Thank you Elizabeth!
How exciting!
I am a kindergarten teacher. Do you think I could do this with 5 or 6 year olds? Is it too late?
In Doman’s book How to Teach Your Baby Math he says that it is best for children between the ages of 0 and 30 months. He says that kids a little older than this may have a chance of learning but the ability is greatly diminished beyond 30 months. 
He says that if they’re a little older than this, you can try teaching numbers one to twenty and if they get it that’s great. Even adults can perceive pretty well numbers from about one to twelve.
“The ability to instantly discern the difference between 98 dots and 99 dots is a wonderful and wondrous ability. However it is not everything. The entire world of higher mathematics is still available to the student even if they are not able to do dots or math equations instantly… Your three-, four-, or five-year-old should not suffer the same fate [not understanding mathematics]. There is no reason for it. If he is too old for the dot cards, then by all means go ahead and begin to teach him numerals. You may have to move a bit more slowly and you will definitely have to approach the teaching of equations in a more conventional vein, but remember his ability to take in raw facts will never be better than it is right now. We have many ten-, eleven-, and twelve-year-old mathematicians who are enjoying trigonometry, and they did not begin their home math programs until the were four or five years old and well beyond the age of doing the quantity cards. Don’t become so in love with the notion of instant arithmetic that you miss the forest for the trees.”
Even though four- and five-year-olds are likely far beyond the dot abilities, they are still much, much faster learners than seven- or eight-year-olds and can learn math, even though they cannot instantly perceive quantities.
There are many available math manipulatives for older children to help them understand the true meaning of numbers. Montessori schools have been teaching three-, four-, and five-year-olds addition, subtraction, and multiplication using simple manipulatives for years. They may be past the instant-math stage but they are much more adept at learning the concepts of math as well as memorizing things such as times tables, etc. Even though Doman probably wouldn’t work in kindergarten, I wouldn’t be afraid to teach the kids basic arithmetic at a much faster pace than is now popular - we seriously underestimate our kids!
I’ve been using a bingo dobber for math dots. They come in many colours, including red, and are quite inexpensive.
Thanx for everything
Sapna
Trying to make sure before I begin teaching . . .
So on day 1, I start with 2 sets of 5, numbers 1-10, three times a day. Then, on day 2, I take away two cards and add two cards. So it will look something like this?
Day 1 (1-10)
Day 2 (3-12)
Day 3 (5-14) . . . and so on?
Then after I get to the 30 or 40 mark (or is it 20 cards?), I start equations? Or do I just keep going to 100 and then start equations after that?
Please help! :wacko:
teachermom: did you read all of the posts?
Actually, on Day one you are supposed to only show one set of five cards (numbers 1-5). Show this three times a day. This is to just get your child interested without going overboard. On the second day, you show two sets of five cards (1-5 and 6-10). You will show these cards three times a day for five days before you start retiring any, so your baby has seen each card 15 times before you put it away.
This is how your schedule will look:
Day 1: introduce numbers 1-5. Show set three times very quickly.
Day 2: introduce numbers 6-10. Show each set three times each very quickly for a total of six extremely brief sessions of math (ten seconds max, each session)
Day 3: show both of your sets three times
Day 4: show both of your sets three times
Day 5: show both of your sets three times
Day 6: show both of your sets three times
Day 7: begin retiring cards. Switch your sets to an odd set and an even set (see instructions in previous post). Retire cards 1 and 2 and introduce cards 11 and 12.
Day 8: retire cards 3 and 4 and introduce cards 13 and 14
Day 9: retire cards 5 and 6 and introduce cards 15 and 16
Day 10: retire cards 7 and 8 and introduce cards 17 and 18
Day 11: retire cards 9 and 10 and introduce cards 19 and 20
Day 12: retire cards 11 and 12 and introduce cards 21 and 22
Day 13: retire cards 13 and 14 and introduce cards 23 and 24
Day 14: retire cards 15 and 16 and introduce cards 25 and 26
Day 15: retire cards 17 and 18 and introduce cards 27 and 28
Day 16: retire cards 19 and 20 and introduce cards 29 and 30
Now you have taught numbers up to twenty. You should now begin teaching addition. You will do addition equations with numbers 1 - 20. At this point you will be doing nine very brief session of math each day - six sessions of quantity and three sessions of equations. See link in previous post for sample schedules that you can use.
While you teach addition you will continue to teach quantity. You can continue to retire two cards a day, but by the time you get to 40 (day 21) you should retire at least three cards per day. You do this to keep the baby interested because babies do not find looking at a bunch of red dots all that interesting, so you must speed up the pace to keep them interested. All you are really doing is teaching them the NAMES of those quantities, because in reality they already know the quantities, just not the names for them.
After two weeks of addition, you start subtraction. After two weeks of subtraction, you start multiplication. After two weeks of multiplication, you start division. After two weeks of division, you move onto problem-solving where instead of showing all three cards of each equation you only show the answer. And after each equation you present your baby with a problem-solving opportunity where he can choose the answer to an equation if he wishes to do so.
You will have finished teaching numbers 1 through 100 by the time you are done with multiplication. After you have taught numbers 1 - 100 you will lastly show the number 0. All that is is a blank card. Teach zero as you did all the other numbers.
Here is the link with the other explanations I was referring to:
http://forum.brillkids.com/general-discussion-b5/maths-equations/msg5832/#msg5832
I hope this helps, I apologize for any confusion. I hope to be making a “how to teach your baby math” Q&A sort of thing very, very soon, that will go over all of the details more thoroughly. God bless and happy teaching!
Some thought about teaching your older baby (18 - 30 months)
I thought I would post this for those of you with older toddlers. Toddlers are very opinionated and so we need to approach teaching them math with careful thought. Once they are interested, they will love it, but we must make sure we don’t overwhelm them and cause them to push us away. Remember, you only get one chance to introduce your child to math. First impressions last the longest. Don’t get so caught up in the excitement of teaching your toddler that you are not sensitive to him. Here is an excerpt from “How to Teach Your Baby Math” by Glenn Doman regarding a child of the ages 18 - 30 months old:
[u]Beginning anything new or different with an eighteen- to thirty-month-old can be a challenge. He is of course highly capable and will move through the first step to the fifth step rapidly once we have a happy consistent program started. There are two important points to remember when you are teaching this little fellow:
- Start his math program gradually
- Move from introducing dot card to beginning equations as quickly as possible.
As each day passes he develops and he assumes his own viewpoint. He begins to have his own likes and dislikes. The eighteen-month-old is not the pure intellect he was at three months. If we are going to begin to introduce language in visual form to an eighteen-month-old we first must remember that he is already an expert at language auditorially. Although he has been talking for months, it is only now that the adults around him can understand his sounds as words. It is not surpising that when he realizes he is at last being understood he has a lot to say and a number of demands to make. It is important to keep in mind that if an idea is his idea it’s a great idea; if an idea originates elsewhere it may not have his approval. No one occupies center stage quite as completely and confidently as this fellow. This is his glory and his program needs to be designed with this in mind. The first thing to rememeber is that you cannot go from no math program to a full-blown math program in a single day with this little guy. Instead of beginning with two sets of five dot cards as outlined in chapter seven, begin with only one group of five cards. This will pique his interest without going overboard. You need to woo him a little. He will love math once he decides that they are his dot cards but at first they are your cards and he doesn’t know them. Show him that one group of five dot cards very quickly and then put them away. Come back at another good moment later. In a few days add the second group of five dot cards. When you begin equations by evolution as his interest grows, introduce a new set of three equations as the days go on. It is best to starve him a little and have him pressuring you for more. As your program progresses, ask him what equations he would like and do those with him. As soon as you have retired dot cards one through twenty, begin equations with him. He will love equations, so don’t wait until you have done one to fifty in the dots to get to equations. He is not a baby. He will want equations more than single dot cards, so get to them as quickly as possible. He will be delighted to major in the third step [problem-solving, sequences, fractions, square roots, simple algebra, etc.] on the Math Pathway and beyond as long as we begin that very first step by evolution rather than revolution. A word about your eighteen to thirty-month-old saying the dots or equations aloud. A child of two, as everyone knows, does exactly and precisely what pleases him most. If he wishes to shout out his equations, he may do so. If he doesn’t wish to say them, he won’t. The point is to teach your child whatever his age may be and recognize his right to demonstrate his knowledge in the way he chooses - or - not at all. [/u]
DomanMom,
Thank you, thank you, thank you. Actually, when I got the email that there was a reply, I thought, I didn’t post in a forum called Re: maths equations. I didn’t even know I did that! So, no, lol, I didn’t read the other posts. I thought I started a completely new thread! I don’t know how that happened. Blame the sleep deprivation and being obsessed with reading too much about early learning. LOL. Thanks and sorry for replying in your thread!
Here is some more information about the various ages of starting a math program with your baby:
[u]Starting with an Infant (Three Months to Six Months)
If you are beginning your math program with a three- to six-month-old, he will be majoring in the first and second steps of the Math Pathway. These steps will be the heart of your program.
The two most important things to remember are:
-
Show the dot cards very quickly
-
Add new cards often
The wonderful thing about a tiny infant is that he is a pure intellectual. He learns anything with a total impartiality and without any bias whatsoever. He learns for learning’s sake, without any strings attached. Of course his survival depends on this characteristic, but it is an admirable characteristic and is no less admirable for being tied to his survival.
He is the kind of intellectual we would all like to be but which very few of us are. He loves everything there is to learn. It is his glory and ours if we are lucky enough to have the opportunity to teach him.
Between three months and six months of age a tin baby is able to take in language at an astounding rate. He is also seeing detail consistently. In short, he is able to absorb spoken language without the slightest difficulty, as long as we make that information loud and clear. He is able to absorb written language as long as we make it large and clear. It is our objective to keep his math cards large and bold so that the baby can always see them easily.
At this stage a baby is using sounds to talk to us. However it will be months before we are able to decode all these sounds as the words, sentences, and paragraphs that they are. In adult terms, then, the baby cannot talk.
He has superb sensory pathways to take in information but he has not et developed the motor pathways sufficiently to get information back out in a way that can readily be understood.
Since this is the case, someone will no doubt ask you how you can teach a baby mathematics when he cannot yet talk.
The baby learns mathematics through the use of his visual pathway and his auditory pathway. He does not learn through the use of his own speech—this is out-put. Learning is by definition the process of taking in new information. It is the process of receiving in-put—not producing out-put.
Learning to recognize quantity is the process of taking in the language of mathematics in its visual form. Speech is the process of putting out language in its oral form.
Recognizing quantity and learning to read numerals are sensory abilities, as is hearing. Talking is a motor ability, as is writing. Talking and writing require motor skills that the baby doesn’t have.
The fact that your child is too young to speak and is not able to say his math cards does not negate the fact that you are increasing and enriching his language by teaching him mathematics.
Indeed such investments in teaching the baby will speed his talking and broaden his vocabulary. Remember that language is language, whether transmitted to the brain via the eye or via the ear.
Reading his dot cards aloud for a fourth-month-old is impossible. This is to his great advantage since no one will be tempted to try to get him to do this. He can therefore “read†his dot cards silently, quickly, and effectively.
At this age a tiny child is truly a glutton for information. He will probably demand more information than you are able to give him. When you begin your math program you may often find that at the end of a session he will demand more. Resist the temptation to repeat his cards or do another group just then. He might happily see even more than the two sets of dot cards that you are showing him daily and still want more.
You can actually show several sets back-to-back with a three- or four-month-old and get away with it for a few months but be prepared to change in the near future because you will need to do so.
Remember he is a linguistic genius—be prepared to feed him with a lot of new information.[/u]
[size=10pt]Part III[/size]
[u]Starting with a Little Baby (Seven to Twelve Months)
If you are beginning with a seven- to twelve-month-old, the two most important things to keep in mind are:
- Keep every session very brief.
- Have sessions often.
A four-month-old will sometimes want to see both of his sets of dot cards one after the other at one session. However such a procedure would be a disaster for a seven- to twelve-month-old.
Use only one group of dot cards at a session and then put them away.
The reason for this is simple. Each day your baby’s mobility will be expanding. At three months he is relatively sedentary. He is a watcher. He will watch his cards for long periods. We adults love this, so we get into the habit of showing him all his cards at one sitting. We get used to this routine; it is easy for us. But each day this baby is changing. He is getting more and more mobile. As soon as he is creeping on hands and knees a whole world of new possibilities opens up for him. He now has a driver’s license and he is just dying to explore. All of a sudden this sedentary little fellow, who saw fifty cards quite happily, is no longer sedentary. He has no time at all for his math. We become discouraged. Where have we gone wrong? He must not like mathematics anymore. Baffled, we give up.
The baby must be baffled too. He was having such a good time learning math and then the dot cards and equations disappeared. It wasn’t that he stopped liking math, it was that his schedule became busier. He now has an entire household to explore. He has all those kitchen cabinets to open and close, all those plugs to investigate, every piece of fuzz on the carpet has to be picked up and eaten before the sun sets. You have to admit that there is an awful lot on a seven-month-old’s plate when it comes to search and destroy. He still wants to explore mathematics too but he cannot afford fifty cards at one time. Five cards at one time is far, far better.
If we provide him with brief session, he will continue to gobble up new information at a mile a minute. It is only when we make him late to his next pressing appointment by taking more than a few seconds that he is forced to abandon ship and leave us sitting alone in the middle of the living room floor.
We adults love to find a nice comfortable schedule and then stick to it no matter what. Children are dynamic, the never stop changing. Just as we have established a routine, the tiny child moves on to a new level and we find we must move with him or be left behind.
Because this is so, always keep sessions brief; then as his mobility expands you will be in the habit of brief sessions, which are a natural part of his busy schedule and fir in with his agenda.
[/u]
[size=10pt]Part IV[/size]
[u]Starting with a Baby (Twelve Months to Eighteen Months)
If you are beginning your math program with a child of this age the two most important things to remember are:
-
Very, very brief sessions.
-
Stop before he wants to stop.
In terms of the Math Pathway you will be emphasizing the first and second and third steps (Chapter Seven). As you work your way up the Math Pathway with a child at this particular stage of development, the most important refinement is to keep the duration of every session very, very brief.
The reason this is so important is that now his mobility development becomes extremely important.
At twelve months, a baby is either walking or beginning the process of moving between people or furniture while holding on with his hands in order to work his way by degrees to his first independent steps. By the time that same child is eighteen months old he will not only have become a good steady walker but he will have begun to run. This is quite an accomplishment in six short months. In order to achieve these spectacular results he must put a great deal of time and energy into feats of physical daring.
At no other point in his life will physical movement assume the importance that it does at this moment. You can be assured that if you were to attempt to follow your baby and simply do each of the things he does physically during the day you would be absolutely exhausted after a single hour of his routine. It has been tried.
No adult is physically up to the rigors of what the average twelve- to eighteen-month-old can handle in a given day.
These physical activities are of great importance to the tiny child. During this period of his growth and development we have to be especially wise about adapting his math program to his intense physical program. Up to this moment in his life a group of five dot cards or three equations at one session may be perfect. However, during this stage this may need to drop to three dot cards at a session or two or even one.There is no single principle of teaching that will take you further than that of always stopping before your child wants to stop.
Always stop before he wants to stop.
Always stop before he wants to stop.
Always stop before he wants to stop.
This principle is true for all teaching of all human beings at all stages of development and at any age.
But it is most especially true for the twelve- to eighteen-month-old.
He needs a high frequency, low duration schedule. Lots of brief sessions suit him. Indeed he needs those brief, treasured respites from his labors.
He will love the entire Math Pathway from the first step of recognizing quantities of dots to the fifth step of sophisticated equations with numerals, but he will need extremely short sessions because he is a man on the move and cannot afford to tarry for very long.
Very short and sweet sessions are best for him.[/u]
A heap of karma to you! 
Elizabeth, thanks for all this valuable information. My son does not like the dots flash cards but he is very interested in maths equations. I didnt know that he can he learn the equations at 2. thanks a lot.
Hi Elizabeth
Sorry for my late reply. 
Thank you so, so much for all of this (you certainly have good karma! Most deserved :biggrin:). You took so much time to explain everything to everyone, and I think it will make a lot of people (myself included) much more likely to follow through with the math program. The fact that your site is offering PowerPoint dot cards and lessons schedules is completely awesome.
I’m one of those parents who started and stopped the math program, because my baby didn’t like it. We did reach the equations (addition and subtraction) but I still was getting a completely bored reaction; sometimes even tears. I think it will be easier to teach my DD on the computer rather than with the physical cards, because she already loves her computer-based lessons (namely Little Reader).
Thanks again Elizabeth. I’m sure your feedback on Little Math will also be invaluable when it comes up for beta-testing…
Maddy
Hi, how do you show the dot cards to your baby? I started showing my baby the first ten dot cards (from 1-10) some weeks ago but I felt he wasn’t much interested when I showed him dot and told him number so I decided to change the way I was doing it and I took only five dot cards (from 1-5) and started showing him dots and counting them.This way please him so much and he enjoys a lot counting dots with me. Now I’m going to start the 5 - 10 dot cards, and I’m not quite sure whether I’m doing it right because now I only have a few dots to count but what about counting 20 or 30 dots, not to say when counting 100! I suppose I’m not doing it right but what can I do? Please help me
There’s no real cookie-cutter way to get a baby interested in numbers. All babies are different so you will have to read your baby’s cues to see what he likes, and find a way to make it fun and interesting.
The first thing is to go very, very quickly. Each card should be shown for less than a second, no longer than it takes to say the name of the number.
The second thing is how many cards you show at once. Seeing ten numbers at once is usually far too much for most babies. Seeing five numbers at once may be too much for some. If he is not interested in seeing five then show him three or two or even one at a time.
Find a ways to make it fun, interesting, and fast. I had a lion puppet that would gobble up the numbers and talk to Hunter about how much fun math was. Be silly. It will take you very far. Try getting your child while he is in his high chair and do something silly with the numbers while you show him, like hide behind one and play peek-a-boo. Like say, “Here comes TWENTY FOUR!!!” with as much enthusiasm as you can muster and then bring it up from under the table and let him see it for a half second, then hide it. “Oh, where did twenty four go?” “Ah! Here is is!!!” and bring it out again and shake it close to his face and tickle him. “Look, what else does Mommy have here? Oh, do you want to see it? Oh, here it comes, here it comes, it’s… TWENTY TWO!!!” Tickle him, laugh with him, and remember he only has to glance at it to absorb the information - tiny kids do not need to stare.
Yes it is probably not a good idea to count them because, like you said, once you get to forty and sixty and one hundred it will not be so easy. Also the goal is for him to learn the names of quantities, of true numbers, not to count them. If he wants to count them, showing them quickly will discourage that and he will quickly learn that this is a different game than the counting one.
I see that your baby is one year and eight months so that would put him in the older toddler category. Have you read the excerpts I have included about teaching the various ages? 18-30 months is here: http://forum.brillkids.com/general-discussion-b5/maths-equations/msg6351/#msg6351
I hope that you find a way to make teaching math to your baby fun and interesting. He will thank you for it for the rest of his life.
Thank you so much for your advice, you always have the right answer for everyone, and are always so kind helping whoever needs it with maths , I will try to follow your instructionds, they are quite interesting and I hope successful. Karma to you !! for all your patience
Elizabeth, do you check whether Hunter is able to know the answers after every 2 weeks of learning a particular set of equations? Or do you just randomly check after finishing all 2-weeks sets of Addition, Subtraction, Multiplication and Division? I know we are not supposed to “test” babies according to Doman. I’m sure you do it with Hunter in a very fun way?
Zaja: I actually did do problem-solving games with Hunter after two weeks of learning something new. When I first taught him addition, I showed him three equations per day for two weeks and at the end of those two weeks, found a time when he was in a great mood and asked him if he wanted to play a game. I would just lay two or three cards down, and ask “Which one is ten plus seventeen?” I was actually amazed when he got them all right and wanted to just tell the whole world. But, most people don’t take kindly to it, so I just kept it to myself.
After a week of subtraction, he appeared bored so I played this game again and he got them all right, so I moved onto multiplication to keep him interested. After five days of multiplication, same thing, and then after three days of division, still the same. If your baby is interested in playing this game with you, than go for it, but keep it short.
Never test - testing would be putting him in the spot to find out what he doesn’t know - “Can tell your Daddy the answer to this equation?” It is ultimately disrespectful to the child because he gets the idea that you don’t believe he can do it. This is the best way to kill the desire to learn math, so avoid it like a plague.
Problem-solving, on the other hand, is really the opposite of testing, because you are letting him demonstrate what he does know if he wishes to do so, not trying to expose what he doesn’t. If you give him two answers to choose from and keep it short, he will love the game as long as you remain joyful and silly. If he picks the wrong answer, don’t scold him “No, that’s NOT the right answer!” He will hate the game if you do this. Simply hold the correct answer closer to his face and say, “THIS is ten plus ten, isn’t it?”
Also, keep it short - stop before he wants to stop. This was one thing I DIDN’T do in the beginning and it proved a thorn in our side - Hunter began to consistently choose the OPPOSITE answer of the correct one to show me he was bored. If this happens - take a hint and don’t push it again. Also, when he began to do that I would say to him, “You get to keep all the wrong answers and I’ll keep all the right answers!” I said this in a silly way, not mean or condemning. He quickly decided that he wanted the right answers and Mommy got to keep all the wrong answers!
Your baby may not want to demonstrate his knowledge, and that is perfectly fine. You can give him an opportunity to problem-solve, but if he chooses not to answer, simply hold the correct answer closer to him and say, “This is five times three, isn’t it?” give him a tickle and a hug and tell him how smart he is, and then PUT THE CARDS AWAY.Try again at another time to see if he is interested in playing. I knew one family on DomanInspiredParenting.blogspot.com who would play the game with each other (Mommy and Daddy) and then when their baby saw them playing, he would creep over to see what they were doing and they would say, “Oh, would you like to have a turn Timothy? Okay, Timothy, which one is 93 divided by 3?” That way it was like a game that they were letting him in on. There are other ways to get your child interested in playing, and as long as you keep it very, very brief and only try every once in a while, there is a good chance that he will want to play with you.
And remember, learning is input, not output. Demonstrating his knowledge is not a necessity to having it. Be gentle with him, take his hints, and don’t push it or you could crush the desire to learn. You only get one chance to introduce your child to math - make it a good one.
Hope this helps, God bless!
karma to you domanmom
thanks so much for all your help on math dots
we did dots one though hundred before she was 9 months old
but stopped after addition because she lost interest in it
i never tested her
and am still not sure if she got it
we are going to start again with subtraction this week (she is now two)
for a long time we weren’t sure if we should just start again at the beginning
doman says never to go back but he doesn’t say anything about a year break from the program
math is really important to us so we will start again at subtraction where we left off
any advice?