Conceptual/hands-on math for upper elementary?

[eternallytired]

I half hate myself for continuing to poke at this topic, but I'm taking my fifteenth new direction with this kid, and I'm hoping someone has a suggestion.

DS9 started math early and strong, but seems to be making less and less progress each year.  I really think that there's some processing/working memory/visual-auditory thing going on with him (he can do BA puzzles, but struggles with the regular problems; he can read music, but can't remember the note names even though we've gone over them daily for months), but the ed psych has a huge wait list, so I'm doing what I can.  I recently picked up Fractions Sense (the Borenson curriculum) for him, and he loved it.  The incremental instruction, visual/hands-on models, and minimal practice worked really well for him.  I've been trying to recreate this success by writing my own similar material for decimals and long division and multi-digit multiplication, but I'd dearly love not to reinvent the wheel.  Does anyone know of any materials similar to Borenson's, but for other math topics?  He's working on fourth grade materials now, but I'm not sure how high his retention has been.  (It's really weird, since he can come up with answers to complicated stuff on his own, but doesn't seem to understand what he's being asked to do on a math worksheet, and verbal explanations seem to make it worse.  I think it was the visual-interactive that really clicked with him.)

[kbutton]

I don't know anything about Borenson, but these are some hands-on products I am aware of. 

http://www.educationunboxed.com/  This site will have at least some concepts.

https://explore.shillermath.com/  This is Montessori-based, so it's multi-sensory.

https://www.enasco.com/c/Education-Supplies/Math-Education-Supplies  I am not sure how much curriculum they have, but they have an entire catalog devoted to just math. 

https://rightstartmath.com/  I think they are also Montessori-based.

 

[Not_a_Number]

On 6/2/2021 at 7:28 PM, eternallytired said:

I half hate myself for continuing to poke at this topic, but I'm taking my fifteenth new direction with this kid, and I'm hoping someone has a suggestion.

DS9 started math early and strong, but seems to be making less and less progress each year.  I really think that there's some processing/working memory/visual-auditory thing going on with him (he can do BA puzzles, but struggles with the regular problems; he can read music, but can't remember the note names even though we've gone over them daily for months), but the ed psych has a huge wait list, so I'm doing what I can.  I recently picked up Fractions Sense (the Borenson curriculum) for him, and he loved it.  The incremental instruction, visual/hands-on models, and minimal practice worked really well for him.  I've been trying to recreate this success by writing my own similar material for decimals and long division and multi-digit multiplication, but I'd dearly love not to reinvent the wheel.  Does anyone know of any materials similar to Borenson's, but for other math topics?  He's working on fourth grade materials now, but I'm not sure how high his retention has been.  (It's really weird, since he can come up with answers to complicated stuff on his own, but doesn't seem to understand what he's being asked to do on a math worksheet, and verbal explanations seem to make it worse.  I think it was the visual-interactive that really clicked with him.)

How's his place value? Because a lot of this stuff comes down to a thorough model of place value. And I don't mean "he can name 10s and 1s" -- I mean, how comfortable is he trading up and down whenever he needs to, sometimes in his head and sometimes on paper, and trading as many things as needed. 

I tend to hand kids a bunch of poker chips and tell them to knock themselves out. We make observations from what they do. It works really well with every single kid I've tried... I don't have a program, though. 

Edited June 4, 2021 by Not_a_Number

[eternallytired]

34 minutes ago, Not_a_Number said:

How's his place value? Because a lot of this stuff comes down to a thorough model of place value. And I don't mean "he can name 10s and 1s" -- I mean, how comfortable is he trading up and down whenever he needs to, sometimes in his head and sometimes on paper, and trading as many things as needed. 

I tend to hand kids a bunch of poker chips and tell them to knock themselves out. We make observations from what they do. It works really well with every single kid I've tried... I don't have a program, though. 

That's the weird thing.  He has no trouble telling me that 4200 is 420 tens or 35 is 3.5 tens.  But it's like as soon as I have him do something on paper--say, a long subtraction problem--he does things like insisting on starting from the largest numbers and working down, without writing out any trades (though he can get it correct about 80% of the time this way).  If I have him write his trades and start from the smallest digit, suddenly he does things like trade a hundred for ten ones.  This is the same kid who randomly informed me at age five that there were 100 fingers/toes in our family, so if two people in our family were sick, then 40% of people were sick.  I feel like it's all up there, but I'm failing him in figuring out how to help him put it on paper (or interpret what the paper is asking).

I've been having him model things with base-10 blocks (not perfect, I know, but at least a concrete model) and that seems to help: he does one that way and then the model sticks in his mind for the rest of his work.  But it's almost like I need to repeat the presentation of the model every day, which is weird to me because he seems to have such a great understanding by the end of each day.  It's very disheartening for me, and he feels like a failure when he doesn't understand what he's supposed to do.

[Not_a_Number]

27 minutes ago, eternallytired said:

That's the weird thing.  He has no trouble telling me that 4200 is 420 tens or 35 is 3.5 tens.  But it's like as soon as I have him do something on paper--say, a long subtraction problem--he does things like insisting on starting from the largest numbers and working down, without writing out any trades (though he can get it correct about 80% of the time this way).  If I have him write his trades and start from the smallest digit, suddenly he does things like trade a hundred for ten ones.  This is the same kid who randomly informed me at age five that there were 100 fingers/toes in our family, so if two people in our family were sick, then 40% of people were sick.  I feel like it's all up there, but I'm failing him in figuring out how to help him put it on paper (or interpret what the paper is asking).

I've been having him model things with base-10 blocks (not perfect, I know, but at least a concrete model) and that seems to help: he does one that way and then the model sticks in his mind for the rest of his work.  But it's almost like I need to repeat the presentation of the model every day, which is weird to me because he seems to have such a great understanding by the end of each day.  It's very disheartening for me, and he feels like a failure when he doesn't understand what he's supposed to do.

So... you can take this with a grain of salt if you like, but I wind up making my (very accelerated and bright) kids use models for something like years before I let them do things without. I think it's actually MORE than normal to need the model often. We tend to think that bright kids who can do calculations have absorbed the model, but actually they often haven't -- they've just learned some shortcuts that always work without ever referring back to the model, and they have the kind of memory that lets those shortcuts stick. (You can generally figure out that they haven't ACTUALLY fully integrated things when the same ideas turn up in new contexts. For instance, I have kids who add and subtract using place value with seeming facility, but then they get lost when they need to trade for division. But the trading idea is the same! So then they probably weren't actually accessing the trades when adding and subtracting -- they were using workaround tricks. This is more common than not at all levels of math.) 

I've worked with lots of bright kids, and most don't have fully integrated models of things because they've never been required to. And that can work OK up to a certain point... until it doesn't. 

I think the point here is that you should keep having him model things with base-10 blocks and you shouldn't worry about how long that takes 🙂 . Models are very tricky to integrate. 

This is why my blog is called Mental Model Math, lol... because I tend to think that we don't spend enough time on the models! 

[Dmmetler]

Also, when you start moving into algebra, algeblocks are pretty awesome. Unfortunately, they’re also expensive, and not terribly common used. If you can manage to go to a math teaching conferences and ETA Hand2Mind is doing a workshop on them, they usually have a nice sample packs included for training/demo purposes that is just right for one kid. Algeblocks work well with base 10 or C-rods, too. I also use Hands on Equations starting when a kid is about at a 4th grade level in math. 
 

 

[EKS]

Math U See is conceptual and hands on and is really good for remediating issues with place value as well as more general spotty weaknesses.  Have him take the placement test and place him where he scores.  You can easily accelerate through the material he already knows (note that I would accelerate rather than skip).

Anyway, I ended up doing MUS Beta-Zeta in about 6 months with a dyslexic kid who had hit a wall with Saxon 7/6.  It worked like a charm.

[Not_a_Number]

3 hours ago, Dmmetler said:

Also, when you start moving into algebra, algeblocks are pretty awesome. Unfortunately, they’re also expensive, and not terribly common used. If you can manage to go to a math teaching conferences and ETA Hand2Mind is doing a workshop on them, they usually have a nice sample packs included for training/demo purposes that is just right for one kid. Algeblocks work well with base 10 or C-rods, too. I also use Hands on Equations starting when a kid is about at a 4th grade level in math. 

I'm a biiiiig fan of starting algebraic reasoning as early as possible. I basically aim my arithmetic at algebra, actually... so in some sense, I start algebra in kindergarten 😉 . Not algebraic manipulations, though -- just practicing with variables, solving equations intuitively, generalizing, and explaining one's reasoning. 

[SoCal_Bear]

try taking a look at Crewton Ramone's House of Math. It's basically Mortensen approach to math.

https://www.crewtonramoneshouseofmath.com/

[Not_a_Number]

8 hours ago, calbear said:

try taking a look at Crewton Ramone's House of Math. It's basically Mortensen approach to math.

https://www.crewtonramoneshouseofmath.com/

Hm, complete with claims about the election being stolen with statements about that being "simple math." Charming. 

Edited June 5, 2021 by Not_a_Number

[eternallytired]

5 hours ago, Not_a_Number said:

Hm, complete with claims about the election being stolen with statements about that being "simple math." Charming. 

That was as far as I got on that site, as well.

[HomeAgain]

1 hour ago, eternallytired said:

That was as far as I got on that site, as well.

I got another page in and saw all his Facebook posts on the side. Nope.

Some ideas for you, though:

Algebricks/Algeblocks (listed above)
Patty Paper Geometry / AngLegs material
Shiller Math
Math U See

My ds uses a highly hands-on, low writing math program.  It has a slight learning curve, but has been a better fit for him.  I hesitate, though, because it uses one set of manipulatives for everything, so we did branch out slightly when it came to percentages and multiplying fractions of fractions.  I brought in money to show 1/10 x 1/10 and slowly work up.

[kbutton]

10 hours ago, Not_a_Number said:

Hm, complete with claims about the election being stolen with statements about that being "simple math." Charming. 

Oh, that's sad to hear!!! I was mostly past that level when I heard about his stuff, so I haven't looked at his site in a long time.

We have a local math/science guy that teaches at a gifted school that has been promoting conspiracies about the pandemic and election both. It's terrible, and he should know better. He's teamed up with the MyPillow guy, sigh.

[*****]

Yes, Crewton's Facebook has gotten too heavily involved in politics since the pandemic, unfortunately.   He is very good with conceptual math and has a ton of videos on youtube.  Mortensen Math is based on Montessori, or at least the idea is (then Math-U-See was developed out of Mortensen).  

Take a look at:  https://www.facebook.com/annasmathpage/        Anna does Mortensen and is very good with her explanations (and stays out of politics!)  

[eternallytired]

17 hours ago, HomeAgain said:

I got another page in and saw all his Facebook posts on the side. Nope.

Some ideas for you, though:

Algebricks/Algeblocks (listed above)
Patty Paper Geometry / AngLegs material
Shiller Math
Math U See

My ds uses a highly hands-on, low writing math program.  It has a slight learning curve, but has been a better fit for him.  I hesitate, though, because it uses one set of manipulatives for everything, so we did branch out slightly when it came to percentages and multiplying fractions of fractions.  I brought in money to show 1/10 x 1/10 and slowly work up.

Thanks!  I had AngLegs on my list after browsing @kbutton's suggested site above.  I actually own Patty Paper Geometry and had seriously considered Math U See way back when (and actually Shiller Math before that), but went with Right Start partly because it uses a variety of manipulatives to model things.  Unfortunately, while we loved A and B, C was both too much review and too much fine motor--particularly since my kids hit it around 5/6--so we jumped ship.  I was able to find something that worked well for my other kids, but not this kid.  Maybe I should look at it again, since several people suggested it.  I hesitate now because it's mastery, so I worry I'd have to invest a ton to get all the levels we'd need to catch up with their program.

What's the low writing math program your DS uses?  I didn't even mention that element, but writing is like torture for this kid, even after OT.

[HomeAgain]

1 hour ago, eternallytired said:

Thanks!  I had AngLegs on my list after browsing @kbutton's suggested site above.  I actually own Patty Paper Geometry and had seriously considered Math U See way back when (and actually Shiller Math before that), but went with Right Start partly because it uses a variety of manipulatives to model things.  Unfortunately, while we loved A and B, C was both too much review and too much fine motor--particularly since my kids hit it around 5/6--so we jumped ship.  I was able to find something that worked well for my other kids, but not this kid.  Maybe I should look at it again, since several people suggested it.  I hesitate now because it's mastery, so I worry I'd have to invest a ton to get all the levels we'd need to catch up with their program.

What's the low writing math program your DS uses?  I didn't even mention that element, but writing is like torture for this kid, even after OT.

We made it from C to E in Right Start before jumping ship in 3rd.  The fractions lessons were torture for my kid because they were not done well, and, if you couldn't tell, we had issues with the amount of writing. 😄  Ds had a really good base from MEP and RS provided too much review, too much fine motor, and too long of a lesson with too many moving parts.  I switched him to Gattegno after he was captivated by one of the videos.  I did start him back at the beginning, but when we finished book 1, I bought the series.

The pro:

• Nearly all lessons are explorations.  They're meant to be as short or as long as needed
• Minimal work can be done in a notebook.  We used centimeter graph paper ones for a long while and then I made him a workbook for book 5.  It was a total of 43 pages, 6 of those being Eratosthenes' Sieve.
• They're available free on Issuu, and the entire series is about $9/book
• The pictures on Amy's Math Page look like they'd go well with it, teaching the same way.
• There are no grade levels.

The con:

• It's super teacher intensive.  Ds can't do much without a facilitator in books 1-5, even though they are all written to be a conversation.  The teaching is the interactive lesson.
• It has a learning curve and requires a comfort level.  I sit down and go through the next book before ds does, teaching myself what the words are trying to illustrate.  Sometimes I end up making short cuts, like a set of foam square units so we're not always putting together blocks.
• There is no book 3.  This bugs us.  I understand why they removed it, since it was work with irrelevant measurements, BUT........this is something that bugs us. I have considered hunting down an older version, but then having one that doesn't match wouldn't be much better.
• There is no standard sequence.  Book 1 ends with multiplying fractions by whole numbers, book 2 has telling time pretty far in.
• They refer to the 4 block as pink.  Ours are a weird pinkish-purple, so we changed it.  Same with the 8 from 'tan' to 'brown'.  I changed the notations in it from T to BW, for example.

 

So, it's not a perfect math program for everyone, but for this specific kid in our house, it was our best option.  We're finishing the series this year (6th) and reassessing after.  I'm thinking of bringing in the Key To series because the pages are still nicely spaced and it'll be good review/work on writing, and then doing Calculus For Young People with him if he stays home again for 7th.

[eternallytired]

On 6/4/2021 at 9:31 AM, EKS said:

Anyway, I ended up doing MUS Beta-Zeta in about 6 months with a dyslexic kid who had hit a wall with Saxon 7/6.  It worked like a charm.

How in the world did you do this without breaking the bank?  Even the used items I'm finding are $40 for the manipulatives (not counting the add-ons for fractions and algebra) and $25 or more for the instructional materials for each level (and that doesn't always include the workbook).  Eeek!

[EKS]

12 hours ago, eternallytired said:

How in the world did you do this without breaking the bank?  Even the used items I'm finding are $40 for the manipulatives (not counting the add-ons for fractions and algebra) and $25 or more for the instructional materials for each level (and that doesn't always include the workbook).  Eeek!

You're right.  It was expensive but I was desperate.

I used the manipulatives with his younger brother, and ended up selling the rest.

[eternallytired]

52 minutes ago, EKS said:

You're right.  It was expensive but I was desperate.

I used the manipulatives with his younger brother, and ended up selling the rest.

Alas!  I was hoping you'd found some less expensive way of doing it.  I may still end up going this route, but I'm going to wait to spend that much until after whatever testing/evaluation they recommend for him this August.  

[PeterPan]

On 6/3/2021 at 11:03 PM, eternallytired said:

a long subtraction problem--he does things like insisting on starting from the largest numbers and working down,

RightStart teaches the to do subtraction from the left. You go through and do all the trades first. Sounds like he's very intuitive on what ought to work and needs the instruction. There are always multiple ways to do things.

[PeterPan]

On 6/6/2021 at 12:03 PM, HomeAgain said:

I switched him to Gattegno

I don't know whether I had never seen this or had forgotten it, but it's good stuff! And as I'm looking through the books, yes that's how my ds thinks. Nice share, thanks!

[Not_a_Number]

1 hour ago, PeterPan said:

RightStart teaches the to do subtraction from the left. You go through and do all the trades first. Sounds like he's very intuitive on what ought to work and needs the instruction. There are always multiple ways to do things.

Oh yeah, I missed this bit... DD8 always did trades from the left until I actually taught her the algorithm way later. 

[eternallytired]

6 hours ago, PeterPan said:

RightStart teaches the to do subtraction from the left. You go through and do all the trades first. Sounds like he's very intuitive on what ought to work and needs the instruction. There are always multiple ways to do things.

Yeah, he reminded me that this is the way RS originally taught it.  I had introduced it the other way at the time, showing how I had learned to do the trades, and the other two kids do it the way I do it--but not YDS.  He is definitely intuitive; he seems to be able to mentally manipulate numbers and can do what I think are the more difficult, puzzle-y elements of BA, but it's the stuff that I think of as being straightforward/rote that seems to trip him up. 

We came to a screeching halt in math this year because--despite working on them with SM2, SM3, and BA3--he still hadn't memorized his multiplication facts (which was absolutely necessary at this point because of his very, very slow processing speed); we couldn't master long multiplication or division or a host of other things until he got those down, and that took something like three months of 20 minute-a-day practice.  (We're not quite done, but he's around 80% mastery now.)  Now I'm busy trying to remind him how we did all these basics while also modeling decimals and long division and...  And I'm wishing I didn't have to generate my own, Borenson-style math worksheets.  But he loves it when I do, and the method seems to work--and it's less expensive than buying a whole new curriculum.  So I guess I read and research and keep plugging.