Math woes

[PeterPan]

I have a theory on the spelling btw. I think the language issues affect their understanding of spelling. My ds was memorizing language whole to part, so spelling was just these bits of memorized data, like those kids memorizing lengths of pi. It was memorized and filed away somewhere like jibberish. Then when we worked on language (parts to whole, making parts have meaning), then SPELLING started having meaning. He started noticing spelling on his own and asking about the spelling of words. 

So things he spelled in Barton aren't there for him now because he wasn't ready to receive them as being connected to meaning, as parts of words that had meaning. They were this other stuff he was just memorizing, like he was memorizing everything. And because he has a phenomenal ability to memorize, he could take it all in.

So it's just my theory, but I've been waiting for moments when spelling has MEANING to him. Like he wants to write it or type on the computer, so we spell it. Or I spell a word I'm about to say to him. In that moment, he knows the meaning and then hears the spelling and can connect them. 

[Lecka]

I have some more opinions.

One, you probably don’t want to mix the operations or introduce operations at the same time.  I know a lot introduce mult/div at the same time and show they are inverse, very very early.

You probably don’t want to do that.  

You probably want to spend months or a year on an operation.  Because — it’s harder to learn if the information is getting jumbled.  And there’s a high chance of this being a consideration.  

Then yes — it’s true, it can add a step of being used to the previous operation, and that’s a reason it can be good to introduce them at the same time.  But you may just deal with this being an extra step or taking extra time, because of the “getting jumbled” issue.  

So — Math-U-See is this way.  I am so not-drawn to Math-U-See, but I think it’s one to look at, and think maybe that’s a feature that could be helpful for learning for retention.  I think you could also just adjust other things to focus on one operation at a time, you don’t have to use Math-U-See.  But I do think it’s something to mention.

Also — I think it’s fine to “do stuff” with the other operations, it’s not like you can’t “do stuff.”  But I would also not be too fast to mix them together too much.  Especially for something that is new or seems like it could be jumbled, because there is too much new information coming at the same time.  

I don’t think this really hardcore but more like — it’s a consideration, and some things where they go out of their way to teach two different things together may not be a good approach.  Or teach it but just focus on one at a time, and then have the “mixing them up” step be a separate step (which — it will probably have to be it’s own step and involve getting confused by both previous things and how the fit together — which is supposed to be avoided by teaching them together in the first place, but — it’s the lesser of two evils sometimes).  

[Lecka]

Also — for some things I’m saying and you’re saying sound familiar — to me it is autism.  These are things that some kids with autism will be like.  So it’s not necessarily going to be the same as dyscalculia or dyslexia.  But it’s also like — I don’t know exactly what “label” this will have.

If anything — maybe working memory.  

There’s a lot of recommendations for working memory, and working memory is often something that does along with autism.

So it could be working memory and I just associate both of those with autism.

But it’s what I think.

I think it’s the kind of thing — if you talked to a teacher who had worked with kids with autism, she would be saying “yep, yep, yep” on some things.  

[Lecka]

Another thing with working memory is — if you are doing a lot of “leading through steps by saying things verbally” this may not be a good fit for lower working memory, because it’s hard to remember.  

This is — a common thing mentioned wrt working memory I think.

 

[Lecka]

Things like — writing things out on a whiteboard, pausing, having the child model, etc, are more things that seem recommended.  

Although you do have to just see what works.  

But there are suggestions for presenting things in a way better for working memory issues — this is something where you could find things on google with recommendations.  

 

[Lecka]

And another thing with working memory and the “jumbled” thing — you see things saying that it’s harder for kids to organize information.  So then it’s more important to present them information in an organized way.  

[Lecka]

https://blog.allaboutlearningpress.com/improving-working-memory/

A blog post from All About Spelling about adapting instruction for working memory.  There are things like this on the Internet that are good.

I think with autism — add more need for making connections and generalizing.  

But you can see what gets you more mileage for sure.  

[Lecka]

I’m just going to add this...  I think if she’s on skip counting, she’s on skip counting as addition practice, as practice in adding 3 to the previous number.  That is a very legitimate stage to be at.

Its only over time that either — one, that develops into a mastery of skip counting as it becomes easier and easier to rapidly do that mental math.  Or, two, you think it’s worth working on rote memory of the skip counting — which I think is totally legitimate, but can come later in the process when doing it as a mental math exercise is going fairly well.

But I do think it’s getting ahead of where she is right now, probably, if she is probably still more ready to be doing mental addition up into the teens and higher numbers.  Which — is a legitimate stage!  But it’s probably a sign to hold off on expecting multiplication right now.  (or — full use of it, or repeated addition, if she may need practice back there as a single skill, and not yet a component skill.... and again many kids do just pull all these things together at the same time, but if she doesn’t it’s good to try to look at components and also think about anything “only memorized” as maybe a component that is not too solid)

Just a thought.  

Edited September 26, 2019 by Lecka

[Heathermomster]

So, my eldest is 2e with maths and reading SLDs but no ASD.

I’m reading the OP and wondering whether there is a visual processing type element that needs to be addressed. 

Anyhoo...I suggest the OP read How the Brain Learns Math by Sousa.  I’m also a huge fan of Ronit Bird; however, I did not use her e-books.  I used the Overcoming Difficulty with Number.  As a mathematician, I believe the OP could read and intuit Bird’s methods easily enough.  She discusses all the pre-skills necessary for multiplication.

 

[4KookieKids]

1 hour ago, Heathermomster said:

So, my eldest is 2e with maths and reading SLDs but no ASD.

I’m reading the OP and wondering whether there is a visual processing type element that needs to be addressed. 

Anyhoo...I suggest the OP read How the Brain Learns Math by Sousa.  I’m also a huge fan of Ronit Bird; however, I did not use her e-books.  I used the Overcoming Difficulty with Number.  As a mathematician, I believe the OP could read and intuit Bird’s methods easily enough.  She discusses all the pre-skills necessary for multiplication.

 

I will look into those books. Thanks.

There definitely are visual processing issues going on as well. Her vision doc tested some different (visual closure and a few other things) and she was below the first percentile in her scores. 😞 Unfortunately, we did 4 months of integrating reflexes and then 8-9 months of vision therapy, every day crying and screaming about how it was too hard and hurt her head, with almost no actual progress in her actual test scores. So... we stopped. Whether that was good or not is beside the point -- I have four kids that ALL have issues like asd, adhd, dyslexia, dysgraphia, anxiety, etc, and I was just losing my mind (even after offering substantial rewards and outsourcing it to DH -- she was too tricky and he couldn't tell that she was cheating on the exercises... He's asd as well and just didn't catch the subtle cheating.)

[Lecka]

Maybe she has trouble lining things up.  

[Lecka]

I have heard other times it’s really hard to do things like that sometimes with autism.  I think the methods aren’t always a good fit at all.  

[PeterPan]

2 hours ago, Heathermomster said:

I’m also a huge fan of Ronit Bird; however, I did not use her e-books.  I used the Overcoming Difficulty with Number.  As a mathematician, I believe the OP could read and intuit Bird’s methods easily enough.  She discusses all the pre-skills necessary for multiplication.

Yes, yes, her print books are great!! She just updated them recently too. 

Basically the progression of ebooks (Dots, C-Rods, Multi) is the content of the first book (Toolkit). So they're interchangeable, either way. I like the ebooks for the embedded videos and the nice chunking of pace. The books have extra games. So either way, sure, yes the books are wonderful. She also has a good FB page and will reply to emails.

2 hours ago, 4KookieKids said:

Unfortunately, we did 4 months of integrating reflexes and then 8-9 months of vision therapy, every day crying and screaming about how it was too hard and hurt her head, with almost no actual progress in her actual test scores.

Oh dear. Well that may explain why things are slow to stick visually, sigh. 

How is her sensory? My dd had that kind of EXTREME reaction, but it turns out she's extreme about EVERYTHING, kwim? Her sensory is just set that way, to overdrive, hypersensitive. 

The other thing is that there's not just one way to work on retained reflexes. There are different methods, systems, exercises people have developed. For my dd, just the reflex work was excruciating. Like seriously excruciating. She was 17, 18, and it was just more than she could bear. The PT we were working with suggested she do *one* exercise in small amounts and wear compression clothing to calm her body down. So the idea was to increase the input with the reflex exercises *very slowly* and do everything sensory wise to calm it back down. We never finished. She knows she needs to, but life is sorta going forward with college and all, sigh.

I also think you could look into other systems of exercises, just to try something different. And again, try only ONE at a time. Not 4 or 5, not lots per day. Just teeny tiny amounts of one thing, figuring out how much that is fluffing it up and learning how to calm it down. My dd, to calm her body, needs weight, textures, colors, compression, music, DARKNESS, scents, etc. 

To get through the VT, which we did before the reflex work (yes, for real, let's pretend this was the Dark Ages), we would give her ibuprofen before the appointments. Then she would sleep afterward. We did almost no school work during those months, and yeah it was pretty awful.

My ds has had more OT, reflex work, and his developmental vision is perfect. So just my suggestion, but if you do one reflex a year, in a few years you'll have some progress and can see where her vision is. But if the issue is her sensitivity, she needs coping skills to manage it, self-awareness to self-advocate. She may even find integrating some of the reflexes *helps* the over-sensitivity. My dd is now on a medication that seems to help too. Medication is a pretty normal thing to be doing in kids with these mixes, and it was an unexpected bonus that her sensory calmed down a bit and became more tolerable. Had I known, clearly I would have pursued medications like this earlier. This particular one is more adult, something a GP suggested, not something her ped had ever put on the table. But right now, seeing it what it can do, I'm saying raise the cup for medications too.

Edited September 26, 2019 by PeterPan

[PeterPan]

So if her visual processing is screwed up because of the other stuff, that's glitching a lot. Here's the thing. You *can* develop splinter skills. It's not ideal, but you can. So maybe research visual memory and go for the splinter skill. RFWP has some stuff. As long as you do it as games, it's not going to hurt and might help. You never know, kwim? Or just give her a calculator and go forward. I mean use your gut but don't use your anxiety. There's a fine balance. Yeah if her visual memory is poor the facts, spelling, etc. will be a mess.

Well foo, I hate that. I like cheerful, this is gonna work out, this is going to be great kind of turnouts. Rats. But keep thinking how to make lemonade out of it I guess.

[4KookieKids]

Thanks, all. I need some time to process all of the responses, because there is just so much information here for me to consider. I really appreciate it.

The reflex work went pretty well for us, actually. We did the exercises faithfully, 3-4 times a day for 4 weeks, and got everything integrated. We just continued for several months to try to make sure things "stuck." It just didn't help the VT struggle at all. And now that we've moved, we're about 2-3 hours from the nearest VT place. lol.

[Lecka]

My older son had midline issues (“crossing the midline”) that were so frustrating.  

I think that’s another post for sure.

Though you never know what could help.

As a comment — maybe it’s hard for her to line up a ruler and yardstick and really connect that if it is hard for her to line things up.  

So this is what I’ve heard for something overall..... when things are being forgotten then that can be called low retention.  The general advice is — to do more before something is considered mastered.  And then to review more.

And then there are a lot of things with the learning process — where you try to present information in a way it is more likely to be retained (if it’s jumbled it is not going to be retained probably), and break skills down into parts. 

But it’s also similar to dyslexia where it’s low-level skills that are hard to stick, and kids go on to do very well when they are showing conceptual strengths.  It is definitely not like it’s a big picture of math ability.  

Something too and I don’t know what other OT issues she might have, but a lot of times manipulatives and hands-on math activities can do double-duty with OT goals.  That’s a common approach, too.  It can also slow things down if a manipulative is hitting some OT weak area.  But those are also something where it can be so slow but then kids do make progress and then you even forget about it after some more time goes by.  

A lot of times you can google OT and a low area from testing and see recommended every day activities.  

There’s a lot of overlap between OT and VT and so a lot of vision things can go along with OT also . 

[Lecka]

I am a writing-processor (or whatever it is called) who thinks from writing things down.  So I’m getting ideas for myself also.  I’m doing daily math with two of my kids right now.  (My kids are in public school so I don’t do everything at the same time.). 

I have been told things from multiple teacher meetings, multiple IEP meetings, and I used to go to a support group and would hear discussion of math woes.  

My almost-11-year-old is doing well right now and I got a (to me very flip!) comment this year of “oh, yeah, a lot of kids do take longer to cement those skills” but then they are making good progress at a higher level.  But (in my case) still behind because of it taking longer at an earlier level.  Sigh.  

[PeterPan]

3 hours ago, 4KookieKids said:

The reflex work went pretty well for us, actually. We did the exercises faithfully, 3-4 times a day for 4 weeks, and got everything integrated. We just continued for several months to try to make sure things "stuck." It just didn't help the VT struggle at all.

Well as perverse as it sounds, I'm glad to hear it, lol. I've felt guilty that VT was hard and assumed it would have gone better if her reflexes had been integrated. But from what you're saying, it would have been hard anyway, sigh. So yeah, with dd I think it was the pain and the sensory hyper-sensitivity. 

What would happen if you did a little BalavisX? I'm just saying as an experiment to see how she does. Not too expensive ($28 book and some squash balls). You just never know what might come together. I would be looking for whole body activities like this. Or things like yoga cards where she looks at something and moves her body. Obstacle courses. Whole body and eyes. We had an OT who would post the list on the board and he would go do a task (whole body) and then come check it off (eyes).

Are you aware of visualization techniques for spelling? Even with her visual processing issues, she still *might* be able to do this. She would look at the word, close her eyes, visualize the word, the manipulate it (spelling it aloud to you backward, whatever). I suppose you could do it with multiplication facts or the tables too. Like RS had us list them out (4,8,12,16,20, next row 24, 28,32,36,40). She would then look at it, close her eyes, visualize, answer questions. I'd probably do one row at a time like that.

It's kind of funny, because when my dd was doing VT they SO wanted her to use visualization as a strategy. And I think by just structure and bent visualization is strong with her, that she's very visual spatial. But because it was weak from the vision problems, she was deferring to auditory processing, even if it was actually a weaker strategy for her, if that makes sense. So just using visualization more was something they really wanted us to do. 

Edited September 26, 2019 by PeterPan

[PeterPan]

48 minutes ago, HeighHo said:

I wanted to mention that what improved my teaching was Ed Zaccaro's Primary Grade Math Challenge, as I could see how 'knowing' progressed thru the four levels of understanding the concept.

Ok, this is kind of revolutionary to me. I have that book from back in the old days with dd, but she never seemed to need it. But you're right, with ds it might be interesting. And maybe somehow she jumped through those stages of learning so easily that I didn't realize they were embedded into the materials. Interesting.

[4KookieKids]

1 hour ago, square_25 said:

I don’t have any experience with teaching autistic kids, just with teaching math, so take this with a grain of salt. Out of curiosity, how much visual work are you doing with her for math? When you say she has her addition facts down, can she use them if playing Blackjack or Addition War?

I honestly don't know. I'm sure that she is correct more than 95% of the time when I ask her something verbally. But I haven't really done it in a variety of situations to know where the fault may lie. As dumb as it is, it's just never occurred to me. Inability to generalize is still a concept *I* am struggling with, having come to the discovery in the last 3 years (though it feels like a lot longer!) that three of my kids and my DH area all autistic. I have to sort through all of the comments above and figure out how to actually evaluate in what contexts she is "good" with things, and in which she is not.

Which brings me to something else that happened today that is relevant to this post. I skipped through a huge chunk of her Singapore 3B book with her (lots and lots of conversions, length, volume, etc.) and went straight to fractions just to see what would happen. It was easy as pie for her. No challenge, no struggle, and she finished three exercises in under five minutes. I know the intro exercises are designed to be basic (intro! lol), but it was just interesting for me to really think about the things she's really good at in the context of things she struggles with. There was no question in her mind what 2/5 meant, when looking at a pie chart that matched it, you know? She could draw them in herself, was comfortable writing fractions to match pie charts, and even started fraction addition. I'm interested to see if simplifying fractions is easy from a visual perspective, and whether doing it without the picture throws her for a loop. 

[4KookieKids]

1 hour ago, square_25 said:

 

This might be her autism, but this also honestly might be that lots and lots and lots of people NEED to work with the conceptual model for a good long while to solidify it. And that conceptual model is usually part verbal and part visual, and trying to move from that model to the abstract language of mathematics before it's solid leads to random symbol memorization and to disconnects which later lead to people's inability to do word problems or in general to connect the math they are doing to anything real. 

I tend to gently push my students (both younger and older ones) into more and more abstract stages but I'm quick to retreat to the model if there's any confusion at all. I've started teaching homeschooling math classes recently and I discovered that while lots of parents told me their kids could add, it did not actually occur to them to add when playing blackjack or addition war (that's why those were my examples, lol.) They just counted up from 1, including some kids that had been in public school in grades 3 and 4. That's a serious disconnect right there! 

What I've focused on with my daughter is making sure all of the symbols are referring to specific things: that she could verbalize or draw or somehow connect the mathematical symbols to the picture. So far, at least, it's paid off. She's really solid on WHEN to add and multiply and subtract and divide, including fairly complicated cases. I've been super unconventional in that we haven't touched the standard algorithms yet at all (she's a very accelerated 7 year old, so she has time), and honestly, it's paid dividends. We've never moved past to something she can very solidly conceptualize in a multitude of ways.

I think the fact that moving on to overly abstract stages before the student is ready is an almost universal problem with almost all levels of math pedagogy... it's not you, it's everyone :-/. And of course, some people DO get it right away, which only exacerbates the issue. 

ETA: With that in mind, I wouldn't try to get her to simplify fractions without a picture yet. Let her use the picture until the idea is crystal clear. And frankly, even with my accelerated kid, that takes a month or two, not days and by the time the picture is solidified, we've in fact done lots of complicated calculations and explored lots of interesting idea. And then eventually, we can remove the picture. 

 

Yes, as I've thought about this more, I think I've just been treating her too similarly to my super math intuitive older child. I never did intended to. But I let her rush through when she seemed bored or impatient, and it just never occurred to me (until things were a complete mess!!) that I needed to take a serious step back and consider how she learns best. I may have ruined her for Singapore permanently at this point, but I won't toss it yet. lol. I downloaded the Ronit Bird books on games and am going to spend a few weeks playing those with her, I think, and including my younger girls as well. I think we may just go back to playing with C-rods for a while, as well, while I figure out my game plan. I found someone local who is willing to let us borrow Math-U-See so we can look it over together and decide if she it would be a good fit and if she would like it. 

I feel like I need a whole new mind set, but so overwhelmed with ideas that I'm not even really sure where to start, besides the games and trying a new curriculum. I've done math clubs and stuff with math intuitive kids and I've spent so long teaching graduate level courses and my aversion to any perceived drill is so strong that I think I put a load on her that was just too much for most kids (even gifted/accelerated ones!), and I feel terrible about it, because I never meant to! I think I saw her giftedness and that things seemed intuitive, and I just did what I'd done before that worked so well for ds10. Sigh. Hindsight's 20/20. She's just such an enigma to me, because some things are SO easy and she hates how boring they are, and others are SO hard, and yet others seem to be both simultaneously (like when she's reading CVC words that are mind-numbingly boring, she says, yet she continues to make mistakes... And we have similar issues sometimes in math.)

[4KookieKids]

1 hour ago, square_25 said:

I dunno whether you've ruined her for anything! Everything will feel pretty different to her when she's on less shaky ground. 

I'm planning to teach my homeschool math classes pretty much entirely through games (very different from what I did with my daughter, but I'm realizing that it's much harder to create hands-on experiences through worksheets in an environment that's not one-on-one), so I think you could do worse than playing lots of games! There are games and game-like things for the majority of the early math concepts. The only thing I'd suggest is being mindful of what games teach what idea :-). Having looked around, some math games seem much more obviously worthwhile than others... 

Plus games will get her to feel better about math in general, I think, if currently she feels confused and not sure of herself!

People are such a funny mix of strengths and weaknesses, aren't they? I don't think my kids are as far from average as yours, but I'm also noticing a serious difference between my two daughters. My first one picked up letters much, much faster than my second. But my second was actually more verbally precocious and still is! She speaks like a 5-6 year old at age 3... and yet it takes serious practice to get her to tell apart her m's from her n's. My first could do this by age 2... 

 

Ha ha. Yes, I was hoping to include her sisters in the games to help give dd8 some confidence and have her help "teach" the younger girls some. I think she's far enough ahead of them that it will only be positive (something I had to consider when I decided against playing nonsense word games with her and the 6 yo, since the 6 yo was reading them better than the 8 yo...). 🙂

Thanks for the encouragement. It's good to just laugh about what a cooky mix of strengths and weaknesses they are when I feel bogged down. 

 

[Lecka]

I think with games and especially between kids or without an adult, keep in mind instructional level of fluency level.

If you play as an adult, and you think you want to make a manipulative model of drawing or write something down, and then say some steps out loud, or model some verbal reasoning or explanation ——— you can make that happen on every turn or model it or say things, etc.

If you have kids playing without an adult it is doubtful they will do that.  

If it’s a game where kids are already at a more fluent level and it is more fluency practice, that will probably go a lot better.  

Games add to working memory demand, because there are the steps of the game to remember plus the math part.  It can mean kids are “just getting the answer” but they aren’t consolidating as much because the working memory is not there for them.  

Kids with more working memory probably can consolidate while also playing a game because they have more working memory.

Kids with less are less likely to.

But then games are still really good for — a fun way to do things but keep it instructional.  And, when it is actually at a fluency level for them and then it’s great to practice.  

But you can play games and think “they’re doing it” but not see the connections happen as desired.  

I think too that’s a really interesting point about linking visual and verbal.  That is known to be more difficult for a lot of kids with autism.  It is known that can be harder to nail down.  I can see where that has been an issue here but I hadn’t thought of it exactly that way.  

[Kanin]

Also keep in mind that when a kid says something is "soooooo boring!" it may be code for "too hard for me."

 

[Lecka]

12 minutes ago, square_25 said:

Because otherwise, the kids are spending just as much time thinking about the rules as about the math! 

 

When the time is right though, that is the level of fluency you want, where they are trying to figure out something unrelated and then bringing in their math on the side. 

[Kanin]

3 minutes ago, square_25 said:

Definitely. But sometimes it also means it's too easy, lol. And sometimes your kid will say "this is soooo hard" when it's actually too boring (my daughter started doing this in kindergarten.) 

Kids... there isn't a perfect dictionary for what they say! 

Oh man, that's so true. You have to be a teacher and a mind-reader!

[prairiewindmomma]

On 9/25/2019 at 5:37 PM, Heathermomster said:

So, my eldest is 2e with maths and reading SLDs but no ASD.

I’m reading the OP and wondering whether there is a visual processing type element that needs to be addressed. 

Anyhoo...I suggest the OP read How the Brain Learns Math by Sousa.  I’m also a huge fan of Ronit Bird; however, I did not use her e-books.  I used the Overcoming Difficulty with Number.  As a mathematician, I believe the OP could read and intuit Bird’s methods easily enough.  She discusses all the pre-skills necessary for multiplication.

 

I also found it helpful to read Sousa, Bird, and other authors books on dyscalculia. It helped me move outside of my comfort zone and really get to the heart of how to teach the kid in front of me. 

[Lecka]

I think too about her scores, when you say it’s lower than other scores, the actual score matters.  If her actual score is about 100 — that is really different than if her actual score is about 85.  2e is broader than this, but there are things written about 2e where a spread is like —100 to 130 — and that is different than if the lower number in the spread is getting a lot lower than 90-100. 

I don’t think you can go “too” much off of test scores, but it is something.

Also, I am pretty sure working memory is one where all kids improve with age, but stay within their percentile.  Sometimes you can look and see what average expectations are for working memory for an age, and then look at percentiles, and adjust to the age expectations that go to a percentile.  

A lot of times you can adjust a teaching method to be more supportive of working memory, while curriculum expects an average child with average working memory.  So then you can add in working memory supports.  

It also means things get easier with age 🙂

 

[Lecka]

There’s kind-of two separate things.

One is working memory, which some people have higher, average, or lower.

Two is how well you know the smaller skills.  If you know the smaller skills really well, to the point they are fluent/automatic, then it’s going to use much, much less working memory.  If you have to stop to think “now how do I do this” about anything (like my oldest right now — he is starting Algebra but he has to stop and think about subtracting a negative number, he has to sit and think it through every time it comes up) then that is going to take up working memory.  

Right now it’s okay for him because it’s something they are working on, but it would cause him to get lost if he was expected to have it at an automatic level in order to understand a further explanation.  

And for my older son he has had testing and I know his working memory is completely average.  

So even an average (or high) high working memory is not so high that someone can get by without things being automatic, at a certain point.  

Edited September 29, 2019 by Lecka

[Lecka]

I worked this morning on my 10-year-old being able to describe what strategy he used to figure out 7x6.  He was starting with 7x5 and then counting up (or adding 6).  It’s so hard for him to say this.  It’s describing two steps and using “first, then” language.  I also have to go over the word “strategy.”

I know he doesn’t “know” 7x6 but he can figure it out quickly this way.  But he does need to be able to say what he is doing (or trying to do), or how can I help him if he’s confused, or talk about what he is doing if he gets a wrong answer?  

 

[PeterPan]

1 hour ago, square_25 said:

the calculations would take so long that by the end of it no one remember what it was we were calculating.

So with my dd, who had very low processing speed and was just constantly crunchy, we would do external RAM (whiteboards, me scribing) and calculators. If the point is NOT the arithmetic but rather the problem solving, then use a calculator. If the point if the arithmetic itself, even then there can be a place for calculators if it reduces fatigue and allows them to learn the overall concept without being bogged down. So not a substitute for learning but to reduce fatigue.

2 hours ago, square_25 said:

I've become very fond of structures that allow you to see an idea "at a glance," so to speak. I think we spend too little time thinking of convenient conceptual framing that would allow kids to do that for all sorts of ideas... 

Bingo. With my ds, I'll draw a frame for the computation or the word problem worksheet will have lines for each answer in the multi-step problems. With my dd we would put a list of words at the top of our whiteboard so she could point or see the word she was trying to retrieve. Anything you need to do, you should do.

[PeterPan]

8 minutes ago, Lecka said:

I worked this morning on my 10-year-old being able to describe what strategy he used to figure out 7x6.  He was starting with 7x5 and then counting up (or adding 6).  It’s so hard for him to say this.  It’s describing two steps and using “first, then” language.  I also have to go over the word “strategy.”

I know he doesn’t “know” 7x6 but he can figure it out quickly this way.  But he does need to be able to say what he is doing (or trying to do), or how can I help him if he’s confused, or talk about what he is doing if he gets a wrong answer?  

 

His method is totally valid, and I'm not sure being able to explain it is a hill to die on. In a situation like that, I'm usually going to have a can of cuisinaire rods in front of me, and I'm going to ask him to SHOW me what he was thinking. Then, because I'm ornery, I'm going to ask him to show me ANOTHER way he could have gotten there.

So he's deriving the facts, and that's terrific. Ronit Bird suggests explaining multiplication as scaling, which is kind of interesting after you think about it. It's sort of like integrals and filling in space under a curve (a very advanced concept). So I might actually say you scaled it with 7s, now could you do it the other way and do it with 6s? He might need to play around with it a bit. He might not have made all the connections and might find that another way of getting there is what makes that number 42 finally interesting and memorable. After all, how often do you go 35 to 42? Haha. But 30 to 42, now that would be super common. So then he's piecing together a 6X5 that he knows and a 6x2 that he knows, and boom he's at 6X7. 

[kbutton]

26 minutes ago, PeterPan said:

With my dd we would put a list of words at the top of our whiteboard so she could point or see the word she was trying to retrieve. Anything you need to do, you should do.

For anyone who is reading this with older kids in mind (like pre-algebra and up), Scaffolded Math and Science (blog/TpT store) has word walls and some structured quick checks for various kinds of problem solving. I think both could help with working memory for tasks older students are likely to see.  

https://www.scaffoldedmath.com/   Her blog has a link to her TpT site. Here are the word walls: https://www.scaffoldedmath.com/p/word-walls.html  

Ooh, I forgot she has some elementary grade stuff! 

 

[Lecka]

I wish it wasn’t a roadblock on his being able to explain things verbally, but it has proven to be a big issue and we aren’t able to get in front of it.  So far at least.  He will get stuck somewhere.  

[Lecka]

For context it’s like — the question is 6x7.  He says 49.  I want to be able to say “what strategy are you using.”  

It doesn’t have to be perfect but it’s not going to work out well if he stares into space and says “I don’t know.”  

I can ask him a series of questions, to see if he is counting up by 7, counting down from 70, etc, but it’s going to be better if he can say it.  

I could show him the distributive property and explain it, but I don’t think it would help him right now to introduce another concept.  

My other kids learned the distributive property earlier in learning about multiplication, and it was fine for them, but I don’t think so for him.  

[Lecka]

I could ask him to write at that point.  That is a good idea.

To some extent it’s a mental organization issue and not just a verbal issue, and he has to use words to organize his thoughts at a certain point. 

I don’t think it’s something where he has worked things out mentally in a visual manner, I think he needs to be able to say it, at a certain point, as part of learning.

But if he could write something down I could help him, and it would be better.  

[Lecka]

I have been doing that with repeating and having him repeat, but I do think it would help him if I wrote it down.  

 

[PeterPan]

1 hour ago, Lecka said:

For context it’s like — the question is 6x7.  He says 49.  I want to be able to say “what strategy are you using.”  

It doesn’t have to be perfect but it’s not going to work out well if he stares into space and says “I don’t know.”  

Maybe he really doesn't know. Maybe he memorized everything and hasn't thought through the math in a chunking, scaling, subitized kinda way. 

So then Ronit Bird and a $15 tub of c-rods.

[Lecka]

He does know.  I heard him today, for 7x8, say “so 48 and add 8” while he was talking to himself. 

 

 

[Lecka]

Well, I have realized that’s probably what I have been modeling for him.  So it’s probably fine for now, but I need to model more if I want him to say more.  And I can definitely write something out where there are just blanks to fill in for the numbers we are using.  

[PeterPan]

2 hours ago, Lecka said:

I can definitely write something out where there are just blanks to fill in for the numbers we are using.  

That's what we do. We model it with c-rods and then write equations on a small whiteboard. More abstract would be draw the rods on the whiteboard, write the equations. And you'd fade that to see it in your mind, write the equations.

[Lecka]

I have thought about this some more -- and I do feel he needs to be able to explain with words, to some extent, so not just going between a model and the equation.  I think it's partly that, I don't think he is doing some great process in every way except that he's not using language.  I think what he says with language is representative of the clarity of his thinking, to some extent.  Not 100% but to some extent.  He's not somebody where it's all clicking except when it's time to translate to language.  

The other thing is he is in public school and ime they don't like it if he can't do it at all, they will want to stay and work on it.  

"Number talks" are really big right now and it's like -- he can't just not participate in them at all.  It's not something I feel I can just skip, because it is something that they want at school.  

And I think it is good, too.  

[Lecka]

I do think that right now, he has a good mental connection for the numbers, for where he is (in the first half of 3rd grade math).  

[PeterPan]

14 minutes ago, Lecka said:

"Number talks" are really big right now and it's like -- he can't just not participate in them at all.  It's not something I feel I can just skip, because it is something that they want at school.  

Depends on what the cause is as to whether it's "fixable" or whether it needs an accommodation in the 504. You might notice *time* and see if processing speed matters. You might notice whether having the questions ahead of time (so he can pre-think) matters. You might notice whether his anxiety/stress/fatigue levels matter. 

He can know everything, but if he is struggling to get it out he might need accommodations. My dd uses in them in college, because some things don't fix. My dd has run into it with classes that require discussion. Sometimes the accommodation is enough and sometimes she finds a way to work around the class. 

Edited September 30, 2019 by PeterPan

[Lecka]

Well, the thing is, I don't want accommodation.  I want remediation of his language issues so he can actually do this.  I am okay with slowing down math for that to happen.  

He's already in a special autism classroom so -- accommodations out the wazoo are already happening lol.  

I do also think it's something that will ultimately hold him back in math.  

[Lecka]

I have just gotten burned too many times with thinking he could move forward and not have the language side keep up.  I really want to have a balance for him.  

Because -- he does have a history of low retention every time I have not done that, and it is happened enough I should be taking the hint at this point.  

I don't "like" It but I think it is where I am.  

[Lecka]

His low retention is like -- it is gone, it might as well have never happened.

It's not like -- oh, he seemed like he forgot it, but then he reviewed, and it came back pretty fast.  

Okay, sometimes it is like that, but that's not what I am talking about when I say low retention.  I'm talking about -- it's really gone.

Not like -- okay, you do a little review, and it's coming back.  

Edited September 30, 2019 by Lecka

[Lecka]

It's not something where accommodations *actually* help.  Accommodations *actually* help when kids *know what is going on.*  

They don't work the same when kids move forward without really mastering the material.  

I agree that when accommodations are working then that is the way to go.  

[PeterPan]

I'm confused, I thought you were talking about your older ds.

[Lecka]

Oh!  Sorry.  No, my younger DS.  

I have got my thoughts in order for when I talk to his teacher, lol.  I just requested a meeting and want to ask some things about his math.  

Edited September 30, 2019 by Lecka