How is it Possible? 309
19
how is it possible
When the problem is on the order of 5 or
for infants to do
instant math?
it is no problem since the adult can perceive the symbol or the fact
successfully from one
The question is not "How is it possible for infants to do instant
math?" but rather, "How is it possible for adults who speak a
language not to do instant math?"
up to about 12
The problem is that in math we have mixed up the symbol, 5,
with the fact,
with some degree of reliability.
310 HOW TO MULTIPLY YOUR BABY S INTELLIGENCE
How is it Possible? 311
From 12
Children who already know symbols, for example 5, 7 10, 13, but
who do not know the facts
to about 20
,
,
the reliability of even the most perceptive adult tends to descend
sharply
From 20
,
upward one is guessing and almost invariably guessing very badly
indeed
312 HOW TO MULTIPLY YOUR BABY S INTELLIGENCE
How is it Possible? 313
I am not able to see
are unable to do instant math.
Tiny children, however, see things precisely as they are, while
adults tend to see things as we believe them to be or as we believe
it is not precisely true to say that I cannot see the above. I can see it
that they should be.
but I cannot perceive it.
I find is maddening that, while I completely understand how
Tiny children can.
children of two years can do instant math, I am unable to do the same.
In order for tiny children to perceive the truth of one (1) which is
The reason I fail to do instant math is that if you say seventy-nine
actually
to me I am able to see only
"
79
314 HOW TO MULTIPLY YOUR BABY S INTELLIGENCE
How is it Possible? 315
We need only to show the child the fact
Very small number of times until the infant is able to perceive and
retain the truth.
The adult mind, when faced with the fact, is inclined to
astonishment, and many adults would rather believe that a child who
"
is able to recognize
And say, This is called one.
"
We next present him with the fact
"
to
"
And say, This is two.
Next we say, This is three, showing the child
is in some way psychic than believe that a two-year-old can
" "
perform a task which we consider to be intellectual in nature and
which we grown-ups cannot perform.
"
The next straw at which we grasp is the belief that the child is not
truly recognizing the number but rather the pattern in which the
numbers occur.
And so on. We need to present each of these a
316 HOW TO MULTIPLY YOUR BABY S INTELLIGENCE
How is it Possible? 317
Any one-year-old worth his salt who has not been sucked into
Columnar way. Thus if we present the fact in this form
recognizing symbols before he recognizes the facts, can tell at a
cursory glance that
" " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " "
we solve the problem by actually counting while the tiny child sees
the truth at a glance.
If we present the truth in columnar form
" " " " " " " "
" " " " " " " "
" " " " " " " "
" " " " " " " "
" " " " " " " "
adults are inclined to count the number of rows across which we see
as 8, and the number down, which we see as 5, and then to use an
arithmetic form which we see as
or whatever other way you choose to arrange the facts are all what
we call 27? Sorry, we fooled you - in fact it s forty, not 27!
Which we grown-ups can see only if you present us with the
8
symbol 40 .
x 5
The kids are not fooled regardless of the form in which you present
40
it and see only the truth, while we adults will actually have to count it
up if you present it in any random pattern or to multiply it if you
or an algebraic form: 8x 5 = 40
present it in an orderly
318 HOW TO MULTIPLY YOUR BABY S INTELLIGENCE
How is it Possible? 319
This incredibly slow process has almost nothing to recommend it
September, April, June and November have
except that it ultimately comes to a correct conclusion. However,
even when it comes to the correct conclusion, which we see as 40, we
have no idea what 40 actually means except by comparison with
something else, such as the number of dollars I earn in a day, or a
month plus ten days. The child sees the absolute truth which is that
days.
And that if you must compare what we call 40 with a month then
what we are talking about it
No more or less and no less
If we must have the comparison with a month then it is fair to say
that any child who ahs been given the chance to see the truth knows
that
As any child can plainly see
How to Teach Your Baby Math 321
20
how to teach your baby math
faced with mathematical problems every day, as are the housewife,
the carpenter, the businessman and the space scientist.
The second reason is even more important. Children should learn to
"Nina, how many dots can you see?"
do math at the youngest possible age because of the effect it will have
"Why all of them, grandmother."
on the physical growth of the brain itself and the product of that
physical growth what we call intelligence.
-THREE-YEAR-OLD NINA PINKETT REILLY
Bear in mind that when we use the word numeral we mean the
symbol that represents the quantity or true value, such as 1, 5, or 9.
When we use the word number we mean the actual quantity of
objects themselves, such as one, five, or nine:
"
" " "
"
"
or
There are two vitally important reasons why tiny children should do
mathematics. The first is the obvious and less important reason:
or
Doing mathematics is one of the highest functions of the human
brain of all creatures on earth, only people can do math.
" "
" " "
Doing math is one of the most important functions of life, since
daily it is vital to civilized human living. From childhood to old age
" " "
"
we are concerned with math. The child in school is
How to Teach Your Baby Math 323
322 HOW TO MULTIPLY YOUR BABY S INTELLIGENCE
In order to begin you will need:
It is in this difference between true value or quantity and its
1. A good supply of white poster board cut into 11" by 11" square
symbolic representation by the use of symbols to represent actual
cards. If possible, purchase these already cut to the size you want.
quantity that tiny children find their advantage over adults.
This will save you a lot of cutting, which is much more time
You can teach your baby to do mathematics even if you aren't very
consuming than the remainder of the material preparation. You
good at doing it yourself. If you play the game of learning
will need at least one hundred of these to make your initial set of
mathematics correctly both you and your child will enjoy it
materials.
immensely. It takes less than a half-hour a day.
2. You will also need 5,050 self adhesive red dots, 3/4" in diameter,
This chapter will give the basics of how to teach your baby
to make cards 1 to 100. The Dennison Company makes PRES-a-
mathematics. Parents who wish to have more information about the
ply labeling dots which are perfect for this purpose.
principles of teaching their babies math are advised to read the book
3. A large, red, felt-tipped marker. Get the widest tip available the
How to Teach Your Baby Math.
fatter the marker the better.
Material Preparation
You will notice that the materials begin with large red dots. They
are red simply because red is attractive to the small child. They are so
The materials used in teaching your child mathematics are
designed in order that the baby's visual pathway, which is initially
extremely simple. They are designed in recognition that mathematics
immature, can distinguish them readily and without effort. Indeed, the
is a brain function. They recognize the virtues and limitations of the
very act of seeing them will in itself speed the development of his
tiny child's visual apparatus and are designed to meet all of his needs
visual pathway so that
from visual crudeness to visual sophistication and from brain function
to brain learning.
All math cards should be made on fairly stiff white poster board so
that they will stand up to frequent use.
324 HOW TO MULTIPLY YOUR BABY S INTELLIGENCE
How to Teach Your Baby Math 325
when we eventually teach numerals he will be able to see these
numerals and learn them more easily than he otherwise would have.
5. Place dots on the cards in a totally random way working outward
You will begin by making the cards that you will use to teach your
from the middle, making certain that they do not overlap or touch
child quantity or the true value of numbers. To do this you will make
each other.
a set of cards containing the red dots, from a card with one red dot to
6. Be careful to leave a little margin around the edges of your cards.
a card with one hundred red dots. This is time consuming but it is not
This will provide a little space for your fingers to curl around the
difficult. There are, however, a few helpful hints that will make your
card and insure that you are not covering a dot with your fingers
when you show the cards.
life easier when you are making these materials:
1. Start with the one hundred card and work backwards down to one.
The higher numbers are harder and you will be more careful at the
start than at the finish.
2. Count out the precise number of dots before applying them to the
card. (You'll have trouble in counting them after you have put
them on the card especially when doing cards above twenty.)
3. Write the numeral in pencil or pen on all four corners of the back
of the card before you place the correct number of dots on the front
of the card.
4. Be sure not to place dots in a pattern such as a square, circle,
triangle, or diamond or a shape of any other sort.
Making the above materials does take some time and depending on
the cost of the poster board can be somewhat expensive, but
compared to the thrill and excitement you and your
326 HOW TO MULTIPLY YOUR BABY S INTELLIGENCE
How to Teach Your Baby Math 327
child will have doing math together it should be worth your effort.
There is a kit now available from the Better Baby Press with these
The path that you will now follow in order to teach your child is
cards already made up for parents.
amazingly simple and easy. Whether you are beginning with an infant
These first one hundred cards are all you need to begin step one of
your math program. or an eighteen-month-old the path is essentially the same.
Once you begin to teach your child mathematics you will find that
The steps of that path are as follows:
your child goes through new material very quickly.
We discovered a long time ago that it is best to start out ahead. For
First Step Quantity Recognition
this reason, make all one hundred dot cards before you actually begin
Second Step Equations
to teach your child. Then you will have an adequate supply of new
Third Step Problem Solving
material on hand and ready to use. If you do not do this, you will find
Fourth Step Numeral Recognition
yourself constantly behind.
Fifth Step Equations with numerals
Remember the one mistake a child will not tolerate is to be shown
the same material over and over again long after it should have been
THE FIRST STEP (Quantity Recognition)
retired.
Be smart start ahead in material preparation and stay ahead. And
Your first step is teaching your child to be able to perceive actual
if for some reason you do get behind in preparing new materials, do
numbers, which are the true value of numerals. Numerals, remember,
not fill in the gap by showing the same old cards again. Stop your
are merely symbols to represent the true value of numbers. You will
program for a day or a week until you have reorganized and made
begin by teaching your baby (at the youngest age possible down to
new material, then begin again where you left off. Start out ahead and
birth) the dot cards from one to ten. You will begin with cards one to
stay ahead.
five.
Begin at a time of day when your child is receptive, rested and in a
good mood.
Use a part of the house with as few distracting
328 HOW TO MULTIPLY YOUR BABY S INTELLIGENCE
How to Teach Your Baby Math 329
factors as possible, in both an auditory and a visual sense; for
will be. Remember also that your child will have had your happy
instance, do not have the radio playing and avoid other sources of
and undivided attention and there is nothing that a tiny child loves
noise. Use a corner of a room that does not have a great deal of
more than that.
furniture, pictures, or other objects that might distract your child
Do not ask your child to repeat the numbers as you go along. After
visually.
the five card has been shown give your child a huge hug and kiss and
Now the fun begins. Simply hold up the "one" card just beyond his
display your affection in the most obvious ways. Tell him how
reach and say to him clearly and enthusiastically, "This is one." Show
wonderful and bright he is and how much you love teaching him.
it to him very briefly, no longer than it takes to say it. One second or
Repeat this two more times during the first day, in exactly the
less.
manner described above. In the first few weeks of your math
Give your child no more description. There is no need to elaborate.
program, sessions should be at least one half-hour apart. After that,
Next, hold up the "two" card and again with great enthusiasm say,
sessions can be fifteen minutes apart.
"This is two."
The first day is now over and you have taken the first step in
Show the three, four, and five card in precisely the same way as you
teaching your child to understand mathematics. (You have thus far
have the first two cards. It is best when showing a set of cards to take
invested at most three minutes.)
the card from the back of the set rather than feeding from the front
The second day, repeat the basic session three times. Add a second
card. This allows you to glance at one of the corners of the back of
set of five new dot cards (six, seven, eight, nine and ten). This new
the card where you have written the number. This means that as you
set should be seen three times throughout the day. Since you now will
actually say the number to your child you can put your full attention
be showing two sets of five cards, and each set will be taught three
on his face. You want to have your full attention and enthusiasm
times in the day, you will be doing a total of six math sessions daily.
directed toward him rather than looking at the card as he looks at it.
The first time you teach the set of cards from
Remember, the more quickly you show him the cards, the better his
attention and interest
330 HOW TO MULTIPLY YOUR BABY S INTELLIGENCE
How to Teach Your Baby Math 331
process of learning math is boredom. Never bore the child. Going
one to five and the set of cards from six to ten you may show them
too slowly is much more likely to bore him than going too quickly.
in order (i.e., one, two, three, four, five.) After that make sure that
Consider the splendid thing you have just accomplished. You have
you always shuffle each set of cards before the next showing so that
given your child the opportunity to learn the true quantity often when
the sequence in which your child will see the cards is unpredictable.
he is actually young enough to perceive it. This is an opportunity you
Just as with reading, at the end of each session tell your child he is
and I never had. He has done, with your help, two most extraordinary
very good and very bright. Tell him that you are very proud of him
things.
and that you love him very much. Hug him and express your love for
him physically, don't bribe him or reward him with cookies, candy, or
1. His visual pathway has grown and, more important, he is able to
the like.
differentiate between one quantity or value and another.
Again, as with reading, children learn at lightning speed if you
show them the math cards more than three times a day you will bore
2. He has mastered something that we adults are unable to do and,
them. If you show your child a single card for more than a second you
in all likelihood, never will do.
will lose him. Try an experiment with his dad. Ask Dad to stare at a
card with six dots on it for thirty seconds. You'll find that he'll have
Continue to show the two sets of five cards but after the second day
great difficulty in doing so. Remember that babies perceive much
mix the two sets up so that one set might be three, ten, eight, two and
faster than grown-ups.
five while the remaining cards would be in the other set. This
Now you are teaching your child two sets of math cards with five
constant mixing and reshuffling will help to keep each session
cards in each set, each set three times a day. You and your child are
exciting and new. Your child will never know which number is going
now enjoying a total of six math sessions spread out during the day,
to come up next. This is a very important part of keeping your
equaling a few minutes in all. Remember: the only warning sign in
teaching fresh and interesting.
the entire
332 HOW TO MULTIPLY YOUR BABY S INTELLIGENCE
How to Teach Your Baby Math 333
Continue to teach these two sets of five cards in this way for five
Principle: Always stop before your child wants to
days. On the sixth day you will begin to add new cards and put away
stop.
old cards.
Here is the method you should use from this point on in adding new
cards and taking out old ones. Simply remove the two lowest In summary, you will be teaching ten cards daily, divided into two
numbers from the ten cards you have been teaching for five days. In sets of five cards each. Your child will be seeing two new cards daily
this case you would remove the one card and the two card and replace or one new card for each set and the two lowest cards will be retired
those cards with two new cards (eleven and twelve.) From this point each day.
on you should add two new cards daily and put away two old cards. Children who have already been taught to count from one to ten or
We call this process of putting away an old card "retirement." higher may attempt to count each card at first. Knowing how to count
However, every retired card will later be called back to active duty causes minor confusion to the child. He will be gently discouraged
when we get to the second and third steps, as you will see shortly. from doing this by the speed at which the cards are shown. Once he
realizes how quickly the cards are shown, he will see that this is a
different game from the counting games he is used to playing and
should begin to learn to recognize the quantities of dots that he is
DAILY PROGRAM
seeing. For this reason, if your tiny child does not know how to count,
(after the first day)
Daily Content 2 sets do not introduce it until well after he has completed steps one through
One Session: 1 set (5 cards) shown once five of this pathway.
Frequency: 3 x daily each set Again, one must remember the supreme rule of never boring the
Intensity: 3/4-inch red dots
child. If he is bored there is a strong likelihood that you are going too
Duration: 5 seconds per session
slowly. He should be learning quickly and pushing you to play the
New Cards: 2 daily (1 in each set)
game some more.
Retired Cards: 2 daily (two lowest)
If you have done it well he will be averaging two new cards daily.
Life Span
This is actually a minimum
of Each Card: 3 x daily for 5 days = 15 x
334 HOW TO MULTIPLY YOUR BABY S INTELLIGENCE
How to Teach Your Baby Math 335
number of new cards to introduce daily. You may feel that he needs
new material more quickly. In this case, you should retire three cards formulas and rituals such as "I put down the 6 and carry the 9." He
daily and add three new ones or even four. will now be able to recognize at a glance forty-seven dots, forty-
seven pennies, or forty-seven sheep.
By now both parent and child should be approaching the math game
If you have been able to resist testing, he may now have
with great pleasure and anticipation, Remember, you are building into
demonstrated his ability by accident. In either case, trust him a bit
your child a love of learning that will multiply throughout his life.
longer. Don't be misled into believing he can't do math this way
More accurately, you are reinforcing a built-in rage for learning that
merely because you've never met an adult who could. Neither could
will not be denied but which can certainly be twisted into useless or
any of them learn English as fast as every kid does.
even negative channels in a child. Play the game with joy and
You continue to teach the dot cards, in the way described here, all
enthusiasm. You have spent no more than three minutes teaching him
the way up to one hundred. It is not necessary to go beyond one
and five or six loving him and he has made one of the most important
hundred with the quantity cards, although a few zealous parents have
discoveries he will ever make in his whole life.
done so over the years. After one hundred you are only playing with
Indeed, if you have given him this knowledge eagerly and joyously
zeros. Once your child has seen the dot cards from one to one
and as a pure gift with no demands of repayment on the child's part,
hundred he will have a very fine idea of quantity.
he will have already learned what few adults in history have ever
In fact, he will need and want to begin on the second step of the
learned. He will actually be able to perceive what you can only see.
Math Pathway well before you get all the way up to one hundred in
He will actually be able to distinguish thirty-nine dots from thirty-
the dots. When you have completed one to twenty with the dot cards,
eight dots or ninety-one dots from ninety-two dots. He now knows
it is time to begin the second step.
true value and not merely symbols and has the basis he needs to truly
understand math and not merely memorize
336 HOW TO MULTIPLY YOUR BABY S INTELLIGENCE
How to Teach Your Baby Math 337
THE SECOND STEP (Equations)
Every time you showed him a new dot card, he saw the addition of
By this time your child will have quantity recognition from one to
one new dot. This becomes so predictable to the tiny child that he
twenty. At this point there is sometimes the temptation to review old
begins to anticipate cards he has not yet seen. However, he has no
cards over and over again. Resist this temptation. Your child will find
way of predicting or deducing the name we have given the condition
this boring. Children love to learn new numbers but they do not love
of "twenty-one. " He has probably deduced that the new card we are
to go over and over old ones. You may also be tempted to test your
going to show him is going to look exactly like twenty except it is
child. Again, do not do this. Testing invariably introduces tension into
going to have one more dot on it.
the situation on the part of the parent and children perceive this
This of course is called addition. He doesn't know what it is called
readily. They are likely to associate tension and unpleasantness with
yet but he does have a rudimentary idea about what it is and how it
learning. We have discussed testing in greater detail earlier in the
works. It is important to understand that he will have reached this
book.
point before you actually begin to show him addition equations for
Be sure to show your child how much you love and respect him at
the first time.
every opportunity.
You can prepare your materials by simply writing two-step addition
Math sessions should always be a time of laughter and physical
equations on the backs of your cards in pencil or pen. A few moments
affection. They become the perfect reward for you and your child.
with your calculator and you can put quite a number on the back of
Once a child has acquired a basic recognition of quantity from one
each dot card from one to twenty. For example the back of your ten
to twenty, he is ready to begin to put some of these quantities together
card should look like this:
to see what other quantities result. He is ready to begin addition.
Beginning to teach addition equations is very easy. In fact, your
child has already been watching the process for several weeks.
338 HOW TO MULTIPLY YOUR BABY S INTELLIGENCE
How to Teach Your Baby Math 339
9 + 1 = 10 5 + 5 = 10
8 + 2= 10 2 x 5= 10 "equals" mean in the same way he learns what the words "mine"
7 + 3 = 10 5 x 2 = 10
and "yours" mean, which is by seeing them in action and in context.
6 + 4 = 10 1 + 2 +3 + 4 = 10
Do this quickly and naturally. Again practice on Dad a few times
until you feel comfortable. The trick here is to have the equation set
up and ready to go before you draw your child's attention to the fact
that a math session is about to begin. It is foolish to expect your baby
to sit and watch you shuffle around for the correct card to make the
equation that you are about to show him. He will simply creep away,
and he should. His time is valuable too.
Set up the sequence of your equation cards for next day the night
20 ÷ 2 = 10 19 - 9 = 10
before so that when a good time presents itself you are ready to go.
30 ÷ 3 = 10 18 8 = 10
Remember, you will not be staying on the simple equations of one to
40 ÷ 4 = 10 17 7 = 10
50 ÷ 5 = 10 16 6 = 10
twenty for long; soon you will be doing equations that you cannot do
in your head so readily or so accurately.
To begin, place on your lap face down the one, two and three cards.
Each equation takes only a few seconds to show. Don't try to
Using a happy and enthusiastic tone simply say "One plus two equals
explain what "plus" or "equals" means. It is not necessary because
three." As you say this you show the card for the number you are
you are doing something far better than explaining what they mean,
saying.
you are demonstrating what they are. Your child is seeing the process
Therefore for this particular equation you hold up the one card and
rather than merely hearing about it. Showing the equation defines
say "one" (put down the one card) and say "plus" (pick up the two
clearly what "plus" means and what "equals" means. This is teaching
card) and say "two" (put down the two card) and say "equals" (pick
at its best.
up the three card) and say " three."
He learns what the word "plus" and the word
340 HOW TO MULTIPLY YOUR BABY S INTELLIGENCE
How to Teach Your Baby Math 341
If someone says, "One plus two equals three" to an adult, what he
Tiny children see the fact and not the symbol.
sees in his mind's eye is 1 + 2=3, because we adults are limited to
Always be consistent about the way you say the equations. Use the
seeing the symbols rather than the fact.
same words each time. Say, "One plus two equals three." Don't say
What the child is seeing is
"One and two makes three." When you teach children the facts, they
will deduce the rules but we adults must be consistent for them to
deduce the rules. If we change the vocabulary we use, children have a
" "
plus equals
"
right to believe that the rules have changed also.
" " "
Each session should consist of three equations no more. You may
do less than this but do not do more. Remember you always want to
keep the sessions brief.
"
or
Do three equation sessions daily. Each of these three sessions will
" "
contain three different equations; therefore, you will be doing nine
different equations daily. Please note you do not have to repeat the
"
or same equation over and over again. Each day your equations will be
" "
new.
Please avoid doing predictable patterns of equations in one session.
"
For example
or "
"
1 + 2 = 3
1 + 3 = 4
or " " "
1 + 5 = 6
etc.
" "
or
"
342 HOW TO MULTIPLY YOUR BABY S INTELLIGENCE
How to Teach Your Baby Math 343
A much better session would be
your lap and you will show each card as you say the number
1 + 2 = 3
"
"
1 + 5 = 7
" " - =
"
"
4 + 8 = 12
By now you will have gone beyond twenty in teaching the dot cards
so you will have an even wider selection of numbers to use to make
Keep the addition equations to two steps because this keeps the
subtraction equations and you should feel free to use these higher
session zippy and crisp, which is much better for the tiny child.
numbers as well.
One hundred and ninety different two-step addition equations that
Now you can stop doing addition equations and replace these
can be made using the cards between one and twenty, so don't be
sessions with subtraction equations. You will be doing three
afraid that you will run out of ideas in the first week. You have more
subtraction equation sessions daily with three different equations in
than enough material here to work with.
each session while you are simultaneously continuing two sets of five
In fact, after two weeks of nine addition equations daily, it is time
dot cards three times daily in order to teach the higher numbers up to
to move on to subtraction or you will lose the attention and interest of
one hundred. This gives you nine very brief math sessions in a day.
your child. He has a clear idea about adding dots; now he is ready to
see them subtracted.
The process you will use to teach subtraction is exactly the same as DAILY PROGRAM
the process you have used to teach addition. This is the same method
Session 1 Dot Cards
by which he learns English.
Session 2 Subtraction Equations
Prepare your dot cards by writing various equations on the back.
Session 3 Dot Cards
Begin by saying, "Three minus two equals one." Again you will have
Session 4 Dot Cards
the three cards that make up each equation on
344 HOW TO MULTIPLY YOUR BABY S INTELLIGENCE
How to Teach Your Baby Math 345
Session 5 Subtraction Equations
Session 6 Dot Cards
to your child. That is plenty. You do not have to do every possible
Session 7 Dot Cards
combination. Now it is time to move on to multiplication.
Session 8 Subtraction Equations
Session 9 Dot Cards
Multiplication is nothing more than repeated addition, so it will not
come as any great revelation to your child when you show him his
first multiplication equation. He will, however, be learning more of
Each of these equations has the great virtue that the child knows
the language of mathematics and this will be very helpful to him.
both quantities
Since your child's repertoire of dot cards has been growing daily
you now have even higher numbers that you can use in your
multiplication equations. Not a moment too soon, because you will
need higher numbers now to supply answers to these equations.
Prepare your cards by writing as many multiplication equations as
possible on the back of each dot card.
Using three cards say, "Two multiplied by three equals six ."
and their names (twelve) beforehand. The equation contains two
elements that are satisfying to the child. First, he enjoys seeing old
" " "
x =
"
" " "
dot cards he already knows and second, although he already knows
" " "
these two quantities, he now sees that his two old quantities
subtracted create a new idea. This is exciting to him. It opens the door
for understanding the magic of mathematics.
He will learn what the word "multiplied" means in exactly the same
way that he learned what the words "plus," "equals," "minus," "mine,"
During the next two weeks you will be majoring in subtraction.
and "yours" mean, by seeing them in action.
During this time you will show approximately 126 subtraction
equations
How to Teach Your Baby Math 347
346 HOW TO MULTIPLY YOUR BABY S INTELLIGENCE
together for less than two months and you have already covered
Now your subtraction equation sessions will be replaced by
quantity recognition from one to one hundred, addition, subtraction,
multiplication equation sessions. You will do three sessions daily
and multiplication. Not bad for the small investment of time required
with three equations in each session. Follow exactly the same pattern
to do so and the excitement and adventure of learning the language of
you have been following with addition and subtraction. Meanwhile
mathematics.
continue the dot card sessions with higher and higher numbers.
We have said that you have now completed all the dot cards, but
Under ideal circumstances your tiny child has seen only real
this is not quite true. There is actually one quantity card left to teach.
numbers in the form of dot cards and has not, as yet, seen any
We have saved it until last because it is a special one and particularly
numeral, not even log 2.
beloved of tiny children.
The next two weeks are devoted to multiplication. Continue to
It has been said that it took ancient mathematicians five thousand
avoid predictable patterns in the equations that you do in one session,
years to invent the idea of zero. Whether that is the case or not, it may
such as
not surprise you to learn that once tiny children discover the idea of
quantity they immediately see the need for no quantity.
2x3 = 6
Little children adore zero and our adventure through the world of
2x4 = 8
real quantity would not be complete without including a zero dot
2x5 = 10
card. This one is very easy to prepare. It is simply an 11" by 11" piece
of white poster board with no dots on it.
These patterns do have a value later in the book. We will touch
The zero dot card will be a hit every time. You will now use the
upon when to bring them to the attention of your child, but not just
zero card to show your child addition, subtraction and multiplication
yet. For the moment we want to keep the tiny child wondering what is
equations. For example:
coming next. The question, "What's next ?" is the hallmark of the tiny
child and each session should provide him with a new and different
solution to that mystery.
You and your child have been enjoying math
348 HOW TO MULTIPLY YOUR BABY S INTELLIGENCE
How to Teach Your Baby Math 349
+ =
" " " " " = "
" ÷
" "
" "
- =
He will learn what the word "divided" means exactly as he learned
what every other word means. Each session contains three equations.
x =
You do three sessions daily so you will cover nine division equations
daily. By now this will be very easy indeed for you and your child.
When you have spent two weeks on division equations, you will
have fully completed the second step and will be ready to begin the
Now we have, in fact, completed teaching all the real number cards
third step on the pathway.
that we need. However, we are not finished with the dot cards. We
will still be using them in many ways to introduce new mathematical
ideas as we go along. THE THIRD STEP (Problem-Solving)
After two weeks of multiplication it is time to move on to division.
If up to now you have been extraordinarily giving and completely
Since your child has completed all the dot cards from zero to one
non-demanding, then you are doing very well and you haven't done
hundred, you may use all these cards as the basis for your division
any testing.
equations. Prepare your cards by writing two-step division equations
We have said much about teaching and much about testing.
on the backs of many, if not all, of your one hundred dot cards. (This
Our strongest advice on this subject is do not test your child. Babies
is a great job for the resident mathematician. If you don't happen to
love to learn, but they hate to be tested. In that way they are very like
have one, try using Dad.)
grown-ups.
Now you simply say to your child, "Six divided by two equals three
."
350 HOW TO MULTIPLY YOUR BABY S INTELLIGENCE
How to Teach Your Baby Math 351
Well what is a mother to do? She does not want to test her child;
she wants to teach him and give him every opportunity to experience
happy, enthusiastic, relaxed way.
the joy of learning and accomplishment.
End of opportunity.
Therefore, instead of testing her child she provides problem-solving No matter how he responds, he wins and so do you, because the
chances are good that if you are happy and relaxed he will enjoy
opportunities.
doing this with you.
The purpose of a problem-solving opportunity is for the child to be
These problem-solving opportunities can be put at the end of
able to demonstrate what he knows if he wishes to do so. It is exactly
equation sessions. This creates a nice balance of give and take to the
the opposite of the test. Now you are ready not to test him but to
session, since each session begins with you giving three equations to
teach him that he knows how to solve problems (and you'll learn that your child and ends with an opportunity for your child to solve one
equation if he wishes to do so.
he can.)
You will find that merely giving your child an opportunity to
A very simple problem-solving opportunity would be to hold up
choose one number from another is all right to begin with, but you
two dot cards. Let's say you choose "fifteen" and "thirty-two" and you
should very shortly move on to opportunities to choose answers to
hold them up and ask, "Where is thirty-two?"
equations. This is a lot more exciting for your child, not to mention
for you.
This is a good opportunity for a baby to look at or touch the card if
To present these problem-solving opportunities you need the same
he wishes to do so. If your baby looks at the card with thirty-two dots
three cards you would need to show any equation, plus a fourth card
on it or touches it, you are naturally delighted and make a great fuss.
to use as a choice card. Don't ask your child to say answers. Always
If he looks at the other card simply say, "This is thirty-two, isn't it?"
give him a choice of two possible answers. Very young children do
while holding up the thirty-two card in front of him.
not speak or are just beginning to speak. Problem-solving situations
which demand an oral response will be very difficult if not impossible
You're happy, enthusiastic, and relaxed. If he does not respond to
for them. Even children who are beginning to speak do not
your question, hold the card with thirty-two dots a little closer to him
and say, "This is thirty-two, isn't it?" again in a
352 HOW TO MULTIPLY YOUR BABY S INTELLIGENCE
How to Teach Your Baby Math 353
like to answer orally (which is in itself another test) so always give
Now the equation sessions will be composed of a variety of
your child a choice of answers.
equations, for example an addition equation, a subtraction equation,
and a division equation.
Remember that you are not trying to teach your child to talk, you
Now would also be a good time to move on to three-step equations
are teaching him mathematics. He will find choosing to be very easy
and see if your child enjoys them. If you move quickly enough
and a lot of fun, but he will quickly become irritated if we demand
through the material the chances are very good that he will.
speech.
Simply sit down with a calculator and create one or two three-step
Since you have now completed all the dot cards and addition,
equations for each card and write them clearly on the back of each
subtraction, multiplication, and division at the initial stages, you can
one. A typical session at this point would be
make your equation sessions even more sophisticated and varied.
Continue to do three equation sessions daily. Continue to show three
completely different equations at each session. But now it is
Equations'.
unnecessary to show all three cards in the equation. Now you need
only show the answer card.
2 x 2 x 3 = 12
2 x 2 x 6 = 24
This will make the sessions even faster and easier. You simply say,
2 x 2 x 8 = 32
"Twenty-two divided by eleven equals two" and show the "two" card
as you say the answer. It is as simple as that.
Problem-Solving.
Your child already knows "twenty-two" and "eleven" so there is no
real need to keep showing him the whole equation. Strictly speaking
2 x 2 x 12 = ?
there is no real need to show him the answer either, but we have
48 or 52
found that it is helpful for us adults to use visual aids when we teach.
The kids seem to prefer it also.
354 HOW TO MULTIPLY YOUR BABY S INTELLIGENCE
How to Teach Your Baby Math 355
Please note that these sessions continue to be very, very brief. Your
child now has nine three-step equations daily with one problem-
40 + 15 - 30 = 25
solving opportunity tagged onto each session.
40 + 15 - 20 = 35
Therefore you are giving him the answer to the first three equations
40 + 15 - 10 = 45
in each session and, at the end of each session, giving him the
opportunity to choose the answer to the fourth equation if he wishes
or
to do so.
After a few weeks of these equations, it is time to add a little
100 50 ÷ 10 = 5
additional spice to your sessions again. Now you are going to give
your child the type of equations which he will like best of all.
50 30 ÷ 10 = 2
Begin to create equations which combine two of the four functions
20 10 ÷ 10 = 1
of addition, subtraction, multiplication, and division.
Combining two functions gives you an opportunity to explore
Your child will find these patterns and relationships interesting and
patterns by creating equations that are related by a common element.
important just as all mathematicians do.
For example:
When you are creating these equations, it is important to remember
if you are using multiplication in the equation that the multiplication
3 x 15 + 5 = 50
function must come first in the sequence of the equation. Otherwise
3 x 15 5 = 40
you can feel free to make up any equations that you wish as long as
3 x 15 ÷ 5 = 9
the ultimate answer to the equation falls between zero and one
hundred since you do not have any dot cards beyond one hundred.
Write these new equations on the back of each dot card.
or
Your problem-solving opportunities should contain these more
advanced equations as well.
After a few weeks time add another function
356 HOW TO MULTIPLY YOUR BABY S INTELLIGENCE
How to Teach Your Baby Math 357
to the equations you are offering. Now you will be giving four-step
in the knowledge that you and you alone have brought about this
equations for the first time, for example:
ability in your child.
You will be astonished at the speed at which your child solves
equations. You will wonder if he solves them in some psychic way.
56 + 20 16 ÷ 2 = 30
56 + 20 8 ÷ 2 = 34
When adults see two-year-olds solving math problems faster than
56 + 20 4 ÷ 2 = 36
adults can, they make the following assumptions in the following
order:
These four-step equations are a great deal of fun. If you were a little
intimidated at first by the idea of teaching your child mathematics, by
1. The child is guessing. (The mathematical odds against this, if he
now you should be relaxing and really enjoying these more advanced
is virtually always right, are astronomical.)
equations just as your child is enjoying them.
2. The child isn't actually perceiving the dots but instead is actually
From time to time you should feel free to show three unrelated
equations as well as those which have a pattern. For example: recognizing the pattern in which they occur. (Nonsense. He'll
recognize the number of men standing in a group, and who can keep
people in a pattern? Besides, why can't you recognize the seventy-five
86 + 14 25 ÷ 5 = 15
pattern on the seventy-five dot card which he knows at a glance?)
100 ÷25 + 0 - 3 = 1
3. It's some sort of trick. (You taught him. Did you use any tricks?)
3 x 27 ÷ 9 + 11 - 15 = 5
4. The baby is psychic. (Sorry but he isn't: he's just a whiz at
learning facts. We'd rather write a book called "How to Make Your
Baby Psychic" because that would be
It is true that he will actually be perceiving what is happening,
while you and I can only see the equations without truly digesting the
information. Nevertheless there is no small pleasure
358 HOW TO MULTIPLY YOUR BABY S INTELLIGENCE
How to Teach Your Baby Math 359
THE FOURTH STEP (Numerals)
even better. Unfortunately we don't know how to make little kids
psychic.)
This step is ridiculously easy. We can now begin the process of
teaching the numerals or symbols that represent the true values or
Now the sky is the limit. You can go in many directions with
quantities that your child already knows so well.
mathematical problem-solving at this point and the chances are
You will need to make a set of numeral cards for your child. It is
extremely good that your child will be more than willing to follow
best to make a complete set from zero to one hundred. These should
you wherever you decide to go.
be on 11" by 11" poster board and the numerals should be made with
For those mothers who would like some further inspiration we
the large, red, felt-tipped marker. Again, you want to make the
include some additional ideas
numerals very large 6" tall and at least 3" wide. Make sure to make
your strokes wide so that the numerals are in bold figures.
1. Sequences
2. Greater than and less than
Be consistent about how you print. Your child needs the visual
3. Equalities and inequalities
information to be consistent and reliable. This helps him enormously.
4. Number personality
Always label your materials on the upper left-hand side. If you do
5. Fractions
this you will always know that you have them right side up when you
6. Simple algebra
are showing them to your child.
It is not possible to cover all of these areas within the scope of this
This is not a consideration with the dot cards you have already
book. However, these areas are covered in more detail in the book
made to show quantity since there is no right-side-up or upside down
to those cards. In fact, you want to show those cards every which way
How To Teach Your Baby Math.
they come up that is why on the back of the dot cards you have
All of these can be taught using the dot cards and indeed should be
labeled all four corners, not just the upper left-hand corner.
taught using the dot cards because in this way the child will see the
reality of what is happening to real quantities rather than learning
how to manipulate symbols as we adults were taught.
360 HOW TO MULTIPLY YOUR BABY S INTELLIGENCE
How to Teach Your Baby Math 361
On the back of the numeral cards, print the numeral again in the
doing three sessions a day of equations with a bit of problem-
upper left-hand corner. Make this whatever size is easy for you to see
solving at the end of each of those sessions, but you have long since
and read. You may use pencil or pen to do this.
finished the six sessions you used to do in order to teach the dot cards
Your numeral cards should look like this:
initially. Now you will teach the numeral cards in exactly the same
way that you taught the dot cards several months ago.
You will have two sets of numeral cards with five cards in each set.
Begin with 1 to 5 and 6 to 10. You may show them in order the first
time but after that always shuffle the cards so that the sequence is
1 2
unpredictable. As before, each day retire the two lowest numerals and
add the next two. Make sure that each set being shown has a new card
in it every day rather than one set having two new cards and the other
set remaining the same as the day before.
Show each of the sets three times daily. Please note that your child
may learn these cards incredibly quickly, so be prepared to go even
3 100
faster if necessary. If you find that you are losing your child's
attention and interest, speed up the introduction of new material.
Instead of retiring two cards daily, retire three or four cards and put in
three or four new cards. At this point you may find that three times
Sometimes mothers get fancy and use stencils to make their cards.
daily is too high a frequency. If your child is interested during the
This makes beautiful numeral cards; however, the time involved is
first two sessions each day but consistently creeps away for the
prohibitive. Remember that your time is precious.
Neatness and legibility are far more important than perfection.
Often mothers find -that fathers can make very nice cards and that
they appreciate having a hand in the math program. At this stage in
your daily program you are
362 HOW TO MULTIPLY YOUR BABY S INTELLIGENCE
How to Teach Your Baby Math 363
third session, then drop the frequency from three times daily to two
the easiest ways is to go back to equalities, inequalities, greater
times daily.
than, and less than and use dot cards and symbol cards together.
You must at all times be sensitive to your child's attention, interest,
Take the dot card for 10 and put it on the floor, then put down the
and enthusiasm. These elements when carefully observed will be
not equal sign, then the numeral card 35 and say, "Ten is not equal to
invaluable tools in shaping and reshaping your child's daily program
thirty-five."
to suit his needs as he changes and develops.
One session would look like this:
At the very most it should take you no longer than fifty days to
complete all the numerals from zero to one hundred. In all likelihood
it will take a lot less time.
Once you have reached the numeral one hundred you should feel
free to show a variety of numerals higher than one hundred. Your
child will be thrilled to see numerals for 200, 300, 400, 500, and
>
12
1,000. After this come back and show him examples of 210, 325, 450,
586, 1,830. Don't feel that you must show each and every numeral
under the sun. This would bore your child tremendously. You have
already taught him the basics of numeral recognition by doing zero to
one hundred. Now be adventurous and give him a taste of a wide diet
= 12
of numerals.
When you have caught the numerals from zero to twenty it is time
to begin a bridging step of relating the symbols to the dots. There are
a multitude of ways of doing this. One of
0 <
364 HOW TO MULTIPLY YOUR BABY S INTELLIGENCE
How to Teach Your Baby Math 365
Your first cards would look like this:
As you work your way up through the numeral cards, play this
game with as many numeral cards and dots cards as you have the time
and inclination to do. Children also like to join in and choose their
own combinations using the dot cards and the numeral cards.
Learning the numerals is a very simple step for your child. Do it
quickly and joyously so you can get on to the fifth step as soon as
possible.
THE FIFTH STEP {Equations with numerals)
Now go back to Step Two of the pathway and follow the
instructions, only this time use new equation cards with numerals
instead of the dot cards. When you have completed Step Two go on
The fifth step is really a repetition of all that has come before. It
to Step Three.
recapitulates the entire process of addition, subtraction,
For Step Three you will need to make some materials suitable for
multiplication, division, sequences, equalities, inequalities, greater
problem-solving opportunities. Now make a quantity of cards to use
than, less than, square roots, fractions, and simple algebra.
which do not have answers written on them. Again use single
Now you will need a good supply of poster board cut into strips 18"
numeral cards to provide your child with choice cards. It will be
long and 4" wide. These cards will be used to make equation cards
helpful if you always write the correct answer on the top left hand
using numerals. At this stage we recommend that you switch from corner of these problem-solving cards along with the problem itself
using red to black felt-tipped marker. The numerals you will be so that you are never at a loss to know what the answer really is.
writing now will be smaller than before and black has greater contrast
than red for these smaller figures. Your numerals should be 2" tall
25 + 5
and 1" wide
25 + 5 = 30
(reverse)
366 HOW TO MULTIPLY YOUR BABY S INTELLIGENCE
How to Teach Your Baby Math 367
Here are some examples of what your materials will look like as
you work your way through the operations that you have already done
with dots.
14 x 2 x 3 = 84
Subtraction Equations
15 x 3 x 2 x 5 `" 45
30 12 = 18
Division Equations
92 2 10 = 80
76 ÷ 38 = 2
192 ÷ 6 ÷ 8 = 4
100 - 23 - 70 `" 0
84 ÷ 28 = 3
Multiplication Equations
3 x 5 = 15
368 HOW TO MULTIPLY YOUR BABY S INTELLIGENCE
How to Teach Your Baby Math 369
will have had a superbly joyous introduction into the world of
458 ÷ 2 = 229
arithmetic. He will have mastered four basic but vital truths in
mathematics.
First, he will have learned about quantity. Indeed he will be able to
differentiate many different quantities from one another.
Continue to use these 2" size numerals long enough to be sure that
Second, he will have learned how to put those quantities together
your child is comfortable with them. When this part of your program
and take those quantities apart. He will have seen hundreds of
is going smoothly, you can begin making the numerals smaller. This
different combinations and permutations of quantities.
must be a gradual process. If you make your numerals too small too
Third, he will have learned that there are symbols that we use to
quickly you will lose the attention and interest of your child.
represent the reality of each of the quantities and how to read those
When you have gradually reduced the numeral size to one inch or
smaller, you will have more space on the cards to write longer and
symbols.
And finally and most important, he will know the difference
more sophisticated equations. As part of your problem-solving
between the reality of quantity and the symbols that have arbitrarily
program at this point your child may wish to choose numerals and
been chosen to represent those quantities.
operational symbols (=, -^, +, -, x, ÷) and make his own equations for
Arithmetic will be the end of the beginning for him because he will
you to answer. Keep your calculator handy you will be needing it!
now easily and happily be able to make the leap from the simple
mechanics of arithmetic to the much more fascinating and creative
Summary
world of higher mathematics. This is a world of thinking and
When you have completed the first through the fifth steps of the
reasoning and logic: not merely predictable calculations but instead a
Math Pathway you will have reached the end of the beginning of your
genuine adventure where new things are discovered all the time.
child's life-long adventure in mathematics. He
Sadly, this is a world that very few have ever entered. The majority
of us escaped from
370 HOW TO MULTIPLY YOUR BABY S INTELLIGENCE
21
mathematics at the earliest possible moment and long before the
the magic is
exciting world of higher mathematics was in view. Indeed it has
always been considered a closed shop where only a lucky few gain in the child
entrance. Instead of arithmetic being a springboard to higher
& and in you
mathematics, it closed the doors to this wonderful language.
Every child should have the right to master this superb language.
You will have bought your child his passport.
There are only two lasting bequests
we can give our children.
One is roots , the other wings.
HOODING CARTER
The most important part of how to multiply your baby's intelligence
is learning what your baby really is and what he has the potential to
become.
You now have learned the basic details of how to teach your baby
as well. But beware we human beings treasure techniques. We love
"know-how." In fact, we Americans pride ourselves on our know-
how. But sometimes we place know-how before "know why" in
importance. We should not do so.
372 HOW TO MULTIPLY YOUR BABY S INTELLIGENCE
The Magic is in the Child& .and in You 373
The principles of how the brain grows and why it grows the way it
The magic is not in the techniques, the magic is in the child. The
does are infinitely more important than the techniques or the how-to's.
magic is in his incredible brain. The magic is in you.
There is no magic in the techniques.
A staff member was once flying from Sydney to San Francisco. It's
The magic is in the child.
a long trip. Sitting beside him was a young mother, brimming over
Do not fall in love with techniques.
with enthusiasm about a recent adventure. He listened delightedly
Instead be certain you have gained a thorough understanding of
while she told him about a marvelous course she had taken in
how the brain grows and why it grows in the way that it does.
Philadelphia called "How to Multiply Your Baby's Intelligence." "
It is infinitely more important.
When she wound down a bit, he asked her, "And do these things
If you learn only techniques, no matter how well you learn them
work?"
you will lack the certainty and confidence that understanding the
"Yes, of course they work," she replied.
principles and philosophy give you. Under these circumstances you
"So you have actually begun to teach your daughter to read and to
will carry out the techniques poorly.
do math and all of those things."
As time goes by and you begin to forget the techniques, your
"Yes, a little," she responded, "and it's fun. But that is not really the
knowledge will degenerate and you will know less and less.
most important thing."
On the other hand, if you truly understand what you are doing and
"Oh, then what is?" he asked.
why you're doing it, your knowledge will grow by leaps and bounds
"Why, our whole lives are changed and they will be forever."
and in the end you will be able to invent more techniques and even
"Really?"
better techniques than we have taught you in this book.
"Of course they are. I've always loved her dearly and now I love her
We have spent years developing these techniques and they are
even more because now I respect her more and understand her much
splendid. What is most important, they work and work well. But there
better. I fully understand the magnitude of the miracle in a way that I
is one thing you must never forget:
never did before.
"Now we love and respect each other more
374 HOW TO MULTIPLY YOUR BABY S INTELLIGENCE
The Magic is in the Child& .and in You 375
than I would have believed possible. As a result, I talk to her and
deal with her in an entirely different way than I ever would have done
doesn't think that it's a joyful opportunity.
before. If I had never shown her a reading word or a single math card
We miss the magic that is born of mother and father and tiny baby
our lives would still have been totally changed by the experience."
learning together. The most magical learning team this world has ever
That mother knew the magic was in her child. We parents are the
seen.
best thing that ever happened to babies, but we have, in the past half
century, been bullied into doing some strange things.
We sometimes are bullied into doing some mighty strange things.
We love our children very much and because we do we put up with
The magic of every child is born in him. It comes with him and if
all the dirty diapers, the runny noses, the momentary terror when for a
we are wise enough to recognize and nurture it, the magic stays with
second we lose sight of them on a crowded beach, the high
him the rest of his life. If we respect the magic we become part of it.
temperatures which seem to happen only at 2:00 a.m., the flying trips
to the hospital and all the rest that goes with the territory of being
Every mother and father has experienced a sense of wonder and
parents and loving our kids.
astonishment when gazing upon their own newborn baby. Every
But when it comes time to introduce them to all of the breath-taking
parent knows that magic. The magic is not in the cardboard and the
beauty that there is in the world everything beautiful that has been
red markers, it is not in the dots , and it is certainly not in the school
written in our languages, all the gorgeous paintings that were ever
system. The magic is not even in the Institutes for the Achievement of
painted, all the moving music that was ever written, all the wonderful
sculptures that were ever carved we wait until they are six years
Human Potential.
old, when it's just about over, and then tragically turn that joyful
The magic is in your child. He has his own unique brand of magic,
opportunity over to a stranger called a teacher who often
unlike any magic that has ever been seen before. Find that magic and
give him yours. If this book provides one mother with a new and
profound respect for her baby, then it will have been well worth the
effort. For this, all by itself, will bring about a powerful and important
376 HOW TO MULTIPLY YOUR BABY S INTELLIGENCE
acknowledgments
change for every mother and baby so touched.
This is what the Gentle Revolution is all about.
If history records who wrote the first book, the information hasn't
filtered down to me.
Whoever he or she was, I'm sure of one thing-it wasn't done without
a good deal of help from other people..
The Good Lord knows that, while I've been working on this book
for forty years in one way or another, I certainly had giant amounts of
help, all of it vital.
In the most direct way, there have been Janet Doman, Michael
Arrnentrout and Susan Aisen, who actually wrote several of the
chapters in their entirety. Those chapters are so brilliantly clear and
incisive that I am at once delighted that they are, while
simultaneously a bit chagrined that the rest of the book is less so.
Lee Pattinson vetted it word for word and removed the splinters of
my split infinitives. Lee's doing so lightened the burden of my long-
time Doubleday editor and friend, Ferris Mack, whose "snide
marginal notes" were witty and
Acknowledgments 379
378 HOW TO MULTIPLY YOUR BABY S INTELLIGENCE
from whence we came-forever, to the tireless twenty-one-year-old
kind enough to render painless the removal of some of my favorite
aspirants.
phrases regarding some of my favorite people .in the whole world.
So also, on every page, are the many thousands of superb children
The hundreds of thousands of words which were in one or another
we have learned from, ranging as they do from the most severely
of the several manuscripts were typed by Greta Erdtmann and Cathy
brain-injured comatose child to the truly Renaissance Children of the
Ruhling, who managed to act as if that endless tedium was actually
Evan Thomas Institute.
enjoyable.
To speak of those children and their individually unique
Michael Armentrout designed the book and, without a single
accomplishments is to laud their endlessly determined and
complaint, put it together in various forms to suit my "whims of iron",
determinedly cheerful and heroic parents who live in a joyous world
which must have seemed endless.
of their own design. To name one or a hundred or a thousand of them
would somehow diminish the remaining thousands. I herewith salute
That peerless Canadian artist and photographer Sherman Hines did
them all-child, woman and man-and bow to them with the most
all the photography, except where otherwise noted.
profound love and respect.
Old Hippocrates, Temple Fay and many other great neurosurgeons
I wish to acknowledge that largely unsung group, the Board of
and neurophysiologists are there on every page, as are the great
Directors of the Institutes, both living and dead, who have given us
teachers I have had. (The dreadful teachers I have had are also there,
their love, devotion guidance and, upon more than one occasion, have
albeit in a different way).
risked their precious reputations to support us when we were
That group of people whom I can only describe as sublime, the
attacking the status quo so jealously guarded by the self-appointed
Staff of the Institutes for the Achievement of Human Potential, are on
and self-anointed "sole proprietors of the truth".
every page, in every word and in the spaces in between. They range
Last, and far from least, I bow gratefully to all who have supported
in age and experience from ninety-year-old Professor Raymond Dart,
the work of the
whose discovery of Australopithecus Africannus Dartii changed
man's idea of who we are, and
380 HOW TO MULTIPLY YOUR BABY S INTELLIGENCE
Institutes down through all the years. They have given us their
unwavering support in financial, emotional, intellectual, scientific and
moral terms and in a thousand other ways.
about the authors
GLENN DOMAN received his degree in physical therapy from the
University of Pennsylvania in 1940. From that point on, he began
pioneering the field of child brain development. In 1955, he founded
The Institutes for the Achievement of Human Potential in
Philadelphia. By the early sixties, the world-renowned work of The
Institutes with brain-injured children had led to vital discoveries
about the growth and development of well children. The author has
lived with, studied and worked with children in more than 100
nations, ranging from the most civilized to the most primitive. The
Brazilian government knighted him for his outstanding work on
behalf of the children of the world.
Glenn Doman is the international best-selling author of the Gentle
Revolution Series, consisting of How to Teach Your Baby to Read,
How to Teach Your Baby Math, How to Multiply Your Baby's
Intelligence, How to Give Your Baby Encyclopedic Knowledge, and
How to Teach Your Baby to Be Physically Superb. He is also the
author of What to Do About Your Brain-Injured Child, a guide for
parents of hurt children. Cur-
382 HOW TO MULTIPLY YOUR BABY S INTELLIGENCE
About the Authors 383
rently, he continues to devote all of his time teaching parents of
mothers. From there she returned to Philadelphia to direct the Evan
both hurt and well children.
Thomas Institute, a unique school for mothers and babies. The early
development program led to the creation of the International School
For more than thirty years Glenn Doman and the child brain
for the children who graduated from the early development program.
developmentalists of The Institutes have been demonstrating that very
young children are far more capable of learning than we ever
Janet spends most of her day nose-to-nose with "the best mothers in
imagined. He has taken this remarkable work work that explores
the world," helping them to discover the vast potential of their babies
why children from birth to age six learn better and faster than older
and their own potential as teachers.
children do and given it practical application. As the founder of The
Institutes for the Achievement of Human Potential, he has created a
comprehensive early development program that any parent can follow
at home.
When Glenn Doman decided to update the books of the Gentle
Revolution Series it was only natural that his daughter help him to
edit and organize the additional information gained over the last three
decades of experience since some of the books were originally
written.
Index
Addition, 337-342 Age, (LeWinn), 185 Computers, 290-291
Fay, Temple, 57-58 From
relationship of, to compared
Two to Five
Klosovskii, Boris N.,
teaching your baby, with human brain,
(Chukovski), 95 Fuller,
128-130 Krech, David, 131-133
196 Alphabet, teaching the, 180-182 Consistency, 214-215
Buckminster,
230-233 Cortex, 59, 137-141 Couplets,
147
Ladies Home Journal
drawbacks of, 235 Approach, 242-246
(May, 1963), 149 Learning
relationship
Genetics vs. environment, 37-
Division, 348-349 Duration of
as a survival skill,
of, to learning, 199-
54 Genius, potential for, 26
teaching sessions, 207-208,
66
201 Attitude, relationship
Guidelines for teaching,
290-291,330-331
brain development and,123-141
of, to learning, 199-
195-220,226-227 reading,
201, 205-206,208--
260
Eaglebull, John, 45-47 Early
print size and, 90 voice level
210 Auditory sense, and
Development Association of
learning, 72-75
and, 90 Lewinn, Edward, 184-
Hearing, and learning,
Japan,
. 72-75
185
40
Bits of Intelligence,
Heredity vs. environment, 37-
186,265,267 Books,
54
McLuhan, Marshall,
Emotional involvement,
introducing,
Human refrigeration
71 Materials
relationship of, to mothering,
256-262 Brain
58
encyclopedic knowledge,
147 Environment,
capacity of, ISO-182 cortex,
Humor, as a teaching
267-280 math, 322-326
best, for learning,
59, 137-141 development of,
tool, 153, 299-
reading, 222-226 size,
227-228 . " .. vs. heredity,
123-
300 Hypothermia, 58
relationship of,
37-54 . Encyclopedic
141 senses and, 221-222
to learning, 209 speed to be
knowledge program, " when
Catch-up phenomenon,
Information, presentation of,
!
shown at,
to start, 197 materials, 273-
124
186-188 Institutes for the
209-210 Math
280 Enthusiasm, relation- . ;
Chukovski, Kornei, 95
Achievement of
Daily Program chart,
ship of, to learning, 199-
Churchill, Winston,
Human Potential,
332-333 effects on brain
201,208-210, 205-206
113,116-117 Ciardi, John, 241
48 Intelligence
growth, 321 material
Equations, 336-349 three-
Color, relationship of, to
Bits of, 186, 265,
preparation,
step, 353-355
learning to read, 225 to learning
267 relationship of, to
322-326 Pathway, 327-370
math, 323 Coma Arousal: The
thinking, 25 Intensity of
when to start, 198 Mood,
Family As A Team
sessions,
relationship of, to learning, 244-245 Organization, Quantity, definition of, encyclopedic knowledge,
205-206, 227 Motor functions, 321 Quantity recognition, 292-293 math, 332 reading,
214, 223-
137- 234-235
327-335
227
139 Multiplication, 345-
Salk,Jonas, 170 Senses, as
348 Reading program, 221-
Permutations, 179-180,
learning tools, 72-75
264 when to start, 197
192-193 Phrases, 246-250
Sensory
Nature-nurture debate, 37-54
Print size, relationship Index
deprivation, 123, 387
Numerals, 359-364 definition
of, to learning, 90,
132-133 functions, 137-
of, 321 equations with, 364-
223,224,257 Repetition, relationship of,
139
368 Numbers, definition
to learning, 90, 212,
Sentences, 250-255
Problem-solving, 217, 349-
of, 321
218,225 Respect,
Sight, and learning, 72-75
358
relationship of, to learning,
Single words, 227-241
Olifactory sense, and 202-203 Retiring cards
Program of Intelli-
Smell, and learning, 72-75
learning, 72-75 Opposites,
gence, 294-300
teaching,
Speed of sessions, relationship Teaching your baby addition, of, 321 Trust, relationship
of, to learning, 209, 229 337-342 alphabet, 230-233, of, to learning, 202
subtraction, 342-345
Starting your program, 199 235 best environment for,
summary of guidelines,
Stopping and re-starting your 206, 227-228 books, 256-262 V.A.T. (visual, auditory, and
219-220,226-227 when to
program, 215 couplets, 242-246 division, tactile), 233 Violin,
start, 199 Testing, drawbacks
Subtraction, 342-345 Suits, 348-349 equations, 336-349 children's abilities for, 43-
of,
Chauncey Gay, multiplication, 345- 45 Vision, and learning,
111-114, 216-217 Time
176 Suzuki, Shinichi, 42, 72-75 Visual
348
best for teaching,
44,51, 107-108 Swimming, differentiation,
opposites, 244-245 phrases,
207-208 to start program, 199
children's 232 Vocabulary actions,
Thinking, relationship of, to
246-250 problem-solving,
abilities for, 39- 240 colors, 243 home, 236-237
intelligence, 25 Touch, and
349-
possessions, 238 self, 233-234
40
learning,
358 quantity recognition,
Voice level, relationship of, to
Tactile sense, and learning, 72-
72-75 True value,
327-335 sentences, 250-255
learning, 90,208
definition
75 Taste, and learning, 72-
single words, 227-241388
75
the insects in the garden, know the countries of the world, discover the beauty of a
OTHER REALTED BOOKS, VIDEOS & KITS IN
painting by Van Gogh, and more. It explains how to^ begin and expand your
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THE GENTLE REVOLUTION SERIES
your child's mind. Paperback $9.95 / Hardback $19.95
HOW TO TEACH YOUR BABY TO READ
Also available: How To Give Your Baby Encyclopedic Knowledge"! Video Tape How To Give
Your Baby Encyclopedic Knowledge Kit
Glenn Doman and Janet Doman
HOW TO MULTIPLY YOUR BABY'S INTELLIGENCE
How to Teach Your Baby to Read provides your child with the skills basic to
academic success. It shows you just how easy and pleasurable it is to teach a young
Glenn Ooman and Janet Doman
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How to Multiply Your Baby's Intelligence provides a comprehensive program that
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will enable your child to read, to do mathematics, and to leam about anything and
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Read Kit
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and how to more fully develop your child's potential. Paperback $12.95 / Hardback
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Glenn Doman and Janet Doman
Also available: How To Multipy Your Baby Intelligence"! Kit
How to Teach Your Baby Math instructs you in successfully developing your child's
ability to think and reason. It shows you just how easy and pleasurable it is to teach a
HOW TO TEACH YOUR BABY TO BE PHYSICALLY SUPERB
young child math. It explains how to begin and expand the math program, how to
Glenn Doman, Douglas Doman and Bruce Hagy
make and organize your materials, and how to more fully develop your child's
How to Teach Your Baby to Be Physically Superb explains the basic principles,
potential. Paperback $9.95 / Hardback $15.95
philosophy, and stages of mobility in easy-to-understand language. This inspiring
Also available: How To Teach Your Baby Math Video"! Tape How To Teach Your Baby
book describes just how easy and pleasurable it is to teach a young child to be
Math Kit
physically superb. It clearly shows you how to create an environment for each stage
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HOW TO GIVE YOUR BABY ENCYCLOPEDIC KNOWLEDGE Glenn Doman
the team of mother, father, and baby is the most important athletic team your child
How to Give Your Baby Encyclopedic Knowledge provides a program of visually
will ever be a part of. It explains how to begin, how to make your materials, and how
stimulating information designed to help your child take advantage of his or her
to expand your program. This complete guide also includes full-color charts, photo-
natural potential to leam anything. It shows you just how easy and pleasurable it is to
graphs, illustrations, and detailed instructions to help you create your own program.
teach a young child about the arts, science, and nature. Your child will recognize
Hardback $24.95
THE WRONG COCKTAIL
WHAT TO DO ABOUT YOUR BRAIN-INJURED CHILD
written by Michael Armentrout
Glenn Doman
In this breakthrough book, Glenn Doman pioneer in the treatment of the brain-
Ages 3 to 6. Paperback $9.95
injured brings real hope to thousands of children, many of whom are inoperable,
and many of whom have been given up for lost and sentenced to a life of institutional NANKI GOES TO NOVA SCOTIA written by Michael
confinement. Based upon the decades of successful work performed at The Institutes
Armentrout
for the Achievement of Human Potential, the book explains why old theories and
techniques fail, and why The Institutes philosophy and revolutionary treatment
Ages 3 to 6. Paperback $9.95
succeed. Paperback $11.95 / Hardback $19.95
For a complete catalog ofAvery books, call us at 1-800-548-5757.
CHILDREN BOOKS
About the Books
COURSE OFFERINGS AT THE INSTITUTES
Very young readers have special needs. These are not met by conventional children's
literature which is designed to be read by adults to little children not by them. The
HOW TO MULTIPY YOUR BABY'S INTELLIGENCE"! COURSE
careful choice of vocabulary, sentence structure, printed size, and formatting is
WHAT TO DO ABOUT YOUR BRAIN-INJURED CHILD COURSE
needed by very young readers. The design of these children's books is based upon
more than a quarter of a century of search and discovery of what works best for very
For more information regarding the above courses, call or write:
young readers.
The Institutes for the Achievement of Human Potential 8801 Stenton Avenue
Philadelphia, PA 19118 USA
ENOUGH, INIGO, ENOUGH written by Janet Doman illustrated by Michael
GD LEARNING RESOURCES SDN BHD
Armentrout
261-3RD & 4TH FLOOR, JALAN TUN SAMBANTHAN
Ages 1 to 6. Hardcover $14.95
50470 KUALA LUMPUR TEL 03-2748488 (3 LINES) 03-274166Z (3 LINES)
NOSES IS NOT TOES written by Glenn Doman illustrated by Janet
EXCLUSIVE DISTRIBUTOR
Doman
Ages 1 to 3. Hardcover $14.95
THE MOOSE BOOK written by Janet Doman illustrated by Michael
Armentrout
Ages 2 to 6. Paperback $9.95
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