back towards selecting kids from
privileged schools (which I had reversed).
(i) for Grades 7-8 (teams of 4) - involving 1200 schools nationwide
(ii) For Grade 11 (teams of 10 - more like ARML) - involving 70
schools (by invitation) nationwide.
National; "Problem solving journal" - once per term for all secondary
ages. Still small - may not survive, but we will see.
Regional: Take home competitions (old established, but not thriving, in
We have two nationwide competitions:
The "Mathematics Olympiad"(/Mathematik-Olympiade
http://www.math.uni-rostock.de/MO started in 1960/61 in former
East-Germany. It is a yearly organized 4-rounds-competition
(/"School-Olympiad", "Regional Olympiad", State-Olympiad",
"Germany-Olympiad"/). Students from grade 5 to grade 12/13 are invited
to participate and have to solve specific problems according to their
age. The first round is a home work round. The best participants qualify
for the next round. The problems for these competitions are posed by
central commissions, which involve university-professors and teachers.
The competition was and still is very successful. Since 1995 students of
all 16 German states have participated. *
*(2) /Bundeswettbewerb Mathematik BWM/
The "Federal Mathematics Competition" (/Bundeswettbewerb Mathematik
http://www.bundeswettbewerb-mathematik.de/ started in the 1970th in
former West-Germany. It is a yearly organized 3-rounds-competition. The
students have to solve the same set of problems in a given year
throughout the state, independent of age. During the first and second
round they work out their solutions at home. The best participants
qualify for the next round. In the last round the students have to stand
through a one-hour mathematical discussion with a university professor
and a high-school teacher. The prize-winners get a prestigious
scholarship of the /Studienstiftung des Deutschen Volkes/. *
How does the
existing AMC structure compare with programs in
The Hong Kong Competitions do not use multiple choice questions. Contestants have to work out the answers. Examples:
HK mathematical high achievers selection contest (for Secondary 1 to 3)
HK Mathematics Olympiad (for Secondary 4 or below)
Enter http://www.ied.edu.hk/math/hkmo.htm and select activities.
Students will be invited to do AIME as a result of the AMC,
and this will lead to the final IMO team. In
2. What competition formats are in use anywhere in the world that do not focus on timed individual problem-solving?
In HK, there is a maths competition sponsored by a commercial organization which does not take the form of timed individual problem-solving. Students get a period of about 3 months to submit their work once started.
The Hang Lung Mathematics Awards is organized by Hang Lung
For each competition, there will be Gold, Silver, Bronze, and Honorable Mention awards with a total award amount of HK$1,200,000. (US$1 = HK$8) Prizes for each winning team will be given out in the forms of team member scholarships, teacher leadership award, school development grant, and MSc tuition scholarship for teachers. Projects submitted for competition will be seriously reviewed in several stages by internationally acclaimed scholars.
Concerning the 1st question, the most important difference
may be the fact that the Australian and the Canadian programs are run
independently of their mathematical associations. In the
Concerning Question 2, I want to emphasize that until recently, there were no multiple choice problems on competitions in Central and Eastern Europe or the former Soviet Union, whose teachers were proficient enough in mathematics to grade essay-type solutions to olympiad-level problems, if they were given appropriate instructions for doing so. Unfortunately, the situation is changing fairly speedily, partially due to the political pressures towards americanization in the field of education. Therefore, if we wish to learn from those countries, we should do so soon.
With respect to competitions with less time pressure, let me
call your attention to
on problem Challenge or National Bank Junior Math Competition to see
what competitions we run from here. These are the only ones produced in
the PMO: it's called '
it has many levels and consists of about 30 problems. for each problem, student has only to tick which of the three possible answers is correct.
do you want me to give some further details about
The Tournament is conducted each year in two stages - Autumn and Spring (northern hemisphere time). The southern hemisphere academic year coincides with this structure.
Each stage has two papers, an "O" level and an "A" level, which are spaced roughly one week apart. The A level paper is more difficult, but offers more points. Students and their towns may participate in either stages or levels, or in all levels and stages.
The Tournament is open to all high school students, with the highest age of students being about 17 years old.
Students are awarded points for their best three questions in each paper, and their annual score is based on their best score in any of the four papers for the year.
There are two versions of each paper, known as the Senior and Junior papers. Students in Years 10 and 11 (the final two years of high school in the Russian nomenclature) are classified as Senior participants and therefore attempt the Senior paper. So that Year 10 students are not disadvantaged their scores are multiplied by 5/4. Younger students, in Years 9 and below, attempt the Junior paper. To ensure that the scoring is fair to all levels of students, Year 8 students have their scores multiplied by 4/3, Year 7 students have their scores multiplied by 3/2 and Year 6 students and below have their scores multiplied by 2.
The competitions in which I am involved are of the timed 5-option mcq model, just like AHSME, the Australian and Canadian
competitions. We have an "Inter-Provincial Mathematics Olympiad"
rather like ARML, which is very successful. We choose our Olympiad teams via a
Talent Search and program of mathematical camps, as you do, but our entire
annual budget is a fraction of yours. Our funding has been largely
corporate, but governmental funding is starting to play a more important
role. Given the economic realities in
We can claim to be better than the
Po Leung Kuk is a renowned welfare organization
and school-sponsoring body in
The PMWC aims to:
· provide an opportunity for the exchange of information of primary school mathematics education throughout the world.
· foster friendly relations among primary school students from different cities.
· discover the mathematics potential of gifted primary students among different cities.
A team consists of a team leader, a deputy team leader and a maximum of four
student contestants. To be eligible to participate in the contest, the students
must be age 13 or under as of September 1 and have not enrolled at a
secondary institution or its equivalent. A qualifying test is sent to schools