When Should Students begin to write the COMC competition?
The Canadian Open Mathematics Challenge (COMC) is a competition
intended, as the name suggests, to challenge our best young mathematical
talents nation-wide. It is not a contest for every student, and it
requires a considerable amount of mathematical maturity.
But it is important that teachers of younger students
with significant mathematical ability encourage these students to begin
writing the COMC at an early age. There are several reasons for this.
The COMC is not for any one specific grade level; students
of all levels are welcome to write it. The literature for the COMC
indicates that the content of the exam should be within reach of the best
grade 10 students. However, it should be clear from the above information
that truly elite students must begin writing even earlier than that or
miss some of the best opportunities available to them.
The questions on the COMC require full solutions, and so
are more stimulating for bright independent thinkers. They will find
this exam much less tedious and routine than the standard multiple-choice
As students progress farther, and into higher-level contests,
the open question format will be used more often. Writing the COMC
is excellent preparation for these tests. In the past there has been
some difficulty with Manitoba students who perform well in the multiple
choice tests but have difficulty making the transition to full answer style
questions in later years. Writing such competitions earlier will
help address this deficiency.
The very best students will lose some significant opportunities
for highest-level competition if they are not writing the COMC at an early
age. Most of the elite competitions and training opportunities
in Canada are by invitation only, and the most significant determiner of
who gets invited is performance on the COMC! Students who do
not write the COMC, therefore, are unlikely to receive invitations to such
things, regardless of their potential. Here is a partial list of
The CMS/Esso National Training Camp is an annual elite Math
Camp for students in grades 8 to 11 that operates by invitation
only, based primarily on performance in the COMC. The focus of this
camp is to train future participants in the Canadian IMO team -- they begin
to work with students showing potential for international-level competition
four years in advance
The Canadian IMO team is a select group of students who write
the International Mathematical Olympiad, the highest-level high school
math contest in the world. The members of the Canadian team are hand-picked
from our best students, with an eye on performance on the most challenging
contests, including the COMC. Of course the students considered first
and foremost for this experience are those who have been groomed for it
through participation in the COMC-dependent National Training Camp, above.
The CMO (Canadian Mathematical Olympiad) is the national
equivalent of the CMO; approximately 50 students across the country write
the CMO each year, plus some regional representatives, but participation
in the CMO is by invitation only; one of the required steps to qualify
for an invitation is participation (and a good performance) in the COMC.
The confusion caused by the above discrepancy is further
exacerbated by the fact that COMC literature is, I believe, sent only to
high schools offering senior classes. Therefore very good students
at Junior High Schools or Middle Schools may not write this exam simply
because their school is not made aware of the opportunity.
Here is my advice:
Bright or enthusiastic students should be encouraged to begin
writing the COMC in grades 9 or 10. Any students who perform in the
top 5 in the province in any of the ranked competitons should begin writing
the COMC at the next opportunity, regardless of their grade level.
If they are below grade 10 in their classes, they should be given supplementary
materials to accellerate their background so that they are prepared for
the basic material. A bright student should do well in this competition
with a minimum of background, but it is hopeless to attempt a problem,
say, regarding cartesian geometry, before cartesian coordinates and
graphs of equations have been seen.
Students who are clearly bound for international competition
in mathematics should begin writing the COMC no later than grade 8.
Of course, it is very hard to identify students of this calibre at an early
age. However, it is possible, for example, to have students in grades
6 and 7 writing the regular competitions for the next year or two (grade
7 students can write the Pascal; grade 6 students can write the grade 7
or 8 Math League contest or the Gauss contest); if they distinguish themselves
at this level, there is a good chance that they are headed for top-level
Don't make COMC participation a large-group activity at any
level before grade 10. Target your best students in the earlier years.
Note, however, that it is quite common for a student who performs only
moderately well in the multiple-choice format to excell in the full solution
format because the latter requires more problem-solving and cognitive skills
while the former requires more mechanical skill and exam-writing strategy.
Keep an eye open for students who may not distinguish themselves in the
traditional ways, but have clearly exceptional problem-solving talent.
These kids will love puzzles and games, enjoy word games and may love to
debate. They will often be loners, and they constantly have new ideas
about everything. Their streak of creative originality will be clear
to all -- whether or not it distinguishes them academically or shows itself
in math class. Don't make the mistake of confusing excellent memory
and recipe-following ability with giftedness in problem-solving -- although
often associated, these are very different skills, and it is quite common
for a student to excel in one and not the other.
NOTE: A selection criterion of secondary importance
for National Math Camp is performance in the Galois (grade 10 Waterloo)
competition. The first 10 students for Math Camp are selected solely from
the COMC results and the Galois competition is figured in for the remaining
Serious competitors should be writing the Galois competition
starting in grade 8. Note that they cannot write the Fryer competition
at the same time -- so this is an option that should only be entertained
for truly excellent students; all others should be writing the Fryer.
If students begin writing the Fryer competition in grade 7 (or earlier)
it will help identify those rare candidates who should move on to the Galois
by grade 8.
This page is maintained by Dr.
R. Craigen of the University
of Manitoba Mathematics Department.
Comments, requests and suggestions welcome.