Has anyone let their younger child use a calculator?

[FairProspects]

I'm at my wit's end. My dyslexic's weakest area in math is calculation. This kid is incredibly spatial and has phenomenal number sense but zero calculation ability and I mean calculates at under the level of a 5 y.o. He has been through mnemonics which have helped some, but he still cannot do 3 + 1 or any other simple addition/subtraction problem on any given day. My 5 y.o. can calculate better and faster than him.

 

Math is taking forever to do 6 problems. We were both in tears today. He has to draw out everything or use a clock as a number line, and nothing sticks after 3+ years. I let him use a multiplication chart, so what is the equivalent for addition/subtraction? Isn't it just a calculator? I'm feeling so stuck. He is starting to hate math which is his favorite subject.

 

Part of the problem is that we are now in multi-step math problems which require several levels of calculations and he wants to give up after the first step because it requires so much effort and cognitive power just to recall the fact answer. I've had it and I'm just done. Nothing will help this kid with fact recall, it just won't. Does it make me a terrible parent to let him use a calculator for simple addition/subtraction only? Is a chart of some kind a better option? What can help him get around this LD?

[Heathermomster]

For 6th grade, DS sat in a NT classroom and used a TI-15 calculator.

 

Geoff, a dyscalculia researcher that goes by eoffg on WTM, recommends using a Soroban abacus. This is the Japanese abacus, not the dual colored RS one. I picked up a plastic one from Amazon. There are texts you can use to teach Soroban use.

 

eta:

http://www.nurtureminds.com/online-store.htm

http://ecommerce.mathsecret.net/products-page/books/

Edited September 25, 2012 by Heathermomster

[anneofalamo]

We love the calculator, to check our problems....it is a great and wonderful end to math.

Together we count blocks to get the answers, and then he checks them while saying it out loud. He even uses a purple pin to circle if right and a red one if wrong.

I am all for making math fun and quick and as painless as possible for everyone! ♥

[PeterPan]

My dd has had a 15-20% difference between her conceptual and computation scores on standardized testing ever since we started testing (2nd grade?), and we couldn't get them evened up no matter how much we worked. This past year we started TT, which is not exactly a rigorous program. Most of what she was doing was review in fact. But somehow in there it clicked. She's 13, so it's probably a combination of things. Really though, working *harder* didn't get her anywhere, and she couldn't understand her way into faster facts either. And she resists mnemonics and visualization and some other things people use. TT did it for her. Easy practice in a humorous context with very short lessons. She got noticeably faster over the course of the level and when we did the testing it was a huge difference.

 

Until then, well you just have to chop lessons and keep it efficient. Does he have an addition table? It can help. How old is he? When dd his, 11 or 12, I forget, her brain utterly fell out. She started going HUH? over 3+4. It was a bad day in the neighborhood, lol. It was always an uphill battle, and then the puberty thing just drove it to where she looked like an idiot, which you KNOW she isn't if you see her scores. And there was a stage with division and stuff where we'd literally do *one problem* a day. You know I think that's part of why TT works, because it separates out the writing and lets them do it all mentally. Regular book math wants them to write everything out. Or we used to do it on a whiteboard. But TT is on the computer and validating their natural bent to do it in their heads. They get this reward (done sooner) when they go faster, and they have these little characters cheering them on.

 

When we went through the *one division problem a day* stage, we would do geometry or something easier for the rest of the math session. So if I had 20 minutes planned, we'd do that one problem and spend the rest of the time on something else.

[Rai B.]

We used a calculator a little bit, because CSMP uses them. I don’t let dd use it for everyday calculations though.

 

I think an addition chart would be the equivalent of multiplication tables. This site has instruction for introducing them (I only use the first couple examples). There are printable charts on Donna Young’s site.

[Guest]

Have you tried Timez Attack? I let my oldest try it during the summer and in a month he mastered all his math facts. He has conceptual understanding from SM and Miquon so I was not worried about that. I just wanted him to get his facts down so that it doesn't slow him down. You do not need to buy the upgrade. The free version worked just great for us!

 

http://www.bigbrainz.com/

[FairProspects]

My dd has had a 15-20% difference between her conceptual and computation scores on standardized testing ever since we started testing (2nd grade?), and we couldn't get them evened up no matter how much we worked.

 

So you do understand what I mean. :) The problem is this is a kid with an 85% differential in conceptual/computation. The calculations are REALLY slowing him down to the point of giving up because of calculating only. I can give him an addition table, but what about double and triple digit numbers? He knows HOW to re-group and all the mental math strategies but he is so dang slow to do it (and he has to draw it all out to "see" it) that it is exhausting for both him and me. The calculations at this point are getting in the way of the actual math, and I'm just not sure how to get around it except with a calculator.

[Mukmuk]

How about keeping your math goals separate, as in, treat arithmetic differently from math understanding? It sounds like your son has great high level skills but poor lower level skills.

 

If the calculator helps as a means to get over the arithmetic for understanding tougher, spatial questions, I would use it. But try to improve his arithmetic skills separately, ie, with manipulatives, an addition table, and so on. Have a separate session to do this even. He will need these skills too, but working on both at the same time may kill his love of the spatial math that he has abilities for.

[Guest]

How about keeping your math goals separate, as in, treat arithmetic differently from math understanding? It sounds like your son has great high level skills but poor lower level skills.

 

If the calculator helps as a means to get over the arithmetic for understanding tougher, spatial questions, I would use it. But try to improve his arithmetic skills separately, ie, with manipulatives, an addition table, and so on. Have a separate session to do this even. He will need these skills too, but working on both at the same time may kill his love of the spatial math that he has abilities for.

 

:iagree: This was how I approached it also. I am against calculators though so I refused to let my boy use one. That was my decision for my own child though. Timez Attack made things visual for him and since it is computer based, it worked great for us. Getting the basic facts down has now helped him work out the higher two digit and three digit in his head a lot faster also.

 

Not saying you should do what I did. Just adding another suggestion for you.

[TippyCanoe]

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[FairProspects]

How about keeping your math goals separate, as in, treat arithmetic differently from math understanding? It sounds like your son has great high level skills but poor lower level skills.

 

If the calculator helps as a means to get over the arithmetic for understanding tougher, spatial questions, I would use it. But try to improve his arithmetic skills separately, ie, with manipulatives, an addition table, and so on. Have a separate session to do this even. He will need these skills too, but working on both at the same time may kill his love of the spatial math that he has abilities for.

 

I think it is even more frustrating than that. If you try to tease out what he knows apart from the fact memorization, he doesn't need the manipulatives because he has an inherent understanding of the meaning of numbers and their composition, he just can't recall the fact. It's part of his dyslexic problem with working memory/word/language recall. The skills and understanding themselves are there, the right number for each fact is not. While we do keep working on it, no amount of drill will make it come (probably not for yrs according to the neuropsych). Even more frustrating is that he is still immature, and when he makes a mistake in calculation that he thinks he should know, he melts down and derails the whole operation for up to an hour while he re-sets.

 

That's why I'm really thinking that it makes sense to move onto something else like a calculator, similar using typing to take the physical part of writing out of the cognitive load. He is overloading cognitively not from the math itself, but from the recall of 3+1, and 7+2, and 100+11 in the same problem. That is too much recall for him and then he overloads because the number recall has been so exhausting that he can't actually focus on what he is learning - like which operations to use to actually solve the darn problem or balancing both sides of an equation.

 

I realize this is not a mainstream choice, but this is not exactly a normal situation. Has anyone at all moved to a calculator for simple calculations on difficult conceptual math (while working on facts at another time)?

[FairProspects]

The spread between dd's conceptual and computational abilities was so huge that it along with her dysgraphia were major reasons she was diagnosed with nonverbal learning disability at age eleven. Like your son, she had advanced number sense and incredible skills in pattern recognition, mused about prime numbers and squares when she was five, and could do equations to solve for things like negative x when she still couldn't accurately count coins or reliably remember what 7 plus 2 equalled.

 

Yup, this is exactly it. Ds has been playing around with solving for E=mc2, but simple addition causes a breakdown into tears. He has been asking for Zaccaro again though, so maybe we will just detour for a few days with that.

 

Right-brained and/or highly visual kids do better when they can use a calculator to do advanced math that engages them, work with their powerful strengths, and take their time to bring their computational skills in line with their conceptual abilities. For many kids like this, the coming together doesn't happen until puberty and/or mid-adolescence. This was true for my dd. She began improving around 8th grade or so, and had a stunning surge at the beginning of 10th. She is doing amazingly well finishing up algebra II, which is actually her favorite school subject right now. She asks her dad for help maybe once a month or once every six weeks or so. She's looking forward eagerly to calculus at the community college this winter. Her computational skills mesh with her number sense so that she knows when an answer is way off -- her own or the book's! She's found a couple of typos in her textbook, confirmed by the solution manual.

 

I know several kids who have developed along these lines. They cause their parents enormous amounts of concern when they're young, because their development doesn't match the way most curricula are laid out or what teachers traditionally expect of kids at certain ages.

 

This is what I've been told to expect, but seeing as it is still years out, it is hard not to worry that I'll mess him up in the meantime by making some of these choices!

 

 

Meanwhile, be sure to feed the visual strengths and show your son that spatial skills are crucial to higher level math. Does he use things like tangrams, origami, pentominoes, ThinkFun games, geoboards activities, visual puzzles, tessellations, pattern blocks, basic graphs, etc.? Does he play chess? Might he like Hands-On Equations, a kinesthetic introduction to algebraic equations that can be used by young kids?

 

All of the above to excess. Except for HOE which I have, but have not started with him. I was planning on doing it after we finish the variables chapter in BA, which for the most part he has enjoyed, but interestingly there has been a bit of a breakdown in balancing both sides of the equation, so HOE might be a more concrete way to demonstrate that to him.

 

GEMS also has several activity-based math units, one on building that dd really loved, and one on probability, for instance.

 

Don't sacrifice a love of math and numbers to a difficulty with calculation. Your son knows the methods and algorithms. Let him use a calculator without guilt!

 

Thanks Doodler! I feel better hearing from someone who has actually pursued this choice and had it work out well.:) I :001_wub: GEMS so I may have to look into those math choices as well. Even though I want to deep down, it seems so hard to make a non-linear choice in math.

[ElizaG]

If I'm understanding correctly, this could be considered a type of dyscalculia. The Eides have some practical suggestions here (not including calculators, though). They also mention David Hilbert, one of the most famous mathematicians of the 20th century, who routinely forgot simple addition facts.

 

I knew there were some famous writers with dyslexia, but it's somehow even more intriguing to think of mathematicians with dyscalculia. The mind is a funny thing. :)

[FairProspects]

If I'm understanding correctly, this could be considered a type of dyscalculia. The Eides have some practical suggestions here (not including calculators, though). They also mention David Hilbert, one of the most famous mathematicians of the 20th century, who routinely forgot simple addition facts.

 

I knew there were some famous writers with dyslexia, but it's somehow even more intriguing to think of mathematicians with dyscalculia. The mind is a funny thing. :)

 

Thanks for the thought, but we've done the full neuropsych eval and it is definitely not dyscalculia (although had we not done the eval I might have thought so too, these issues can look a lot like each other). We're just dealing with dyslexia here. I do agree that the mind is a complicated thing! :)

[TippyCanoe]

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[Guest]

I respect everyone's right to do what they feel is best for their children. As a parent myself, I cannot advocate for something I would not do with my own children. The wait and see approach has nothing to do with the kind of person I am. I have always been of the mentality that an obstacle is something to overcome and that has been the driving force in my life.

 

I also don't put my kids in packages, VSL, right brained, left brained or whatever. Each child is unique and that is how I approach my own children when I am trying to help them get past something that is slowing them down or affecting their life somehow. So far it has served me well :) but since my "limited" experience is not enough, lets take Temple Grandin as an example of a strongly visual learner. She learned how to read with phonics, had no problem learning her math facts (that I have ever seen in her books) but did have an issue with Algebra. I am a visual learner also. I was slow at learning my math facts but did higher level math from a younger age also and was the person everyone came to after a test or exam. I had no issues with Algebra. These are just two examples of course but maybe, just maybe, our kids don't really fit in these neat little packages that everyone is trying to create these days ;).

 

This is my approach with my kids. I have been observing them and what makes them tick since birth. I try to know my kids first before trying to figure out what will work for them. Have I made mistakes? Sure!!! I make changes and move on knowing that the answer will come. I pray a lot :) and then I observe some more. My kids are two unique little people and it is my job to find what will work for them. I make it my job :)!

 

To the OP, I hope you find the best solution for your child :).

Edited September 25, 2012 by Guest

[peacefully]

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[FairProspects]

I don't actually have The Mislabeled Child, I checked it out from the library at one point but returned it. It is on my wish list to buy. What is interesting to me is that remediating ds's working memory didn't come up at any of our appts, and it seems like it would have if it was a pressing issue, but maybe I'll have to go back through the report and see if I missed something. The fact that the working memory was significantly disparate was mentioned in that I should expect glitches, but as far as I know it is already above age-level, just not to where it would be if he wasn't dyslexic.

[TippyCanoe]

nm

[peacefully]

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[Guest]

Doodler, I purposely made my comments as general as I could because I didn't have the time, energy, or the intention of entering into a debate. Also, this being a public forum, there are many more readers than posters and I felt the need to express another point of view. Since you seem to have taken offense to my comments though, I will reply.

 

I most definitely agree that labels are useful. However, you are taking a well established in the medical world label, backed by lots of research, and comparing it to a label that if I judge by posts I have seen on this forum about it, lumps every child with learning difficulties under its umbrella.

 

Your child has Asperger's, while the OP's child has dyslexia. They may have certain common issues but what may have worked for yours may not necessarily work for hers. When you compare Temple Grandin and how she presents compared to your daughter and husband I feel puzzled :001_huh:. Isn't this why it is called a spectrum disorder? Temple Grandin will be the first to admit to that and the categories she talks about in her books, based on her own observations (as she clearly states in her books and speeches), and which are specific to autistic kids, make so much more sense to me than the generalizations made by the right brain supporters. This is relevant to those on the spectrum though and does not have anything to do with this thread.

 

Doodler, you are telling the OP to give her child a calculator with no guilt rather than kill her child's love of math. How can you make such an assumption without knowing her child :001_huh:? Yes, each learner needs a different approach and you obviously exhausted all the options with your child before making that determination. I am all for solutions but a solution for one child may become a crutch for another. Can you make that determination and tell the op or any other parent to give their child a calculator with a clear conscience? What about if the child needs to write an age/ grade appropriate test? What will that do to the child's self-confidence much less love of math?

 

You talk about my huge misunderstanding but you have totally missed the point of my posts and intentions. You like to philosophize and I am more practical in my way of thinking. My mind automatically starts thinking solutions. It's just the way my mind works ;)! Perhaps this is why I can relate to Temple Grandin.

Edited September 26, 2012 by Guest

[Heathermomster]

Chiming in to say that I would just use the calculator, personally. ;) I also wanted to add my comment about what you said here:

 

I wanted to mention that remediating my ds's working memory made a dramatic difference in his ability to recall facts and do multi-step problems mentally. My ds's basic processing glitches are still there, but once his working memory was functioning at age-level, it was as if he had more cognitive "space" to do his mental work. Everything became easier—writing, math, narration, etc. I could almost imagine that his mental whiteboard became larger, so that while he still had a somewhat scrambled picture on his whiteboard, he wasn't constantly running out of room and having to erase and start over. This was just so, so huge for him.

 

Do you have The Mislabeled Child? The Eides offer some suggestions for improving working memory in the memory chapter in that book. Many of their suggestions are very similar to the exercises that our SLP gave to my ds. I just wanted to throw that out there because the working memory issue affects not just the ability to recall math facts, but some of the other recall difficulties that you've recently mentioned in other threads.

 

I see now that I will be purchasing the Eides book...

 

YLLEK, Would you please give one example of a working memory exercise? How long do these wm exercises take? What do they involve? Are they digit span exercises?

[Heathermomster]

I realize this is not a mainstream choice, but this is not exactly a normal situation. Has anyone at all moved to a calculator for simple calculations on difficult conceptual math (while working on facts at another time)?

 

For my own child, I stress conceptual understanding above arithmetic. I insist that he show me his work, which isn't always advised either. As stated earlier, DS used a calculator for 6th grade. I wouldn't dream of asking him to calculate decimal division or silly amounts of arithmetic. Averaging a large amount of numbers is best done using a spreadsheet in my view.

 

The math we are doing at the moment doesn't really require a calculator. Even when using the calculator, DS will sometimes enter the wrong information. He has been known to grow impatient, plug and chug, and not recognize the answer is incorrect by a large margin due to problems with estimation.

 

Use the calculator. It's certainly not a perfect solution, but life is better with one. Make sure you get one with a multiline screen so that he can ensure that he's entering his numbers correctly.

 

Totally an aside here...I pulled DS from his private school of 8 years over a calculator. The teacher in charge of the middle/high math dept totally opposed calculator use, even for a diagnosed math disability. It chuffs me every time I think about it.

Edited September 26, 2012 by Heathermomster

[myboyluvsdinos]

This book has worked very well for my dyslexics:

 

"Two Plus Two is Not Five"

by Susan Greenwald

 

They have it on Amazon.

 

It gives them a different "hook" in order to remember addition and subtraction facts. As an example, it teaches the 4+7=11 fact family by pointing out these three numbers are the "straight line" numbers -- all the other numbers have curves.

 

If you use it as it is intended (10 min. a day with flashcards as described in the beginning of the book), it really does work. It's not a full math program, just a way of memorizing those darn facts.

 

Also, Times Tales DVD can be very successful for some kiddos.

[EKS]

I allowed both of my children to use a calculator for Singapore's Challenging Word Problems. It allowed them to focus on the problem solving and they loved it because they thought they were getting away with something.

 

You can also make an addition chart, BTW.

[FairProspects]

Doodler, you are telling the OP to give her child a calculator with no guilt rather than kill her child's love of math. How can you make such an assumption without knowing her child :001_huh:? Yes, each learner needs a different approach and you obviously exhausted all the options with your child before making that determination. I am all for solutions but a solution for one child may become a crutch for another. Can you make that determination and tell the op or any other parent to give their child a calculator with a clear conscience? What about if the child needs to write an age/ grade appropriate test? What will that do to the child's self-confidence much less love of math?

 

With all due respect, Doodler and I have had extensive private conversations over the a couple of years and she is privy to far more information about the situation than general readers of this board will know. She DOES know the situation and I appreciate her input. As for testing, thanks for your concern, but ds has a documented 504 plan that will give him a scribe, and he is certainly capable of writing/drawing out all needed math algorithms and pictures, he is just slow to do so.

[FairProspects]

FWIW, the working memory thing was barely mentioned during our NP appointments too. I got the feeling that our NP didn't feel it was a pressing issue at all, but merely explained some of the "glitches," as you say. It was our SLP who made the whole working memory deficit thing a priority.

 

I don't mean to harp on it if this isn't your son's issue. It's just that sometimes your wording of your son's issues seems as if I had written it. By all means, I think that pursuing a non-linear approach to math or writing or whatever will probably address most of the issues that you are encountering right now, but it occurred to me to mention the working memory angle because you had identified that particular issue and because it really helped make every task (interest-driven or not) so much easier and smoother for ds once we had it sorted out.

 

It is a good thought, and is worth working on now perhaps. At the time there were other immediate concerns, but now that many of those have been addressed, it might be time to revisit the working memory issue. I think I am just doubtful because I feel like I got burned with the dysgraphia. We worked so hard on remediation, and it got to a point where everyone was stumped and really nothing could be done to improve ds's fluency. I realize they are different issues, but I think in the back of my head, I'm just assuming we will reach a place where we just have to cope with the glitches in the working memory too.

Edited September 26, 2012 by FairProspects

[peacefully]

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[peacefully]

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[TippyCanoe]

nm

[eoffg1]

FairP,

You wrote that he is 'incredibly spatial', but are you confusing this with visual?

As you said that 'he still cannot do 3+1 or any other simple addition/subtraction'.

 

But 3+1 isn't something that we 'do', but something that we concieve of.

Where we spatially concieve of a quantity, which we learn to call 3.

But before we give it a name, we need to concieve of this sized quantity.

We concieve of it with spatial thinking, by forming a spatial association.

As an automatic process.

So that if you look at a group of 2 or 3 or 4 objects, you will immediately recognize the size of the group.

But if you look at a group of 5 or 6 or 7 objects ?

Then their wont be an immediate recognition of the size of the group?

But to count 5,6 or 7 objects ? You wont need to count them, one by one?

Rather, your spatial thinking will divide the objects in groups, such as 3 and 3, or 2 and 4, and then add them together as a group of 6.

Where this immediate spatial recognition of groups of 2, 3 or 4 objects. Is the foundation of our conception of math.

So that if you look at 2 or 3 or 4 objects, you are aware of the quantity, before you associate it with the word or symbol of 2,3,or 4.

But when spatial thinking doesn't form instantly these groups of 2,3 or 4 ?

Their is no immediate sense of 3 as a group.

So that when you said that he 'cannot do 3+1'?

When you look at 3 objects plus 1 more object, in front of you?

You might consider what you actually 'do', to count them?

Rather the 'doing' would involve recognizing the size of the group.

 

So that this spatial concieving of different sized groups, precedes learning the names and symbols of numbers, to represent them.

This quantity is 3.

As opposed to, 3 is this quantity?

[FairProspects]

No, that's not what I mean. If he sees the objects in front of him, he will recognize them immediately. I mean when he needs to answer 3 + 1 = __ as it is written out in symbols, he doesn't have immediate fact recall, and he has to use a number line to remember that the symbol we write and the word we say for that quantity is 4. The concept is there in his head - he just has difficulty getting it out. That language recall overloads him, particularly in multi-step math problems with lots of smaller calculations. This is because of his dyslexia, partly because of slow processing speed, partly because of word retrieval issues, and partly because of a relative deficit in working memory. :)

Edited September 26, 2012 by FairProspects

[rafiki]

nt

[Heathermomster]

No, that's not what I mean. If he sees the objects in front of him, he will recognize them immediately. I mean when he needs to answer 3 + 1 = __ as it is written out in symbols, he doesn't have immediate fact recall, and he has to use a number line to remember that the symbol we write and the word we say for that quantity is 4. The concept is there in his head - he just has difficulty getting it out. That language recall overloads him, particularly in multi-step math problems with lots of smaller calculations. This is because of his dyslexia, partly because of slow processing speed, partly because of word retrieval issues, and partly because of a relative deficit in working memory. :)

 

How does he do with multiple choice math questions? I'm curious to know whether that would help with the basic math practice. A choice between three possible answers...

Edited September 26, 2012 by Heathermomster

[FairProspects]

How does he do with multiple choice math questions? I'm curious to know whether that would help with the basic math practice. A choice between three possible answers...

 

Interesting you should ask, because I just discovered from letting him play with a computer math program that he rocks multiple choice. I couldn't believe how far up in the math he could go when he had possible answers. I'm not sure if that seems fair though, since it doesn't seem to be the equivalent of producing the answer yourself? :confused:

[Heathermomster]

Interesting you should ask, because I just discovered from letting him play with a computer math program that he rocks multiple choice. I couldn't believe how far up in the math he could go when he had possible answers. I'm not sure if that seems fair though, since it doesn't seem to be the equivalent of producing the answer yourself? :confused:

 

I think it's fair. I see it as a way to get around the dysgraphia. I'm trying to sort out in my head, a way to use multiple choice in a teachable (not testable) way. I don't know if I'm making sense.

[peacefully]

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[FairProspects]

Choosing among multiple-choice answers was one of the very first accommodations that our SLP asked that I provide for my ds because of his word retrieval difficulties. It was such a relief to me to have that information, to know that my ds understood the information that he was encountering and could remember it. It really helped me see that his issue was primarily one of retrieval and not some other learning issue.

 

You gals are such an interesting bunch! I love talking with you all. I learn something new every day. Maybe I should let him use that math program more then.

[Heathermomster]

I've read your posts before and I forget how different our children are, yours with the retrieval business and mine with the processing speed....Anyhow, have you thought about just making a number line and laminating it? I was thinking a line for small numbers, up to 20 maybe... perhaps, he could use the number line as a visual cue and not have to redraw a line whenever he is stumped.

 

The thing is, as these kids advance with math, they will still have to deal with exponents and coefficients, and not the big numbers but the little ones.

 

I recall seeing math software a few years back where you could type in the equations too. Both of our boys may be a candidate for that one day. I'm having a random thought morning.

Edited September 27, 2012 by Heathermomster

[TippyCanoe]

nm

[Guest]

Some food for thought for anyone interested:

 

http://voices.washingtonpost.com/answer-sheet/daniel-willingham/willingham-the-leftright-brain.html

 

http://psychology.about.com/od/cognitivepsychology/a/left-brain-right-brain.htm

 

http://www.lastwordonnothing.com/2012/07/24/unraveling-the-left-brainright-brain-theory/

[Tiramisu]

Just a note on the working memory issue: dd's neuropsych evaluation showed no working memory deficits. The only oddity she displayed was that she didn't put a random list of items into categories for later retrieval, but simply went down the list from the top as she remembered it. The categorization function appeared on its own (that is, without any targeted work or therapy) a year or two later: right around age thirteen.

 

If a child has a neural network in which webs of association are what leads to automaticity/retrieval rather than a more straightforward mental filing system (math facts here), then it makes sense that it takes time for that web of associations with abstract numbers and addition/subtraction/etc. facts to develop and mature. It also makes sense that for many kids like this, retrieval, even when automatic, will be a tad slower as the brain searches all those different filing boxes rather than simply opening one. This does not mean that working memory or an LD is necessarily at work, merely that the computational facts are accumulated and stored differently. Some kids may need more time on timed exams later on, but some won't; dd finished the math sections of her CHSPE and community college placement tests with enough time to go over problems she wasn't sure of, twice. Note again, this is as a sixteen year old. It didn't happen in the elementary years.

 

Doodler, I'm wondering about how this jives with abstract categorical reasoning as measured by Picture Concepts on the WISC IV. This was dd's area of significant weakness. It seems like your thinking could fit together with it. (This question may be off track since dd didn't have trouble in early math, only much later on, and we do have some working memory and processing weaknesses, too, just not as significant.)