Dyscalculia and calculation/procedure

[kbutton]

I'm trying to think through calculator use as well as other potential accommodations for my son in math. All work takes him forever and ever, regardless of subject.

My son has dyscalculia that is for calculation more than anything else. He has co-morbid dyslexia, ADHD, auditory processing issues, motor issues (including dysgraphia due to a connective tissue disorder), visual processing challenges (also due to connective tissue disorder), etc. Here are his WJ scores for math and his WM and processing scores--they are all composite/scaled scores, and the diagnosis is discrepancy based (pretty big). The processing speed is a VAST improvement over previous testing, lol! Both WM and processing are even more discrepant to IQ than his achievement scores are.

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Removed scores

Please don't quote the score portion in case I decide to delete it later.

His overall IQ is comfortably into the gifted range with hills and valleys in all the subtest groupings. 

I don't think he needs remediation at this point--his overall math intuition and number sense is intact. He did tons of multi-sensory math in the early years. Geometry is probably his weakest point after procedural information, and I think that's largely because it's so much visual processing and is fine motor intensive. His mistakes, even now, are usually procedural or in writing things down incorrectly. He works much more efficiently with a scribe, but he often still doesn't want the scribe to write steps down--I think the working memory and processing speed are behind that part. When he was learning multi-digit everything, he did partial quotient division and things like that at first. 

After MUS Primer/Miquon, he used Singapore (US Edition) for several years. He was one year ahead in Singapore (finished through 5A and B in 4th grade), and I didn't find SM US Edition to be great for 6th grade with my older one, so we made the leap to MM topical units this year. He works across several books at once. I have to hold him back from wanting to do all the early algebra and probability units, and he tends to like anything that is strong on concepts. He's really bogged down in the Fractions, Decimals, and Percents. Like, a small section takes forever to complete even with scribing, and he's all but rolling on the floor and is SoVeryTired. (Fatigue is also real and very pervasive, sometimes, with his connective tissue disorder, so I have to sort out what is real and what is drama.)

I have no problem with using a calculator, but I would like to know how people do this practically speaking--what is allowed on the calculator vs. longhand (including if it's maybe half and half or some combination). Also, it's become clear that while he's not losing his conceptual understanding of fractions, decimals, and percents, he is finding that he's losing the relationships between them in the weeds of remembering the steps to convert them all. There are so many ways to use them interchangeably, and MM is determined to teach and use them all, lol! 

Practical ideas? Suggestions for additional supports in addition to a calculator (maybe reference sheets for some of the fractions/decimals/percents)?

We did pick up a basic calculator that uses adding machine tape (yard sale!)--I told him that's so we know he's using the calculator for individual steps--he cheekily asked, "You mean so I don't just use the percent key?" 

Edited August 12, 2019 by kbutton

[Pen]

1. I would not hold him back from more conceptual math that he wants to do.  Maybe he could move ahead on algebra and probability and come back to fractions, decimals, percents. 

2. The adding machine seems like a good step. Paper will also let him check that he keyed numbers in correctly.  

3. A basic Casio or Texas Instruments type calculator can calculate percents and convert fractions. And yes, that can be a problem, but, what does he think he wants to do “when he grows up”?  Will it be something that longhand math is required for—other than for entrance exams (and even some of those increasingly allow calculators)? 

If not, I’d consider letting him use a calculator most of the time along these lines Texas Instruments TI-30XS MultiView Scientific Calculator https://www.amazon.com/dp/B000PDFQ6K/ref=cm_sw_r_cp_api_i_wEGtDbQC5Y9K7 provided he is willing to look at what it shows on screen and think about what process the calculator has used.

[Pen]

Texas Instruments MultiView TI-34 Scientific Calculator - 4 Line(s) - 16 Character(s) - LCD - Solar, Battery Powered 34MV/TBL/1L1/A https://www.amazon.com/dp/B00OFRMLFG/ref=cm_sw_r_cp_api_i_2MGtDbAS2BVNP

Can show even more steps on screen.

 

Ds with dysgraphia does almost everything in his head... which started to be a problem in Algebra 2 when it was too much for his head.  He’s in ps now and calculators like the first I linked are REQUIRED for middle and high school— not merely allowed. 

 

Edited August 10, 2019 by Pen

[kbutton]

38 minutes ago, CuriousMomof3 said:

How old is he?

I keep seeing people referencing signatures, but I can't see them.

11.5 and starting 6th grade. I don't have a signature.

[Pen]

On my number 1, of letting him move ahead with algebra and probability, I think it’s extremely important to support the gifted side of 2E kids.  It’s where they can be happy and soar.  And some mathematicians are better at concept math and not much good on calculation, just as some gifted writers aren’t good spellers.

 

[kbutton]

24 minutes ago, Pen said:

what does he think he wants to do “when he grows up”?

He doesn't know. It will need to be something that is not physically intense and has good benefits unless we've moved to universal healthcare at that point. 

[kbutton]

2 minutes ago, Pen said:

On my number 1, of letting him move ahead with algebra and probability, I think it’s extremely important to support the gifted side of 2E kids.  It’s where they can be happy and soar.  And some mathematicians are better at concept math and not much good on calculation, just as some gifted writers aren’t good spellers.

I keep hearing that fractions, decimals, and percents are what holds up the advanced math, so I guess I am leary of that. But then I hear stories about how that motivated kids to nail those concepts too. I do wonder if coming back to those topics would be fine--I feel empowered to at least give it a whirl.

My older one is so quirky without dyscalculia that I'm a bit gun-shy on not nailing every.little.thing before moving on. I am not sure that being pickier with my older one would've changed his outcome though (displays some really novel thinking but forgets/remembers it all very eclectically--storage and retrieval of concepts is very idiosyncratic). 

[Lecka]

I think you might be able to move slower on the topic compared to what would be possible with MM topical?  Can you stay on an easy level of questions longer?  Maybe longer than there are problems of that type provided in MM?  

I think I would try to cut it down and slow it down before doing too much with a calculator, depending on the kinds of numbers involved in the problems.

Is this fraction/decimal/percent stuff he really ought to be doing mentally?

Or is it like — doing procedural math with numbers and then that is the hang up?  For that I think a calculator is a lot more fine.

If he needs more of going back and forth between things with easier numbers, that is fine.

I think MM can move through things fast, and when that fits it is great, but when it doesn’t I think it’s a fast-moving curriculum in ways.  And, with using more hard numbers or hard problems, maybe. 

Which is good but it doesn’t have to be all done at the beginning.

There can be more easy problems spread over time.  

I think for the mental math — converting between fractions/decimals/percents with common numbers has a big memory element, though.  I think that is a big part of what is important for moving on or causing trouble in higher math. 

But also — if it’s only memorized and easy/common numbers used — that is a problem, too. But I would doubt that more if he is strong with concepts.  

[Kanin]

39 minutes ago, kbutton said:

I do wonder if coming back to those topics would be fine--I feel empowered to at least give it a whirl.

Maybe he'll be so interested/motivated with algebra that he would be willing to put in the work to understand fractions, for example. There's no way to know unless you try! 🙂 

[Lecka]

I think there is a huge gap between — having some issues in a rigorous math program...... and moving up in math without understanding some foundational concepts.

These are not equivalent things.  

Not that it’s not a concern at all — but it sounds like it might be okay if he is not at the ideal MM level right now.  

[PeterPan]

There's no reason not to use a calculator. Hand it to him. Make sure the buttons are of a size that he can comfortably manipulate with his other physical issues. 

When my dd was that stage, I challenged her to decide whether it was *faster* to answer a given question using a calculator or no. If the point is computation, obviously have him compute. But for my dd, when the point was something other than computation I needed to let her use the calculator to drop her fatigue. Otherwise she was wearing herself out processing computation rather than learning the concepts.

If it worries you, have him drill his math facts once in a while. But really, doing fractions should keep them fresh. I have no idea why you're holding him back. Let him forward into the things that interest him and run units concurrently. 

[Pen]

15 hours ago, kbutton said:

He doesn't know. It will need to be something that is not physically intense and has good benefits unless we've moved to universal healthcare at that point. 

 

So it could involve math—like payroll dept in corporation with excellent benefits— but that would be math with calculator and computer help

[Pen]

Maybe also a variety of resources explaining things different ways would help?

 

[Pen]

I am a James Tanton fan:

https://gdaymath.com/courses/fractions-are-hard/

Tanton tends to be conceptual. 

 

Sal Khan on fractions might be worth your son watching on videos also— Khan tends to be procedural. 

[lewelma]

Here in NZ, all students do a 'numeracy' unit in 7th, 8th, 9th, and 10th grade while concurrently working their way up the math ladder.  This unit is longer in 7th grade than in 10th, but even in 10th grade it is for 6 weeks.  As a tutor, every single one of my students (including the gifted ones) need a bit of revision for fractions all the way through 10th grade.  Expect it.  Do NOT try to have a kid MASTER numeracy before letting them do other stuff, especially a 2E kid. 

As for using a calculator, absolutely have him use it every day.  Calculators are tools that allow students more brain space for higher level thinking.  My students will use them for 2 digit multiplication and division, some 2 digit subtraction if It is a bit mucky with negative numbers, converting fractions to decimals to create percents, etc.  I try to encourage them to continue to do all fractions by hand, but that would exclude some of the really hard ones that I have seen in MUS (subtracting fractions with different denominators that require carrying or some such). 

Ruth in NZ

[kbutton]

19 hours ago, Lecka said:

I think you might be able to move slower on the topic compared to what would be possible with MM topical?  Can you stay on an easy level of questions longer?  Maybe longer than there are problems of that type provided in MM?  

I think I would try to cut it down and slow it down before doing too much with a calculator, depending on the kinds of numbers involved in the problems.

So, I was hoping that while he did several other MM units, he would get through the F/D/P unit in pieces by the end of the year. Just getting him to do a page could sabotage half of math, lol! 

I am open to cutting things down, but I think I find that hard with MM--they might do several different things on one page whereas cutting down Singapore meant just cutting down to odds or evens or something like that. 

We do skip stuff that is repetitive from where we left off in Singapore though. I go through each book on the computer, and then I sometimes print out only half the book because we've done the equivalent of the first half.

Also, MM has some grade-level suggestions for how the topical units line up--I am trying to use them as a loose comparison, and I think this is a book they would have the kids finish before moving on, but I can check that for sure. 

I might need to have him do more of a type of problem to slow it down. That's possible. I think the sheer number of methods is a lot of it--there are so many options.

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Is this fraction/decimal/percent stuff he really ought to be doing mentally?

Or is it like — doing procedural math with numbers and then that is the hang up?  For that I think a calculator is a lot more fine.

If he needs more of going back and forth between things with easier numbers, that is fine.

I think MM can move through things fast, and when that fits it is great, but when it doesn’t I think it’s a fast-moving curriculum in ways.  And, with using more hard numbers or hard problems, maybe. 

Which is good but it doesn’t have to be all done at the beginning.

There can be more easy problems spread over time.  

Some is sort of mental, some is meant to be harder--if you are meant to use dividing the numerator by the denominator to get a decimal, it's intentionally going to make you practice your 9's for math facts. Or you 7's. Some number that is less intuitive than doubling a smaller number (which is how both my kids have extended the few math facts they know and is something that always worked quite well with Singapore. So, he might be fine doing a division problem with 9's (with groans) or making a decimal this way (with groans), or learning how to extend division problems to include a decimal answer vs. a remainder (with a big groan), but when he's doing it all disguised as a fraction to decimal problem, he just kind of feels picked on, lol! 

There is a lot of "directed" instructions for each exercise whereas Singapore often doesn't care with method you use or is quite happy to give you numbers that allow you to practice MORE mental math with numbers that aren't as taxing.

Most of the time, he has done all of the underlying skills in Singapore and even some of the combined skills. Then, MM makes it more annoying and adds in two or three more methods on top of it. I do think that the methods would be good for him--my other son tended to be a one-shot wonder with fewer methods, and then he wouldn't go broad with algebra methods--he wanted to just keep using math and logic to bypass algebra altogether (which demonstrated a CRAZY good set of reasoning skills but ultimately ran out of gas). 

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I think for the mental math — converting between fractions/decimals/percents with common numbers has a big memory element, though.  I think that is a big part of what is important for moving on or causing trouble in higher math. 

But also — if it’s only memorized and easy/common numbers used — that is a problem, too. But I would doubt that more if he is strong with concepts.  

He is pretty good on converting with common numbers--he has the capacity to do that if the steps aren't too long. When they get longer, he writes stuff down wrong that was right in his head. Like 31 will become 13 (and often multiple transcription errors in the same problem). But yes, for common numbers, he's great. 

For big math problems that are things he's been doing forever, such as multiplication and division, we do let him use a calculator. If the point is to remember the algorithm as review, he uses the calculator for the same steps he'd do to write it down. If it's just computing an answer in a word problem where the numbers are large multi-digit numbers, we let him plug in the answer the shortest way and don't worry about steps.

Also, I cut the number of multi-digit problems of all operations way back--Singapore never bothered to do such big or cumbersome numbers. 

[Pen]

Is he fine with the print size and density?

[kbutton]

18 hours ago, PeterPan said:

There's no reason not to use a calculator. Hand it to him. Make sure the buttons are of a size that he can comfortably manipulate with his other physical issues. 

When my dd was that stage, I challenged her to decide whether it was *faster* to answer a given question using a calculator or no. If the point is computation, obviously have him compute. But for my dd, when the point was something other than computation I needed to let her use the calculator to drop her fatigue. Otherwise she was wearing herself out processing computation rather than learning the concepts.

If it worries you, have him drill his math facts once in a while. But really, doing fractions should keep them fresh. I have no idea why you're holding him back. Let him forward into the things that interest him and run units concurrently. 

I think we are already doing this in some areas--see my reply to Lecka about the two different ways we use a calculator so far. I do run units concurrently. I did that even in Singapore where everything was grade level. If we were getting bogged down, we'd liven it up with a different unit for a while. I think the only holding back at this point is equivalent to you need to eat your broccoli once in while with that candy bar.  Or, maybe more like, "Once all those candy bars are gone, all you'll have left is broccoli, and then we'll all be sorry with you [because he'll be whining and a lot more frustrated than]." 🙂 

[Lecka]

I don’t think Math Mammoth sounds like a great fit, if he did better with Singapore. 

I think — it sounds like he will be fine for using a calculator in the long term.  Can you see if the kinds of problems in another curriculum’s problem sets would give him less trouble?  

Or make up some problems to be the same type, with easier numbers, and thin out the harder MM problems.  

There is a general principle with learning a new thing — first do things that are easier, then harder.  Part of that can be doing the same problem type, and then a little later mixing the problem types.

It doesn’t mean you never mix the problem types — it can just come later.  

There’s nothing wrong with making things a little easier when someone is getting frustrated, but also not totally backing off.  

It sounds like you have a good idea of what is giving him a hard time, and what would be something he could get and be more successful with, which would be providing good practice and hopefully a confidence booster and making the whole thing less frustrating.  

I think there is a big gray area between on one side, no harder numbers.  And on the other side, all harder numbers.  There’s a big place in the middle.  But I do think some rigorous programs like to hang out on the hard side!  And probably some like to hang out on the easy side.  But I think you can adjust for this to be appropriate challenge. 

Honestly I don’t know if it really sounds like it is a dyscalulia issue, or if this is just a harder area for him.  

I don’t think it’s good to hold him back or see him too frustrated, though.  But I think there could be a middle ground. 

And with a calculator too, he could use it some and not some, even on the target problems — maybe.  It could be worth trying to see how it went, if it seems productive or not.  

Just my opinion.  

[Lecka]

Okay, this is a general thing, too.

Look at his behavior.  Is it as soon as he sees the problem?  The book?  Is it after a few problems?

If he can do some without whining, cut to one less than that; and add one or two a week and see if it’s better.  

If he’s mega whining at the sight of the book, go easier and slowly include harder problems.

Then — ideally you start to see what is fatiguing etc without wondering as much about the behavior side.  

There is still “demands too high, or reinforcement too low.”  It’s just — hard to mix that in with skills.  But in general — you would reduce skill difficulty to something acceptable, and then slowly ramp up.  

That might be overkill if he is whining but basically doing it.  Maybe then he would be open to some discussion about what he thinks is fair or reasonable for him to accomplish some amount of math with some amount of appropriate behavior.  

 

[kbutton]

4 hours ago, Pen said:

Maybe also a variety of resources explaining things different ways would help?

I think he's covered that way, honestly.

4 hours ago, Pen said:

I am a James Tanton fan:

https://gdaymath.com/courses/fractions-are-hard/

Tanton tends to be conceptual. 

 

Sal Khan on fractions might be worth your son watching on videos also— Khan tends to be procedural. 

How many million sites does Tanton have? Lol. I get really lost looking for things on his site, and that's a different one than I've seen before. 

I find the Khan site completely counterintuitive as well. Sorry. I am better with print resources that I can spread out in front of me so that I can figure out the big picture. 

[Lecka]

Do you notice if he makes more transcription errors with fatigue?  That is so frustrating I think; and I don’t know if scribing or you watching him is an option.  Or if he will make the same error after he has written it down incorrectly once.  

If it is fatigue related I think it does mean to cut down, mix in easier problems, or something.  

[kbutton]

6 minutes ago, Lecka said:

I don’t think Math Mammoth sounds like a great fit, if he did better with Singapore. 

I think — it sounds like he will be fine for using a calculator in the long term.  Can you see if the kinds of problems in another curriculum’s problem sets would give him less trouble?  

Or make up some problems to be the same type, with easier numbers, and thin out the harder MM problems.  

There is a general principle with learning a new thing — first do things that are easier, then harder.  Part of that can be doing the same problem type, and then a little later mixing the problem types.

It doesn’t mean you never mix the problem types — it can just come later.  

There’s nothing wrong with making things a little easier when someone is getting frustrated, but also not totally backing off.  

MM has only really been a problem with F/D/P because they have so many strategies and then combine them with so many picky numbers. Last year was about the worst one ever with keeping a routine and with my son's fatigue level, and yet I think he actually got more math done with less complaining about it than any other year. Also, the instructions and the concepts are written to the student in short snippets, which he needs. He gets really overwhelmed with having to listen to me presenting something first--listening is not good. Ever. MM cuts me out of the loop in that regard but in a positive way. He doesn't mind talking to me after he's done some work or if he gets stuck. He doesn't usually get stuck either--it's more that he's misinterpreted the directions and thinks he's stuck, but somehow that is better for him than trying to have someone TALK while he's thinking about math. At all. Ever. 

I do think I can make up some side problems with easier numbers and thin out the harder MM. 

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It sounds like you have a good idea of what is giving him a hard time, and what would be something he could get and be more successful with, which would be providing good practice and hopefully a confidence booster and making the whole thing less frustrating.  

I think there is a big gray area between on one side, no harder numbers.  And on the other side, all harder numbers.  There’s a big place in the middle.  But I do think some rigorous programs like to hang out on the hard side!  And probably some like to hang out on the easy side.  But I think you can adjust for this to be appropriate challenge. 

Honestly I don’t know if it really sounds like it is a dyscalulia issue, or if this is just a harder area for him.  

I don’t think it’s good to hold him back or see him too frustrated, though.  But I think there could be a middle ground. 

And with a calculator too, he could use it some and not some, even on the target problems — maybe.  It could be worth trying to see how it went, if it seems productive or not.  

Just my opinion.  

The entire dyscalculia diagnosis was a surprise to me, honestly. But the psych watched him and seems to think that ADHD is not the whole story. She made it clear though that she thinks his number sense is intact and it's just calculation--I guess that's a thing. 

I am feeling like I can be more adventurous about the calculator at this point.

[Lecka]

The thing about fatigue is if someone is stressed they may be more fatigued because of the stress.  It’s something where — reducing the stress can help.  

But it may not be a permanent relationship of fatigue to a certain thing.  Partly from learning; partly from the stress going down.  

The lower working memory demands when the numbers are ones he has an easier time working with, will help; but so will just less stress.

I also wonder if you see some certain numbers he has “worked around” using — can you single those out for practice separate from them coming up in the problems?  That can be a good kind of strategy, too, and maybe he does need more practice there.  

But the thing is you could be addressing that and then allowing more calculator use, too.  You can decide what your purposes are for the things you are doing, and maybe it can be a point where he uses a calculator but still is addressing some tricky numbers.  

[Pen]

4 minutes ago, kbutton said:

I think he's covered that way, honestly.

 

That’s good then.  

4 minutes ago, kbutton said:

 

How many million sites does Tanton have? Lol. I get really lost looking for things on his site, and that's a different one than I've seen before. 

I find the Khan site completely counterintuitive as well. Sorry. I am better with print resources that I can spread out in front of me so that I can figure out the big picture. 

 

G’day is for the lower arithmetic levels.  

Thinking mathematics is more upper levels.  

And maybe something for educators and math team kids?

 

They interconnect, I believe. 

There are print books by Tanton, for all of it, including an encyclopedia 😳 of math, but I was trying to link you to free resources 😉

 

[Lecka]

I agree you can be more adventurous with the calculator!  

And when there’s too much variety being presented then repeating the same type and then adding mixing them as a separate step — is often a good strategy.

If you do that, you might also cut the number or difficulty down the first time you mix them, because being mixed is itself increasing the difficulty level.

The mixing of the problem types does add a lot of complexity!  It is good complexity, but reducing it is a way to make it easier; and it doesn’t mean you will never mix them.  It’s something that can be a step in the process or not, as needed.  

[kbutton]

28 minutes ago, Pen said:

Is he fine with the print size and density?

In this case, probably--it's very visually organized, and he doesn't have to look up at a board and back at his papers, but thanks for mentioning this. It might not be optimal even if it is tolerable. His genetic mutation means that the fibers that hold his eye lens in place are not normal. Those fibers are connected to the muscles that accommodate for switching between near and far. We know that he has trouble when that is part of the equation. Overall, his visual development is glitchy, but I don't have access to our dev optometrist anymore. He has a good ped ophthalmologist, but often they just go by a huge range of normal vs. optimizing. I need to broach this with her. 

And for follow-up, outside of good therapy for convergence, his condition means that any other data about vision therapy for something like accommodation doesn't apply. Or data about myopia. Or pretty much anything else, lol! His convergence is good. 

[kbutton]

41 minutes ago, lewelma said:

Here in NZ, all students do a 'numeracy' unit in 7th, 8th, 9th, and 10th grade while concurrently working their way up the math ladder.  This unit is longer in 7th grade than in 10th, but even in 10th grade it is for 6 weeks.  As a tutor, every single one of my students (including the gifted ones) need a bit of revision for fractions all the way through 10th grade.  Expect it.  Do NOT try to have a kid MASTER numeracy before letting them do other stuff, especially a 2E kid. 

As for using a calculator, absolutely have him use it every day.  Calculators are tools that allow students more brain space for higher level thinking.  My students will use them for 2 digit multiplication and division, some 2 digit subtraction if It is a bit mucky with negative numbers, converting fractions to decimals to create percents, etc.  I try to encourage them to continue to do all fractions by hand, but that would exclude some of the really hard ones that I have seen in MUS (subtracting fractions with different denominators that require carrying or some such). 

Ruth in NZ

That is reassuring!!! In the US, we just give calculators and then teachers complain when kids don't switch between mental math and a calculator, lol! We literally hand over the calculator at the point when the students are just getting comfortable with changing gears and then don't go back to mental math...ever. 

So, besides using the calculator, I need to expect refreshers and build it in. That sounds really balanced.

[Pen]

My recollection is that MM had visually dense pages.  A lot of small type, packed in problems, not much white space

Fwiw, I wasn’t thinking of the G’day site on fractions for you, but rather for your son himself. It has far fewer problems and much more thinking to try to understand the underlying math. Rather than lots of computation practice.  It’s sort of the opposite of MM iirc. 

[kbutton]

17 minutes ago, Lecka said:

Do you notice if he makes more transcription errors with fatigue?  That is so frustrating I think; and I don’t know if scribing or you watching him is an option.  Or if he will make the same error after he has written it down incorrectly once.  

If it is fatigue related I think it does mean to cut down, mix in easier problems, or something.  

Yes, but he also makes them without fatigue. But fatigue is so, so real. When we went to a conference for people with his medical issues, fatigue and handwriting were the themes over and over with school. IEP level fatigue. Official school plans for how to make up work level fatigue.

He doesn't like to be watched, but then he's not so fond of pounding his head against a wall because I didn't catch something.

I say with all love and an equal amount of frustration that he's basically Goldilocks but with short brown hair, and he can't help it, usually. Sometimes he catches himself being extra-Goldilocks and has a good laugh at himself.

He's doing a really good job of stringing those units out to eternity, so I am guessing I can follow his lead. 😉 That is not meant to be snarky at all--I feel a lot better, and I think I can find my way forward. 

[Lecka]

Honestly I have experienced more nuanced use of calculators.  

We would have problems on tests where we weren’t supposed to use a calculator and in class be expected not to always pull out a calculator, but pull it out for some big multiplication or something.

But what Lewelma says sounds great 🙂  That is a good system.  

[kbutton]

9 minutes ago, Pen said:

My recollection is that MM had visually dense pages.  A lot of small type, packed in problems, not much white space

Fwiw, I wasn’t thinking of the G’day site on fractions for you, but rather for your son himself. It has far fewer problems and much more thinking to try to understand the underlying math. Rather than lots of computation practice.  It’s sort of the opposite of MM iirc. 

It is probably just how you are thinking, but a textbook that isn't meant to be written in was worse, which is how Singapore was. There was no room to work problems, except in the workbooks. I would say that the type is smaller. The pages are larger, which means more on a page. I would not say it doesn't have white space, but I probably view white space organizationally vs. as a quantity. (And we did use US Edition Singapore--I don't know it looks compared to the Standards edition. Compared to Dimensions, I think MM has more space too.)

ETA: He might enjoy the site. Thanks!

Edited August 10, 2019 by kbutton

[Lecka]

That is too bad about the fatigue.  I’m glad you could hear about it at the conference!  It’s got to be good to know for both of you.  

[lewelma]

Here is an example of the numeracy assessment for 10th grade in NZ. Notice, you are not told exactly what to do or in what order.  Notice also that you must make assumptions, which you must discuss to earn an excellence (an A).  Like how many days will be in your month? Is it fair that both students contribute the same if they earn different amounts?  Can they actually keep to the saving plan?  Will the exchange rate change, or the ticket prices while they are saving over the period of a year? The daily amount is only an estimate and is rounded, so how will this impact your final number? etc.  There is no one set answer, and you need at the end when you give your answer, to also note that there should be a bit of a buffer due to the uncertainty of the prices, so you should suggest that they save for LONGER than is actually calculated numerically. This is what numeracy can look like at a high level. 

Also, note that you have to show proper mathematical communication, so be logical and ordered and write up what you are doing at each step, but you absolutely can use a calculator. But organizing your thinking and mathematical working is a part of the assessment. 

Introduction

Mike and Huia are planning to travel to England for a holiday. They plan to be in England for three months, and during that time take a three-week bus tour through France and Spain.

This activity requires you to calculate the amount of money Mike and Huia will need to save for their trip and how long it will take them to save it.

You will work independently to complete this activity.

Show your calculations. Use correct mathematical statements. Clearly communicate your strategy and method at each stage of the solution. You will be assessed on the quality of your discussion and reasoning, and how well you link this to the context.

Task

Use the following information to find out how much money Mike and Huia will need to save and how long it will take them to save it.

Mike and Huia estimate that for each day they are in England, between them they will need on average NZ$250 (to the nearest $50) when they are not on the bus trip.

Huia earns $850 each week. Mike earns $790 each week. Huia is able to save two fifths of her income and Mike 35% of his income to put towards the trip.

The cost for the return air tickets is $2500 each.

The cost of travel insurance is $385 plus GST (15%) for the two of them.

The three-week bus trip costs 2000 Great Britain pounds per person.

Edited August 10, 2019 by lewelma

[kbutton]

5 minutes ago, Lecka said:

Honestly I have experienced more nuanced use of calculators.  

We would have problems on tests where we weren’t supposed to use a calculator and in class be expected not to always pull out a calculator, but pull it out for some big multiplication or something.

But what Lewelma says sounds great 🙂  That is a good system.  

My high school class was known for rampant cheating, so we didn't have much nuance, lol! Middle school--no calculators. Elementary school--"What's a calculator?"

[kbutton]

4 minutes ago, lewelma said:

Here is an example of the numeracy assessment for 10th grade in NZ. Notice, you are not told exactly what to do or in what order.  Notice also that you must make assumptions, which you must discuss to earn an excellence (an A).  Like is it fair that both students contribute the same if they earn different amounts?  Can they actually keep to the saving plan?  Will the exchange rate change, or the ticket prices while they are saving over the period of a year? etc.  There is no one set answer, and you need at the end when you give your answer, to also note that there should be a bit of a buffer due to the uncertainty of the prices, so you should suggest that they save for LONGER than is actually calculated numerically. This is what numeracy can look like at a high level. 

Also, note that you have to show proper mathematical communication, so be logical and ordered and write up what you are doing at each step, but you absolutely can use a calculator.

Introduction

Mike and Huia are planning to travel to England for a holiday. They plan to be in England for three months, and during that time take a three-week bus tour through France and Spain.

This activity requires you to calculate the amount of money Mike and Huia will need to save for their trip and how long it will take them to save it.

You will work independently to complete this activity.

Show your calculations. Use correct mathematical statements. Clearly communicate your strategy and method at each stage of the solution. You will be assessed on the quality of your discussion and reasoning, and how well you link this to the context.

Task

Use the following information to find out how much money Mike and Huia will need to save and how long it will take them to save it.

Mike and Huia estimate that for each day they are in England, between them they will need on average NZ$250 (to the nearest $50) when they are not on the bus trip.

Huia earns $850 each week. Mike earns $790 each week. Huia is able to save two fifths of her income and Mike 35% of his income to put towards the trip.

The cost for the return air tickets is $2500 each.

The cost of travel insurance is $385 plus GST (15%) for the two of them.

The three-week bus trip costs 2000 Great Britain pounds per person.

That is very interesting and practical!

[lewelma]

http://ncea.tki.org.nz/Resources-for-Internally-Assessed-Achievement-Standards/Mathematics-and-statistics/Level-1-Mathematics-and-statistics

1.1 is numeracy

1.5 is measurement. 

There are a number of example assessments on this page for numeracy and measurement.  All are really interesting - both the academic and vocational tracks.  They all must meet the standard, so are at an equivalent level. 

Edited August 10, 2019 by lewelma

[kbutton]

7 minutes ago, lewelma said:

http://ncea.tki.org.nz/Resources-for-Internally-Assessed-Achievement-Standards/Mathematics-and-statistics/Level-1-Mathematics-and-statistics

1.1 is numeracy

1.5 is measurement. 

There are a number of example assessments on this page for numeracy and measurement.  All are really interesting - both the academic and vocational tracks.  They all must meet the standard, so are at an equivalent level. 

Bookmarked! I am going to show these to his math tutor. (ETA: OLDER son's tutor...sorry to be confusing.)

Edited August 10, 2019 by kbutton

[Lecka]

At my 11th-12th grade school they made homework only count for 10% (maybe not in all classes but in the classes I took it was this way).  Then you could cheat or do group work on homework and the math teacher would think it was fine either way.  

In 9th-10th grade sometimes we had open-homework quizzes that would have problems just like the homework problems.  Homework was not weighted that high but higher than 10% for sure.  

They did sometimes change some questions or numbers to problems between classes before and after lunch so people couldn’t cheat off of someone in an earlier class.  

[Pen]

I love that NZ assessment!

[kbutton]

@Pen , I saw your other thread about Exploding Dots. I will look to see what else he does with that concept, but that's a lot like Decimal Street in MUS and what they do with chips (not sure if that's the right word) in Singapore. 

His talking speed and accent might lose my son, though he might not mind backing up and re-listening. 

[Pen]

5 hours ago, kbutton said:

@Pen , I saw your other thread about Exploding Dots. I will look to see what else he does with that concept, but that's a lot like Decimal Street in MUS and what they do with chips (not sure if that's the right word) in Singapore. 

His talking speed and accent might lose my son, though he might not mind backing up and re-listening. 

 

There are books too if conceptually it’s helpful but talking is too fast or too hard an accent.  

 

eTa the MUS decimal street seems to be new since we did MUS— but the blocks themselves are similar.  We didn’t use much Singapore other than the bars so I don’t know about their chips.

Waldorf used stories with math squirrels and acorns / or fairies and magic pebbles / or knights and jewels (etc$ ) which were similar—but the math got lost for some kids in the stories.

one could of course use pennies, dimes, $1 bills, $10 bills, $100 bills as manipulatives

(Maybe play money!!!) 

but the Dots is very easy to use even for large values If one has something that erases to write on or even a sand tray.  And it takes little dexterity to use in some such form.  

And, of course, a good Abacus is also similar. But there is much more dexterity needed

Edited August 11, 2019 by Pen

[Pen]

Or “ chisenbop” for that matter is similar , and most kids always have the manipulatives with them at their fingertips!   But it’s harder to teach, learn, and do— again even just in terms of dexterity. 

[Pen]

Reference sheets:

I suggest he make up his own reference sheets, or his own notebook of reference sheets (anything he feels would help), but so that his own making them up would be part of the learning.  Check them to be sure they are correct before he starts using them so that he won’t internalize an error on his personal reference sheet

[Heathermomster]

I don’t know that there is right way to introduce a calculator.  By 7th grade, DS used a calculator and a laminated multiplication sheet.  If you think your DS will benefit from a fraction and decimal information sheet, print up a sheet, review it with him, and hand it over.  DS needed a calculator with a large display, but even with a large display, he was prone to input errors.  There were times when the calculator was of no benefit so I took it away.  He often practiced math facts for 5-10 minutes in the morning using the computer.  Math fact practice was a separate exercise from an actual math assignment.

James Tanton is awesome.  I taught DS how to factor, multiply polynomials, and derive the quadratic equation using the galley method that Tanton promoted during algebra.  I watched his videos and used one of his Thinking Math volumes.  Basically, Tanton taught me, and then I taught DS.  DS has never watched or heard of JT.  When we used Khan, it was to review a concept that DS was struggling to learn from me.  I sat with DS as he watched KA, and we worked problems together.  Might I add that some of those Khan problems were a bear.

I never expected my dyscalculiac to self teach. Now I did promote going online and seeking answers when there was an issue, but DS often did not always know the right question to ask.  I guess I’m trying to say, use the resources that Pen mentioned for yourself..  I sat down and repeatedly worked through his explanations and contacted JT directly because some of his answers were incorrect.  

My DD is about to finish Singapore 5, and it was loaded with fractions, decimals, and word problems. I’ve been thinking a lot about how helpful the bar models were.  Your maths disabled DS covered that information a year early. Did he understand the math at that time? Have you considered repeating Singapore 5A and portions of 5B and then moving on?  Maybe supplement with Hands-on Equations and start teaching integer math.  Throw in the Dragon Box game and call it good.

 

Edited August 11, 2019 by Heathermomster

[PeterPan]

15 hours ago, kbutton said:

His talking speed and accent might lose my son, though he might not mind backing up and re-listening. 

You can download the exploding dots workbook and teach it yourself.

[kbutton]

5 hours ago, Heathermomster said:

My DD is about to finish Singapore 5, and it was loaded with fractions, decimals, and word problems. I’ve been thinking a lot about how helpful the bar models were.  Your maths disabled DS covered that information a year early. Did he understand the math at that time? Have you considered repeating Singapore 5A and portions of 5B and then moving on?  Maybe supplement with Hands-on Equations and start teaching integer math.  Throw in the Dragon Box game and call it good.

Yes, he did, and MM has a similar approach, so he still gets bit of it here and there. In his WJ scores, applied problems are his highest score--he does really well with word problems.

He did really well with the MM Integer unit. 

[kbutton]

4 hours ago, PeterPan said:

You can download the exploding dots workbook and teach it yourself.

I will look to see if it covers where he is right now.

Some of what is being posted is on the young side for him, and I was going to see if the dots activities reached up into a range where he was having issues with things. But basically, he could use the MUS version of dots to add and subtract 3-digit numbers (both as the minuend and subtrahend) with regrouping in preschool. It was a long time before he did those things with an algorithm, and it was confusing, but got there okay. Division and multiplication algorithms were hard--too much directionality, for starters! But the concepts were solid, and he eventually learned. 

[kbutton]

Also, my son isn't exactly self-teaching, but he does prefer to interact with the book first. So, I'm not expecting him to teach himself, but it's maybe not the dynamic that is expected either. 

I have multiple algebra resources, all of which have their pros and cons for him, and I can switch between them fairly well at this point. It was more of a struggle with my older one, but now that I have a feel for how algebra programs vary in the order they teach topics and things like that, it's not as much of a guess for me. 

I just hear a lot about F/D/P concepts holding kids up. I am thinking maybe that's not us so much. 

[kbutton]

5 hours ago, Heathermomster said:

James Tanton is awesome.  I taught DS how to factor, multiply polynomials, and derive the quadratic equation using the galley method that Tanton promoted during algebra.  I watched his videos and used one of his Thinking Math volumes.  Basically, Tanton taught me, and then I taught DS.  DS has never watched or heard of JT.  When we used Khan, it was to review a concept that DS was struggling to learn from me.  I sat with DS as he watched KA, and we worked problems together.  Might I add that some of those Khan problems were a bear.

I think maybe some of my best efforts might be to see what resources he has for algebra and head that direction. I like to see where we are going, and having multiple methods to teach quadratics would be nice. My older son could probably use yet another run through on those! 

I do use Math Equals Love blog and sometimes Scaffolded Math and Science. I think maybe their stuff is organized in a way that makes more sense to me.