Kids' Math Help: The Story of Mathino
By Marsh Kaminsky
"I don't like math, and I'm not good at it." Those annoying words
are uttered all too often today by children and adults alike.
Americans frequently say them with pride, accompanied by a smirk, as
if being a math wimp was some kind of badge of honor. As a Certified
Public Accountant, my livelihood depended on math. Much of my life
revolved around my ability to understand, nurture and massage
numbers. How could I prepare tax returns without knowing math?
With that in mind, I sat on the edge of my four year-old son's bed
one evening, preparing to read him Green Eggs and Ham. As I looked
at the book, I wondered whether he would grow up to dislike numbers
and become a certifiable math wimp like so many others. The thought
made me cringe. After stewing about this for a week, I made a
decision that is forever etched in my memory. "I will teach Daniel
mathematics!" I remember shouting those words to no one in
particular. My son probably wondered what his silly Daddy was
The next day a little voice in my head asked me a reasonable yet
disquieting question: "Okay, big shot, what do you know about
teaching math to a little kid?" I wanted a way to teach him math
that would ignite his interest in the subject. Knowing my son and
his very short span of attention, I knew my project was doomed
unless he really enjoyed what he was doing. So how do I proceed?
A few days after my teaching decision, I went to Harrahs casino in
Reno for some much needed rest from enduring yet another murderous
tax season. I soon found myself watching my money slowly disappear
at a 21 table. It must have been fated, because I began to think
about how one cannot play 21 unless one can do simple addition. I
did not know it at the time, but Harrahs just showed me the way.
Card games are the answer!
I started by acclimating my son Daniel to the look and feel of
playing cards and the numbers on them. I did this by teaching him
the simple game of War. While War reinforced the concept of more or
less, it did little else in teaching him math. Worse yet, because
the outcome of a game of War is determined by pure luck, there is
never any strategic thinking involved. But on the plus side, I saw
how much he enjoyed our uninterrupted time together. In fact, I was
enjoying it too. Furthermore, I could not fail to notice how much he
enjoyed competing with me. His competitive nature and desire to win
turned out to be crucially important factors in the lessons that
would soon follow.
Next, I thought back and remembered a card game called Casino my
father taught me when I was a teen. While I sensed that Daniel was
not quite ready for quadratic equations, I figured he could handle a
card game that involved simple addition to the number ten. Well, if
he ate up War, he soon gorged on Casino.
The object of Casino is to "capture" as many cards as possible,
particularly those with point values such as the four aces. One way
to capture a card is by a simple match -- a player matches a card in
his hand with one on the table. Hence, a player can capture a five
if he has a five in his hand. It took about two minutes to explain
that to him. There are, of course, other ways of capturing cards
which, as one might guess, involve addition. A player, for example,
can capture a 3 and a 5 with an 8 in his hand. What's more, a player
can "build" numbers -- a procedure that creates mathematicians.
Building is exciting as it involves a strong element of risk. I
might put a 3 on a 4 and build 7s. If Daniel had a 7 in his hand, he
could capture my build. Furthermore, in an attempt to steal my 7s
build, he could change it to a card he had in his hand. To
illustrate, he could add a five from his hand and change my 7s to a
12. Nothing gave him more pleasure than that.
From the onset, my major goal was not to stuff my son's head full
of math facts. Sure, I wanted him to know the basics, like the
addition and multiplication tables by heart. But I did not want him
to learn math (algebra in particular) as I did in high school by
memorizing meaningless formulas where I'd plug in some numbers.
Overall, I guess I wanted him to be enthralled with mathematics and,
of course, to think mathematically. I know kids will learn if they
are bored, but they will learn so much more if motivated by a sense
of joy and fun. That's how kids are. Now that I think about it,
adults are like that too.
We played Casino constantly -- maybe a few hundred games over the
next four or five months. Because of the constant practice, Daniel
became quite adept at simple addition.
One day I had a brainstorm that changed everything. If a player, I
wondered, could put a 2 on a 5 and build 7s using addition, why
couldn't he/she build 3s instead by using subtraction? I taught
Daniel the new "rule" and he accepted it immediately. Not yet six
years old, Daniel had no idea that subtraction was a school subject.
He thought it was just another rule of the game. After a few months
of playing with both addition and subtraction, he asked me, "Any
more new rules, Daddy?" His words were music to my ears.
"The new rule is called multiplication. Want to try it?"
Since multiplication is just a fancy way of adding the same number
more than once, I approached him with that strategy. "Daniel, five
times three is simply a way to add the number three, five times."
After a few days of practice with this new intriguing rule, he got
Adapting multiplication to Mathino (somewhere along the line we
changed the name) was a problem since the largest number in the game
is twelve. The trouble was .... the product of a two number
multiplication is frequently more than twelve. However, my knowledge
of a tax depreciation method called "summing of the digits" provided
a solution. In short order, Daniel learned that 8 x 8 really equals
10 because the sum of the digits of the product (64) equals 10. He
was enthralled with this new rule.
Now I was on a roll! After a few months of practice with
multiplication, I gradually began to introduce four more new rules:
division, powers, roots and negative numbers. I suspect that if I
could have incorporated integral calculus into the game, his
competitive spirit would have prompted him to learn that too.
Mathino is a deceptively easy math game. Played at its simplest level
with just addition, a four or five year old child can easily pick up
on the play of the game in less than an hour. But at its most
sophisticated level with addition, subtraction, multiplication,
division, negative numbers, powers and roots all being played in
tandem, Mathino would challenge a college math professor.
During a game, I never allowed Daniel to use a calculator. Instead,
I provided him with hard copy multiplication and power tables.
Daniel sometimes spent five or more minutes going through mental
math calculations before deciding on a favorable move. I never
hurried him as I knew that this constant mental practice was
acclimating his brain to the world of mathematics. I was also
fascinated by his grasp of intricate strategic nuances. Whether he
knew it or not, he was also learning odds, percentages, logical
thinking skills, along with the importance of a good memory
Besides all the other things that Mathino taught him, I used the
game to show him how to win graciously and how to lose without
having a snit.
The following incident happened when Daniel was in the first grade.
His teacher called and told me that they were discussing the number
five in class when Daniel raised his hand and piped in with, "A five
is not just a five. It is also a two plus three, a seven minus two,
a negative two plus a positive seven, a five times one, ten divided
by two, and the square root of twenty-five!" The teacher said she
almost fell over. Such is the power and magic of Mathino.
Throughout the last twenty years I must have decided at least ten
times to market Mathino. From years of teaching the game to many
young students and teachers, I knew it would be a great success. But
somehow, something always happened to interfere with those plans.
One of those happenings was a case of Multiple Sclerosis. Now at
sixty three years old and confined to a wheelchair, I no longer have
the strength to market the game. But on the other hand, I know that
Mathino is far too good a math teaching tool to just let it wither
and die. Accordingly, I have decided to freely share the game with
parents and teachers. That way, I know Mathino will live forever.
Marsh Kaminsky of