This article is about comparing the MATHCOUNTS results of students whom I coached in 1999 and 2000, with different methods in a private learning centre - Ho Math and Chess. I feel the main reason of improvements was due to different coaching methods used in these two years. Students want to participate BC MATHCOUNTS as individuals may find this paper resourceful since individual participation is allowed in 2002/2003 in BC, Canada .
In 1999, I had an opportunity to coach some students who came from a private school (mainly from Vancouver Crofton school) and were interested in participating MATHCOUNTS, but were not able to because they could not get sponsored by a teacher from their own school. I got permission to organize them as the Vancouver Ho Math and Chess Learning Centre team. I trained them 2 hours a week starting from September until the week before the competition.
How did I start to prepare them for the competition? I had a quick glance at the 1999 MATHCOUNTS School Handbook and realized that there was a lot of work to be done to help these students perform well. These grade 8 mathletes had very strong math background and some of them had advanced a level which was above their peers at school. This was an easy part of my training in the sense that they did not have weakness in their school math but the biggest challenge was how to speed them up to the competition level. I started training them by giving out Warm-Up and Workout problems contained in the MATHCOUNTS School Handbook. Based on my evaluation of the students' results, I would attempt to teach the concepts behind the problems so that they would understand better. But quickly I discovered that at the grade 8 math level, there was a lot of material in MATHCOUNTS beyond their ability. Being a first time coach, I realized that I need to have a good understanding of the scope of the problems covered in the MATHCOUNTS competition. The MATHCOUNTS School Handbook is great for providing diversified problems for students to work on, but it is difficult for me to teach concepts required in solving these problems all at once since each Warm-Up or Workout covers a wide spectrum of concepts.
I went through the entire 1999 problem index in the back of Handbook to find out what kinds of problems are included in MATHCOUNTS . My impression is there are problems which have not been covered in grade 8 and need to be taught. If I only gave students problems in Handbook, I knew that they would not do well in MATHCOUNTS for the reason there are some materials which they have not learned at school. The first thing I did was to find out what they knew and what they need to learn. Using the Problem Index, I determined what areas need to be taught. In 1999, I mainly used Handbook to try to group problems with the same subjects such as Algebra, Geometry, Number Theory etc. together. Most of the time, I used cut and paste method and handed questions to students. This teaching method was frustrating and I wanted to have a reference book so that I could concentrate my efforts in teaching instead of cutting and pasting. While I was teaching I also started to write down my own teaching notes.
The second year (2000), I purchased a MATHCOUNTS Competition Database (1998 Edition, a collection of past competition problems from 1983 to 1998, School level to Chapter, State, and to National level) from EducAide Software (The database includes both past competitions problems and Handbook problems). I started to take on my coaching method as a research project - I wanted to see if teaching students in a structured way with organized subjects gathered from the previous MATHCOUNTS Competition Database would make any difference in scores. The feedback from students was the students liked the way my lecture was presented.
Every week I presented with one or more subjects, and after the presentation students would get chance to work on problems which I generated from the Database. Students' tests would be marked and I would go over problems which they could not get. The results between 1999 and 2000 are as follows:
Name
Ranking (1999, 2000)
Sprint (1999, 2000)
Target (1999, 2000)
Andrea
23, 13
7, 17
8, 14
Meghan
16, 15
11, 17
8, 14
Matthew
13, 6
9, 21
12, 16
Olivia
27, 21
8, 18
4, 10
Matthew
18, 9
10, 20
8, 14
It shows that students made tremendous progress in the second year, with two of my students placing in the top 10 list. MATHCOUNTS Competition Database gives me the power to have an excellent historical overview on the depth and knowledge level of problems. I was able to use the Database combined with my knowledge of what students would have learned in school math classes to create a workbook which I think would help students do well in math competitions. The goal of the second year was to analyze what a grade 8 student need to know for the possibility to get on the top 10 list in MATHCOUNTS. I mainly used the competitions Database to do the work. I went through each chapter in Database and analyzed each question to see how complex the problem is and if students need to be taught for the concept required to solve the problems. This tedious task eventually leads to my publishing of a workbook - Math Contest Preparation.
My analyses of the Database are as follows:
Arithmetic
Students are expected to have acquired the math concepts covered in this section such as fractions, decimals, %, digits, place value, rounding, order of operations scientific notation etc. I taught students the radicals and exponents using grade 10 textbook. There are lots of continued fractions and to express as common fractions. I showed students how to use the Euclidean Algorithm to create the continued fractions so students would understand continued fractions better. There are many contest questions which are important to know, but I could not put them as one chapter. I collected all those important concepts together and went through with students, examples such as changing a repeating decimal to a fraction, base conversion etc. One of the difficulties that I encountered in coaching MATHCOUNTS is the VOCABULARY and FORMULAS section in MATHCOUNTS School Handbook. The list is representative of terminology used in the problems. The list is long and I had managed to teach all terminology listed.
Algebraic Expressions & Equations
Factorial
Since the knowledge of factorial is required in combination and permutation, I had introduced factorial, combination and permutation to students and encouraged them use these knowledge in solving probability problems.
Trinomial factoring
Example: Find the trinomial a perfect square .
Sum and Product problem What is the positive difference between two integers whose sum is 30 and whose product is 221?
I used the grades 9 and 10 factor problems to train students so that they could factor trinomials using the cross-multiplication in intuitively way. (I gave minimum 200 such questions to work on.) .
Absolute-value equation
I created a table which gives summary of different Absolute-Value Models.
Inequalities
One or 2 variables inequality equations.
Systems graphing
This area is difficult for me to coach since most of the students do not have any knowledge in terms of graphics of parabola, absolute-value equation, and slope etc. I had to use the grade 10 book to teach slope, and the basic knowledge of transformation, graphing of inequality. The best way of covering these concepts is to use the real contest data in MATHCOUNTS I used the Database to produce questions for students to work on after my presentation.
Functions
Used the questions in Database after my presentation.
Exponents
Used the exponents in grade 10 to train students.
Miscellaneous problem-solving
Coin or natural number problems, Sum and difference problems, Traveling (with current or without), work problems etc. with multi-methods are offered for different types of problems.
Geometry
The geometry in MATHCOUNTS covered many areas and I have found the best way of coaching is to produce those problems from Database. The concept of slope (WU 12-4, WU 16-2) and distance (WU 4-2) between 2 points are normally covered in grade 10, so I decided to use the materials in grade 10 to teach. Other important concepts such as the relationship of lines, space diagonal, side lengths and angles of triangles are taught in grade 10 but is useful in MATHCOUNTS, so they were taught to students.
Number Theory
MATHCOUNTS is very heavy in counting shapes or paths. If these problems do not appear in the competitions, they may appear in the countdown. Number theory forms the foundation of having a good math contest preparation. Counting shapes, divisibility, primes, trailing zeros, GCF, LCM, remainders, counting paths, modular arithmetic were all taught. I emphasized the POP (Product Of Prime) method to solve the # of factors problems. The relationship between POP and the # of factors is not mentioned in school textbooks. For defined operations, counting systems problems, I also used Database.
Probability and statistics
I used the textbook to introduce the basic concepts of mean, median, mode, range, and frequency, I also used the questions from Database on data interpretation.
General mathematics
I decided to teach the students to the level of grade 10/11 algebra math. As a result it pretty much covered the section of general mathematics
Summary
After 2 years of training students, I discovered that by teaching students the concepts required in MATHCOUNTS, students appreciated more and gained confidence in participating. My goal of teaching them the knowledge required to do well in MATHCOUNTS was achieved by offering them chance of learning these concepts in a well-organized and structured way.
Please note that this article was written in 2001 and perhaps much information and MATHCOUNTS fromat have changed a lot but I feel that my training method is still applicable. I trained my own son Andrew to be the youngest Canadian chess master when he was 12 and later he became a FIDE chess master. The subjects of training in chess or math are different but the principle of methodology is more or less the same. By comparing the training methods of teaching both chess and math, I concluded one effective factor that will surpass any training methods one would ever find that is the training itself has to be altruistic.
There were many nights that I could not sleep well because I was still "dreaming" on how to find a way to overcome Andrew's weakness. There were numerous times that I was frustrated because I could not find a way on how to raise my students' math ability. From my personal coaching experience I can say that when one coach really puts in 100%, no 200% into helping children then their performance will be a big surprise.
Those students whom I coached earlier including my own daughter were still in my mind and my learning center has since evolved into the international stage. Many of my earlier workbooks had been tested on them, so I would like to thank all of you.
The workbook Math Contest Preparation is now not sold publically but only through Ho Math and Chess franchisees. My dedication on math and chess teaching research has allowed me to create the Geometry Chess Language (patents applied), Frankho chess maze, Ho Math and Chess Teaching Chess Set.
February, 2008
Frank Ho is the founder of the only international child education franchise dedicated to teaching children math through integrated math and chess. He invented the world's first math and chess integrated workbooks using Geometric Chess Language (Patents applied), Frankho Chess Mazes, and Ho Math and Chess Teaching Set. Math and chess worksheets make the math learning more fun and engaged, as a result, children become more observant in processing iniformation and become more alert when playing chess. In additional improving children's math marks, Ho Math and Chess workbooks are an excellent training tool for for improving problem solving skills and improving memory and brainpower.
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