Math - giving wrong answer phenomenon

Early Learning Teaching Your Child Math
1

Hi all,

As you know I try to teach my daughter Math. For this purpose I have read some thread in this forum and some blog article of DomanMom. There she wrote e.g. that her “Hunter” usually got wrong answers if she took videos. There she also write why learning Math isn’t like learning Geography.

That’s make me thinking a lot.

Obviously it isn’t easy teaching Math like teaching to read. Not every parents are successful in teaching Math.
Obviously children tend to give more wrong answer (than in other subject) when asking to do choose right number or problem solving.

My daughter e.g. always give the right answer when we ask her things (picture or real life) like “where is the elefant, where is the windmill etc.”. Even if we ask her for the things she knows very well, she doesn’t get fed up and give a wrong answer.
But why she answer 50 - 50 by math!?

Can anybody share this experiences? Thanks in advance.

2

I somehow share the same experience. My dd is 50-50 correct on identifying quantities. However, on equations, she is mostly correct. On identifying things around the house, she is 100% correct at ALL times, she would not get bored no matter how many times we ask her.

Domanmom once commented on Texaslady222’s blog that her son is the only other child she knows that can do Doman math (recognizing quantities & instant calculations).

The IAHP also admits that not all are successful with the program. I wonder why is this? Most success stories here are of reading & EK. What could be the factors involved in making Doman math work?

My DD enjoys seeing the dots/icons in LM but when I show her a math flashcard, i can see her face that she is unsure.

3

Thank you for your reply Nadia.

I guess that for doing Math they need to be in a certain condition (relaxed, alpha state…) !?

Well, I am a bit disappointed about Doman Math because of the high failure rates and that they do not explain that well in their book (they write only positive things).

4

to be honest, I am still awaiting some solid proof of this working out, Doman math I mean, though I do show Kyle quantities everyday, but he usually dont want to watch it except when I talk of ZERO!!!
for me the fact that they give 50% wrong answers again increases my doubt! I have never tried Kyle on quantities thought he loves to test himself on LR, in Dhivehi and English!
sO are there any parents who have been successful on Maths with a kid rather than infants or toddlers who cant totally tell you that they can gather quantities without counting?

5

Perhaps DomanMom will provide an update on Hunter’s progress.
You might find this site interesting:

http://domaninspiredparenting.blogspot.com/2008/11/math-dots.html Just realised that this is Texaslady22’s site.

“This is the first time we’ve been a bit frustrated with Doman, though. I’ve read of so many parents who do the full math program and their child excels and then just suddenly “loses” the math ability…how does that happen? Why does that happen? It seems like they really need to do more research in this area.”

It might be better to mainly use the LM grid arrangements to safeguard against confusing your baby. Also consider incorporating the Ten Frame method.

I taught understanding with building blocks, toy currency, an abacus (rows of ten beads) and cards with 10 dots alongside a set of cards covering the range 1-9. All three of my children have a good understanding of maths.

XXXXX XXXXX + XXXXX XXXXX =25
XXooo ooooo XXXoo ooooo

This is a ten frame approach-the circle should be a faint outline of the icon that you are using-butterfly, truck, dot etc. Leave a larger gap between 5 and 6 and also increase the space between rows 50 and 60 to make it easier to recognise the quantities. You could also make a slightly less noticeable adjustment to the gap between rows 30 and 40 and 80 and 90

Ultimately it is up to you to decide which approach to adopt but I can state that the random approach recommended by GD didn’t produce the results claimed in the book.

XXXXX XXXXo 3x9=27 clearly 30-3
XXXXX XXXXo
XXXXX XXXXo 3x9= 6x5-3

Why waste time with random arrangements that your babies might not be able to subitize. Random arrangements could be restricted to developing estimation skills-which is larger etc.
Chris.

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Dear Chris,

Could you please tell me where can I find more information about your method of teaching math?

And maybe you can provide us with some pictures of how you teach? (or more description)

How old are your children when you started with the Ten Frame Method? How long have they been doing that? What can they do in Math now?

I find the Doman Method is maybe “too good to be true”. It seems not to work for every child!?! I would switch to your method after trying more Doman Method. Thank you for sharing us your experience so we all can learn from it.

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Dear Aguh,

Please visit http://forum.brillkids.com/teaching-your-child-math/number-sense-series-ten-frames/ for more information on ten frames k :slight_smile:

I occasionally use this maths site with my son: http://www.conquermaths.com/

My children are now 18, 15 and 12.

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We have a large family ( 23 nieces and nephews, and a lot more cousins, etc. :biggrin: ), many of which used Doman method ( I would say 8/10). The ages at present anything from 18 years old and down. I was not involved in their school, but observed some of the resuts on the occasion, and also talked with their parents. Four of their parents are actually professional educators, and they did try other methods, primary with teaching other children. They all, after try and error, say that they will definetly chose Doman’s method for early education over anything else. Later on in life, they did introduce other age appropriate learning methods ( most of the children were incredibly early learners, so they were ahead of their age group in their schooling) for math, etc. But they definetly say that from personal experience and results, they will be starting with Doman Method, even if you do not see immediate results and it seem like the child is not showing progress. As much of this method of learing is a preparation for other ones later in life.

They also used combination of other schools, like Montessori, etc. Adapting it. When I asked them about the “results” factor, they agree that it is about giving baby knowledge and opportunities and making it fun, and letting the baby figure it out and develop on its own pace, not expecting him or her to perform on cue. It is not about raising uop geniuses, but rather helping each kid to progress and be challenged according to his or her own potential and pace.

Just thought to share it

9

Thank-you Skylark for your comments K :slight_smile:

I would also suggest starting with GD maths to teach quantity and numerals-babies clearly derive pleasure from seeing quantity cards in the early stages. Random arrangement cards are also ideal for teaching concepts like greater than, less than, not equal to, provided the quantities are far enough apart. My children could always correctly answer this type of question which supports the claim that GD maths develops number sense and a mental number line.

My children learnt the numerals 1-100 and beyond very quickly thanks to GD maths but I do not believe that babies can subitize large quantities and perform complex calculations by mentally manipulating quantities as claimed in the book.

Other activities- What comes next?

What to do Prepare a set of black and white cards
Place some cards on the floor that follow a sequence and ask “What comes next”. This activity develops logical thinking skills and was used by Richard Feynman’s father. BBWBBWBB? BWBWBW? You could also use shapes circle,circle,square,circle,circle,square,circle,?

Encourage counting every day - count everything , four plates, four knifes at the table, number of buttons on shirts, cats in the garden etc. Whilst walking comment on the number of ducks in the pond, people waiting for the bus, dogs having a walk.

Use wooden blocks and construct a tower of ten and ask your child to build a tower next to yours-count as they build the tower and show/discuss how many more blocks are needed to finish the tower. This activity will teach number bonds to ten 9 can be seen as 1 less than 10 etc.
This activity can be extended to teach place value-e.g. show a numeral card and build the number. I used cards with spots to construct the larger quantities -e.g. numeral 24 constructed from 2 ten cards and a card with 4 dots

Introduce activities that encourage your children to categorise by size-find the biggest and smallest doll, prepare a set of cards and arrange in order of size also introduce the appropriate language-largest,smaller,smaller,smallest. The cards could contain the same picture varying in size.

Teach shapes and discuss when you are out-how many circles can you find-road signs , wheels, hubcaps etc

To begin with, early number activities are best done with moveable objects such as counters, blocks and small toys. Most children will need the concrete experience of physically manipulating groups of objects into sub-groups and combining small groups to make a larger group.

These are just a few of the activities that you could introduce alongside GD maths.
Chris.

10

Thanks Chris1

When I went through Domanmoms site, I found this article and heres part of it that I found explains a lot… and some pointers she added at the bottom…

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.

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Those of you with older children might like this maths site: http://www.conquermaths.com/

You can try free example lessons - click on try it free and then click on Free Lesson no signup required.

Chris

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Hi Kyle’s Mom

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.

The Simplest Explanation Ockham’s Razor: That children are unable to subitize these quantities and read gestural cues or guess when asked to pick the correct card.

Think Like A Maths Genius,by Arthur Benjamin and Michael Shermer, is an excellent book on the art of calculating in your head. Arthur Benjamin states that his many years of teaching experience has convinced him that rapid math is a skill that anyone can learn provided that you practice the right way. I doubt that asking babies to answer questions like 12x13-76= is the right way.

Perhaps someone could contact DomanMom for an update.

13

Dear Aguh, more details as requested:

Teaching the mental process of rapid calculation.

Left to right

Addition problem: show the numeral sum 34+41=75

Demonstrate how to build 34 by using three 10 spot cards and a 4 spot card, do the same for 41.

This needs to be done quickly, say 10,20,30,34 as you place the cards.

Transfer the 10 spot cards from 41 to 34 and count/state the total, then transfer the remaining 1 spot card and state the answer.
To solve 34+41 you first add 40, then add 1. After adding 40, you have the simpler problem 74+1, which equals 75.

This activity will promote an understanding of quantity and teach the appropriate mental process involved in calculating the answer.

34+41 = 74+1 = 75
First add 40. Then you add 1

With younger children you can teach an understanding of numerals by showing a numeral card and constructing the quantity. Show your child, for example, a 20 numeral card and place two ten cards side by side on the floor. Then cover the unit space on this numeral card with any unit numeral, read aloud the adjusted numeral and then place the appropriate spot card on the floor.

This can also be done in reverse-take four 10 spot cards and a 4 spot card and place them on the floor , counting the total as you place the cards-10,20,30,40,44. Then take a 40 numeral card and say 40, then take the smaller 4 unit numeral card say 4, use this to replace the zero on the 40 card and say 44.

These activities should be repeated daily.

Chris.

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Thank you very much Chris. I am figuring out how the Ten Frame Method works from your description. I didn’t find much info through google. Maybe I have to ask you more later. :wub:.

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I find this quite intesting.
http://www.acceleratedlearningmethods.com/functions-math.html

The Functions of Rapid Math Calculation
Here, we discuss the functions of math from the left brain perspective and how doing math through the right brain allows you perform complex math equations faster than a computer.

A Left Brain Math “Genius”

Before discovering the incredible right brain functions of math, I saw a guy on TV dazzling the viewers with his amazing rapid math skills. Somehow, he was able to add, subtract, multiply and divide large random numbers very quickly. I wanted to do math like him so I bought the course.

At first his rapid math system seemed fairly simple. Basically, I learned to group together and temporarily store different chunks of numbers in my ming from an equation while putting together other chunks, then assembling them all at the end for the answer. It worked great but what I found is, if I made one wrong calculation along the way, of course the final answer was wrong at the end.

Also, as I progressed through the lessons the equations became more and more difficult. I found trying to keep multiple chunks of numbers in my mind just got too mental. My brain ended up shutting off to this system (and I may have popped a few screws from my head along the way) so I dropped the course.

Looking back, what I know now is that this “math wizard” really did have incredible rapid math abilities and figured out a system that works - for the left brain. That may be fine for some, but for contrast, let’s look at a faster way much younger children are solving even larger equations - the right brain way!

Right Brain Rapid Math Calculation

Equations solved by A. T., Nagoya (age 2 yrs-8 mths). © The Shichida Method.Here’s the scenario: You walk into a classroom and observe young children concentrating on their lessons. As you walk around you notice a little girl saying rather large numbers out loud as she’s looking at a small writing board. This interests you, so you wonder over to see what she’s looking at. What you find is amazing: She’s shouting out the answers to six-digit math equations! You ask her how she does it. An assistant comes over to answer your question because the student doesn’t speak English. She simply says, “She sees the answers in her mind.”

Ok, you’re kidding, right? How can someone, let alone a child, instantly see the answer to a math equation in her mind? She must have memorized the answers to some pre-written equations! Well, I’ve seen it myself and it’s real. As fantastic as it sounds, people are capable of solving complex math equations faster than a computer. Let me tell you how real rapid math calculations are possible!

Mathematics is not like Geography
In his book, How To Teach Your Baby Math (see at right), Glenn Doman says, “Mathematics is not a subject like geography but a way of thinking and reasoning.” The functions of math are really just a series of visual symbols that we arrange into other symbols. Following this idea, Doman and Shichida developed math programs using symbols instead of numbers and actually succeeded in teaching math to babies and very young children. Although the methods used by Doman and Shichida vary slightly, they both generate the right brain visual input allowing complex equations to be solved instantly.

Instant Rapid Math Calculation Through the Subconscious Mind
Solving large math equations instantly is not a function of conscious (left brain) mathematical calculations. The answers automatically come from the subconscious where they are calculated instantly. Through the right brain, we literally see a picture of the correct answer in our mind’s eye. However, we need to be in the right state of consciousness to see it. Think of it like baseball: If you’re not in the right spot on the field at the right time, you won’t catch the ball that was just batted to you. In most cases, being in the right place to receive the answers that appear in your mind takes certain training.

It’s True! I Can Do It Too!

Ok. Here’s my experience with rapid math calculation.

Sometimes, when looking at numbers on paper I can hear my mind saying, “I need to add these.” Or, “I need to multiply these.” Instantly, the answer appears in my mind. It happens so quickly that often I hardly take notice. Sometimes, the answer will appear and then, in another instant, it’s gone. When I do make conscious (left brain) contact with the answer appearing in my mind, I write the answer down.

What I just described doesn’t happen all the time but when it does, my logical left brain tells me it can’t be right so I usually verify it by hand or by using a calculator. What I find is my instant answer is always correct.

Dr. Shichida’s Research Confirms This Ability

Child educator and pioneer in right brain education, Dr. Makato Shichida, tells us there are a great many five- and six-year-old children all over the world who can correctly multiply and divide five- and six-digit numbers in seconds. He believes that this is the right brain activity of fast calculation and imaging mechanisms. In fact, he verified his supposition using data from Positron Emission Tomography (PET) testing of brain waves. This data shows that the right brain function of highly skilled abacus users are active when carrying out arithmetic operations. This contrasts with the rest of us, for whom the left brain is more active when doing arithmetic with a calculator. Remember, earlier we mentioned that the use of symbols in math equations activate the right brain’s instant math abilities. The abacus uses a series of visual symbols - beads.

So, if we want to train our children to calculate faster than a computer, we’ll need a suitable math program and exercises we can use to develop our right brain’s natural imagery and visualization abilities. This will enable our conscious awareness to see what our subconscious is showing us, which in this case, are answers to math problems.

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So far, so good. I’m getting sceptical about Doman Math. The failure rate is high.

e.g. http://www.childandme.com/doman-math-does-it-work/

Nevertheless, I still want to give my child the opportunity.

17

Though I was intimidated by the high failure rate and the non-verbalization part of it initially, I am now more inspired by Domanmom’s blog (http://grhomeschooling.blogspot.com/search/label/Math). It is clear from her blog that she is reinforcing math in many other ways apart from just flashcards, and Hunter definitely seems to have a good understanding of the subject.

I feel it is not fair to generalize that Doman math does not work. If it does not work, then it should not work for anybody. But if a couple of people are having success with it, then I guess it is something do-able. There are several factors which could alter the success of any method…consistency of the program, child’s interest (in dots particularly) etc. I do not think teaching Doman math can cause any harm. So I guess we can give our children the opportunity. …And now that we have LM with the several icon options, it might help keep the child’s interest levels up.

After all, if a child has a pleasant feeling toward math and if he is comfortable with numbers later in life, I think that is what matters the most. If Doman math helps them achieve this comfort level with mathematics, then I guess its worth a try.

Questers.

18

I have recently seen an infographic with some tips for parents on how they can help their kids with studying. It is not easy still, but at least some hints that can make the life of teaching parents easier. Here it is: http://www.homework-desk.com/blog/parents_helping_kids_wtih_hw_/.

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I guess wrong answers in maths is one of the major problems that the children face during their school.

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Indeed, it does depend on different factors. I used LM with both boys at different ages and we’ve had Doman dots in different ways and programs. But I haven’t been consistent nor used it beyond the first semester or so, I think.

As for understanding math, I would go for Montessori method and Mortensen Math. The second one is discussed here in the group, you shall see the last post from Sonya, who showed me how fun and easy actually we and the kids can learn and use math http://forum.brillkids.com/teaching-your-child-math/mortensen-math/msg107051/?topicseen#new, and there are parents really into this on the Facebook group designed for that.

As for giving wrong answers, Crewton Ramone from Crewtone Ramone’s House of Math (Mortensen Math master trainer) talks a lot about guided discovery, getting the ‘no’ out of our lessons and instead using questions and positive ways of helping the child see and think. And it’s really quite natural for repetition to occur till the child will see/understand things and will give the right answers. We should pursue understanding of concepts, not right answers from the start (and thus frustrating ourselves and the kid if she makes mistakes) when teaching, in my opinion, or at least this is how I understood things.