## Monday, November 17, 2008

### The Math Mystery

"Mathematics is not a subject like geography, but a way of thinking and reasoning."
- Glenn Doman
How to Teach Your Baby Math

It finally hit me, the meaning of those words. For fourteen long months I have been endlessly wrestling with the answer to a very troublesome question: Why does the Glenn Doman math program have such a high failure rate, children simply "losing" all that they were taught?

It was a disturbing question indeed. A revolutionary idea had been presented - that babies could understand mathematics (and understand it well, very well) if we presented it to them in an honest, factual, and joyous way. But then a peculiar speculation was made: where are all the kids who were raised on Glenn Doman math? And even worse, even more so disheartening, were the ever-increasing stories of failure with the Glenn Doman math program. "I tried it, and my kids appeared to be able to recognize quantity, but they lost their ability when they got older."

I had heard this story line many times in the past fourteen months as I browsed online forums, websites, and blogs, and was beginning to become more and more perplexed: "How could a child just 'lose' his ability to understand math and numbers?"

For a long time I was able to justify this "loss" of information and understanding with a simple enough, yet not completely satisfying, solution: The children had lost their ability to perceive quantity because they had not gone far enough with the program, their parents weren't consistent enough and the duration was too short, so the kids started to learn but lost it before they had a chance to get firmly grounded. It was really a matter of "use it or lose it".

The theory seemed reasonable enough, but incomplete, and I still had many questions. As long as the only stories I heard were "They appeared to be able to recognize quantity but then they lost it", and no stories of people actually going through the entire program (arithmetic, problem-solving, numerals and all), my story was sufficient.

Then one day several weeks ago, I met and conversed with a parent on the brillkids forum who shared their experience with the Doman math program, and things were starting to get more and more confusing. They shared how they had done the program and their children lost the ability, and they had called the Institutes who had apparently stated that all children lost the ability to do math after their third birthday! I knew there was an explanation about the statement from the Institutes, but the more perplexing part was that this parent was saying that they had done the entire math program, all the way through, with each of their children, yet it proved of no use as all their children lost their abilities after age three. Although they did admit that none of their children were ever able to do arithmetic (while toddlers at least), so it's questionable about how thorough or how consistent the program was, it still presented a difficult mystery and a million more questions with no one to answer.

Then something incredible happened: I called the IAHP and got some simple, yet incredible answers that at the time didn't seem so profound but as I have let things settle in my brain (and they have been spinning for, like I said, the past fourteen months) everything about the failures with the math program now make sense, and this puzzle is no longer such a mystery.

Here is the phone conversation I had with Ms. Breyer. The Institutes can be reached at 1-800-344-TEACH

“Good afternoon this is Connie Breyer.”

“Hi, this is Elizabeth calling…”

“Oh yay! [laughs] Good, I’m glad you called back. Yeah, so, let’s get this thing straightened out. Um, yeah, so what forum is this?”[She originally had called me but I had to call her back because of a crying baby!]

“Um, this particular forum was on a website called brillbaby.com

“Oh yeah we’re hearing a lot about that!”

“Oh really? Well that’s neat…But, yeah, what this person was saying is that they had had a lot of success with the reading program but had tried the math program and it didn’t work, and they phoned you and said that you stated that the ability would not be retained past three years old which didn’t make any sense to me, considering you still sell and promote stuff for the math program and why would you sell stuff that you say doesn’t work?”

“Well, now, the thing is that in the book it does say that there is this window of opportunity and it closes somewhere between two-and-a-half and three-years-old. Um, after that age, usually, the children cannot see, they cannot distinguish the quantity, in the same way that you and I cannot distinguish 88 dots from 89 dots. You and I, the only way we’d know is by counting. But a tiny baby – a child – can distinguish which one is 88 and 89 instantly.”

“Well now, I knew that there was that window of opportunity but like, with my son, he started with the math program when he was almost 30 months and did great, and that was a year ago he’s 3 ½ now and can still perceive quantity, so, shouldn’t children who are trained with this program, the ability be retained?”

“There are some children that are able to retain the ability to distinguish quantity but that is not the norm. The point of the whole program, is to set a foundation for math, for the rest of their lives. Once they understand that a number is a quantity, not an abstract numeral, then everything that has to do with mathematics makes logical sense. Adding, subtracting, multiplying, dividing, everything. Once they have that, then they’re set for life, and then they are able to transfer the quantities to numerals. But it’s that understanding that never goes away.”

“But, now, when they’re older, they can still understand math, and do instant equations and such?”

“Oh yes absolutely. Our children are fabulous mathematicians.”

“Oh okay, well, that makes a little bit more sense then…”

“Yes there’s just something that happens in our brains that makes it so we no longer can distinguish the quantities.”

“Hmm… well that’s really interesting.”

“That’s why we don’t recommend starting our program, with children older than three years old, because we can’t guarantee that it will work. There definitely are some children though who are four and five and can pick it up but,”

“Now I’ve heard that, with autistic people, sometimes, even when they’re older they can sometimes still distinguish the quantities, even without training.”

“Like Rainman?”

“Yes…”

“Yes, and for our brain-injured program, we teach the dot cards no matter how old the children are. They are neurologically that age, even though they’re not chronologically. So, we use that program with all of our children [in the brain-injured program], even if they’re adults.”

“So, is that making any more sense then? At first it was like, hope they don’t turn everybody off to our program.”

“Yeah, no, we wouldn’t want that and I’m really glad that you were able to clear these things up for me.”

“Yes, me too, and I’m so glad you took the time to call, it looks like you’ve done a fabulous program with your child. And, he has that now for life.

I then told her some thank you's for their wonderful organization and such, and told her about how I had found their books at the library and have really enjoyed learning with my son. She was a wonderfully kind lady and the phone call was not only informative but delightful.

Hanging up the phone, I was, on one hand, a little bit disappointed: So Hunter won't be able to look at a flock of birds, or a pile of cereal, or a stack of pennies and instantly be able to tell that it's 93, no more or no less? Such a "cool" and useful ability was something I was not too excited about letting go of, of him losing.

But then there was the other thought, the other perspective, the "Ah ha!" moment. As I let things settle and reflected on what was said in this phone conversation, suddenly it was all starting to make sense. "The point of the whole program, is to set a foundation for math, for the rest of their lives..." Those words rung through my head over and over again. Yes, a foundation, a foundation, to set a foundation of what math is and what it means and how it works, and this foundation - this understanding - will go on with them for the rest of their lives. That's the point, that's the goal, that's the secret to success. Does it work? "Oh yes absolutely". I knew it did, I knew it could: I had seen it with my own eyes, with my own child, that tiny kids really can do math, really can perceive quantity. The words "fabulous mathematicians" rang comfortingly again and again as I contemplated the ramifications of this conversation.

What were the ramifications? Well, I had always thought that if quantity training was initiated before the third birthday, then the child would have that for life, which is why so many stories of kids losing that ability just didn't make sense. But after this conversation, it is all beginning to be clear why quantity training is not enough.

You see, babies are born with the ability to perceive quantity. The Doman program is not actually teaching quantity recognition but rather labeling it. A tiny child can already tell the difference between 28 and 29 without any training - they just don't have a name for it. All the Doman program does is gives quantities names and teaches the names for putting those quantities together and taking them apart ("plus", "minus", "multiplied by", "divided by"). This is not teaching the tiny child anything new, per se, but simply giving them labels for things they already innately know.

But teaching them names is not enough. The child must progress to the point where he doesn't just see the numbers on a card (which he will soon not be able to do anymore) but that he sees the numbers in his head. He must be able to manipulate the numbers in his head, he must know them front and back, knowing not only the number but its relation to other numbers, knowing that "fifty" is half of 100 and 1 less than 51 and 30 less than 80. He must know that "twenty eight" is a third of 94 and half of 56, that it's the product of 2 and 14, and 7 and 4, that it's the sum of 20 and 8 and the difference of 30 and 2. If it's all in his head, he'll have it for life, and he must get to that point before he loses the ability to "see" quantity.

This is the point where we will get back to the original statement in this post, the moment where it finally hit me about the meaning of Glenn Doman's words: "Mathematics is not a subject like geography, but a way of thinking and reasoning."

It hit me as I was reading a new blog post, a Doman friend who does the math program also, with very tangible results. But she was perplexed about how her son, now two, has never been able to verbalize his answers. He can easily pick out the correct dot card when you ask him what 24+54-21 is, but if you ask him for a verbal response, even to a simple addition equation, he just makes something up, like shouting "two!" for 10+24. This is nothing new to me: Hunter does the same thing. I've discussed this odd behavior before, but for some reason when I was reading about it this time, something clicked, and it all made sense.

I realized, little kids at this stage cannot yet verbalize the answers because mathematics is not like geography - it is a way of thinking and reasoning. If math was simply about memorizing a set of facts - What is the capital of France? Who was the fifth President? What sound does the letter A make? - it would simply be a matter of recalling the correct answer, the corresponding fact. But math, in the way that babies can do it, is not about memorizing facts: it is a way of thinking and reasoning.

When you tell him an equation, a mental process is going on in his head that is nothing like the process that goes on when you ask him the capital of China. He's being trained to think mathematically, and in the beginning verbalizing what he sees in his mind will not be as easy as verbalizing other facts he knows, because they are completely different tasks. It's not as easy to recall the fact "sixty-eight" as it is to recall the fact "George Washington". Although this may seem somewhat strange to us, as we were taught math by mere memorization of times tables and algorithms, but what is going on in a baby's mind is completely different and it's not like geography.

The goal, therefore, in training babies in math, is to get them to be able to verbalize, that is, it's to get them to know the numbers in their head instead of just being able to see them with their eyes on paper. Training him to think and reason is the goal, but he must learn mathematics thoroughly before he gets to the stage where he can no longer see the numbers on paper - they must be completely internalized, so when you say "seventy-three" he knows exactly what that number is and isn't, and he can manipulated the numbers strictly in his mind without the aid of visual dots.

For some final thoughts on the issue of "making the math permanent" for your child, I will end on a quote from the forum member who brought up the phone call with the Institutes in the first place:

"If you ask a fluent reader to explain how they read they would simple state that they can. It is possible that the mental manipulation of quantity develops to the stage where the entire process takes place at a subconscious level."

That is the goal, for a child to truly master mathematics so that it is permanent in their being and always remains with them. Here is the conclusion of steps that must be taken in order for a child to go onto be proficient in instant mental calculation:
1. Parents must, first and foremost, create in their child a rage to learn mathematics. Some children do not like the math program initially because we are teaching them something they actually already know. A child must love his numbers, must adore his numbers, for true learning to take place.
2. On being consistent: Consistency is of utmost importance as your child will learn best this way. By taking breaks, whether days, weeks, or months, your child may forget a great deal of what was learned or even worse, lose interest.
3. On being timely: Spending an extended amount of time on one thing would likely bore the child and cause him to lose interest. It's important to keep your lessons new and exciting to retain the desire to learn it.
4. On being thorough: Being thorough is important, as you want to be sure to cover the material well, so he knows it well. We're not talking about endless drilling here, but about making it a part of life, talking about it frequently, and playing lots of games with numbers to be confident he knows the material well.
5. It's important to try and follow the program as much as possible as outlined in the book. For example, don't teach numbers 1-100 all the way through to your 2-year-old without introducing arithmetic - he will want to progress to interesting things quickly, so don't hold him back.
6. Parents should not wait an extensive amount of time to introduce numerals. It is important that numerals be learned while he is still able to see quantity, so that he is able to see the connection and relationship between the two.
7. Parents should exercise extreme foresight to keep lessons interesting and to keep the desire to learn mathematics at a high. Keep in mind the cardinal rules of teaching, like always stopping before your child wants and to only teaching when you're both in a splendid mood. Keep lessons brief and frequent. If your child loves math, it will take a great deal to stop him from learning it. This is the most important factor for success.

As I mentioned in a previous post, we're now introducing numerals in a countdown to Christmas and Hunter has been doing very well with them. I'm not sure why Hunter is an "odd ball" and is able to still perceive quantity at so late of an age, but thank God that he is! I hope that this post has been informative to all of you who have wondered about the Doman math program but haven't been able to put together the pieces.

"At that time Jesus answered and said, I thank thee, O Father, Lord of heaven and earth, because thou hast hid these things from the wise and prudent, and hast revealed them unto babes. Even so, Father: for so it seemed good in thy sight."
Matthew 11:25-26

1. Dear Domanmom,
I´m also a Doman mom in Chile, Southamerica. My son´s 4, and I started at 2,5 months. In the last 2 years I have introduced other educational methods as well: waldorf, montessori, classical, m.i., etc. What I have learned is that the brain does not "absorb, learn, rationalize, etc" different subjects the same way. For instance, it is not possible that the flash cards have the same effect on the same child when they are language or when they are quantity. Because, as Doman says about mathematics not being a subject, NOTHING is. History can be a recollection of data or an understanding of sociology or political moves. My son knows how to add and subtract and I never taught him, he undersatnds fractions and we are starting algebra. I am amazed, puzzled and interested in the human brain since he was born. I have started my own research and a few of the conclusions I have arrived to (AND it´s not easy to arrive to a personal conclusion) is what I just stated. Another important thing, I don´t agree with this "window" of opportunity. Of course, mine is just an opinion against scientific investigations, BUT if your child is older, the only thing different you have to do is find the way to access that part of the brain that is supposedly closed. If before you showed dots and that was doing it, now, maybe, you can do a previous activity and afterwards do the dots. The brain absorbs anyway, we just have to "work" it differently. Doman taught me that, the flexibility of the brain.
Hope you comment,
Andrea H.

2. Hi Elizabeth,

Thanks for your thoughtful post.
I learned about you from the brillkids forum, and I'm not sure if you ever did use the Little Math software.

I have it and am wondering if you were in my position, having a 13 month old boy, would you use the software to just replicate the Doman math curriculum, or would you feel comfortable using the preset curriculum that comes with Little Reader.

Thanks again!
mom2ross

3. Hi Elizabeth,

Thanks for your post. My son is 3 yrs old and I have been wondering how to retain his ability to do math which he could before.

Thanks for your effort and sharing your struggle in the whole process. Your findings is a relief for us. Now I know how to enjoy the program more instead of being worried why my son lost the ability.

The passage you shared from the Bible is inspiring!

George

4. Hi,
Thanks for a fascinating post!
Tamar

5. thank you so much for the info....it's great ....now i understand the program better!!!!!

6. Thank you!
I'm just about to start the math program with my baby girl and as I was seaching for information I found your blog. All I really want to say is thank you for giving me this understanding of what the Doman´s method will give my daugther. A life long understanding of math!
/A mom in Sweden

7. this post is great. Thank you so much1

8. Thank you for this article. I successfully taught my now 10-yr-old and 8-yr-old sons to read using the Doman method when they were babies. However, I always felt unsuccessful with the infant math program because my sons did not seem to retain the information. After reading your article, I was encouraged! My 10-yr-old is a math whiz, consistently scoring perfect to almost perfect scores on National Standardized tests. He is taking Algebra I in school as a 10-yr-old so obviously is mathematical reasoning abilities are very strong. My younger son is not advanced to the same degree, but he is one year ahead in math. I am expecting another child soon and had been reconsidering the Doman math program so your article helped me a lot. I also appreciate the Scripture that you presented.