My Experience of Coaching Mathcounts Math Contest Preparation

My Experience of Coaching Mathcounts Math Contestdecimals, %, digits, place value, rounding, order of
Preparationoperations scientific notation etc. I taught students
Frank Ho   BC certified math teacher   Founder ofthe radicals and exponents using grade 10 textbook.
Ho Math and Chess Learning Centre   Vancouver,There are lots of continued fractions and to express
BC, Canada   This article is about comparing theas common fractions. I showed students how to use
MATHCOUNTS results of students whom I coachedthe Euclidean Algorithm to create the continued
in 1999 and 2000, with different methods in a privatefractions so students would understand continued
learning centre - Ho Math and Chess. I feel the mainfractions better. There are many contest questions
reason of improvements was due to differentwhich are important to know, but I could not put
coaching methods used in these two years. Studentsthem as one chapter. I collected all those important
want to participate BC MATHCOUNTS as individualsconcepts together and went through with students,
may find this paper resourceful since individualexamples such as changing a repeating decimal to a
participation is allowed in 2002/2003 in BC, Canada .fraction, base conversion etc. One of the difficulties
In 1999, I had an opportunity to coach somethat I encountered in coaching MATHCOUNTS is the
students who came from a private school (mainlyVOCABULARY and FORMULAS section in
from Vancouver Crofton school) and were interestedMATHCOUNTS School Handbook. The list is
in participating MATHCOUNTS, but were not able torepresentative of terminology used in the problems.
because they could not get sponsored by a teacherThe list is long and I had managed to teach all
from their own school. I got permission to organizeterminology listed.
them as the Vancouver Ho Math and Chess LearningAlgebraic Expressions & Equations
Centre team. I trained them 2 hours a week startingFactorial
from September until the week before theSince the knowledge of factorial is required in
competition.combination and permutation, I had introduced
How did I start to prepare them for the competition?factorial, combination and permutation to students
I had a quick glance at the 1999 MATHCOUNTSand encouraged them use these knowledge in solving
School Handbook and realized that there was a lot ofprobability problems.
work to be done to help these students performTrinomial factoring
well. These grade 8 mathletes had very strong mathExample: Find the trinomial a perfect square .
background and some of them had advanced a levelSum and Product problem What is the positive
which was above their peers at school. This was andifference between two integers whose sum is 30
easy part of my training in the sense that they didand whose product is 221?
not have weakness in their school math but theI used the grades 9 and 10 factor problems to train
biggest challenge was how to speed them up to thestudents so that they could factor trinomials using
competition level. I started training them by giving outthe cross-multiplication in intuitively way. (I gave
Warm-Up and Workout problems contained in theminimum 200 such questions to work on.) .
MATHCOUNTS School Handbook. Based on myAbsolute-value equation
evaluation of the students' results, I would attemptI created a table which gives summary of different
to teach the concepts behind the problems so thatAbsolute-Value Models.
they would understand better. But quickly IInequalities
discovered that at the grade 8 math level, there wasOne or 2 variables inequality equations.
a lot of material in MATHCOUNTS beyond their ability.Systems graphing
Being a first time coach, I realized that I need toThis area is difficult for me to coach since most of
have a good understanding of the scope of thethe students do not have any knowledge in terms of
problems covered in the MATHCOUNTS competition.graphics of parabola, absolute-value equation, and
The MATHCOUNTS School Handbook is great forslope etc. I had to use the grade 10 book to teach
providing diversified problems for students to workslope, and the basic knowledge of transformation,
on, but it is difficult for me to teach conceptsgraphing of inequality. The best way of covering
required in solving these problems all at once sincethese concepts is to use the real contest data in
each Warm-Up or Workout covers a wide spectrumMATHCOUNTS I used the Database to produce
of concepts.questions for students to work on after my
I went through the entire 1999 problem index in thepresentation.
back of Handbook to find out what kinds ofFunctions
problems are included in MATHCOUNTS . MyUsed the questions in Database after my
impression is there are problems which have notpresentation.
been covered in grade 8 and need to be taught. If IExponents
only gave students problems in Handbook, I knewUsed the exponents in grade 10 to train students.
that they would not do well in MATHCOUNTS for theMiscellaneous problem-solving
reason there are some materials which they haveCoin or natural number problems, Sum and difference
not learned at school. The first thing I did was to findproblems, Traveling (with current or without), work
out what they knew and what they need to learn.problems etc. with multi-methods are offered for
Using the Problem Index, I determined what areasdifferent types of problems.
need to be taught. In 1999, I mainly used HandbookGeometry
to try to group problems with the same subjectsThe geometry in MATHCOUNTS covered many
such as Algebra, Geometry, Number Theory etc.areas and I have found the best way of coaching is
together. Most of the time, I used cut and pasteto produce those problems from Database. The
method and handed questions to students. Thisconcept of slope (WU 12-4, WU 16-2) and distance
teaching method was frustrating and I wanted to(WU 4-2) between 2 points are normally covered in
have a reference book so that I could concentrategrade 10, so I decided to use the materials in grade
my efforts in teaching instead of cutting and pasting.10 to teach. Other important concepts such as the
While I was teaching I also started to write downrelationship of lines, space diagonal, side lengths and
my own teaching notes.angles of triangles are taught in grade 10 but is useful
The second year (2000), I purchased ain MATHCOUNTS, so they were taught to students.
MATHCOUNTS Competition Database (1998 Edition, aNumber Theory
collection of past competition problems from 1983 toMATHCOUNTS is very heavy in counting shapes or
1998, School level to Chapter, State, and to Nationalpaths. If these problems do not appear in the
level) from EducAide Software (The databasecompetitions, they may appear in the countdown.
includes both past competitions problems andNumber theory forms the foundation of having a
Handbook problems). I started to take on mygood math contest preparation. Counting shapes,
coaching method as a research project - I wanted todivisibility, primes, trailing zeros, GCF, LCM, remainders,
see if teaching students in a structured way withcounting paths, modular arithmetic were all taught. I
organized subjects gathered from the previousemphasized the POP (Product Of Prime) method to
MATHCOUNTS Competition Database would makesolve the # of factors problems. The relationship
any difference in scores. The feedback frombetween POP and the # of factors is not mentioned
students was the students liked the way my lecturein school textbooks. For defined operations, counting
was presented.systems problems, I also used Database.
Every week I presented with one or more subjects,Probability and statistics
and after the presentation students would getI used the textbook to introduce the basic concepts
chance to work on problems which I generated fromof mean, median, mode, range, and frequency, I also
the Database. Students' tests would be marked and Iused the questions from Database on data
would go over problems which they could not get.interpretation.
The results between 1999 and 2000 are as follows:General mathematics
NameI decided to teach the students to the level of grade
Ranking (1999, 2000)10/11 algebra math. As a result it pretty much
Sprint (1999, 2000)covered the section of general mathematics
Target (1999, 2000)Summary
AndreaAfter 2 years of training students, I discovered that
23, 13by teaching students the concepts required in
7, 17MATHCOUNTS, students appreciated more and
8, 14gained confidence in participating. My goal of teaching
Meghanthem the knowledge required to do well in
16, 15MATHCOUNTS was achieved by offering them
11, 17chance of learning these concepts in a well-organized
8, 14and structured way.
MatthewP.S.
13, 6Please note that this article was written in 2001 and
9, 21perhaps much information and MATHCOUNTS format
12, 16have changed a lot but I feel that my training
Oliviamethod is still applicable. I trained my own son
27, 21Andrew to be the youngest Canadian chess master
8, 18when he was 12 and later he became a FIDE chess
4, 10master. The subjects of training in chess or math are
Matthewdifferent but the principle of methodology is more or
18, 9less the same. By comparing the training methods of
10, 20teaching both chess and math, I concluded one
8, 14effective factor that will surpass any training
It shows that students made tremendous progress inmethods one would ever find that is the training itself
the second year, with two of my students placing inhas to be altruistic.
the top 10 list. MATHCOUNTS Competition DatabaseThere were many nights that I could not sleep well
gives me the power to have an excellent historicalbecause I was still "dreaming" on how to find a way
overview on the depth and knowledge level ofto overcome Andrew's weakness. There were
problems. I was able to use the Database combinednumerous times that I was frustrated because I
with my knowledge of what students would havecould not find a way on how to raise my students'
learned in school math classes to create a workbookmath ability. From my personal coaching experience I
which I think would help students do well in mathcan say that when one coach really puts in 100%, no
competitions. The goal of the second year was to200% into helping children then their performance will
analyze what a grade 8 student need to know forbe a big surprise.
the possibility to get on the top 10 list inThose students whom I coached earlier including my
MATHCOUNTS. I mainly used the competitionsown daughter were still in my mind and my learning
Database to do the work. I went through eachcenter has since evolved into the international stage.
chapter in Database and analyzed each question toMany of my earlier workbooks had been tested on
see how complex the problem is and if studentsthem, so I would like to thank all of you.
need to be taught for the concept required to solveThe workbook Math Contest Preparation is now not
the problems. This tedious task eventually leads tosold publically but only through Ho Math and Chess
my publishing of a workbook - Math Contestfranchisees. My dedication on math and chess
Preparation.teaching research has allowed me to create the
My analyses of the Database are as follows:Geometry Chess Language (Canada copyright
Arithmeticnumber 1069744), Frankho chess maze, Ho Math and
Students are expected to have acquired the mathChess Teaching Chess Set.
concepts covered in this section such as fractions,