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Can we talk math/dyscalculia?


PeterPan
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I've been thinking about this, and what might be the best way to "feed" him.  You could just add another session of RB, and that might be okay, but I was wondering:  what if you did totally different things for one or two 10 minute sessions?  Geometry:  tangrams, geoboards, Montessori constructive triangles and binomial cubes; read Math Start books, do some work on time:  not telling time, but a visual schedule of your daily routine, a timeline of his life, some calendar stuff; some Montessori seriation exercises (pink cube, brown stair, etc), patterns, strategy games and logic problems, c-rod PLAY/ building (didn't someone once post a pre-Miquon book that they did with their child?).  Sort of laying indirect preparation for other approaches, but not drilling or remediation focused.  Maybe look at MEP and their Reception program for some "talking math?" 

 

I don't know much about this, but does he have any understanding of "ten" at all?  I'm wondering if even if he doesn't have ten down solid, if he could understand it as a WHOLE, he could start to do some stuff with place value, using the place value blocks or c rods? 

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I've been thinking about this, and what might be the best way to "feed" him.  You could just add another session of RB, and that might be okay, but I was wondering:  what if you did totally different things for one or two 10 minute sessions?  Geometry:  tangrams, geoboards, Montessori constructive triangles and binomial cubes; read Math Start books, do some work on time:  not telling time, but a visual schedule of your daily routine, a timeline of his life, some calendar stuff; some Montessori seriation exercises (pink cube, brown stair, etc), patterns, strategy games and logic problems, c-rod PLAY/ building (didn't someone once post a pre-Miquon book that they did with their child?).  Sort of laying indirect preparation for other approaches, but not drilling or remediation focused.  Maybe look at MEP and their Reception program for some "talking math?" 

 

I don't know much about this, but does he have any understanding of "ten" at all?  I'm wondering if even if he doesn't have ten down solid, if he could understand it as a WHOLE, he could start to do some stuff with place value, using the place value blocks or c rods? 

Yes, these are good ideas!  Thank you!  You're making some ideas go through my head that hadn't been there before.   :)

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I suspect dyscalculia is like dyslexia, with symptom lists online that don't really get to the core/crux of what they're looking for diagnostically.  Lots of kids will have issues with math facts due to needing lots of repetition/context to learn and due to processing speed.  That's not really the same as a lack of number sense, which seems to be the core issue of dyscalculia.  Now this is probably an EXTREME example, but someone wrote me saying their dc is doing calculus successfully but can't tell you 5+5+5.  Diagnosed dyscalculia.

Yes, I agree with this - like currently the most popular dyslexia  theory is a phonemic issue - yet although DD so clearly has phonemic issues that does not encompass the whole of her issues.    And it is so hard to separate the two - the slow math facts can appear to be a number sense issue just as the slow phonemes can appear to be a phonemic issue.  For example, even though DD has no trouble with dot patterns - she still does not 'bridge'  without my telling her to do so and oh so very slowly going through it in her head - so very alike when I would have her do phonemic replacements/deletions.   And yes I can imagine my DD able to do calculus and still flubbing 5+5+5.  She can do DragonBox 12+ and basic pre-algebra - and still is so slow at any plain old arithmetic type of calculation past the 'math facts' (and wants to write it down to work it). It just adds a whole 'nother level of difficulty for her to add that 3rd 5 even though it would seem such a simple problem.

 

I have thought multiple times about going through a RB book with her - figuring that we would whip through it if she doesn't actually need it.  The only thing that has really stopped me is that RB is a little too amorphous to me - lots of games and not much clarity on what to do when, or when to move on.  And the order as you have said is very unclear - I would be very interested if you could write up what you understand after communicating with her.   And the other thing I have been thinking about doing is trying out a soroban abacus to see how that goes.

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Yes, I agree with this - like currently the most popular dyslexia theory is a phonemic issue - yet although DD so clearly has phonemic issues that does not encompass the whole of her issues. And it is so hard to separate the two - the slow math facts can appear to be a number sense issue just as the slow phonemes can appear to be a phonemic issue. For example, even though DD has no trouble with dot patterns - she still does not 'bridge' without my telling her to do so and oh so very slowly going through it in her head - so very alike when I would have her do phonemic replacements/deletions. And yes I can imagine my DD able to do calculus and still flubbing 5+5+5. She can do DragonBox 12+ and basic pre-algebra - and still is so slow at any plain old arithmetic type of calculation past the 'math facts' (and wants to write it down to work it). It just adds a whole 'nother level of difficulty for her to add that 3rd 5 even though it would seem such a simple problem.

 

I have thought multiple times about going through a RB book with her - figuring that we would whip through it if she doesn't actually need it. The only thing that has really stopped me is that RB is a little too amorphous to me - lots of games and not much clarity on what to do when, or when to move on. And the order as you have said is very unclear - I would be very interested if you could write up what you understand after communicating with her. And the other thing I have been thinking about doing is trying out a soroban abacus to see how that goes.

There are conflicting theories about dyscalculia having sub-types. It is entirely possible to have issues with arithmetic and fully comprehend advanced mathematics. The problem is, so many students never reach advanced math because the student despises math and thinks they are no good or their teachers are very short sighted. A friend of mine lives next door to a physicist with dyscalculia. It can happen.

 

I can't really see the point in going through an RB book. I almost think something like Dynamo Math would be more fruitful. Maybe someone who has used Dynamo could relate their experiences. I used RB surgically with my DS, picking out activities to specifically reinforce problem areas. The last half of Overcoming Difficulties with Number has been priceless to DS when it comes to promoting algebraic thinking. Foerster's Algebra chapter 3 or 4 (too lazy to get up and look) has been great as well because it teaches proofs. That is where DS saw all the math from grade 5 and upwards coalesce. I am speaking from the perspective of a STEM major.

 

DS actually enjoys algebra. His problems are rooted in his handwriting and processing speed. For problem solving, the only thing that seems to help has been me sitting with DS every day and talking through problems and using a white board. DS also could not get by without MUS blocks (only because they are hollow on one side and that is great for identifying neg integers) and Algebra Lab blocks. James Tanton's arithmetic book from his Thinking Mathematics series has been great too. For factoring and multiplying polynomials, Tanton teaches the area model (same as RB) and the galley method.

 

Earlier today, there was some discussion about c-rods. We never knew, saw, heard, or touched them until RB used them to demonstrate multiplication. DS learned his multiplication tables in about 6 weeks after I followed RB's recs. I am fairly certain RB and c-rods forced me to finally recognize that I could home educate.

 

Geoff has recommended Soroban in the past and speaks very eloquently as to why. Like dominoes or other manipulatives, the Soroban is the tool to teach counting and numbers sense. The individual bars of the Soroban abacus literally represent place value, and there is nothing abstract about that. The trick with the Soroban is that once 10 is mastered, the bead moves for basic arithmetic are then mastered. I see teaching bead moves as a potential sore spot for getting a student stuck in the abacus weeds. I am assuming repeated practice is supposed to overcome any issues because the process of bead moves for each math function does not change.

 

My real time experience with Soroban is limited to my DD, and she blew through all the basics. It seemed pointless to use an abacus to calculate 7+8 when DD could just tell me.

 

From what I can tell by reading, Soroban is taught incrementally and in baby steps. Pre-k type Soroban instruction doesn't seem to push counting beyond adding 1s and 2s and setting the thing. One of my Soroban activity books literally shows dice, the number represented on the abacus, and the typeface number. I don't know why I am bothering to explain this other than to say, if someone wanted to use Soroban for their struggling learner, I expect you would have to go back to ground zero and teach from the absolute beginning with counting and move up. For the WTM abacus thread that was linked previously, pre-k students with no prior formalized math instruction were being taught with the abacus. Instruction manuals for Soroban are now being released and sold which make teaching so much easier than the freebie, toothache inducing ones found online.

 

I am not trying to persuade anyone to change their math teaching habits. When I first started thinking about Soroban, I was very confused about it. I understand a little better and only wish there was a program with a full scope and sequence that included Soroban. Blessings all, h

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Yes, I agree with this - like currently the most popular dyslexia  theory is a phonemic issue - yet although DD so clearly has phonemic issues that does not encompass the whole of her issues.    And it is so hard to separate the two - the slow math facts can appear to be a number sense issue just as the slow phonemes can appear to be a phonemic issue.  For example, even though DD has no trouble with dot patterns - she still does not 'bridge'  without my telling her to do so and oh so very slowly going through it in her head - so very alike when I would have her do phonemic replacements/deletions.   And yes I can imagine my DD able to do calculus and still flubbing 5+5+5.  She can do DragonBox 12+ and basic pre-algebra - and still is so slow at any plain old arithmetic type of calculation past the 'math facts' (and wants to write it down to work it). It just adds a whole 'nother level of difficulty for her to add that 3rd 5 even though it would seem such a simple problem.

 

I have thought multiple times about going through a RB book with her - figuring that we would whip through it if she doesn't actually need it.  The only thing that has really stopped me is that RB is a little too amorphous to me - lots of games and not much clarity on what to do when, or when to move on.  And the order as you have said is very unclear - I would be very interested if you could write up what you understand after communicating with her.   And the other thing I have been thinking about doing is trying out a soroban abacus to see how that goes.

Maybe just start with one of the ebooks?  I find them quite clear and easy to work with.  The $50 printed books sort of have that look of wow, how would I know what to do, but with the ebooks I feel very comfortable.  They're very tight in the sense of explaining the concept you're trying to see, giving you a game to see if they can work on it and learn it, and you just rinse and repeat till it sticks, then move on to the next page/lesson.  Tight, straightforward, no guessing.

 

So yes, RB in our correspondence said to go dots, c-rods, multiplication (at which point you've worked through the jist of Toolkit) and then go into Overcoming.  

 

If she has the disability, are you sure it's worth it to go back?  Maybe it's time to give her the calculator and go forward?  

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http://www.moebiusnoodles.com/2014/07/abacus-finger-math/

 

ETA:  QWIRKLE is a big hit with my youngest.

Interesting!  And you're right, I haven't tried QWIRKLE on him yet.  I showed him the soroban finger counting tonight and he LOVED it.  We used it to add together 14 and 24 to get the days till Christmas for a paper chain.  It went so well, I think I might get out some Singapore CWP books I have and see if he could do those using the soroban finger counting.  This could totally work.

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Heather, this workbook series http://www.amazon.com/gp/product/1941589014/ref=ox_sc_act_title_1?ie=UTF8&psc=1&smid=ATVPDKIKX0DER  seems similar to what the person in that other thread described that they were doing in their soroban class with a tutor.  It does indeed have daily drill and it seems predicated on some pre instruction.  I think the real issue is that a student who is not struggling with number sense and the basics is probably going to FLY with the soroban and get very advanced very quickly.  RightStart has them doing 4 digit addition in 1st grade, basing it on the theory that if you really GET it, the number of digits doesn't matter.  

 

So geodob says to make friends with the soroban?  Cool.  Now that I see how well the finger counting can click, I could actually see ds doing the soroban.  I'm just going to take my time and let it come together.

 

And your comment about them hating math is interesting.  It explains why some people take these kids and do all kinds of OTHER math.  (probability, geometry, etc.)

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With the example of soroban finger counting above:

http://www.moebiusnoodles.com/2014/07/abacus-finger-math/

 

I have two important changes to this?

Firstly, the little finger is used for 1, rather than the index finger.

 

The main reason for this, is that MRI studies, gave shown that when we think of 1 ?

That in our motor cortex, neurons for the little finger on our left hand, light up.

With each finger in turn, for 1 to 4.

So this is why it is important to start by extending the little finger on the left hand.

 

Then the next most important thing?

Is that in the above link, you'll see that the 'fingers are spread apart' as they are extended.

 

A critical difference I made, is that when a finger is extended?

That it is pressed up against the finger next to it !

 

The crucial difference with this, is that when the fingers are pressed together?

They are felt and sensed as a Group !

Where I would ask you to simply try it, and compare the difference between having the first two fingers extended.

Where they are spread apart, and then touching each other ?

 

(But importantly, keep your Thumb inside against your Palm)

 

When spread, the fingers remain as 1 and 2.

But when touching, the idea of 1 disappears.  As they are just felt as a group of 2.

 

Perhaps you could also try extending all fingers on your left hand, pressed against each other?

 

Then spread them apart at the middle. So that the group of 4, has now been Divided, into equal groups of 2.

 

 

Returning them to a group of 4.

Then try 'taking away' a finger on one side ?

Where depending on which outside finger is 'taken away'?

It will form either 1 and 3, or 3 and 1.

 

Further, you try extending all fingers on both hands?

Then spread both groups of 4 on each hand, down the middle?

 

So that we have 4 groups of 2 fingers.

Where these can be used to 'feel' multiplication?

Playing with them, and retracting and extending the groups in order?

2,4,6,8.

8,6,4,2.

 

Though I would note, that the focus with this approach?

Is with developing a way to Concieve of numbers and and how to do different operations with them.

Where after practicing it for a while?

The fingers no longer need to be moved/ used?

As it develops a 'Motor Memory' of finger positions for each number.

Where calculations can then be done, by 'imagining' the movement of finger/ thumbs.

 

So that their is a real 'Sense of Number'.

Where numbers are felt.

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Though in regard to buying a Soroban Abacus?

The one that I would recommend, is a simple 3 row one, that is called the Pacchi.

Which can be used to count up to 999.

 

I'll add a link, where you'll see the Pacchi in the top left corner of the page.

Where it can be bought for $21 , which also covers postage from Japan.

http://www.soroban.com/english/shopping/

 

Though my whole focus, is rather with developing a way to concieve of numbers and math.

Where Number Sense, is making sense of numbers.

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Geodob, you're losing me on the multiplication with fingers.  If we do that, then we broke all the rules for assigned hand and finger values, right?  And how would you go higher?  (3s?)  

 

I'll go look for the Pacchi.  It seems like a good idea to go simple at first.

 

He enjoyed the finger soroban so much, I'm looking forward to trying it on him again.  Thank you for sharing this with us.  It's funny because it's something you had explained a year ago. Guess we just weren't ready for it then.

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Maybe just start with one of the ebooks?  I find them quite clear and easy to work with.  The $50 printed books sort of have that look of wow, how would I know what to do, but with the ebooks I feel very comfortable.  They're very tight in the sense of explaining the concept you're trying to see, giving you a game to see if they can work on it and learn it, and you just rinse and repeat till it sticks, then move on to the next page/lesson.  Tight, straightforward, no guessing.

 

So yes, RB in our correspondence said to go dots, c-rods, multiplication (at which point you've worked through the jist of Toolkit) and then go into Overcoming.  

 

If she has the disability, are you sure it's worth it to go back?  Maybe it's time to give her the calculator and go forward?  

 

Thanks OhElizabeth!  

 

FWIW, I don't actually believe DD is dyscalculic - and definitely not at a 'give the calculator' level because she can do it on paper and pencil.  Especially since she finally has her math facts at a reasonable speed.    What she can't do is any of the mental math type processing.  Bridging in particular stands out to me.  She understands the idea, she can do it if I explicitly ask for it albeit ever so slowly and.... she does not apply it in real life. 

 

I think she needs the same incremental/repeated practice at bridging and other such mental math techniques as she did for phonics.   And right now to address this I am doing what is essentially equivalent to what I originally did for phonics  - a little of this, a little of that - when what I really need is the math equivalent to "LIPS".  

 

I am going go to look at RB c-rods book - I believe someone said earlier in this thread that c-rods are excellent for working on bridging. 

 

Complete aside: you know it's interesting how writing something out here brings out facts that I have just glossed over when thinking about them- like DD is still struggling with 'tracking' when reading (loses places, skips lines- VT type tracking exercises have been no help) BUT she doesn't have that same issue with columnar math calculations.  So maybe it's not tracking at all?  Yet another thing to mull over :unsure:

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Complete aside: you know it's interesting how writing something out here brings out facts that I have just glossed over when thinking about them- like DD is still struggling with 'tracking' when reading (loses places, skips lines- VT type tracking exercises have been no help) BUT she doesn't have that same issue with columnar math calculations.  So maybe it's not tracking at all?  Yet another thing to mull over :unsure:

Hmm, have you had her eyes checked by a dev. optom. to actually see what's going on?  Just because she's having issues with tracking, that doesn't mean it's the only problem or the root problem.  The issues with tracking can actually be caused by convergence, where the brain switches eyes because the images don't resolve.  They lose their spot when the eyes switch, making it *look* like a tracking problem.  

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Hmm, have you had her eyes checked by a dev. optom. to actually see what's going on?  Just because she's having issues with tracking, that doesn't mean it's the only problem or the root problem.  The issues with tracking can actually be caused by convergence, where the brain switches eyes because the images don't resolve.  They lose their spot when the eyes switch, making it *look* like a tracking problem.  

Yeah, we've done VT twice.   VT sped up her reading both times but did not affect the skipping/losing place in any way.    The 2nd time the VT people told me that she just needed to do more of their tracking sheets - completely discounting me when I told them she had done 100's of those during and after the first VT ( "You must not have done them correctly"  :001_rolleyes: - it's not like the things are rocket science)  The high noon site has tracking books exactly like what our VT office used.  

 

Hmm, I wonder if it's a midline issue - I seem to remember someone on this board talking about that.  Off to research...  (and sorry for the thread derail)

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Dunno.  Ds tracks fine for what the VT doc is looking for but skips at the midline, just the midline, per the OT.  She likes S'cool Moves/Focus Moves and BalavisX, so that's what we're doing.  The midline issues can affect vision and also language.  And of course with what geodob is saying they affect number sense.  Wild.  That's why I'm spending a lot of time on it right now, including it in our day each day, because I figure it's better to improve the brain and then let the academics come, rather than struggling for academics with what is a brain issue.  And since the midline stuff in Focus Moves is crazy hard for him, I feel like we're at least on-track.  Well crazy hard isn't accurate.  Challenging.  Sometimes it's hard to sort out what is impulsivity and what is midline, but the activities are definitely challenging.

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Dunno.  Ds tracks fine for what the VT doc is looking for but skips at the midline, just the midline, per the OT.  She likes S'cool Moves/Focus Moves and BalavisX, so that's what we're doing.  The midline issues can affect vision and also language.  And of course with what geodob is saying they affect number sense.  Wild.  That's why I'm spending a lot of time on it right now, including it in our day each day, because I figure it's better to improve the brain and then let the academics come, rather than struggling for academics with what is a brain issue.  And since the midline stuff in Focus Moves is crazy hard for him, I feel like we're at least on-track.

Is the Focus Moves just posters?  Their amazon blurb is a little confusing to me.   Did you buy the S'cool Moves book too?

 

(didn't realize that you were talking about midline & tracking recently LOL! must be why it popped into my head)

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My son's tracking was a midline issue.  But -- I think it was obvious -- I think they would have told you at VT that it was a midline issue.  I took my son for a COVD eval and he told me the same thing, and two OTs saw it.  They all said he had a "jump" or a "skip" when he came to the middle of a page.  He also (for a while) would skip a line where a new paragraph started and it was indented.  He would just skip down to the next line that was not indented. 

 

The two OTs were both seeing this just by watching his eyes while he read.  The COVD saw it when he had some goggles attached to his face (and had seen it elsewhere too, I guess).  He said that he didn't think he would even be able to read with the goggles, he was surprised when he did read the passage and answer the comprehension questions.  This was with my son doing speech therapy and 2ish years of solid reading before going to the COVD.  When he was younger, I was told he had minor CI and then that he no longer had CI (convergence insufficiency).  At the first eye exam where it was brought up, I was told he could grow out of it or just develop the skill as he did more reading-type activities. 

 

But, it was the OT midline activities that helped his tracking.  He did straight-up tracking, too, where it was following things with his eyes.  But he was doing the usual midline stuff, too, with the physical activities that did not have anything in particular to do with his eyes. 

 

With the private OT she quietly told me to stand and watch my son's eyes while he read, she was surprised I couldn't see what she was talking about.  But I could never see it.  It seemed like some weird hippie stuff to be honest.  The first person to tell me about it was the school OT (that my son liked) who dresses in a hippie way and smells like incense.  Lots of long necklaces and jewelry.  I was skeptical about it, but then 2 other people told me they saw the same thing.

 

But overall -- it seems like they would have told you they were seeing this, if they were seeing this.   Although -- I definitely went into the private OT and said "here is the crazy thing they told me at school" and I went to the COVD asking about it, too. 

 

Edit:  Part of me wonders if they would see it at a VT screening, for a child who is not reading?  B/c it is observed during reading.  I had an impression that the COVD was already seeing it before the goggles part, but I guess I am not sure.  I think my son had some ways of compensating, too, that he could do for some things. 

 

Edit 2:  There used to be another poster (I want to say Shellers, but it could be another name) whose son was very similar with the midline thing, too, and who also had dyslexia and was using Barton.  At the time it sounded like she was being told very similar things and her son was doing OT and also had handwriting challenges (my son has handwriting challenges).  So there have been a few people at least who have been hearing about the midline/tracking thing, but then other people's kids do not have the same issues even when it is tracking. 

 

 

Edited by Lecka
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Is the Focus Moves just posters?  Their amazon blurb is a little confusing to me.   Did you buy the S'cool Moves book too?

 

(didn't realize that you were talking about midline & tracking recently LOL! must be why it popped into my head)

You know me, totally hack, lol.  I bought Focus Moves but not the S'cool Moves book.  So yes, $10 for the Focus Moves ebook.  It said in the description it includes the posters for you to use, so I figured they'd be like pdfs you could print and actually use, right?  Nope, they sell the posters as a separate set for $50 printed and then include these small, non-clickable jpegs in the ebook.  So, since they mean for you to use them and say you can and I can't figure out how in the jolly world to make the practice in an ipad when the point is to SEE them and track and USE them, I made the file big on my screen, did screen shots, and pulled them into a Pages/Word file and printed them.  They're fuzzy but more than adequate for our purposes.  And with the pages printed in page protectors, it's easy to keep them all in a notebook and move just the ones we're working on to the front.  That to me is practical.  Pages in the Kindle app are too slow.  I have no clue what they were thinking.  If they ever read this, I wish they'd get it sorted out and make it easier for people.  

 

The OT has the $50 posters set and they're nice.  For a homeschooler, the 8 1/2X11 pages in page protectors make a lot more sense, kwim?  Well that's not true.  She pins her posters on an easel and runs tape on the floor for the midline.  It's a really nice set-up.  If you have $50 lying around, knock yourself out.  I'm just saying how I'm doing it at my pricepoint.

 

What I've been doing, and not saying I'm as good as an OT here, is picking 4-5 pages and doing them every day with him for a week.  By the end of the week some are ready to drop off.  The ebook has challenging variations for many of the posters and I usually add some myself.  Like I'll take the poster through a 2nd week having him do the same task with the addition of a metronome.  LOVE multi-tasking like that!  

 

Btw, on the S'cool Moves site they show a dots and 8s kit that you can make yourself in 10 minutes on a mac.  I assume you can on windows as well.  It's just colored circles in random patterns...  I made 4 variations and printed them and put in page protectors.  They're part of our morning warm-up now.  They work on rapid naming and I've been having him read the 2nd sheet a 2nd time with the metronome.  That gets him read 2 pages a total of three times.  The next week we rotate to the other two pages I made so he doesn't memorize them.  He's visibly getting faster.  The Focus Moves book includes some rapid naming posters, but they're REALLY hard, wow.  I'd encourage you to take the 10 minutes or whatever and make some dot pages.  We've been doing them a few weeks now (2 or 3, my mind is getting blurry) and I still don't think he's ready for the RAN pages in Focus Moves.  They're THAT hard.  Oh, I guess that's skewed by his apraxia.  The posters in Focus have you reading shapes and letters and things, and I just feel like sticking with colors is better for him for now.  You'll see things like beginning well and not being able to hold it together to the end.  

 

There's a poster Focus Moves that has basic hand motions that we add the metronome in on as he's gotten better.  He's so impulsive that I use it to target EF, yes, but also just to slow him down and get him to focus.  Sometimes moving really rapidly is masking a lack of control.  

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All of the figure 8 stuff also is working on crossing the midline.  

 

I went to an OT seminar thing about a month ago, and there are a lot of options. 

 

Honestly this is stuff that I was not involved in, I let my son just go to OT and go to school OT.   I was more concerned with him practicing the handwriting that he was also doing in OT, I was not into the midline stuff.... then once I saw how it helped him, the lightbulb went off then.  But just for additional things -- my son was having trouble swimming, he had trouble dribbling a ball, he didn't know how to skip, etc -- lots of just general coordination things. I didn't even realize until I saw how much he improved with these kinds of things.  It was the biggest gain of OT. 

 

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Lecka, I'm like you.  The OT had him flat on his back, was having him track something (pen, whatever), and says CAN YOU SEE IT?  And I'm like NO, I can't see it...  So whatever.  That's what I pay them for, lol.  And the VT doc screens but it's not like this in-depth thing, just a screening.  And there are tolerances developmentally.  She's not trying to elicit every single nuance in a screening, just to make sure he's within reasonable tolerances developmentally.  If they're within those tolerances and have no complaints, there's no issue from their perspective.  There's more to it, but that's the jist.  

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All of the figure 8 stuff also is working on crossing the midline.  

 

I went to an OT seminar thing about a month ago, and there are a lot of options. 

 

Honestly this is stuff that I was not involved in, I let my son just go to OT and go to school OT.   I was more concerned with him practicing the handwriting that he was also doing in OT, I was not into the midline stuff.... then once I saw how it helped him, the lightbulb went off then.  But just for additional things -- my son was having trouble swimming, he had trouble dribbling a ball, he didn't know how to skip, etc -- lots of just general coordination things. I didn't even realize until I saw how much he improved with these kinds of things.  It was the biggest gain of OT. 

Yup.  Ds is looking more coordinated in gymnastics.  It's fascinating to watch.

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Some thoughts on living math books: 

 

Penrose the Mathematical Cat (maybe?) 

Math Start books by Stuart Murphy

Is he too young for The Phantom Tollbooth?

You might look at the I Hate Mathematics book (I hate the title, but it is really excellent) and pick out some activities

Sir Cumference books

Full House by Dayle Dodds

A Very Improbable Story

If You Were a Quadrilateral/ Polygon/ Fraction (Math Fun series, I think?)

Once Upon a Dime

Kathleen Stone's books

The Mission of Addition/ The Action of Subraction/ How Long or How Wide?/ A Fraction's Goal

12 Ways to Get to 11

Measuring Penny

Me and the Measure of Things

How Big is a Foot?

What Time Is It, Mr. Crocodile?

When a Line Bends, a Shape Begins

How Much Is a Million/ If You Made a Million/ Millions to Measure

Math Curse/ Grapes of Math/ Math for All Seasons

One Grain of Rice

Anno's Math Games/ Multiplying Jar/ etc

What's Your Angle, Pythagroas?

Toads and Tessellations

Hershey's Kisses Addition Book

Math Appeal

Math Potatoes

Math Fables

My Half Day

Whole-y Cow

My Even Day

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OhE, with Dyscalculia, their is often a difficulty with concieving of the idea of ' multiplication', and the idea of the division of a quantity?

 

Where the example that I gave, is about developing a way of concieving of multiplication and division.

Which is distinct from 'learning' multiplication and division.

So that Dyscalculics might learn 'two plus two is four', and 'two times two is four'.

But they have no concept of what this actually means?

 

Where my real concern, is with developing a way to 'concieve of math', as a foundation.

So that learning math, can then be made sense of.

 

Though I really need you to try doing it, to understand it?

 

So that with your left hand, and the back of it facing toward you.

With your thumb under your palm.

Extend your 4 fingers as a group, all pressed against each other.

Importantly, they can felt as a 'group of 4'.

As opposed to: 1,2,3,4 fingers.

 

Then with the fingers pressed against each other?

Spread them apart in the middle.

To form 2 groups of 2 fingers.

 

Which can be felt as Division of 4.

That is equal on both sides.

 

But then, if you extend 'both hands', to form a group of 4 fingers on each side.

We can feel them as a combined group of 8.

Where we can 'take away' one hand, leaving 4.

Then 'add' the hand again, to form 8.

 

But then with both hands extended, with their groups of 4.

Next, spread both hand groups down the middle.

Forming 4 groups of 2.

Where these 4 groups of 2, can be used to develop a 'feel' and sense of multiplication.

As multiples of 4.

 

But essentially, the focus is with developing a way concieve of numbers.

Then to concieve of the ideas of adding, taking away, dividing and multiplying.

As well equivalence, and the groups on both sides being equal.

 

Though if you explored doing this with your hands/ fingers?

Then you might appreciate how this provides a way to make sense of math?

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Geodob, outside of using the finger method that your are describing to develop the feeling of numbers and assuming that objective is achieved...where do you go from there?  What is the best method to apply that new sense of feeling the numbers?  Does she go to dots or transfer to c-rods?  What would be the next step? 

Well I can answer that one at least in part.  We're going to go fingers directly into use.  And then fingers BACK to c-rods.  I was looking at some online books last night that use soroban and unit blocks interchangeably, since conceptually there's little difference.  But for practical purposes, my theory right now is to get him USING his finger soroban.  So today we ripped off another piece of his paper chain but we counted to 37 first on our finger soroban, removed one, discussed how that's what the paper chain quantity will be when we rip one off, then he ripped one off.  So I want to give the quantities meaning.  And I'm squeezing his fingers (5 thumb and 3 and the 2 tens as we say 3-ten 8, etc.).  It seems good to me and real.  Since he likes to solve problems, I'm interested to start him on SM CWP.  I *think* I have the CWP 1 books lying around.  I think he just needs to USE the fingers and let them be real and let him establish quantity as connected to something real.

 

I'm also trying to start talking with him about the hours and noticing the hours when we do things.  I think that has eluded him entirely.  Frankly, if you knew how I live it wouldn't be shocking, lol.  In college I only looked at the minute hand on the clock.  Everything was relative by minutes.  Just sorta weird I guess, lol.

 

So I think bringing in the crods will be useful later to work from fingers to paper maybe.  Right now though I'm just wanting to keep it real a while and let him own it.  Once he owns it, then we'll connect or extend it to other things.  Or as RB says, the written is merely notation for what they already understand.  We can do an awful lot with fingers.  And when it occurs to him he has run out of fingers, then soroban abacus.  And when it occurs to him it would be useful to write, then write.  

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Your plan sounds good, and you may never require a Soroban abacus because Soroban is premised around complements to 5s and 10s and how to apply a carry.  Abacus is really all about the bead moves associated with the device and reading the answer.  Here is an example of what I mean...

 

With Soroban, suppose you are adding 4+1...Set the Soroban to 4.  There are no more beads to add, just one heavenly bead, SO you have to figure out how to manipulate the 5 bead (heavenly bead) to add +1.  With Soroban, you have to add the 5 bead and take away 4 earthly beads to derive the answer.

Adding 4+1 is the equivalent of adding 4+ (5-4)...Lower the heavenly bead to the bar and remove the 4 earthly beads.  You are left with the abacus set to the answer 5.  

 

Singapore on the other hand has a +1 strategy.  There is no thinking about removing complements or pushing beads around.  Count on by 1 and be done with the answer.  If you are not interested in all the complements business, I would not bother with an actual Soroban.  Just use the finger methods to display numbers up to 99 with traditional Singapore counting.  It sounds like you are already doing that so keep it up.

 
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Yes, with fingers and soroban you have to do a trade to go from 4 to 5 *and* a trade at 10.  With slavonic you're only trading at 10.  He doesn't seem confused by that and it's sort of an interesting physical way of making them attend to those relationships in things that make 10 and 5.  With slavonic it's still there but the 5's get relegated to visual.  I never felt like dd bought into the slavonic/RS abacus and visualized with it and used it.  Of course her developmental vision was off so she wasn't.  It's more just a practical question of whether it's worth the effort to do the trades at 5 and 10 or just 10.  Advantage of the soroban would of course be the kinesthetics of it.  Should be easier to visualize too, I would think.  I mean, it's just a memory thing.  

 

What I noticed in the soroban thread and the soroban books on amazon was the common denominator that you had to be willing to drill it to automaticity.  If you're not willing to do that, the slavonic is going to make a LOT more sense as it will be immediately readable and representative.  Functionally, the methods are going to be almost identical for what you can do and represent.  

 

The only reason it intrigues me so much is because he's such a kinesthetic/tactile learner. I like the idea of having quantities go right from his fingers to his brain.  I might as well do this.  I've done weirder things, lol.  I mean Dvorak for typing?   :lol: 

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Their is a critical difference between the Soroban as a 5 base system, and other Abacus that use a 10 base?

 

Which is basically because the human brain uses a 5 Base system.

Which is also what Number Sense is..

Using spatial thinking, the brain can automatically recognize and form groups of 2, 3 and 4 random objects.

But 4 objects is the limit. 

5 objects require adding 1 to 4, or 3 to 2.

 

So that while our number system carries at 10.

Our brain actually carries 5. 

Where we can instantly recognize the 4 beads on a Soroban as a group.

But we can't do this with 10 bead abacus.

 

While the finger soroban can be used for up to 99.

Which establishes the foundation.

The 3 row Pacchi Soroban I noted above.

Extends this up to 999.

Which maps onto thousands, millions, billions.

 

Though using the Pacchi, also develops a visual memory of the 'number patterns'.

 

But this doesn't just develop a 'feel for number's?

Rather it develops a way 'concieve of numbers'.

Where their is no need to then use dots or C-rods, as numbers and how manipulate them ?

Is already able to be concieved of.

The 'times tables' can be explored as patterns created of the Pacchi.

 

To start with, the numbers to be formed and calculated, can be given verbally.

Once proficiency has developed?

Then a change to presenting the numbers to be formed and calculated, can be given visually as written numbers.

After forming the answer on the Pacchi.

It can then be written down on paper.

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Yes, with fingers and soroban you have to do a trade to go from 4 to 5 *and* a trade at 10.  With slavonic you're only trading at 10.  He doesn't seem confused by that and it's sort of an interesting physical way of making them attend to those relationships in things that make 10 and 5.  With slavonic it's still there but the 5's get relegated to visual.  I never felt like dd bought into the slavonic/RS abacus and visualized with it and used it.  Of course her developmental vision was off so she wasn't.  It's more just a practical question of whether it's worth the effort to do the trades at 5 and 10 or just 10.  Advantage of the soroban would of course be the kinesthetics of it.  Should be easier to visualize too, I would think.  I mean, it's just a memory thing.  

 

What I noticed in the soroban thread and the soroban books on amazon was the common denominator that you had to be willing to drill it to automaticity.  If you're not willing to do that, the slavonic is going to make a LOT more sense as it will be immediately readable and representative.  Functionally, the methods are going to be almost identical for what you can do and represent.  

 

The only reason it intrigues me so much is because he's such a kinesthetic/tactile learner. I like the idea of having quantities go right from his fingers to his brain.  I might as well do this.  I've done weirder things, lol.  I mean Dvorak for typing?   :lol: 

I am a huge fan of Soroban over Slavonic for arithmetic.  If you drill enough with the Soroban to get the moves down for basic addition and subtraction, I assumed the student would then move back to the more usual style of math and incorporate the mental strategies of the abacus (like a student using a calculator or fact sheet) where applicable.  

 

RB teaches multiplication using a visual model with the distributive property, and it is so worth the effort of learning.  The payoff has been huge for DS, who learned how to factor a quadratic equation in under 10 minutes.

 

I've always thought you could manage this, and that is why I suggested it upthread.  :D

 

OhE, you know I contacted RB too, but I will mention this to anyone reading the thread.  I contacted RB directly and asked her to recommend a math curriculum for DS.  RB had no rec because she tutors students where they are, using her own methods.  I'm assuming math remediation is only to get the student up to speed so that they can re-enter typical coursework.  Unfortunately, most of us are going to be modifying just about every math curriculum that we touch.

 

Thank-you Geoff for clarifyng the method for teaching a child to conceive numbers with their fingers together and counting a 1 by starting at the pinkie.  Details matter.  He went back further than RB.  Who'd have thought that possible?  I have been walking around with Spock hands.

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Oh Heather, you're hilarious, lol.  But, I don't mean to be tacky, but if you're such a fan of the soroban, why didn't you stick with it for your dd?  It wasn't necessary or was tedious for her?  Didn't work because of fine motor issues?  Was overly problematic to actually make happen?  

 

See that's what I've been thinking through.  It's great to have theories, but getting things DONE is more important than theories, lol.  My opinion is spaghetti on the wall, so splat it all and see what sticks.  

 

Geodob's explanation of soroban over slavonic fits with what I saw with dd, that the RS abacus never really DID the magic it should have, at least not for her.  But the soroban is so unusual for us, not part of our culture, so I'm very concerned about my ability to implement it well.  Methinks I need to find some Saturday school for it.   :D  But you know, sometimes the magic is the dc, not us.  So maybe if I just start with it and things click we'll be cool?  

 

This is not what you asked, but I'll tell you that what I'm hearing backchannel from someone who effectively dealt with fully diagnosed, triple confirmed dyslexia, was a mix of math experiences in lots of situations (science projects, living books acted out, exploring live with math, etc.) and a mix of other aspects of math besides computation (patterns, HOE, geometry, probability, etc. etc.)  It wasn't really about a curriculum at all, because curriculum focuses on computation.  Her point is the dc could be wicked smart at OTHER types of math and have the reality be that with their disability computation is NEVER going to be a strong point.  So literally in that scenario when you make math only about computation you're working ONLY to their disability and never to their gift.  So I think there has to be some balance.  I do agree it's screwed up to say the only parts of math that matter are computation and that patterns, algebraic thinking, NOTHING else matters till they're 12 and the system says they may begin to explore other types.

 

So what I've decided to do is plow forward with bits of HOE, bits of *other* types of math (geometry, algebraic thinking, patterns, etc.) and let the computation grow as well.  Multi-pronged, multi-splat.  That's my theory.  But I could be all wrong, lol.  I figure even if I'm wrong, I'm at least not wrong for him.  He's learning every day and making connections and they're real and good.

 

We have to get a bit further with the concept of 10s to be ready to do the first soroban workbook from amazon.  Actually, just the finger counting may have prepared him enough.  I've had this sort of trepidation, lol.  It's only a small amount of money, but it's the kind of thing you either do or don't do.  I don't see much value to piddling with it.  

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Heather, look at this!  http://www.mathabacususa.com/mental-math-using-abacus.html  This tutoring place says they keep the kids on fingers for calculations through 99 and through K5.  Then when they're competent through 99 on their fingers doing computation, doing evens/odds, word problems, etc., THEN they switch them over to the beaded version.  Cool, that means my gut (that that could work) was RIGHT!  :D

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OhE, I blame Geodob for my interest in Soroban.  I was looking for an alternative to help DS and possibly help DD if she had maths disability.  Dyscalculia irritates me due to the lack of info to help our kids.  Anyhoo..

 

My DD simply doesn't need a Soroban.  The girl can add and subtract sideways.  She mentally bridges.  I can find no compelling reason at this moment to continue with Soroban.  Also, I prefer a math program with a spelled out scope and sequence.

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I wish this brain stuff could be turned into a curric to use with dd! We've started using MindUP, which is an emotional intelligence curric based on neurology and dd is now using amygdala and hippocampus in regular conversation. She would like the idea of doing hard maths to make the neurons in her (such and such area of her brain) tougher.

 

Anyway. Maybe once she's graduated I'll know enough to write it myself.

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I'm teaching two older boys (10.5 and 13) who don't have any basic number sense at all. I'm so interested in this conversation! They have trouble separating wholes into parts (realizing that 5 is the same as 1 and 4, etc), consistently counting, and more. When you put five blocks and three blocks next to each other, they start counting from the beginning rather than beginning with 5 and "counting up." I'm using Ronit Bird with them and so far they are doing well with dot patterns and Cuisenaire rods.

 

Have any of you used a Rekenrek? It looks a little like an abacus, but it's much simpler: https://www.enasco.com/product/TB22807J It helps students understand that numbers are wholes, but can also be broken into parts. It also helps them add or subtract without counting by ones. So for adding 5 + 3, since you slide the entire chunk of red beads to the left, it's instantly "5" without counting, and then adding 3 is easier. I'll let you know how it goes once I try it out.

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I'm teaching two older boys (10.5 and 13) who don't have any basic number sense at all. I'm so interested in this conversation! They have trouble separating wholes into parts (realizing that 5 is the same as 1 and 4, etc), consistently counting, and more. When you put five blocks and three blocks next to each other, they start counting from the beginning rather than beginning with 5 and "counting up." I'm using Ronit Bird with them and so far they are doing well with dot patterns and Cuisenaire rods.

 

Have any of you used a Rekenrek? It looks a little like an abacus, but it's much simpler: https://www.enasco.com/product/TB22807J It helps students understand that numbers are wholes, but can also be broken into parts. It also helps them add or subtract without counting by ones. So for adding 5 + 3, since you slide the entire chunk of red beads to the left, it's instantly "5" without counting, and then adding 3 is easier. I'll let you know how it goes once I try it out.

I have not heard of that.  Interesting!

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I'm teaching two older boys (10.5 and 13) who don't have any basic number sense at all. I'm so interested in this conversation! They have trouble separating wholes into parts (realizing that 5 is the same as 1 and 4, etc), consistently counting, and more. When you put five blocks and three blocks next to each other, they start counting from the beginning rather than beginning with 5 and "counting up." I'm using Ronit Bird with them and so far they are doing well with dot patterns and Cuisenaire rods.

 

Have any of you used a Rekenrek? It looks a little like an abacus, but it's much simpler: https://www.enasco.com/product/TB22807J It helps students understand that numbers are wholes, but can also be broken into parts. It also helps them add or subtract without counting by ones. So for adding 5 + 3, since you slide the entire chunk of red beads to the left, it's instantly "5" without counting, and then adding 3 is easier. I'll let you know how it goes once I try it out.

I think you're asking for the result (addition and subtraction) before you build the foundation.  The entirety of the Dots ebook by RB is spent on subitizing.  Which of her books are you using?  In Toolkit she mingles c-rods and dots, yes, but all with the goal of working on subitizing.  All of the addition and subtraction facts come when they can subitize.  We spent MONTHS going through each digit.  Actually we're STILL not finished with the Dots book.  

 

RB introduces the abacus beads and you build your own.  Instead of skipping steps, I encourage you to start at the beginning of Toolkit, or Dots or whatever you're using and work your way through, doing every single step to complete understanding, no matter how tedious.  If you're using Overcoming, it sounds like you may need to back up and get Toolkit.  

 

Do you know you can also write RB?  You can contact her through her website and through her FB page.  She writes back and is very nice.  :)

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I think you're asking for the result (addition and subtraction) before you build the foundation.  The entirety of the Dots ebook by RB is spent on subitizing.  Which of her books are you using?  In Toolkit she mingles c-rods and dots, yes, but all with the goal of working on subitizing.  All of the addition and subtraction facts come when they can subitize.  We spent MONTHS going through each digit.  Actually we're STILL not finished with the Dots book.  

 

RB introduces the abacus beads and you build your own.  Instead of skipping steps, I encourage you to start at the beginning of Toolkit, or Dots or whatever you're using and work your way through, doing every single step to complete understanding, no matter how tedious.  If you're using Overcoming, it sounds like you may need to back up and get Toolkit.  

 

Do you know you can also write RB?  You can contact her through her website and through her FB page.  She writes back and is very nice.   :)

 

Thank you! Oh yes, we're going sloooooow. We haven't been doing anything other than subitizing, but I do feel some pressure because I'm in a school - alternative, yes, but still they wants some results! I agree that going faster than the kids can handle will just perpetuate the same problems. I think the Rekenrek will be great for when we *hopefully* get to adding and subtracting! :)

 

So far we've mostly been counting, using the c-rods to make the "stories" of the numbers 1-5, finding the "numbers inside" 1-5, matching dice to irregular dot patterns to numeral cards. I hope I'm on the right track...

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Thank you! Oh yes, we're going sloooooow. We haven't been doing anything other than subitizing, but I do feel some pressure because I'm in a school - alternative, yes, but still they wants some results! I agree that going faster than the kids can handle will just perpetuate the same problems. I think the Rekenrek will be great for when we *hopefully* get to adding and subtracting! :)

 

So far we've mostly been counting, using the c-rods to make the "stories" of the numbers 1-5, finding the "numbers inside" 1-5, matching dice to irregular dot patterns to numeral cards. I hope I'm on the right track...

How much are you working on this per day?  Ronit Bird gets to all of this.  You might consider working on it multiple short sessions a day to pick up the pace.  There's no difference between your R abacus and the beaded version you'd make in RB.  (conceptually I mean)  Which book are you using?  I think the instructions are in Toolkit and I know they're in her C-Rods ebook.  

 

Anyways, you might consider working multiple short sessions a day with breaks between to let the brain recover.  So work 15 minutes three or four times a day.  Or 20 minutes 3X/day.  Bam, bam, bam.  Kwim?  

 

A lot of therapy work benefits from *intensity*.  That doesn't mean pushing it hard but more frequency to push the brain, push the brain a bit more.  I see it creating breakthroughs with my ds with dyslexia.

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Though what this highlights to me, is the need to really understand what is different about the number 5 ?

 

Which relates to how our brain concieves of numbers?

Where basically it is able to concieve of 2 or 3 or 4 objects, as different sized groups of individual items.

Which can retain their individual identity.

 

But 4 is a critical cross over point for the brain?

Where 5 objects lose their individual identity, and can only be concieved of as group.

 

While our written number system carries a 9, to form one group of 10.

 

The brain actually carries after 4, to form one group of 5.

Where this term "Number Sense'?

Numbers are just the symbols and words.

 

Where it is really 'Group Sense'?

Groups within groups.

 

I might mention the traditional Japanese approach to learning math?

Where they avoid teaching children the names and symbols for numbers?

Until around the age of 9.

But typically, a 9 year old Japanese child, has the math skills of a 12 year old Western child,

Before they even know the names and symbols for numbers,

But what they have developed, is the ability to concieve of different size groups within groups.

To concieve of patterns within these groups.

Which they later learn, are called 'multiplication tables'.

 

Though the effect that this different approach has for children with math difficulties and Dyscalculia?

Has been difficult to define?

As no children have been reported with math difficulties and Dyscalculia?

 

Where the only difference, is with the way that math is introduced to them.

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How much are you working on this per day?  Ronit Bird gets to all of this.  You might consider working on it multiple short sessions a day to pick up the pace.  There's no difference between your R abacus and the beaded version you'd make in RB.  (conceptually I mean)  Which book are you using?  I think the instructions are in Toolkit and I know they're in her C-Rods ebook.  

 

Anyways, you might consider working multiple short sessions a day with breaks between to let the brain recover.  So work 15 minutes three or four times a day.  Or 20 minutes 3X/day.  Bam, bam, bam.  Kwim?  

 

A lot of therapy work benefits from *intensity*.  That doesn't mean pushing it hard but more frequency to push the brain, push the brain a bit more.  I see it creating breakthroughs with my ds with dyslexia.

 

I see them for a full hour every day (woo hoo!). I taught them tally marks today, and one of them REALLY loved it. We're using a combo of Ronit Bird and Math U See, sooo... we'll see how it goes!

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