maths equations

[DomanMom]

Maddy:

Yes, actually, that is my son back in December of last year. We had really just started then, he only knew up to twelve. But yes, before he turned three we had learned quantities up to one hundred, addition, subtraction, multiplication, and division.

About your concern about kids losing their abilities (or rather, perhaps the fact that they didn't even learn it at all - they were just reading gestures!) I don't have the clearest answer to give you. I have met many, many parents who have had wonderful success with the reading program, but only one other parent who has had success with the math program. That other person is the author of domaninspiredparenting.blogspot.com.

Why is this? I don't really know. The trend for the math program either seems to be 1) Their baby hated it and so they dropped it. This is actually what happened to us - I first read the book in August of 2007, and Hunter learned numbers one through ten, but then refused to look at them so we took a three month break until I improvised, made it more exciting (you can read other posts about our silly puppet "math lion" who loves math and gobbles up numbers), and he became interested again. We made it a very, very quick game and he loved it. My speculation is that the reason babies get bored with it and refuse to look at it is because looking at a bunch of red dots isn't very interesting, after all, if they are born with the ability to perceive quantity then they already know the quantities they just don't know the names we've given them yet (i.e. "twenty-seven")

The second trend I have come across with the math program is parents like the commenter on your blog, who taught their baby the dots but did not finish the whole program. Of the "success stories", other than the blog author I mentioned above, most do not admit that they actually taught their child arithmetic or say how long they did the math program - one "success" story told of how they did the dots when their son was a baby, and when he was three and in preschool he caught onto the math worksheets really quickly. But this is far from the projected results of the book, and makes one wonder if the dots really did any good or if we're just fooling ourselves into pretending it had an impact.

But, I can tell you that I know that it has worked with my son. As for reading body language, this hasn't been our experience in his ability to perceive real quantity. How do I know? Well, I have seen him pick the card with 81 dots on it in a pile of 80, 79, 82, 81, and 83. Not once or twice, but hundreds of times with hundreds of combination of numbers - he always gets the right one! In fact, usually I don't even know which one is the right answer because I shuffle them all and then lay them out - he has to bring me the card and I look at the numeral on the back to make sure it's the right one! So there's really no way that I could give the answer away with my body language because I don't even know which one is the answer! And if you're wondering if maybe he just memorized the patterns - no, I have used several different cards with many different patterns, and it doesn't matter which one I used or even if he's never seen the cards before, he still knows how many dots are on there.

But the most convincing way that I know that he really can perceive quantity and really does know the true meaning of numbers is in his ability to solve equations. I followed the Doman program and showed him addition equations for two weeks, subtraction, multiplication, division, etc. I never acted it out for him (i.e. adding one Cheerio to two Cheerios). All I did was show him the facts - "one" (show him the one card) "plus two" (show him the two card) "equals three" (show him the three card). After seeing about nine different equations a day for two weeks, he could solve any addition equation I presented to him. After one week of subtraction he appeared bored, so I gave him some problem-solving opportunities and he could solve any subtraction equation. After five days of multiplication he did the same. After three days of division he did the same. He has never memorized his multiplication tables. He has never had division acted out for him. He has not seen every addition problem under the sun. But he understand math, and knows the true meaning of the equations we were made to memorize only in the abstract.

I can't say I fully know why so many have failed on this simple program. Perhaps because it is not really simple at all - I have spent many hours pouring over what equations to teach, and have spend long energy trying to make it interesting and fun for him so that he can learn. It pains me to see parents who want to teach their baby math but fail for one reason or another. I hope that by telling my story and providing parents with resources - such as printable dots, and the most time-consuming thing: schedules of equations - that I can help as many children as possible to learn the meaning behind the symbols we use in math and be able to master this simple language. Perhaps the other reason so many parents have failed is because they don't really believe it is possible, and therefore give up before they've even truly started. Maybe I can help by telling everyone that it is possible to teach a tiny child math, and that it is a great and noble thing to do. It's been such a joy for us, I just pray that as many people as possible who can hear the good news will hear it, and will press on with joy and love to teach their own child.

I hope this helps, if you want to know more you can visit my blog on blogs under the title of math: http://worldsbesteducation.blogspot.com/search/label/Learn%20Math

[kmum]

Elizabeth - I checked out your blog.  It is very inspiring! Thanks for all the great information.

[prince]

sapna  i have just started with equations with my kid... i do not use any educational dvd... i just do it on powerpoint slides..i take help of the link  http://worldsbesteducation.org/math.aspx  provided by Elizabeth .. they r a great help...as eiizabeth has explained here in same topic i now do exactly that way. im adding here a file to show how i do it...


sp note ...experts can also comment on the method n provide suggestion or correction for the same

[chispa]

Hi!  This is amazing!  I really want to start with my Andrew.  Elizabeth, does it matter what the pattern of the dots is?  How about the color of the dots?

Thanks for the website.  I will be printing the schedule and cards.  I just thougt I could make the first ones with the dots from "garage sales' that you can get in the stores.

Thanks again!

[DomanMom]

No it doesn't matter what pattern the dots are in as long as it is a random pattern. I.e., you do NOT want to put the dots in any kind of shape or pattern like squares, triangles, stars, or rows - just put them on there completely randomly.

Also, the color does not specifically matter - red is ideal, just because it is the most attractive color to the baby, but not necessary to learn quantity. I have been using black cards because you can print them out of your computer quite cheaply.

And yes, while you can make dots from the "garage sale" stickers you talk about (this is how Doman instructs you to do it), making numbers one through one hundred is a tedious, difficult task - I did this when I first started and it probably took me at least ten to twenty hours to cut all the paper, put on all the dots (5,050), and write the numerals on the back - not fun! This is why I created a version you can print out on your computer.

I would recommend getting all your materials ready before beginning, because your baby will learn at a mind-boggling speed. It will take you at most eight weeks to teach numbers one through one hundred, and in all likelihood he can easily learn it in six or even four! It's always good to be one step ahead of your baby, so you want to start ahead and stay ahead!

Hope this helps - I really need to put together at least some kind of questions and answers forum on this math program because so many people keep asking about it, and I'm afraid I'm leaving stuff out. But as for now if you can, check out the book How to Teach Your Baby Math by Glenn Doman from your local library or you can get it on Amazon.com for around $10.

[chispa]

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?

[DomanMom]

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!

[kmum]

I've been using a bingo dobber for math dots.  They come in many colours, including red, and are quite inexpensive.

[Sapna1322]

Thanx for everything

Sapna

[teachermom]

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!

[DomanMom]

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!

[DomanMom]

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:



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:

1. Start his math program gradually
2. 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.

[teachermom]

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, , 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!

[DomanMom]

Here is some more information about the various ages of starting a math program with your baby:

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:

1.   Show the dot cards very quickly
2.   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.

[DomanMom]

Part III

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:

1.   Keep every session very brief.
2.   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.

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