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My 9 year old dd struggles with memorizing math facts.  She has most of the addition facts, some subtraction facts, and few multiplication facts (0,1,10), but her understanding of math is very good.  I have been working on her facts using Math U See, but I am not sure if I should I continue on with our regular program (we are using Teaching textbooks) at grade level and continue to work facts.  Math U See at the beginning levels is way too easy for her other than memorizing facts?  What to do?

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I just tried (from reading your other thread) Reflex math with my son last night.  He liked the free trial, and has agreed to it.  We are just starting on it.  He has made progress with a computer math facts program at school, but extended-day learning ends on May 2nd and he needs to keep working through the summer.  But he has made progress.  

 

In the meantime -- for a lot of things he is fine with a "math book."  For his math book -- every page is a number.  Then he has copied out the skip counting for that number.  

 

He also has a grid for the multiplication facts.  

 

He can use them for a lot of mult/div fine (he is 9 and in 3rd grade).

 

However -- he has just had a unit including fractions, and it is very hard for him to see that 8/24 is the same as 1/3 when he does not have any instinct that "24/8=3."  He has been able to do a lot of things fine, but just some things he did not understand.  For that area and for least common denominators, I do not have a good solution.  We have been drawing the arrays and then coloring them so he can see they are the same -- but it is not something I am finding to be a good solution for him, though it s also a work in progress.

 

Overall though I am happy (so far) with him in his regular program and as there are things where his math facts are holding him back, address it.  This has been the first time that he has not been pretty fine using his math book and grid.  The math book seems like it is helping him with his skip counting.  Skip counting is still difficult for him, he does not totally have all of them memorized, and he is also unsteady sometimes and stalls -- but he is improving, it is just not like "oh he knows it now."

 

For now I am (honestly) skipping subtraction (he counts on his fingers quickly but does not "know" very many at all) because I read a little and had a take-away of ----- it does hurt kids not to know multiplication as they get into fractions and percents and things like that -- they need the feel for multiplication.  But there is not anything like that with subtraction (it just slows computation down, sigh sigh sigh).  

 

So I am on the side of trying to not hold back areas outside of computation.  When my son does MAP testing and we get his scores, there are 5 sections of math and only one is computation.  It is not the end-all be-all of math.  But -- it is important, too.  But I would try not to hold everything back b/c of one area, if she is doing well otherwise. 

 

I will also mention -- another poster here has done Timez Attack and contacted the company for a way to give more response time.  We had tried that last year and it was good but I didn't know about that, and it got frustrating b/c he could not answer fast enough.

 

On Reflex on the trial he was able to answer fast enough, but he is a year older now and has some more familiarity with typing number on the computer etc. etc.  

 

But anyway -- if she can have a grid or math book (and she could have a page listing math facts for a number too, for addition/subtraction if she wanted) that has been a good solution here up until this pesky unit with the 8/24 stuff.  And, it has really only been on sheet of word problems, and he got a B on the unit test for the unit.  But -- it is clear it is coming up in the near future.  I am planning for him to do 30 minutes a day from now on and hope he can be more solid before 4th grade starts.  

 

(My son is solid-to-good in math -- and that is with a lot of difficulty with his handwritng and with his math facts...... iow he is pretty darn good at every other thing about math, for the most part, he is compensating for his weak areas with his strengths, and coming out as solid-to-good.  He has a good understanding for the most part.  I think his program at school is good, they do a lot with manipulatives and using dry-erase boards -- so there is that, too.  But I would really try to separate math facts out, if they are the weak area.  Maybe divide things up in some way, over the day.  I am not familiar with TT though so I don't know if it is one where it is easy to make adjustments here and there, or how close your daughter is to getting into fractions where the multiplication stuff might be more important for the concepts.)  

 

 

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My DS learned addition and subtraction facts to 20 using Saxon.  He was sitting in a classroom at that time.  I recall him reviewing self made flash cards daily.  If you are not pleased with MUS, maybe look at RS math.

 

DS has a maths disability as well.  For multiplication and division facts, I followed the steps laid out in Ronit Bird's book and used c-rods and the area model of multiplication.  For facts practice, DS used math software and a 10 keypad to enter answers quickly.  

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Thanks.  I am not displeased with MUS; I just really want to use it to learn math facts.  I have heard many people say get those math facts before you move on, but I think that might be unrealistic for a dyslexic kid. 

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I think it is ideal to get those math facts before you move on.  Yes.  I agree.

 

But if there is some reason that it is not practical -- then it is on to Plan B and individualizing and making the best of things and using strengths.  

 

Personally a lot of people don't understand that you cannot just get kids to learn math facts easily just by doing some flash cards or something.  Like -- I have been trying for two years, really.  In first grade I was not focusing on math facts at all, only reading, and math was his strong area (besides math facts, but it was not such at thing in 1st grade).

 

But I really think some people just do not realize how HARD it is, and do not realize that for some things, kids with lower results have been working HARDER than kids with higher results.  

 

If it seemed like it was possible to pause and not lose progress in other areas, and possible to spend a short amount of time and get caught up, that would be different.  But I think math facts are a long haul here -- they are not something where I can just go "okay hit it hard for a little while."  It is just not how it is.  

 

Though I am hoping for progress before 4th grade, too.  He has surprised me with his computer math facts learning -- I am impressed.  

 

He is counting up with skip counting, but can get the answer quickly, for the most part.  He does not know the skip counting for every number without some counting (vs. memorized) but really -- he has made some progress.  

 

But yes, I agree, everything would be easier if he knew his math facts better.  Yes.  But I don't think it is practical to hold it up.  

 

If you like MUS for math facts ----- go for it!!!!!!!  Maybe she can just have two math programs and do them at different times. I actually like that at my son's school -- they have math facts separately from math block, and so his not-liking of math facts hasn't rubbed off on "math" b/c they are separate to him in a way.  

 

 

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Thanks.  I am not displeased with MUS; I just really want to use it to learn math facts.  I have heard many people say get those math facts before you move on, but I think that might be unrealistic for a dyslexic kid. 

According to Ronit Bird, knowing addition and subtraction facts to 20 is a precursor to multiplication.  The book that I linked will provide helps for addition and subtraction facts too.

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I am seeing my son fine with multiplication. He understands subtraction fine and can count on his fingers for ones he is less-solid on.  He just does not have the straight memorization of the facts.  He does not have the "fluent recall in 3 seconds."  Even for the ones where he is not counting but just thinking of them, I don't think he is that fast.  

 

I honestly think what I see is just this difficulty with memorizing, the same thing that made it so hard for him to learn letter sounds, phonics, Dolch words, the words "eleven, twelve, thirteen, fourteen, fifteen," our address and phone number, his middle name (he still asks me his middle name), the days of the week, the months of the year (he still doesn't know), and just some other things like that.  He just is not good at remembering things like that.  

 

Next school year will be long division with mixed operations in each problem, though.  I hope he can be farther in subtraction by then, too.  

 

If "know" means -- understands addition to subtraction to 20, he does know in that sense.  He is just so slow and still counts on his fingers.  Sometimes he can't think of answers that he has known fairly consistently.  It is similar to reading -- he was reading quite a while when he would still randomly forget a letter sound.... it didn't mean he needed to go back to letter sounds.... he just has what people call "glitches" sometimes or he freezes up or he just doesn't think of things that he knows to some extent.  But what I have seen with reading, is that it has gotten better and better with more practice.  Now he hardly ever does it.  

 

It's also true I have focused more on reading as I have always been told he is good in math except for math facts, and they do them separately at his school to some extent, they are very big on conceptual understanding and word problems, but of course want the kids to know math facts, too.  But while he is good at conceptual understanding and word problems, I think they do let him slide by a little more than they would if he had the opposite situation.

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Give her a multiplication chart and just keep trucking!  I know that you need to have those facts down or it encumbers your math work later... but the great thing about giving them a multiplication chart is that THEY get tired of looking things up and eventually learn them.  One of my kids did redesign her chart with a color scheme giving each factor a different color, and the product was a blend of the two factor colors.  Worked for her!  If you stop and stall on memorizing facts you will nurture a despising of math. 

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Give her a multiplication chart and just keep trucking!  I know that you need to have those facts down or it encumbers your math work later... but the great thing about giving them a multiplication chart is that THEY get tired of looking things up and eventually learn them.  One of my kids did redesign her chart with a color scheme giving each factor a different color, and the product was a blend of the two factor colors.  Worked for her!  If you stop and stall on memorizing facts you will nurture a despising of math. 

 

 

That is what I was doing, and she understands the concept of multiplication well.  But then I read that you should get all facts down before moving on.  Maybe I will continue to work math facts via MUS, but continue on with our other math program so she can progress in math.  Thanks, everyone.

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The idea of math facts as something that can be memorized is interesting?

It perhaps defines the difference between the Western and Eastern approach to math?

Where a math fact is a relationship between variables that can be scientifically proven.
 
With the Eastern approach,  children use manipulatives/ abacus, to explore and prove the relationship between variables.
In Japan, traditionally children don't learn the names and symbols for numbers, until around 9 years of age.
But they are already able to do math, and prove it on an abacus.
As they know the process to prove a math fact.
Memorizing plays no role, as they understand math facts.
 
Where math is understood as different patterns of relationships, between variables/ numbers.
As a process of manipulating variables to prove a math fact.
 
The idea of memorizing math facts, is a contradiction of math as a process.
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The idea of math facts as something that can be memorized is interesting?

It perhaps defines the difference between the Western and Eastern approach to math?

Where a math fact is a relationship between variables that can be scientifically proven.
 
With the Eastern approach,  children use manipulatives/ abacus, to explore and prove the relationship between variables.
In Japan, traditionally children don't learn the names and symbols for numbers, until around 9 years of age.
But they are already able to do math, and prove it on an abacus.
As they know the process to prove a math fact.
Memorizing plays no role, as they understand math facts.
 
Where math is understood as different patterns of relationships, between variables/ numbers.
As a process of manipulating variables to prove a math fact.
 
The idea of memorizing math facts, is a contradiction of math as a process.

 

I started DS with Math in Focus and his understanding of math and relationships is progressing much better now.  It is slow going at times because it is all mental math and understanding of concepts and number relationships, instead of rote memorizing and regurgitating numbers.   But some of the other parents don't see it as progress because he cannot recite his math facts off the top of his head.  Can he do the math problems mentally?  Yes.  Is his conceptual understanding of math increasing?  Yes.  Every day.  And it is slowly becoming apparent to me that actually understanding the math is more valuable, at least to us, than being able to rapidly recite the math facts.  This post of yours, geodob, is helping crystallize my feelings regarding this.

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My husband is mildly dyslexic and as a kid never did memorize math facts. He just kept doing math, and got his math facts over time. He went on, in college, to double major in mechanical engineering and mathematics. He does very well with lots of math.

 

our eldest daughter has trouble memorizing math facts, however, when she doesn't have to calculate she goes great guns on the rest of math. The conceptual stuff she gets amazingly fast. It's just the arithmetic she doesn't like. Because of this, and because of my husband's experience,I don't require her memorizing her math facts. She counts very quickly on her fingers, the addition and most subtraction have come with time. She has a multiplication grid that she is allowed to use when doing her math. I've noticed that these facts, too, are also being memorized without effort, over time.

 

different people learn in different ways. Try various methods to see what works best for your child. Unless there is some reason but they must have particular math facts memorized don't stress it. I found that removing the pressure has freed up my DD's brain for learning a lot of things more quickly.

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This process started when DS came home and was late 5th grade. DS learned his multi and division facts by first verifying he could instantly recognize dot patterns. I followed that up with ensuring he could decompose numbers and then teaching him the distributive and commutative properties of multiplication. For about 15 minutes per day, he used c-rods, metric graph paper, and colored pencils. As we reviewed and proved the concepts on paper and with concrete manipulatives, he also practiced counting on. Eventually, he started multiplying in his head and then he knew them. On occasion, I make him practice with a computer.. For a child to learn new info, they have to internalize the process and the process has to make sense. That can take some time, and we have used mnemonics. Over the years, DS has learned to compensate. DS and I both enjoyed the process of learning multiplication because the methods were new and did not involve rote memorization. If a child never learns all their facts, they still need a strategy to derive them accurately and on paper if necessary.

For subtraction, he learned a process called mental bridging which involves a novel way to use number lines. All of these steps are in the book I linked up thread. Things would have been much better had I known and applied the strategies when DS was third grade.

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My two boys are also using the free trail of Reflex Math currently.  My ds10 is mildly dyslexic.  I did not want to spend money to practice match facts especially when I had several other ways to practice facts for free.  However, my boys love it and they are averaging 20 minutes per day each on their math facts sometimes up to 25 minutes.  When we were playing math games or doing flashcards we only got about 5 minutes before the boys were begging to be done.  Reflex math is really holding their attention and the games/rewards is proving to be a real incentive to log in each day and play.  So far in the 5 days we've used it both of their math fact fluency has increased.

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My DS learned addition and subtraction facts to 20 using Saxon.  He was sitting in a classroom at that time.  I recall him reviewing self made flash cards daily.  If you are not pleased with MUS, maybe look at RS math.

 

DS has a maths disability as well.  For multiplication and division facts, I followed the steps laid out in Ronit Bird's book and used c-rods and the area model of multiplication.  For facts practice, DS used math software and a 10 keypad to enter answers quickly.  

Heathermomster, have you tried using the Ronit Bird Dyscalculia Resource book?  I have had it in my basket at Amazon forever.  It is so expensive I have not purchased it, but I thought it might be worthwhile to have around.  I haven't' found anyone personally that has used it, though....

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That is what I was doing, and she understands the concept of multiplication well.  But then I read that you should get all facts down before moving on.  Maybe I will continue to work math facts via MUS, but continue on with our other math program so she can progress in math.  Thanks, everyone.

I haven't used MUS, so perhaps that is their recommendation.  I have seen other programs recommend that as well.  However, I ignored it it BECAUSE I knew my kids understood the concept well (and that they eventually would learn their facts), but for them (all very VSL, no dyslexia Dx) drilling facts only made their retention worse.  And it made math a dreaded subject.  Oldest DD went from public school (where she had a timed drill sheet every day in 2nd and 3rd grade) hating math and thinking she sucked at it to loving math - FAVORITE SUBJECT - and solidly finishing AoPS preA at 11. The difference was we had to tap into her way of thinking, stop drilling facts, and let her soar with what she could understand and do in her head.  I am not saying that everyone is the same, but for VSL kids (which by nature all dyslexics are) everything I have read as anecdotes and from professionals is that drilling math facts with them won't help.  You can try some of the visual math fact programs (they have cute stories and pictures to help them memorize the facts).  I found that a nicely produced, color multiplication table at their disposal, AND using multiplication in the context of more meaningful problems, worked for us.

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Heathermomster, have you tried using the Ronit Bird Dyscalculia Resource book?  I have had it in my basket at Amazon forever.  It is so expensive I have not purchased it, but I thought it might be worthwhile to have around.  I haven't' found anyone personally that has used it, though....

Yes, I own that book and The Overcoming Difficulties with Number.  I prefer the Overcoming Difficulties to the Dyscalculia Toolkit because it addresses multiplication, division, and math reasoning strategies in more detail.  The DT is mostly games and activities to teach more basic number sense, complements to 5 and 10, place value, and calculations above the number 10.  

 

ETA:  ODwN refers to activities in the Dyscalculia Toolkit, so that's a wee bit of an annoyance. 

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Yes, I own that book and The Overcoming Difficulties with Number.  I prefer the Overcoming Difficulties to the Dyscalculia Toolkit because it addresses multiplication, division, and math reasoning strategies in more detail.  The DT is mostly games and activities to teach more basic number sense, complements to 5 and 10, place value, and calculations above the number 10.  

 

ETA:  ODwN refers to activities in the Dyscalculia Toolkit, so that's a wee bit of an annoyance. 

I do have ODwN and the Dyslexia Toolkit, although I find it hard bouncing between them.  But I am not certain I am clear on what you are saying....sorry.  Are you saying that you also own The Dyscalculia Resource book too?  Or just Overcoming Difficulties with Numbers and The Dyscalculia Toolkit ("just" being a relative term since those are both very useful books and rather expensive :) ).  I am wondering if the Dyslexia Resource book might have things DD would be more interested in doing for fun.  She likes puzzles and games, which DR seems to be, but it looks like it may be very similar to what is in the D Toolkit.  I don't want to duplicate.

 

FWIW, I love Ronit Bird.  I think so many issues with math would go away in schools if kids started out with more of this approach when they are developmentally ready (whatever age that might be)...but I wish the books were in much bigger print.  The small print is killing my eyesight.   :(

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I am thinking about the Ronit Bird book for summer, it is not something I would be able to do after school (public school).  Plus I can use it with my younger kids.

 

Part of it, I know his school is really good about the developmental things, and the manipulatives.  They use Math in Focus and I think they do a good job with it.  He is doing things I did not see until much later in school.

 

But ------ he has some problems, too, I wonder if maybe he does have some gaps.  OR if he just has a hard time memorizing.  

 

But more ways to target the same thing can be good for him, even if it is "just memorizing."  Even another way might be more effective.

 

Though it can't just be "a different way of playing math fact games." He is on to that.

 

However ----- I am embarassed to say this, but my husband has recently gotten involved with a card game called Magic:The Gathering.  When his work schedule allows it, he is playing in tournaments 2 nights a week.  My son and I play with him, and it has helped my son with his addition and subtraction.  He is actually pretty good at this game, and it is a strategy game.  He can play against adults when my husband takes him to the card shop.  My husband is a better player, he usually finishes in the top 6 or 8 out of 50.  But there are 4 or 5 players who always beat him and trade around for getting the top places. 

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I haven't used MUS, so perhaps that is their recommendation.  I have seen other programs recommend that as well.  However, I ignored it it BECAUSE I knew my kids understood the concept well (and that they eventually would learn their facts), but for them (all very VSL, no dyslexia Dx) drilling facts only made their retention worse.  And it made math a dreaded subject.  Oldest DD went from public school (where she had a timed drill sheet every day in 2nd and 3rd grade) hating math and thinking she sucked at it to loving math - FAVORITE SUBJECT - and solidly finishing AoPS preA at 11. The difference was we had to tap into her way of thinking, stop drilling facts, and let her soar with what she could understand and do in her head.  I am not saying that everyone is the same, but for VSL kids (which by nature all dyslexics are) everything I have read as anecdotes and from professionals is that drilling math facts with them won't help.  You can try some of the visual math fact programs (they have cute stories and pictures to help them memorize the facts).  I found that a nicely produced, color multiplication table at their disposal, AND using multiplication in the context of more meaningful problems, worked for us.

 

This sounds exactly like my DD12.  Very visual in approach to everything.  She also is very independent-minded: if she wants to do something there is no stopping her, and if she doesn't there is no way to make her.  We had her tested for dyscalculia when they tested her for other things -- she is not dyscalculic.  Dysgraphia, horrible short-term memory, very slow processing speed, ADD (primarily inattentive, and very strongly so) -- in short, a very poor fit for your usual school classroom.  My challenge now on all of her studies is keeping her challenged enough, now that she doesn't have to take tests within a specific amount of time and can change learning approaches when stuff doesn't make sense.

 

My eldest niece, age 14 and a high school freshman, used to think she was stupid and horrible and math.  She got a teacher one year who actually paid attention to how DN14 thinks and learns, and all of that changed.  This year DN14 has been inducted into some math genius society (can't remember the name right now), and has been scoring very highly is some college tests (testing in to take dual credit courses next year).

 

Ever since I've really looked at kids in general and watched their minds click I have failed to see any who are not amazingly smart in their own way.  There is no such thing as a stupid kid, just a kid who hasn't been able to figure out how to play the game by the rules currently in use.  I've been telling my kids that "stupid" is knowing better and doing/not doing whatever anyway.  That is the only definition acceptable in our family now.

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To the op, you're not crazy.  For us there was a big gap between when dd understood the math and when she was fluent in it.  In other words, with her standardized testing there was a significant gap between her conceptual and computation scores.  In improved in 7th grade when we switched mid-year to Teaching Textbooks.  TT is not brilliant conceptual instruction, but it's gentle spiral.  All I'm saying is the facts.  We had done everything within reason (flashcards, math tables to reference, abeka drill books, extra practice books from the BJU math, Flashmaster, card games from RS, etc. etc. etc.) and what finally got her there was either age or spiral or a combo of the two.  

 

So when somebody says they're using card games at age 7 (or what have you) and not seeing a budge, it makes sense why.  You're using an auditory channel with a VSL dc.  If the dc has visual processing problems but still by virtue of brain structure is likely to be VSL, then you do VT first to get that fixed.  And as for the people who say it's all age and comes later, I can only say the truth, that for us it was later.  No amount of oral card games budged her computation speed.  Yes she has low processing speed.  I think for her TT worked because it was short lessons with humor, with a story, with multiple modalities at once at the time when her brain was ready thanks to a bit more age and the VT.

 

I like RonitBird and the understanding it develops, but I doubt it will turn out any different for my ds than RS did with my dd as far as facts.  She UNDERSTOOD them.  It's just that it didn't confer to fact speed on written math.  Now I take that back.  RB does a bit better about getting it to connect to visual.  (so you have a visual 4 and a visual 1 leading to a visual 5 as you say it)  RS was so auditory for her, even though it was supposed to be so visual.  Dunno.  Just saying you're not the only one, and I agree with not ruining their math lives over it.  

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Though this discussion raises question about the current limited definition of Dyscalculia, as an inability to concieve of different sized quantities?

Which are represented as numbers, verbally and visually.

But their is a small part of the brain behind the left ear, called the Angular Gyrus.

One important role of this, is to make connections between the conception of different sized quantities, and the symbols and words to represent them.

Which also connects the sounds of words, with the written letters that represent them.

 

Where perhaps you might consider the idea of infants learning the names and symbols for letters, before they are introduced to words?

This letter is this sound, as opposed to this sound is this letter.

Which would seem absurd?

Learning to read and write, and later to speak.

 

But in Western countries, most babies are introduced to and learn the names and symbols for numbers.

With no concept, of what they actually represent?

Where the problems that this creates, needs to be recognized.

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Though this discussion raises question about the current limited definition of Dyscalculia, as an inability to concieve of different sized quantities?

Which are represented as numbers, verbally and visually.

But their is a small part of the brain behind the left ear, called the Angular Gyrus.

One important role of this, is to make connections between the conception of different sized quantities, and the symbols and words to represent them.

Which also connects the sounds of words, with the written letters that represent them.

 

Where perhaps you might consider the idea of infants learning the names and symbols for letters, before they are introduced to words?

This letter is this sound, as opposed to this sound is this letter.

Which would seem absurd?

Learning to read and write, and later to speak.

 

But in Western countries, most babies are introduced to and learn the names and symbols for numbers.

With no concept, of what they actually represent?

Where the problems that this creates, needs to be recognized.

Once again you have flipped my world upside down...going off to ponder life for a bit.  :)

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Though this discussion raises question about the current limited definition of Dyscalculia, as an inability to concieve of different sized quantities?

Which are represented as numbers, verbally and visually.

But their is a small part of the brain behind the left ear, called the Angular Gyrus.

One important role of this, is to make connections between the conception of different sized quantities, and the symbols and words to represent them.

Which also connects the sounds of words, with the written letters that represent them.

 

Where perhaps you might consider the idea of infants learning the names and symbols for letters, before they are introduced to words?

This letter is this sound, as opposed to this sound is this letter.

Which would seem absurd?

Learning to read and write, and later to speak.

 

But in Western countries, most babies are introduced to and learn the names and symbols for numbers.

With no concept, of what they actually represent?

Where the problems that this creates, needs to be recognized.

So is there something you can do to stimulate the Angular Gyrus?  Or is it just more recognizing what's going on and remediating?  Is it considered a developmental delay the way EF is?  Is it something where we'd actually be better off going a different route entirely?  We're starting to get that sound to written, math visual to math word, etc., but it's REALLY slow going. If there's something I can do to make our work more effective, I'd be all for it.  Ds is, as you're saying, struggling with those connections in both the math and reading. We've gotten up through 5 in the Ronit Bird stuff, as in he can play a game about things that make 5 using the nuggets.  That's it.  He can't tell you how many fingers he has.  When presented with a 3 die and a 6 die, he'll still start over and count them.  It's just crazy.  And on the testing we've done, his IQ extrapolations are pretty high, in the bright or gifted range.  

 

It's not really an apraxia issue with him per se, because he can retrieve the words and isn't present in all kids with apraxia.  That's why I've been assuming when we get him eval'd at some point he'll get dyslexia and dyscalculia labels.  I just haven't seen a lot concrete on why those two things seem so connected in him, so your point on the AG is fascinating.  

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I've been thumbing through the On Cloud Nine book by Bell and Tuley, and it's interesting.  Perhaps, those of you that have used LMB's Visualizing and Verbalizing can explain it better.  Basically, the premise of On Cloud Nine math is to go from concrete --> imagery --> computation.  Cloud 9 math identifies weak concept imagery as the cause of some math problems.  In contrast, RB goes more concrete --> picture--> computation.  The lag for my child is the picture--> computation stage.

 

DS started heavily with integer math this semester.  He'd been introduced previously but is really applying it now.  While simplifying an expression, he has to stop and image the manipulative.  If he does not, there's a good chance he'll make a mistake.  Getting him to slow down, visualize, and be patient are problems because he's not accustomed to using his spatial talents that way, and he's a teen aged boy.

 

 I wonder sometimes whether I should have emphasized the imagery aspects of the math earlier.  With LMB and even Soroban abacus instruction, the student is introduced to  number with the manip and then told specifically to stop right there, close your eyes, and use your mind's eye to image the number.  The student must deliberately associate the number value with the manipulative...I suppose over time, the student internalizes the imagery step and just does it.  

 

For three years now, DS has used manipulatives with the emphasis of proving why 5+2 equaled 7 or why 3 times 4 was the same as 4 times 3.  Never once have I stopped DS and told him to image the problem until this semester. When he does stop and image, he gets the problem correct. I don't know whether any of what I'm saying makes since.  I expect the visualizing takes time and consistent practice.

 

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Though this discussion raises question about the current limited definition of Dyscalculia, as an inability to concieve of different sized quantities?

Which are represented as numbers, verbally and visually.

But their is a small part of the brain behind the left ear, called the Angular Gyrus.

One important role of this, is to make connections between the conception of different sized quantities, and the symbols and words to represent them.

Which also connects the sounds of words, with the written letters that represent them.

 

Where perhaps you might consider the idea of infants learning the names and symbols for letters, before they are introduced to words?

This letter is this sound, as opposed to this sound is this letter.

Which would seem absurd?

Learning to read and write, and later to speak.

 

But in Western countries, most babies are introduced to and learn the names and symbols for numbers.

With no concept, of what they actually represent?

Where the problems that this creates, needs to be recognized.

I'm curious to know, does vestibular issues and ear infections affect the Angular Gyrus?

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Heather, have you had them checked by a developmental optometrist?  RB is catching the need to visualize and use visual patterns with their careful attention to the dot arrangements.  It's in there as a technique she's using, even though she's not stopping and asking them to visualize it.  V&V doesn't replace the need for VT, and to me it goes in looking for the end product without asking the precursor questions.  

 

I'm being paged to do sticker books.

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Just stopping by to say -- Reflex math is going well here.  But I am curious from other users -- do kids remember long term?  

 

I am sad to say, I think my son is improving right now b/c, a couple of years ago he decided he was bad at math facts, and since then has been just getting out of working hard on them (or avoiding them, whatever).  Or maybe things are clicking more for him this year.

 

He has hated it so much in the past, particularly in 2nd grade (when I got him out of timed math facts, which were upsetting him).  Maybe enough time has passed, maybe the sweet woman at extended-day learning helped him. 

 

At his school they do manipulative, then picture, then abstract.  There are times when some kids are on picture and some are on abstract, and it seems to work out.  I think next year in 4th they are going to have separate math levels for the first time.  

 

I will be following up on this, more in the summer.  I would SO like him to be solid when he starts 4th grade.  

 

Reflex is working out.  He is not having trouble typing, though I will type for him once in a while.  We make deals for what he can do if he gets a green light.  He usually doesn't do it all at once, he does it in 2 or 3 spurts.  I am tying it to his viewing of Minecraft walk-throughs.  He is engaged with the coins, and buying things for his avatar.  

 

I am concerned if he will remember long-term, but I think that it is at least good enough -- he will be at a point where it will not be *so hard* to practice to keep them up.  

 

I do want to make sure he is understanding everything, too, but for now -- I am pleased with how Reflex is going.  

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Heather, have you had them checked by a developmental optometrist? RB is catching the need to visualize and use visual patterns with their careful attention to the dot arrangements. It's in there as a technique she's using, even though she's not stopping and asking them to visualize it. V&V doesn't replace the need for VT, and to me it goes in looking for the end product without asking the precursor questions.

 

I'm being paged to do sticker books.

Yes, DS was evaluated by a VT, and there were no problems that way.

 

ETA:  Maybe the visualizing is a specific strategy that needs to be taught to the maths disabled student.  

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Their has been some interesting research done in Japan, with older students who grew up using the Soroban abacus.

Which looked at the brain processes when these students do math?

Where these students had developed a 'mental abacus'.

What they found, was that when thought of a number?

It triggered a response in their brain's motor cortex, as if their fingers had just formed that number on a Soroban.

So that numbers are felt. 

Then when they do a math calculation, it uses an imaginary movement of the fingers.

 

This has parallels with people who are born deaf and learn sign language.

Where letters/words are concieved of as finger/ hand positions.

Then when they are thinking, they feel the words as a sequence of movements.

So that with a 'mental abacus/ soroban', a math calculation is carried out as a sequence of imaginary movements.

 

This is actually a more efficient way of doing math.

Where in Japan, a popular game, is having races with a calculator.

As they aren't slowed down with having to verbalize and visualize numbers, through the calculation.

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