至于我原来的“先教识字，后教数学” 的说法，可能是从How to multiply Your
Baby’s Intelligence 那本书上出来的，因为这本书同时介绍了其它四本书的内容。
我想他的说法只是个建议，不用过于拘泥。如果你想要先从数点卡开始的话，可以
试试看。孩子学不会他会不感兴趣的，会让你知道。Glenn Doman 的教法不会因此
就失效了。不过我会尽量把作者的原文找出来。
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THE FIRST STEP (Quantity Recognition)
Your first step is teaching your child to be able to perceive actual numbers,
which are the true value of numerals. Numerals, remember, are merely symbols
to represent the true value of numbers. You will begin by teaching your
baby (at the youngest age possible down to birth) the dot cards from one
to ten. You will begin with cards one to five.
第一步是教孩子看出真实数量的能力。先开始教一到十，从卡一到五教起。
Begin at a time of day when your child is receptive, rested and in a good
mood.
选一个孩子接收能力强，精神不错，情绪好的时候开始。
Use a part of the house with as few distraction factors as possible, in
both an auditory and a visual sense; for instance, do not have the radio
playing and avoid other sources of noise. Use a corner of a room that does
not have a great deal of furniture, pictures, or other objects that might
distract your child visually.
选择一个安静的地方，在视觉和听觉上都尽量减少分散注意力的因素。
Now the fun begins. Simply hold up the “one card” just beyond his reach
and say to him clearly and enthusiastically, “This is one” Show it to
him very briefly, no longer than it takes to say it. One second or less.
Give your child no more description. There is no need to elaborate.
Next, hold up the “two card” and again with great enthusiasm say, “This
is two.”
接著，举起“二” 卡，再次充满热情地说：“这是二。”
Show the three, four, and five card in precisely the same way as you have
the first two cards. It is best when showing a set of cards to take the
card from the back of the set rather than feeding from the front card. This
allows you to glance at one of the corners of the back of the card where
you have written the number. This means that as you actually say the number
to your child you can put your full attention on his face. This is ideal
because you want to have your full attention and enthusiasm directed toward
him rather than looking at the card as he looks at it.
Remember the more quickly you show him the cards the better his attention
and interest will be. Remember also that your child will have had your happy
and undivided attention and there is nothing that a tiny child loves more
than that.
Do not ask your child to repeat the numbers as you go along. After the five
card has been shown give your child a huge hug and kiss and display your
affection in the most obvious ways. Tell him how wonderful and bright he
is and how much you love teaching him.
Repeat this two more times during the first day, in exactly the manner described
above. In the first few weeks of your math program sessions should be at
least one half-hour apart. After that, sessions can be fifteen minutes apart.
The first day is now over and you have taken the first step in teaching
your child to understand mathematics.(You have thus far invested at most
three minutes.)
第一天结束了，你已经迈出了教孩子理解数学的第一步（此时你最多花费了三分钟）
.
The second day, repeat the basic session three times. Add a second set of
five new dot cars (six, seven , eight, nine, and ten). This new set should
be seen three times throughout the day. Since you now will be showing two
sets of five cards and each set will be taught three times in the day you
will be doing a total of six math sessions daily.
The very first time you teach the set of cars from one to five and the set
of cards from six to ten you may show them in order (i.e. one, two, three,
four, five). After that initial showing make sure that you always shuffle
each set of cards before the next showing so that the sequence in which
your child will see the cards is unpredictable.
At the end of each session tell your child he is very good and very bright.
Tell him that you are very proud of him and that you love him very much.
It is wise to hug him and to express your love for him physically.
Do not bribe him or reward him with cookies, candy, or the like. At the
rate he will be learning in a very short time, you will not be able to afford
enough cookies from a financial standpoint and he will not be able to afford
them from a health standpoint. Besides, cookies are a meager reward from
such a major accomplishment, compared with your love and respect.
不要用饼干糖果一类的东西去贿赂他。
Children learn at lighting speed ━ if you show them the math cards more
than three times a day you will bore them. If you show your child a single
card for more than a second you 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 great difficulty in doing so. Remember that
babies perceive much faster than grown-ups.
Now you are teaching your child two sets of math cards with five cards in
each set, each set three times a day. You and your child are now enjoying
a total of six math sessions spread out during the day, equaling a few minutes
in all.
The only warning sign in the entire process of learning math is boredom.
Never bore the child. Going too slowly is much more likely to bore him than
going too quickly. Remember that this bright baby can be learning, say,
Portuguese at this time, so don’t bore him. Consider that splendid thing
you have just accomplished. You have given your child the opportunity to
learn the true quantity of ten when he is actually young enough to perceive
it. This is an opportunity you and I never had. He has done, with your help,
two most extraordinary things.
1. His visual pathway has grown and, more important, he is able to differentiate
between one quantity or value and another.
2. He has mastered something that we adults are unable to do and, in all
likelihood, never will do.
Continue to show the two sets of five cards but after the second day mix
the two sets up so that one set might be three, ten, eight, two and five
while the remaining cards woud be in the other set. This constant mixing
and reshuffling will help to keep each session exciting and new. Your child
will never know which number is going to come up next. This is a very important
part of keeping your teaching fresh and interesting.
Continue to teach these two sets of five cards in this way for five days.
On the sixth day you will begin to add new card and put away old cards.
继续用这种方法教这两组卡五天。在第六天开始引进新卡，让一些旧卡退休。
Here is the method you should use from this pint on in adding new cards
and taking out old ones: simply remove the two lowest numbers from the ten
cards you have been teaching for five days. In this case you would remove
the one card and the two card and replace those cards with two new cars
(eleven and twelve). From this point on you should add two new cars daily
and put away two old cards. We call this process of putting away an old card
“retirement.” However every retired card will later be called back to
active duty when we get to the second and third steps as you will see shortly.
Daily Contents: 2 sets
One Session: 1 set (5 cards) shown once
Frequency: 3 x daily each set
Intensity: -inch read dots
Duration: 5 seconds per session
New cards: 2 Daily (1 in each set)
Retired Cards: 2 Daily (two lowest)
Life Span of Each Card: 3 x daily for 5 days = 15x
Principle: Always stop before your child wants to stop
In summary, you will be teaching ten cards daily, divided into two sets
of five cards each. Your child will be seeing two new card daily or one
new card for each set and the two lowest cards will be retired each day.
Children who have already been taught to count from one to ten or higher
may attempt to count each card at first. Knowing how to count causes minor
confusion to the child. He will be gently discouraged 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
game he is used to playing and should begin to learning to recognize the
quantities of dots that he is seeing. For this reason if your tiny child
does not know how to count, do not introduce this until well after he has
completed steps one through five of this pathway.
Again one must remember the supreme rule of never boring the child. If he
is bored there is a strong likelihood that you are going too slowly. He
should be learning quickly and pushing you to play the game some more.
If you have done it well he will be averaging two new cards daily. This
is actually a minimum 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 daily and add three new ones or even four.
By now both parent and child should be approaching the math game with great
pleasure and anticipation. Remember, you are building into your child a
love of learning that will multiply throughout his life. More accurately,
you are reinforcing a built-in rage for learning that will not be denied
but which can certainly be twisted into useless or even negative channels
in a child. Play the game with joy and enthusiasm. You have spent no more
than three minutes teaching him and five or six loving him and he has made
one of the most important discoveries he will ever make in his whole life.
Indeed, if you have given him this knowledge eagerly and joyously and as
a pure gift with now demands of repayment on the child’s part, he will
have already learned what few adults in history have ever learned. He will
actually be able to perceive what you can only see. He will actually be
able to distinguish thirty-nine dots from thirty-eight dots or ninety-one
dots from ninety-two dots. He now knows true value and not merely symbols
and has the basis he need to truly understand math and not merely memorize
formulas and rituals such as “I put down the 6 and carry the 9.” He will
now be able to recognize at a glance forty-seven dots, forty-seven pennies,
or forty ━seven sheep.
If you have been able to resist testing, he may now have demonstrated his
ability by accident. In either case, trust him a bit longer. Don’t be misled
into believing he can’t do math this way merely because you’ve never met
an adult who could. Neither could any of them learn English as fast as every
kid does.
You continue to teach the dot cards, in the way described here, all the
way up to one hundred. It is not necessary to go beyond one hundred with
the quantity cards, although a few zealous parents have done so over the
years. After one hundred you are only playing with zeros. Once your child
has seen the dot cars from one to one hundred he will have a very fine idea
of quantity.
继续用这里说的方法教授点卡，一直教到“一百” 卡。没有必要学过一百。
In fact, he will need and want to begin on the second step of the Math Pathway
well before you get all the way up to one hundred in the dots. When you
have completed one to twenty with the dot cards it is time to begin the
second step.
