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Math Woes (and some reading/language discussion beginning on p.4)


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Understanding # 2:  We can think of big numbers as being composed of smaller numbers combined.

 

Activity #1:  Introduce numbers inside with Ronit Bird

Here are a couple videos where she models looking for smaller numbers inside a bigger number.  

 

 

I usually start with a couple lessons where I take just 1 of the following numbers: 2, 3, 4, 5 or 6 and demonstrate finding the numbers inside.

Activity # 2: Play these two Ronit Bird Games

 

 

(I'll add that the act of sitting with your kid, and making these cards is a great chance to review the numbers)

Here's the game board

http://www.ronitbird.com/wp-content/uploads/2013/09/Game-Numbers-Inside.pdf

Activity #3: Explore this concept with real life objects.

I love to do this in the context of cooking.  

Make dominos by spreading a graham cracker with peanut butter, and placing a pretzel rod down the middle. Give your kid 5 raisins, and have them see how many "5" dominos they can make.  

Make pizza on a pita, cut it in half.  Give your kid 5 pepperonis (or whatever topping they like that's a piece) and see the different ways you can make it.

Make cupcakes give your kids two colors or skittles or m & m's, have them make a 5 pattern with 2 colors.  

If you don't like cooking, you can also do this with red circles and black circles to make "lady bugs".  

(Note: I'm using 5 a lot here, because while I'd do all of the numbers, I'd spend a lot of time on 5.  Because 5, like 10 is kind of a magic number in math, so I want those facts to be really automatic)

Activity #4: Play with my favorite app

http://androidapk-s.com/app/912574293/domino-addition

There are a couple apps out there called domino addition, but this is the best.  It's also free.  It's also available on Android.  

In this app, the big idea is that you see a domino with pips on both sides, and then choose the number that tells you how many pips there are altogether.  That's really the whole activity.  But there are so many settings.  For example, you can choose the sums (I'd start with 1 to 5 until those are really solid), you can choose to make the color of the pips change when you tap them, which is really nice when you're counting.  You can also make the pips moveable, so you can literally side the two sides together.  And you can set the pips so they appear and then disappear forcing you to subitize.

Activity #5: Extend what you've learned to things in a 5, or a 10's frame.

Look at these two apps:

http://androidapk-s.com/app/416444482/what-s-hiding

http://androidapk-s.com/app/418083871/10-frame-fill

If you're doing any kind of behavior plan or pacing board or count down to a special event, use a 5 or 10 frame to organize it.  

Activity #6: Play a game with Five or Tens Frames

Make a set of playing cards with 5 frames, where the 5 frames are exactly in the middle so they can be flipped.  Use cheap cards that are a little see through, and use dark colored sharpie and dark colored price stickers https://www.amazon.com/iMlabeller-Sticker-Stickers-Teaching-Inventory/dp/B07QKD85NT/ref=sr_1_3?dchild=1&keywords=price+stickers+circle+yard+sale&qid=1614004745&sr=8-3

 Have your kid help you make the with 0, 1, 2, 3, 4, and 5.  

Play matching games like go fish or memory where instead of asking for the same number, you ask for the number that they need to add to make 5 (e.g. if I have a card with 2 dots, I count or subitize the empty spaces and ask for 3).  Check your work by flipping the cards on top of each other to show how they make 5.  

Yes, of course your kid will cheat.  But he won't cheat until he can see the patterns in his head.  Which is the point. 

Make another set with 10's.

Also watch this ridiculous video. 
 

Activity #7: Extend what you're learning to objects the kid has to organize.

https://everydaymath.uchicago.edu/about/understanding-em/games/two-fisted-pennies-game.html (I'd play with 5 first, and then with 10)

 

Activity #8: Play with your fingers

Painting finger or toe nails (I mostly do toes, because a lot of kids working on this skill are also working on keeping their fingers out of their mouths) is a fun activity here.  I like to spend time planning how to paint nails, by giving kids counters in various colors and a graphic organizer I made by tracing their 2 hands or feet. Have them tell you the numbers they want for each color, and then spend some time arranging them just so (e.g. do you want a pattern?  one color on each hand) and then paint their nails to match.  

Activity #9: Go back to Ronit Bird and explore odds and evens

I really like the way she models teaching odd and even in the Exploring Numbers with Dot Patterns book.  But that video is not on youtube.  

Basically, you want to give kids experience taking a number and seeing if you can divide it into two equal groups.  

I like the Dominos Addition app for this.  I'll set it for up to 10, and have it give me a problem with the pips set to moveable but not color changing, and then we'll try to share them equally.

One of the really major understandings we're looking for is that some numbers can and some numbers can't, and it's true regardless of who is sorting.  This sounds really obvious to those of us who have good number sense, but a lot of times when I give a kid the app with 7 pips and tell them to try to share it evenly, they'll try and try, and then tell me that they can't, can I show them how.  They come to the task assuming that all numbers can be shared evenly.  We'll often pass the app around, and have everyone try.  The kids need to see that parents can't do it either.  You want to get that understanding that this quality -- being able to be divided equally into two groups is a stable attribute of a number. 

Once they have the sense of trying to divide up a number into two groups, then I turn it into a game.  I assign one player "odds" and one player "evens".  We either make a domino using the app, or we roll two dice, and then we try to arrange it.  If we can share it then whoever is "even" gets a point.  If not then who ever is odd gets a point 

Once they can do it with rearranging we make it harder in the following ways:

Play it with fingers:  Do Rock Paper Scissor style "shooting", where each player puts up any number of fingers on one hand.  Then put the two numbers together.  So, if I have a 4 and you have a 2, we have 6.  Then one person "puts" the 6 on their hands (5 and 1), try finding another way to make 6 that has the same number of fingers on both hands.  See if it's odd or even, and give that person a point, or the right to make whatever decision you're odds and evening about.  

Play it with actual dominos -- draw a domino from a pile, and figure out if it's odd or even (note: at this point, I have not drawn a connection between the idea of odds and evens and skip counting.)  Give him manipulatives to figure it out, or encourage him to use his fingers.  

Once he's playing the game well (and this is a game that can take kids a while to get, so feel free to sit with it), then I'd make a number line with cards that say 0, 1, 2, 3, 4, 5, 6, 7, 8, and 10.  Place the even dominos under the numbers that show the total.   Look for that pattern of every other number.  

Activity #10: Apply this to graphing.  

Keep doing lots of graphing as described above, but start looking for patterns in the way things divide.  Since you'll always have 6 people graphing you'll have lots of chances to look at how that 6 can be divided up.  Make a graph with just 5 people and make predictions.  What will happen if Dad chooses this when he comes home from work?    What will happen if Dad chooses that?  

 

If you made it this far, I'll also say that I agree 100% with @Lecka that there's a risk of implying to kids that numbers end at 10.  You want to keep the idea that there are numbers beyond 10 out there.  One thing you can do is work on rote counting to 20, like when you're washing hands or playing hide and seek.  Also, when you're reviewing counting with 1:1, have some sets that are 11 or 12 or 13.  Another thing you can do is to sometimes "accidentally" have problems that will go a little further.  So, if you're sorting dominos, have the 11's and 12's in there.  When they come up say "I'll do that one", and just model briefly a number above 10.  If you're playing the Make 5 or Make 10 game with the cards and the frames, sometimes try to combine 2 cards that will make a number too big.  Point out the circles that overlap, talk about where you'd put them. Talk about needing another frame.  If you're playing the odds even number game with your fingers, sometimes add in a third player.  See how sometimes it works, and sometimes you have a number you can't fit on your fingers. Take off your shoes and talk about how you can use your toes, or ask someone to lend you their fingers.  Kid doesn't have to be able to do the math with those numbers at this time, but you want to get the idea out there that there is math that can be done with those numbers.  

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This is why I love c-rods, and I think why Ronit Bird loves them, too. With my students, we'd find a c-rod, say, the number 8, then find other ways to make 8... 4+4, 2+3+3, etc. Then we'd pretend to g

Thank you!   I definitely will check that out.  I am always interested in new resources, and that isn't one that I know.   For me, because the kids I teach are close to finishing their school ca

Understanding # 1:  Number is a permanent attribute of a set.  Or, in simpler terms, 4 is 4 is 4.  Activity #1:  Introducing numbers like in Ronit Bird. One change I'd make, is

17 hours ago, PeterPan said:

Yup, all in on the genetics. Were you thinking there's a connection to the synthesia? Ds does not have an MTHFR defect but dd and I do. 

Sorry, my comment was meant to be anecdotal, not diagnostic (no trained subject matter expertise). When I read your post I was struck by how *valuable* your advice was.  Something can seem statistically improbable, be on the differential dx, and, in fact, turn out to be involved in a systemic problem. That's the extent of my comment, that your advice is good.

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@BaseballandHockey — those are great.

It’s funny, there are so many things I do with my kids that I don’t even THINK about, so then I don’t mention it to other people. Like, until I taught my homeschooling classes, I didn’t realize people don’t all have their kids show numbers on fingers. Both DH and I do it naturally (“You have 5 more minutes!”), we prompt the kids to do it, but I never even thought about the fact that some kids simply miss out on this practice entirely. That was one of the things I dearly wished I had enough time for in my classes — having the kids reclaim their fingers as tools. 

In the same way, I do often show “numbers within numbers,” and I do focus on ones they are already comfortable subitizing when I’m splitting things up, but would I think to mention this to someone? No. I wouldn’t. It’s just something I do naturally. 

I have an eventual goal of making a math app that’s focused on mental models, and I really need to write some of these early concepts down for future reference, because I’m just not mindful of it in the same way as I’m mindful of the stumbling blocks when we’re, say, working on equals signs or operations or graphing functions.

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50 minutes ago, Not_a_Number said:

@BaseballandHockey — those are great.

It’s funny, there are so many things I do with my kids that I don’t even THINK about, so then I don’t mention it to other people. Like, until I taught my homeschooling classes, I didn’t realize people don’t all have their kids show numbers on fingers. Both DH and I do it naturally (“You have 5 more minutes!”), we prompt the kids to do it, but I never even thought about the fact that some kids simply miss out on this practice entirely. That was one of the things I dearly wished I had enough time for in my classes — having the kids reclaim their fingers as tools. 

In the same way, I do often show “numbers within numbers,” and I do focus on ones they are already comfortable subitizing when I’m splitting things up, but would I think to mention this to someone? No. I wouldn’t. It’s just something I do naturally. 

I have an eventual goal of making a math app that’s focused on mental models, and I really need to write some of these early concepts down for future reference, because I’m just not mindful of it in the same way as I’m mindful of the stumbling blocks when we’re, say, working on equals signs or operations or graphing functions.

I'm sure that @Cake and Piis already doing those things too.  But kids with these kind of issues definitely benefit from having it be more explicit and structured.  

I would look at the apps I shared.  They do a fantastic job of presenting visual models. 

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8 minutes ago, BaseballandHockey said:

I'm sure that @Cake and Piis already doing those things too.  But kids with these kind of issues definitely benefit from having it be more explicit and structured.  

I would look at the apps I shared.  They do a fantastic job of presenting visual models. 

No, I’m sure you’re right. That’s exactly what I think — that it’s important to be mindful of these activities. Whenever I’ve become mindful of something I do “naturally,” I do a better job.

As for visual models, I think I have a decent idea of what a good way to present quantity is. I think “recognizable patterns” are a good idea, for example — dice, ten frames, etc. Are there main ideas for how to present it in a clear way, you’d say?

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22 hours ago, Not_a_Number said:

By the way, to demonstrate how poker chips work with DD4 -- I just asked DD4 about 23 + 25, and she thought about it, said "I'll do the blues first" (for us, blues are 1s), counted on for 5+3, then added the 2 + 2 greens (which are 10s for us) via memory, and got 48 😄 . 

She obviously has a LOT of working memory, or this wouldn't work, and I'm sure she can't yet carry in her head. But she does have a very straightforward VISUAL model for what's happening. 

And here’s a picture of DD4 with her poker chips 🙂 . She has recently learned to put them into the ten frame shape before trading, so that’s what she was doing.

I’m just posting in case it helps anyone visualize what we do. I know it’s not currently the right answer for the OP! 

 

CFAF6067-1103-4C6B-9D3A-61C670F9D1DB.thumb.jpeg.0e3c7515b2236125cc0fe2dae4eb8a01.jpeg

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1 hour ago, BaseballandHockey said:

I'm sure that @Cake and Piis already doing those things too.  But kids with these kind of issues definitely benefit from having it be more explicit and structured.  

I would look at the apps I shared.  They do a fantastic job of presenting visual models. 

Obviously, I know all the posters here are super knowledgeable, so at the risk of suggesting something already well-known:  Have you thought about JUMP Math? Well known Canadian program that emphasizes mathematical models and understanding.  Their Grade 1 Teacher samples has a lot of complementary ideas to the strategies you've been outlining (...I think.... you all are the experts...)  My son is in the (Cdn) Grade 5 (we're in the US, the Cdn books were cheaper at the time...) and the first page of his Grade 5 workbook explicitly teaches counting on with diagrams and have the students practicing it for the entire page. In any case, just throwing it out there.....

https://jumpmath.org/jump/us/samples_usa  

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5 minutes ago, Clickie said:

Obviously, I know all the posters here are super knowledgeable, so at the risk of suggesting something already well-known:  Have you thought about JUMP Math? Well known Canadian program that emphasizes mathematical models and understanding.  Their Grade 1 Teacher samples has a lot of complementary ideas to the strategies you've been outlining (...I think.... you all are the experts...)  My son is in the (Cdn) Grade 5 (we're in the US, the Cdn books were cheaper at the time...) and the first page of his Grade 5 workbook explicitly teaches counting on with diagrams and have the students practicing it for the entire page. In any case, just throwing it out there.....

https://jumpmath.org/jump/us/samples_usa  

Thank you!  

I definitely will check that out.  I am always interested in new resources, and that isn't one that I know.  

For me, because the kids I teach are close to finishing their school career, priorities shift.  There are things in a typical first or second grade curriculum that we teach because they lay the foundation for upper level skills that my students won't get to before graduation.  So, I find that I need to draw from multiple resources, and create things that fill in the gaps. 

None of this applies to @Cake and Pi .  There's a huge difference between a 7 year old working on these skills and a 17 year old.   

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38 minutes ago, BaseballandHockey said:

For me, because the kids I teach are close to finishing their school career, priorities shift.  There are things in a typical first or second grade curriculum that we teach because they lay the foundation for upper level skills that my students won't get to before graduation.  So, I find that I need to draw from multiple resources, and create things that fill in the gaps. 

A premise of Jump is that math should be taught very, very incrementally with models.  The series goes up to Grade 8. Rainbow Resources is actually the easiest place to see each grade levels' Table of Contents.  For some grades, incl. Grade 8,  they show or allow you to download sample pages. I'm interested in the Grade 8 myself because it has linear equations.

https://www.rainbowresource.com/category/13420/JUMP-Math-Assessment-and-Practice-Books.html

The Jump math URL I gave you in my previous post also has samples, and a very large resource of (free) teaching materials (powerpoints, etc.)  Just as a note, always buy the American versions of the books (will have a US Flag in the corner, as opposed to the Canadian flag).  Canadian standards follow a different scope and sequence entirely.

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16 hours ago, BaseballandHockey said:

I would love to talk about this in the context of the classroom.  What do you teach?

I'm a SpEd teacher, reading/spelling/writing and math. Mostly grades K-5. With math, I find that the admin I work with are mostly concerned with having "a program" to point to in IEP meetings. They aren't open to the idea of teaching specific skills unless there is "a program" being used. When I try to explain the mismatch between a boxed program with its own progression of skills and teaching what an individual kid needs, they have no idea what I'm talking about. We could start another thread so we don't derail this one. 

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3 minutes ago, Kanin said:

I'm a SpEd teacher, reading/spelling/writing and math. Mostly grades K-5. With math, I find that the admin I work with are mostly concerned with having "a program" to point to in IEP meetings. They aren't open to the idea of teaching specific skills unless there is "a program" being used. When I try to explain the mismatch between a boxed program with its own progression of skills and teaching what an individual kid needs, they have no idea what I'm talking about. We could start another thread so we don't derail this one. 

I'd love that!

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9 minutes ago, Kanin said:

I'm a SpEd teacher, reading/spelling/writing and math. Mostly grades K-5. With math, I find that the admin I work with are mostly concerned with having "a program" to point to in IEP meetings. They aren't open to the idea of teaching specific skills unless there is "a program" being used. When I try to explain the mismatch between a boxed program with its own progression of skills and teaching what an individual kid needs, they have no idea what I'm talking about. We could start another thread so we don't derail this one. 

There *are* some programs aimed at dyscalculia. The dyslexia school near us has their own program, and they're well enough known I wouldn't be surprised if they sell it. The posh ps near us has a curriculum that is said to have tiers of intervention and work for math disability. I just couldn't bring it in reach because it's marketed to schools. 

So I can see where parents and people advocating from that perspective want curriculum and I can see where teachers want freedom. As a parent doing that free teaching, I can say eventually it comes back to bite you; even I find myself wanting curriculum, lol. 

Fortunately, techniques like RB plug into a curriculum. 

But you know it totally shows the gap there, because they may have a different tune for SLD Reading. With that are they allowing OG trained people to do custom work, or are they wanting a curriculum there too?

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On 2/21/2021 at 5:43 AM, Not_a_Number said:

Do you know what I mean about trading being the definition and everything else flowing out of it?

I think so? Yes? I think our mental models are reversed, though. It goes the opposite direction in my head with trading flowing from place value instead of the other way around. Both models accomplish the same thing and seem to contain the same components. Maybe it's just a difference in how we each first made sense of quantity in our early days?

Except... I go straight to trading when working in other bases... which again may be because that's the way I first understood other bases. Different mental models in different bases. Very inconsistent, lol.

On 2/21/2021 at 5:43 AM, Not_a_Number said:

For what it’s worth, I wasn’t even trying to do place value with my homeschool class kids who weren’t comfortable working until 20.

It sounds like you are working with kids who see "12," know it is called "twelve," can count to twelve, but don't realize that twelve is a 10 and two 1s until you teach that to them, which you do only after they're comfortable with working until 20. 

I was perhaps trying to go about this in the opposite direction. I was thinking that place value might make numbers 11-20 accessible to DS 7 since he's had such a hard time conceptualizing them. Learning to count and name numbers and quantities 11-20 was one of his IEP goals last year, but he never got beyond rote counting. DS 7 sees "12" and says "twenty" or "one two." He sees "20" and also says "twenty" or "two zero" or just "two," and has been at this point for at least the last year and a half.

On 2/21/2021 at 5:43 AM, Not_a_Number said:

Even for adding 1 or 2? I have to say, I absolutely don’t use place value for 199+1 or something like that — I do rote counting. I wouldn’t do it for bigger additions, but it’s a handy trick for me.

They didn't do any counting with addition. We did a bunch of work with the abacus and with visualizing, so they wouldn't need to count on. They'd just visualize a quantity and then some more and mentally subitize. With my kid who has trouble visualizing I focused more on +1 being "the next number" and +2 being the "next even" or "next odd" number. Perhaps this is actually a kind of counting and we're really talking a difference in semantics?

On 2/19/2021 at 2:42 PM, BaseballandHockey said:

Understanding # 1:  Number is a permanent attribute of a set.  Or, in simpler terms, 4 is 4 is 4. 

It's good that you began at the beginning with these lists of activities. I started trying stuff out with DS 7 last week. I *thought* he knew that quantity didn't change when it was rearranged, but apparently I was mistaken!

In general, do you you find it's better to run through all this with 0-5, then start over with 0-10, or is it better to focus on one task at a time first with 0-5 and then with 0-10 before moving on to the next task?

I'm veering off topic here, but do you happen to have recommendations for beginning reading instruction as well...? Do you know of a curriculum or program for teaching reading to kids with significant language disabilities? DS 7 has had two years of sped preschool, two years of public kindergarten with 4 hours per week in the resource room with the O-G trained Learning Specialist, two summers of public summer school, and about 6 months of private language and literacy (O-G) targeted therapy spread out over the last year and a half. At home we've gone through the entire Explode the Code primer set (Get Ready, Get Set, and Go for the Code) TWICE and done a letter of the week type program. And, he still doesn't know the entire alphabet. Teaching him feels like trying to fill a cracked bucket with water.

Thanks again for typing out all those activities to work on, the apps, and the videos. I also got the RB Dyscalculia Toolkit book and am reading though it now.

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10 minutes ago, Cake and Pi said:

I think so? Yes? I think our mental models are reversed, though. It goes the opposite direction in my head with trading flowing from place value instead of the other way around. Both models accomplish the same thing and seem to contain the same components. Maybe it's just a difference in how we each first made sense of quantity in our early days?

I think you will find it very hard to define what a number like 7745 means without trading! You can try, but I bet you'll have trouble 😉 . 

 

11 minutes ago, Cake and Pi said:

Except... I go straight to trading when working in other bases... which again may be because that's the way I first understood other bases. Different mental models in different bases. Very inconsistent, lol.

I would guess that's because you weren't taught place value when you first interacted with base 10 numbers, so you had to figure it out yourself by trial and error. But with other bases, you had someone guiding you. 

 

12 minutes ago, Cake and Pi said:

It sounds like you are working with kids who see "12," know it is called "twelve," can count to twelve, but don't realize that twelve is a 10 and two 1s until you teach that to them, which you do only after they're comfortable with working until 20. 

That's correct. That would be when I'd feel reasonable tackling place value. 

 

12 minutes ago, Cake and Pi said:

I was perhaps trying to go about this in the opposite direction. I was thinking that place value might make numbers 11-20 accessible to DS 7 since he's had such a hard time conceptualizing them. Learning to count and name numbers and quantities 11-20 was one of his IEP goals last year, but he never got beyond rote counting. DS 7 sees "12" and says "twenty" or "one two." He sees "20" and also says "twenty" or "two zero" or just "two," and has been at this point for at least the last year and a half.

This is where I was really, really wondering whether seeing a yellow and two greens would make it easier for him to name the numbers. Whether it'd be easier to remove the written numbers and let him interact with place value visually for a long, long, long time. And yes, I understand he wouldn't have any feeling for how big anything was for a while; that's why I was suggesting games that would allow him to explore this weird new way of expressing quantity.

However... 

 

13 minutes ago, Cake and Pi said:

It's good that you began at the beginning with these lists of activities. I started trying stuff out with DS 7 last week. I *thought* he knew that quantity didn't change when it was rearranged, but apparently I was mistaken!

... this seems like a bigger problem! So then his mental model of quantity is shaky. I wouldn't try place value without a mental model of quantity, because place value requires understanding that a 10 is a 10 is a 10. You need to feel very firm in the 10-ness of 10. 

 

15 minutes ago, Cake and Pi said:

With my kid who has trouble visualizing I focused more on +1 being "the next number" and +2 being the "next even" or "next odd" number.

That's exactly counting on, in my opinion. I almost always use counting on with my kids for +1 and +2. Occasionally for +3. 

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8 minutes ago, Not_a_Number said:

I think you will find it very hard to define what a number like 7745 means without trading

... It's 7 big cubes, 7 square flat thingys, 4 bars, and 5 tiny cubes. 😄 Obviously that doesn't count as a formal definition mathematically speaking, but that's how the number exists in my mind in it's most basic form -- no trading involved.

Now, trading absolutely starts happening when I try to manipulate 7745 on a larger scale, by, say adding or subtracting 2153. But if I'm just adding or subtracting a 1- or 2-digit number I'll be zoomed into that vertical number line jumping up or down it, and there's no trading there either. 

3 hours ago, Not_a_Number said:

... this seems like a bigger problem! So then his mental model of quantity is shaky. I wouldn't try place value without a mental model of quantity, because place value requires understanding that a 10 is a 10 is a 10. You need to feel very firm in the 10-ness of 10.

Yep. I was pretty floored. I sincerely thought he had this already. Maybe he used to. It's definitely time to back up and camp out, though.

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Just now, Cake and Pi said:

... It's 7 big cubes, 7 square flat thingys, 4 bars, and 5 tiny cubes. 😄 Obviously that doesn't count as a formal definition mathematically speaking, but that's how the number exists in my mind in it's most basic form -- no trading involved.

And how big are the big cubes? You're going to have to define how many square flat things are in a cube to actually finish your definition. Your definition may be intuitive for you, but it clearly doesn't define it for anyone else 😉 . The question is: how could you define 7745 for another person without trading? And I think you'll find that you basically can't. 

 

Just now, Cake and Pi said:

Now, trading absolutely starts happening when I try to manipulate 7745 on a larger scale, by, say adding or subtracting 2153. But if I'm just adding or subtracting a 1- or 2-digit number I'll be zoomed into that vertical number line jumping up or down it, and there's no trading there either. 

One is certainly allowed to have more than one way to manipulate a model 😄 . 

 

Just now, Cake and Pi said:

Yep. I was pretty floored. I sincerely thought he had this already. Maybe he used to. It's definitely time to back up and camp out, though.

How did you test it? What did you do? 

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1 hour ago, Not_a_Number said:

How did you test it? What did you do?

I laid out 5 tally sticks, 4 parallel to each other and the 5th across and on top of the other 4. He's learned that this is 5. So I asked him how many there were and he answered "five." I took the top stick off and moved it a few inches to the side as he was watching, then asked again how many there were, but this time he said "six." I put it back and he said there were 5 again. I told him I was just moving the stick, directed him to watch closely, and put it off to the side again, and again he said there were 6. I asked him to count them, which he did and then told me there were 5. I tried various other arrangements of the 5 sticks (a pentagon, group of 2 and a group of 3, a zig zag pattern) and he came up with different answers each time before I had him count them. Of course, in between each trial I reminded him that the sticks were all the same and I wasn't going to give or take any. He was able to parrot back to me that there were fives sticks, but then when I moved them it was like he was totally guessing about how many there might be.

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5 hours ago, Cake and Pi said:

I laid out 5 tally sticks, 4 parallel to each other and the 5th across and on top of the other 4. He's learned that this is 5. So I asked him how many there were and he answered "five." I took the top stick off and moved it a few inches to the side as he was watching, then asked again how many there were, but this time he said "six." I put it back and he said there were 5 again. I told him I was just moving the stick, directed him to watch closely, and put it off to the side again, and again he said there were 6. I asked him to count them, which he did and then told me there were 5. I tried various other arrangements of the 5 sticks (a pentagon, group of 2 and a group of 3, a zig zag pattern) and he came up with different answers each time before I had him count them. Of course, in between each trial I reminded him that the sticks were all the same and I wasn't going to give or take any. He was able to parrot back to me that there were fives sticks, but then when I moved them it was like he was totally guessing about how many there might be.

I’m very glad @BaseballandHockey chimed in so you could test this!! That does sound like he’s having issues with quantity. It sounds like Ronit Bird is a good idea, as are all the other suggestions that address this.

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7 hours ago, Cake and Pi said:

I sincerely thought he had this already. Maybe he used to. 

the definition of an SLD

 

11 hours ago, Not_a_Number said:

So then his mental model of quantity is shaky.

Yes, number sense is the underlying component of dyscalculia. Now SLD math is broader and can be a bunch of things, but with dyscalculia we're specifically saying the number sense is affected. So op is on the cusp of thinking that's what she's seeing and I'm saying go there, use the term, assume it.

5 hours ago, Cake and Pi said:

I laid out 5 tally sticks, 4 parallel to each other and the 5th across and on top of the other 4. He's learned that this is 5. So I asked him how many there were and he answered "five." I took the top stick off and moved it a few inches to the side as he was watching, then asked again how many there were, but this time he said "six." I put it back and he said there were 5 again. I told him I was just moving the stick, directed him to watch closely, and put it off to the side again, and again he said there were 6. I asked him to count them, which he did and then told me there were 5. I tried various other arrangements of the 5 sticks (a pentagon, group of 2 and a group of 3, a zig zag pattern) and he came up with different answers each time before I had him count them. Of course, in between each trial I reminded him that the sticks were all the same and I wasn't going to give or take any. He was able to parrot back to me that there were fives sticks, but then when I moved them it was like he was totally guessing about how many there might be.

This is the convergence of autism and dyscalculia. Not only does he not have the number sense, but what he does have has not yet generalized. It's what happened with my ds, where he would know it with one thing and totally not with the next. 

You have RB Toolkit, so back up to her earliest lessons for number sense. All those lessons she does with dots/beads/dominoes, you need to repeat 6 ways to see if the concept will generalize. So can he see *1* popsicle stick in the array you laid out? That's it, just one. And do that with popsicle sticks and repeat with dominoes dots and glass beads and cute little turtle math manipulatives and m&ms and cookies you bake together. Over and over till no matter what it is he recognizes a *1* in there. And then you do this with *2*. 

She has games and whatnot to make it not so boring, but that's the jist. If he's looking at a field of 2, he should see two *1s*. And eventually, he'll see larger fields like 7 and be able to see 1+6, 2+5, 3+4, 1+1+1... etc. 

Sometimes the best way to go forward is to back up. 

Edited by PeterPan
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3 minutes ago, PeterPan said:

Sometimes the best way to go forward is to back up. 

Oh, totally. I see this at higher levels ALL THE TIME. If you miss a foundational concept, you can’t really go forward until that concept is there.

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I have had major setbacks with my son with retention.  He really may have known it before!  On some level.  If he has known it before, he can know it again.  It’s also easy to assume kids know things, and I have had major setbacks that way, too.

I am pretty sure my son could count items before he started Touchmath, but it does help kids to associate quantities.  

Something I feel like — we want kids to mix things up, but sometimes it is good if it’s the same way every time for a long time.  
 

To be honest I don’t know/remember everything with my son at this level.

But holding up fingers for 1-5 can be something.  Having him count his own fingers.

Also using a number line or a hundreds chart (but maybe a hundreds chart is too much right now — maybe a number line...... or maybe a ten frame that you make out of tape where it is multisensory and will be the same for a long time) and lay things in/on it and count.  
 

Though it sounds like he could do that bc the tally sticks.  Unless he has just memorized “say 5” on some level.  But doing that is a start!

Laying things out very orderly to count them, mix them up, then *lay them out very orderly again.*. Or don’t mix them up — remove one item and scoot the other ones over so visually it is connected.  With memory issues I think it can need to be more smooth visually and not “mix things up because you think they will remember what was just happening.*. Like — not to never do it, but to have more things be smooth visually.  
 

I have an opinion that a lot of dyscalculia things are not made for this level or for low working memory.  Edit:  I have to go...  but I think concept formation is also important and would be done not just with counting

Edited by Lecka
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5 minutes ago, Lecka said:

Something I feel like — we want kids to mix things up, but sometimes it is good if it’s the same way every time for a long time.  

Yeah, I think that can really solidify ideas when done right, and not just for kids with dyscalculia.

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I looked back and saw the Ronit Bird videos -- I had not seen ones like that before.  Ones I have seen have looked more advanced to me -- these do look good to me.  

Kids are so different, it is hard to know.  But my son had a lot of issues with "concept formation."  This was meant as -- the most basic kinds of abstract thought.  For an example of something my son worked on -- being able to identify ten examples of an item as all belonging to that same item label.  For example -- ten different spoons that were not all exactly the same size (or that looked different from each other, but would obviously be spoons).  That means getting past knowing some specific spoons are called spoons, to identifying it as a category/label and being able to sort items as being spoons or not.  He would get stuck on four or five examples of an item, and have a very hard time adding more items.  This is a level of abstract thought that is -- very basic, but it is also abstract, because you have to "form" a "concept" of what it means to be a spoon.  

Then another example is ordering things in order.  To put things in order -- at some level you have to understand what it means to put things in order.  Well -- this is also abstract in its way.  For an example -- for 3 sequence cards to put in order -- when my son had trouble understanding this as a concept (I think to some extent, not understanding what he was supposed to do) -- but one of the sequence card sets had 3 pictures, and it showed a boy going up a ladder on a slide, then on the slide (doing down the slide), then at the bottom of the slide.  You would think that would be so easy and obvious -- well, it was hard for my son, and he was on that level for a while.  

To some extent, this is my understanding -- there are still plenty of math concepts to work on, but if it is hard to understand sequencing as a concept, it is going to be hard to understand ordering numbers and relating to numbers as going in an order.  If it is hard to line things up from smallest to largest, too, then it is going to be hard to line up numbers and understand they are also going from smallest to largest.  

Then there is a lot of stuff with sorting.  As far as sorting goes -- sorting by color can be extremely hard.  Because -- how do you explain to someone "pay attention to what color it is" if that is hard to understand.  Because -- color is abstract, all different things are the same color, and it's confusing.  

From talking to other parents, it is impossible to tell sometimes that a certain child is struggling with this kind of thing.  They could be very, very strong in other ways.  But from talking to parents -- kids who would have a hard time sorting by color, would also have a hard time understanding numbers.  There is a level of them being abstract.  

Receptive sorting was one of my son's very strongest skills when he was little, so he was good at sorting.  He still had to spend a lot of time to learn -- but it was something he picked up more easily.  

Anyway -- there is a lot of sorting stuff to try to help kids form abstract categories.  My son had low expressive language, so with sorting it didn't require him to talk.  

This is the kind of thing he did at school (from pre-school when he went to special needs pre-school) and with ABA.  He did the kind of ABA where they use the VB-MAPP with early learners.  

If this kind of thing is part of what is going on, then working on any kind of abstract category should be helping with the concept of "we put things in categories and link them to an abstract category" or whatever.  This gets very confusing -- I have had it explained to me many times.  Anyway -- if it is an abstract concept kind of issue, then every abstract concept of any kind will help, because it will all be strengthening that kind of concept, and it should all help with "the concept of numbers."  

Your son could be farther in concept formation overall, and it could be "just math" or "just numbers."  This is definitely a thing, too, and what I think of more as dyscalculia.  If it is this way with other abstract concepts -- then it is tying into language, too, in a huge way, and it is very associated with autism.  

 

Edited by Lecka
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14 hours ago, Cake and Pi said:

I think so? Yes? I think our mental models are reversed, though. It goes the opposite direction in my head with trading flowing from place value instead of the other way around. Both models accomplish the same thing and seem to contain the same components. Maybe it's just a difference in how we each first made sense of quantity in our early days?

I'm with you.  I don't see these are two separate things, or one as primary over the other.  

To me, if there's a core mental model, it's the idea that numbers can be broken up into parts, and place value is a convenient way to represent those parts that makes conceptualizing and calculating with bigger numbers possible.  Trading is a way that we explore, and make sense of, and work within that framework.  

14 hours ago, Cake and Pi said:

Except... I go straight to trading when working in other bases... which again may be because that's the way I first understood other bases. Different mental models in different bases. Very inconsistent, lol.

It sounds like you are working with kids who see "12," know it is called "twelve," can count to twelve, but don't realize that twelve is a 10 and two 1s until you teach that to them, which you do only after they're comfortable with working until 20. 

I was perhaps trying to go about this in the opposite direction. I was thinking that place value might make numbers 11-20 accessible to DS 7 since he's had such a hard time conceptualizing them. Learning to count and name numbers and quantities 11-20 was one of his IEP goals last year, but he never got beyond rote counting. DS 7 sees "12" and says "twenty" or "one two." He sees "20" and also says "twenty" or "two zero" or just "two," and has been at this point for at least the last year and a half.

Does he do the same thing in reading?  

I think that place value will make it more accessible to him.  I just think he needs a stronger understanding of numbers as being made up of parts, and that he needs to explore that with numbers he can subitize first. He's really young.  He'll get there.  

14 hours ago, Cake and Pi said:

They didn't do any counting with addition. We did a bunch of work with the abacus and with visualizing, so they wouldn't need to count on. They'd just visualize a quantity and then some more and mentally subitize. With my kid who has trouble visualizing I focused more on +1 being "the next number" and +2 being the "next even" or "next odd" number. Perhaps this is actually a kind of counting and we're really talking a difference in semantics?

I don't really know what you mean by counting if you don't mean saying "the next number" after a number.  

14 hours ago, Cake and Pi said:

It's good that you began at the beginning with these lists of activities. I started trying stuff out with DS 7 last week. I *thought* he knew that quantity didn't change when it was rearranged, but apparently I was mistaken!

In general, do you you find it's better to run through all this with 0-5, then start over with 0-10, or is it better to focus on one task at a time first with 0-5 and then with 0-10 before moving on to the next task?

I would probably do the "4 is 4 is 4" stuff with 0 - 5, while still doing counting and number recognition to 11, and then when that's approaching solidity with that, do the "little numbers inside of big numbers" things with 0 - 5 and a little bit of the "4 is 4 is 4" stuff, and maybe counting and number recognition to 12.  I think that place value 0 - 20 will come easier if he has at least a few numbers in that range that he already recognizes, and I also agree with @Lecka that if we always stop at 10 then kids can get the sense that 10 is "the big number", which obviously is problematic. 

14 hours ago, Cake and Pi said:

I'm veering off topic here, but do you happen to have recommendations for beginning reading instruction as well...? Do you know of a curriculum or program for teaching reading to kids with significant language disabilities? DS 7 has had two years of sped preschool, two years of public kindergarten with 4 hours per week in the resource room with the O-G trained Learning Specialist, two summers of public summer school, and about 6 months of private language and literacy (O-G) targeted therapy spread out over the last year and a half. At home we've gone through the entire Explode the Code primer set (Get Ready, Get Set, and Go for the Code) TWICE and done a letter of the week type program. And, he still doesn't know the entire alphabet. Teaching him feels like trying to fill a cracked bucket with water.

I have lots of ideas!  Do you want to start a different thread?  Or should I put them here?

14 hours ago, Cake and Pi said:

Thanks again for typing out all those activities to work on, the apps, and the videos. I also got the RB Dyscalculia Toolkit book and am reading though it now.

I kind of forgot to come back, when I said I would.  So, I'm glad you reminded me.  I'll work on the next thing. 

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2 minutes ago, BaseballandHockey said:

I would probably do the "4 is 4 is 4" stuff with 0 - 5, while still doing counting and number recognition to 11, and then when that's approaching solidity with that, do the "little numbers inside of big numbers" things with 0 - 5 and a little bit of the "4 is 4 is 4" stuff, and maybe counting and number recognition to 12.  I think that place value 0 - 20 will come easier if he has at least a few numbers in that range that he already recognizes, and I also agree with @Lecka that if we always stop at 10 then kids can get the sense that 10 is "the big number", which obviously is problematic. 

I agree.  I would focus on 0-5, but include up to 11 for now 🙂

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6 minutes ago, BaseballandHockey said:

I'm with you.  I don't see these are two separate things, or one as primary over the other.  

I bet you can't define 7745 without trading. You just can't. It's where it comes from. Everything else flows from the idea of having units of different sizes such that each unit is worth x times as much as the previous one. (For us, x is the quantity equal to our total number of fingers, but it's the same idea for other values of x, which gives different bases.) 

Liping Ma calls this understanding the understanding of "decomposing a unit of higher value." That's the one thread that is essential to a deep understanding of place value. That's what she says, and that's what firmly believe. 

 

6 minutes ago, BaseballandHockey said:

To me, if there's a core mental model, it's the idea that numbers can be broken up into parts, and place value is a convenient way to represent those parts that makes conceptualizing and calculating with bigger numbers possible.  Trading is a way that we explore, and make sense of, and work within that framework.  

You can have a robust idea of quantity without any understanding of place value at all. Most typically developing children are very firm on the idea of quantity and breaking numbers up and have very limited place value understanding. I understand that for the kids you work with, that's not where they get stuck, but for the kids I've worked with, that has been unambiguously true.  

Edited by Not_a_Number
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3 minutes ago, Not_a_Number said:

I bet you can't define 7745 without trading. You just can't. It's where it comes from. Everything else flows from the idea of having units of different sizes such that each unit is worth x times as much as the previous one. (For us, x is the quantity equal to our total number of fingers, but it's the same idea for other values of x, which gives different bases.) 

 

You can have a robust idea of quantity without any understanding of place value at all. Most typically developing children are very firm on the idea of quantity and breaking numbers up and have very limited place value understanding. I understand that for the kids you work with, that's not where they get stuck, but for the kids I've worked with, that has been unambiguously true.  

I think you can have a robust idea of the quantity of 7 or 20 without understanding place value.  I don't think you can have a robust understanding of the quantity of 1,234,567,890 without an understanding of place value. 

I also don't think you can have fluency with place value with experiences working with it, which will involve skip counting, and trading.  

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Just now, BaseballandHockey said:

I think you can have a robust idea of the quantity of 7 or 20 without understanding place value.

Of course you can. And you should have that robust sense before you even get started on place value. 

I mean, we don't have to record 20 using place value at all. We could use Roman numerals and write XX. Why not? It represents the same quantity... 

 

Just now, BaseballandHockey said:

I don't think you can have a robust understanding of the quantity of 1,234,567,890 without an understanding of place value. 

Agreed. 

 

Just now, BaseballandHockey said:

I also don't think you can have fluency with place value with experiences working with it, which will involve skip counting, and trading.  

We never did skip counting, actually. I don't really believe in it, at least for the kids I've worked with. I just jump to multiplication. For the kids I work with, skip counting gets them stuck on "counting" instead of thinking in "copies." But we did a LOT of trading. Constant trading. 

My kids can skip count now, but they learned to multiply first. 

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3 hours ago, PeterPan said:

the definition of an SLD

Yes and no.  SLD is partially defined by discrepancy, and it isn't completely clear to me whether this is a global delay that impacting a wide variety of skills, or something that's more specifically impacting math.  

I'm not sure it matters here.  If I thought this was dyscalculia vs. a more global delay, I wouldn't suggest dramatically different interventions at this point, and what I'm suggesting isn't really any different from what I'd do if someone forced me to teach math in a structured way to a typical preschooler who was at the same point. 

3 hours ago, PeterPan said:

Yes, number sense is the underlying component of dyscalculia. Now SLD math is broader and can be a bunch of things, but with dyscalculia we're specifically saying the number sense is affected. So op is on the cusp of thinking that's what she's seeing and I'm saying go there, use the term, assume it.

This is the convergence of autism and dyscalculia. Not only does he not have the number sense, but what he does have has not yet generalized. It's what happened with my ds, where he would know it with one thing and totally not with the next. 

You have RB Toolkit, so back up to her earliest lessons for number sense. All those lessons she does with dots/beads/dominoes, you need to repeat 6 ways to see if the concept will generalize. So can he see *1* popsicle stick in the array you laid out? That's it, just one. And do that with popsicle sticks and repeat with dominoes dots and glass beads and cute little turtle math manipulatives and m&ms and cookies you bake together. Over and over till no matter what it is he recognizes a *1* in there. And then you do this with *2*. 

She has games and whatnot to make it not so boring, but that's the jist. If he's looking at a field of 2, he should see two *1s*. And eventually, he'll see larger fields like 7 and be able to see 1+6, 2+5, 3+4, 1+1+1... etc. 

Sometimes the best way to go forward is to back up. 

Yes 100% to the bolded.  

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Skip counting helped my son with counting numbers past 20.  It helped him be able to remember “what number comes after 29?” etc because he could think back to how he learned to skip count by 10s.  I think it is an important pattern to learn just for counting higher numbers, if that does not come easily.  

I think skip counting by 5s is needed for telling time on a clock, and desirable for counting nickels.  And that skip counting by 10s is desirable for counting dimes.  

Baseball and Hockey — where we lived when my son was in pre-school and Kindergarten, they included sequencing and sorting activities on their list of math skills, so those could be considered math skills.  Not like there wouldn’t be other math activities, but it was fair to work on sequencing and sorting as math skills.  That changed from 1st grade, but it was what they had for pre-school.  Anyway — you would be able to legitimately stay you were working on math while doing sorting or sequencing, you wouldn’t “have” to do just numbers and counting.  

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2 minutes ago, Lecka said:

Skip counting helped my son with counting numbers past 20.  It helped him be able to remember “what number comes after 29?” etc because he could think back to how he learned to skip count by 10s.  I think it is an important pattern to learn just for counting higher numbers, if that does not come easily.  

I think skip counting by 5s is needed for telling time on a clock, and desirable for counting nickels.  And that skip counting by 10s is desirable for counting dimes.  

You don't have to skip count. You can just define it as multiplication. It doesn't look very different in practice for things like "what's 10 after 20", to be honest, it's just a different starting point. You start with "3*10 means three 10s added together" and you work from there. At the beginning, you do wind up doing things like "two 10s and another 10," which is skip counting. 

Edited by Not_a_Number
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3 minutes ago, Lecka said:

Skip counting helped my son with counting numbers past 20.  It helped him be able to remember “what number comes after 29?” etc because he could think back to how he learned to skip count by 10s.  I think it is an important pattern to learn just for counting higher numbers, if that does not come easily.  

I think skip counting by 5s is needed for telling time on a clock, and desirable for counting nickels.  And that skip counting by 10s is desirable for counting dimes.  

Baseball and Hockey — where we lived when my son was in pre-school and Kindergarten, they included sequencing and sorting activities on their list of math skills, so those could be considered math skills.  Not like there wouldn’t be other math activities, but it was fair to work on sequencing and sorting as math skills.  That changed from 1st grade, but it was what they had for pre-school.  Anyway — you would be able to legitimately stay you were working on math while doing sorting or sequencing, you wouldn’t “have” to do just numbers and counting.  

Yes, to the bolded 100%.  I actually was going to talk about sequencing as my next skill, because I think it's critical.  I didn't start there because I wasn't clear if that was the weakness that was contributing to the specific place value problem.  It might be, and even if it isn't the problem here, working on those skills while waiting for maturation in other skills makes a lot of sense.  

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Just now, BaseballandHockey said:

Yes, to the bolded 100%.  I actually was going to talk about sequencing as my next skill, because I think it's critical.  I didn't start there because I wasn't clear if that was the weakness that was contributing to the specific place value problem.  It might be, and even if it isn't the problem here, working on those skills while waiting for maturation in other skills makes a lot of sense.  

What are sequencing skills? 

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7 hours ago, Not_a_Number said:

Of course you can. And you should have that robust sense before you even get started on place value. 

I mean, we don't have to record 20 using place value at all. We could use Roman numerals and write XX. Why not? It represents the same quantity... 

 

Agreed. 

 

We never did skip counting, actually. I don't really believe in it, at least for the kids I've worked with. I just jump to multiplication. For the kids I work with, skip counting gets them stuck on "counting" instead of thinking in "copies." But we did a LOT of trading. Constant trading. 

My kids can skip count now, but they learned to multiply first. 

So, I think this is the same problem as counting on.  That in my mind skip counting is a developmental conceptual thing that every kid needs, and that your kids almost certainly have.  I can't really imagine how one would teach place value and trading without some sense that if I have 3 tens that's thirty, and I can add another ten via trading and it's 40.  Similarly, if @Cake and Pi is saying that her kids understand "the next even number is . . . " then they are, in my mind skip counting on a conceptual level. 

Now, that doesn't mean you have to memorize the skip counting pattern for 6's and use that information in a Touch Math style way.  I totally agree that that's a strategy that works for some kids and not others.  

Edited by BaseballandHockey
because I wrote that skip counting is something "every kid has" when clearly I meant needs
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7 minutes ago, BaseballandHockey said:

So, I think this is the same problem as counting on.  That in my mind skip counting is a developmental conceptual thing that every kid has, and that your kids almost certainly have.  I can't really imagine how one would teach place value and trading without some sense that if I have 3 tens that's thirty, and I can add another ten via trading and it's 40.  Similarly, if @Cake and Pi is saying that her kids understand "the next even number is . . . " then they are, in my mind skip counting on a conceptual level. 

I think I know what you're saying. You're saying people need to understand the concept that you can "count in groups" -- that their sense of quantity is robust enough to support the idea of "one more 6 than three 6s makes four 6s." I absolutely agree with that! 

 

7 minutes ago, BaseballandHockey said:

Now, that doesn't mean you have to memorize the skip counting pattern for 6's and use that information in a Touch Math style way.  I totally agree that that's a strategy that works for some kids and not others.  

I've found that strategy very counterproductive for the kids I've taught, especially the weaker ones. One of them asked me "do I start at 0 or 6 when I skip count 6s," which just made me feel terrible. She had absolutely not internalized the point of skip counting. She just knew to say the pattern 😕 . She did much better in a more flexible model. 

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Sequencing is putting things in order.

It can be like steps of getting dressed.

Or it can be biggest to smallest.

Things like that.  
 

It can also be like “first we plant the acorn, then the oak tree starts to grow, then there’s a big oak tree.”  
 

Edit:  all kinds of things, really.  Anything that goes in an order, or could be put in an order.  

Edited by Lecka
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Just now, Lecka said:

Sequencing is putting things in order.

It can be like steps of getting dressed.

Or it can be biggest to smallest.

Things like that.  
 

It can also be like “first we plant the acorn, then the oak tree starts to grow, then there’s a big oak tree.”  

Got it, thank you. That's another skill I never had to work with with my kids because it came naturally. It's a good thing to think about. 

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1 hour ago, Lecka said:

Sequencing is putting things in order.

It can be like steps of getting dressed.

Or it can be biggest to smallest.

Things like that.  
 

It can also be like “first we plant the acorn, then the oak tree starts to grow, then there’s a big oak tree.”  
 

Edit:  all kinds of things, really.  Anything that goes in an order, or could be put in an order.  

All of these are great examples,

It's a really good example of how the lines between math and literacy in Preschool and Kindergarten curriculum is really fuzzy, because both are so tied up with language.

If we use words like next, then, and after to retell a story, we call it literacy.  If we sequence number cards, or put shapes in order by size, we call it math, but there are lots of things in the middle where it's really gray.  

 

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10 hours ago, Lecka said:

I looked back and saw the Ronit Bird videos -- I had not seen ones like that before.  Ones I have seen have looked more advanced to me -- these do look good to me.  

Kids are so different, it is hard to know.  But my son had a lot of issues with "concept formation."  This was meant as -- the most basic kinds of abstract thought.  For an example of something my son worked on -- being able to identify ten examples of an item as all belonging to that same item label.  For example -- ten different spoons that were not all exactly the same size (or that looked different from each other, but would obviously be spoons).  That means getting past knowing some specific spoons are called spoons, to identifying it as a category/label and being able to sort items as being spoons or not.  He would get stuck on four or five examples of an item, and have a very hard time adding more items.  This is a level of abstract thought that is -- very basic, but it is also abstract, because you have to "form" a "concept" of what it means to be a spoon.  

Then another example is ordering things in order.  To put things in order -- at some level you have to understand what it means to put things in order.  Well -- this is also abstract in its way.  For an example -- for 3 sequence cards to put in order -- when my son had trouble understanding this as a concept (I think to some extent, not understanding what he was supposed to do) -- but one of the sequence card sets had 3 pictures, and it showed a boy going up a ladder on a slide, then on the slide (doing down the slide), then at the bottom of the slide.  You would think that would be so easy and obvious -- well, it was hard for my son, and he was on that level for a while.  

To some extent, this is my understanding -- there are still plenty of math concepts to work on, but if it is hard to understand sequencing as a concept, it is going to be hard to understand ordering numbers and relating to numbers as going in an order.  If it is hard to line things up from smallest to largest, too, then it is going to be hard to line up numbers and understand they are also going from smallest to largest.  

Then there is a lot of stuff with sorting.  As far as sorting goes -- sorting by color can be extremely hard.  Because -- how do you explain to someone "pay attention to what color it is" if that is hard to understand.  Because -- color is abstract, all different things are the same color, and it's confusing.  

From talking to other parents, it is impossible to tell sometimes that a certain child is struggling with this kind of thing.  They could be very, very strong in other ways.  But from talking to parents -- kids who would have a hard time sorting by color, would also have a hard time understanding numbers.  There is a level of them being abstract.  

Receptive sorting was one of my son's very strongest skills when he was little, so he was good at sorting.  He still had to spend a lot of time to learn -- but it was something he picked up more easily.  

Anyway -- there is a lot of sorting stuff to try to help kids form abstract categories.  My son had low expressive language, so with sorting it didn't require him to talk.  

This is the kind of thing he did at school (from pre-school when he went to special needs pre-school) and with ABA.  He did the kind of ABA where they use the VB-MAPP with early learners.  

If this kind of thing is part of what is going on, then working on any kind of abstract category should be helping with the concept of "we put things in categories and link them to an abstract category" or whatever.  This gets very confusing -- I have had it explained to me many times.  Anyway -- if it is an abstract concept kind of issue, then every abstract concept of any kind will help, because it will all be strengthening that kind of concept, and it should all help with "the concept of numbers."  

Your son could be farther in concept formation overall, and it could be "just math" or "just numbers."  This is definitely a thing, too, and what I think of more as dyscalculia.  If it is this way with other abstract concepts -- then it is tying into language, too, in a huge way, and it is very associated with autism.  

 

All of this!  Everything you've said here I agree with 100%.

I'll add that since @Cake and Pi asked specifically about place value, I was only thinking of offering numeracy ideas, and I'll come back with more.  But there are absolutely other pieces of math, in measurement, and geometry, and sorting, and time concepts that are important, and interspersing those with concepts of number can be a great way to give a kid a little space to allow number concepts to absorb and solidify, while you wait for some developmental leap.  

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My son did some Reading Mastery.  

He did a sight words program that ---- okay, it helped him, but it also led to some "known problems with sight words programs" issues.  I was so mad at the time that they would use a sight words program, and the program they used, if you google it, says it's for kids they don't think can learn to sound out words, and the goal is functional sight words to read -- like -- the men and women signs on a restroom door.  Maybe that is an exaggeration.  But at the time -- I was so mad about it, but really, in retrospect, I do think it helped him.  And he was not *only* doing that program.  

It is hard for me to remember exactly.  Reading Mastery explicitly teaches blending, and when he did it, they made index cards for him so he could practice the same few words over and over.  It is similar to Teach your child to read in 100 EZ lessons ------ but it had more to it.  They are both direct instruction programs.  

My son had "low retention" when he was doing early math skills.  

With low retention -- basically this means forgetting things.  

This means slowing down, reviewing more, practicing more, and looking for more ways to generalize (do the same kind of thing with a different activity or in some different way).  It means always reviewing, and devoting a LOT of time to reviewing.  

There are "review box" methods where you space things out for review.  You could (for example) write an activity or skill on an index card.  Have review sections in a box.  Have things mixed into daily review, weekly review, monthly review, and then just review.  You can move something from the weekly review section, to the monthly review section, after it's been remembered 4 times in a row (or more -- if you consistently see that cards moved to monthly review are not retained well, then you can increase the time they stay in weekly review before they go to monthly).  And then after monthly review -- there can just be "mastered" but still go through that here and there.  

That is what is recommended for low retention.  So -- it is good to just be going through and reviewing all the time, anyway, so -- I would say always be doing a mix of things.  

And often spend more time on review than on new things.

Where often things are set up -- to spend more time on something new, and less time on review.  It is vice-versa with low retention.

My son's retention improved as he got older and also as he got solid on some skills that had been hard for him for a long time.  Then he did start to have an easier time.  

I would also say -- for some things, you want a high % right to move on.  This can be hard if you get into "is it wrong, or did he just not feel like doing it?"  You can do it again the next day when he's definitely not tired.  

Also be careful about giving hints, without realizing it, or presenting things in a way where answers can be memorized -- this is a good teaching method, but it's important to know if a non-memorized answer can be come up with.  

Discrete trial training, from ABA, in my experience is good about this.  It is all about -- in my experience -- keeping a review box kind of thing, and making sure that answers are kept track of, and if hints are being given -- which is good for learning -- it is conscious that that answer is known with a hint, not without a hint.  

You might ask your ABA provider for information about it.  There might be some good ideas you would want to use.  

I was also going to say, for some things, you want a really high % correct before moving on to new material that needs the old material mastered..... because it's really easy for an answer that has a 50/50 chance of being correct, to make an average higher, when really -- maybe there is still some confusion there.  

I also wished and hoped that my son could leapfrog in math, since it was obvious language was going to be a long road.  Well -- I know this happens for some kids.  But for many kids -- they go together, and for a lot of kids there just is not a leapfrog.  

It can come across like this happens a lot, because I hear about it a lot, but from what I have seen -- those are more of exceptions.  

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You can start on blending without all letter names/sounds learned.  This can help with retention over time.  
 

Do you have a speech eval with info about phonemic awareness?  


You can use a review box also and work with 8 letters (or something) and slowly add new ones.  
 

I know we had “ram” as a card and he would have to go over just that word and blending the sounds for a while, and it could be one thing while doing other letter activities or phonemic awareness or listening.  

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https://autismclassroomresources.com/how-can-we-best-teach-reading-to-students-with-autism/
 

This is a post by someone I like, about teaching reading to children with autism.

 

Not that I would not teach reading at all — but it can be small part of a language program with language goals.  It can depend how fast kids go with reading — they can adjust.  A lot of times people do a mix of highlighting the child’s strongest area while keeping up some work on weaker areas including the pesky weakest areas.  My son was weaker in reading but had some other language-type skills, while other kids took off with reading but might be going slower with something like — answering questions with wh words.

It just depends, but language skills might be things like wh words and ffc (feature, function, and class).  Or describing pictures.  Or describing sequence cards using “first, then, next.”  Or using the word “not.”  Those kinds of things can be part of reading/language.  For what I am familiar with — there are things like VB-MAPP and ABLLS. There is another one that is older and less language-y that our public school system used.  I believe this was it (I’m not 100% sure). https://www.amazon.com/gp/aw/d/0890796831/ref=dbs_a_w_dp_0890796831
 

I don’t know if you have stuff like this and are supplementing academics.  
 

But it sounds like you have a newer autism diagnosis and might not have looked into stuff like this. There is a lot out there.  
 

 

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2 hours ago, Lecka said:

You can start on blending without all letter names/sounds learned.  This can help with retention over time.  

I know this isn't autism-specific, but we did 100 EZ Lessons, and that's exactly what they do -- they start with a few letters and teach blending with those letters along the way. It worked well for both my kids, especially for DD4, who actually seriously struggles to internalize letters and letter combinations. Actually, for DD4, we had to slow it down even further... but she got it all down and is now a strong reader. 

Anyway, I think it can work well to introduce blending before all the letters are learned. 

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You also might see if there are different IEP services available if you ask them to change his qualifying condition to autism.

Some places are that way.  
 

Maybe after corona or just if you wanted to see some time.  

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I am sorry, I keep meaning to come back to this, but I'm having a busy week.   I'm just going to address the philosophical piece right now, because I'm kind of turning into a pumpkin, but I will come back and tell you how to put this in action.  In the meantime, I agree with everything  @Lecka  said.  

I'll also add that a lot of what I'm going to say is going to sound like heresy to many people on a Classical Education Board where people love phonics and copywork.

I'm a big fan of Karen Erickson at the Center for Literacy and Disability Studies at UNC Chapel Hill.  I love her work.  In her book, Comprehensive Literacy for All (Teaching Students with Significant Disabilities to Read and Write)  she talks about several models for literacy, one of which divides up the knowledge we need to read and write into four categories:

Conceptual Knowledge (knowledge about the functions of print, and about themselves as a learner)

Procedural Knowledge (knowledge related to letters, sounds, and words)

Oral Language Knowledge and Comprehension

and 

Metalinguistic knowledge related to phonological and syntactical awareness. 

Often times students arrive at school, or at school age if they're homeschooled with many of these skills already built.  They might have strong oral language.  They might understand the reasons and ways that people use print, and see themselves as people who are becoming literate.  They might already know some things about letters and sounds and words, and be able to play with sounds and syntax.

Kids with dyslexia often arrive at the same age with most of those skills, and very specific deficits in procedural knowledge, and the phonological piece of metalinguistic knowledge.  

For kids in both of those categories, it can be very appropriate to narrowly focus on phonological and procedural skills, using either a high quality phonics curriculum written for general education, or an Orton Gillingham Program.  These programs can be the final piece in the puzzle of learning how to read, and can lead to a lot of success.  For families and teachers of typical kids, or kids with very specific disabilities, like dyslexia, it can seem as though these are all that kids need to learn to read, but in reality, kids are just integrating this new knowledge and skill with what they already knew.  

When a child comes to school or reaches school age in homeschool, with delays that impact them more globally this doesn't work.  I want to be clear that I'm not using global delays as a synonym for ID.  It doesn't seem like that's what's going on here.  But it does seem as though right now your @Cake and Pi little guy has some delays in underlying skills such as engagement, self regulation, joint attention, language, attention etc  .  . that impact him across multiple domains of development.  In those cases, kids are going to need a program that weaves together all 4 strands, and that puts a lot of emphasis on that contextual strand, and the oral language strand.  In addition, we need to careful that we aren't accidentally teaching procedural skills in a way that interferes with that conceptual knowledge development. 

To give an example of what I mean, I'll take the task of writing.  At a conceptual level, writing is what happens when I have a thought that is formed in words inside my head.  I take that thought and transfer the words to paper, representing them with letters that stand for the sounds in the words, and then someone else looks at the paper, translates those letters into sounds in their head and now the thought that was in my head is in their head too.  It's really kind of a magical thing. 

Some kids come to Kindergarten or even preschool knowing that.  They're sneaking in under your arm and asking you what you're writing, and they're approximating writing in their play, and they're thinking of words to ask you to spell for them, and then showing the words to Daddy.  For those kids, who are solid on that concept of how print works, it can work really well to spend a large chunk of "school" working on letter names or sounds, or doing copywork, and kids can get that this is a task they need to do so that one day it will be easier for people to read the thoughts they put down on paper. 

But for a kid who gets to school age, and whose conceptual knowledge of how print works is shaky, focusing on skills in isolation, whether that's letter names, or handwriting, or sight words, can reinforce the wrong ideas.  They can easily come to see writing as a test to pass, or as a guessing game, and that misunderstanding can both hinder their ability to apply what they are learning in any kind of context, and their engagement in doing the hard work to remember what they're supposed to be learning at all.  And so, we need to figure out ways to work on letters and sounds and sight words and phonological awareness that keep making and sharing meaning in the center of our process, and that also help students both develop their vocabulary and syntax, and apply their vocabulary and syntax to the tasks of reading and spelling.  

I'll be back! 

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OK, I'm back.  

So, how do we teach kids procedural knowledge like phonemic awareness and letter names and sounds while simultaneously teaching kids that these are powerful things that can be used in meaningful ways?  How do we help kids engaged and motivated?  them and revisiting them in their working memory, which is what builds memory?

Here are a few activities I particularly like.  A lot of this comes from Karen Erickson, who I referenced above, combines with my own experiences.

One place I would slightly disagree with Karen Erickson is that she makes a big deal about the dividing line between emergent reading instruction and conventional reading instruction, and has a list of 4 questions you can ask to tell which one to do.  In my experience, that line is far muddier than she makes it out to be, and many kids benefit from a mixture of Emergent and Conventional activities for a long time.  That's where I'm guessing @Cake and Pi's  little guy is, so I'm going to make suggestions from both those lists, although I'm just going to make some of them here, because of time. 

Emergent Reading Strategies

Shared Reading

This is basically bedtime style reading where you and the child share a book and talk about what you're reading.  I'm guessing you're already doing this.

Interventions for Oral Language

The stronger his vocabulary and syntax are, the better he'll be able to use these things to support his reading and writing.  As @Lecka pointed out, speech therapy and oral language need to be a high priority.  

Shared Writing: Predictable Chart

if you asked me to pick one activity I found particularly powerful for teaching early reading and writing it would be this one.  

Basically, in this activity you start by using sentence strips or strips of paper, to write sentences that follow a pattern, each accompanied by a picture.  For example, I might make a book that has pictures of loved ones, and text that says "Name loves Mommy".  "Name loves Daddy".  "Name loves Grandma".    Or I might make simple line drawings of my kid doing various things and write "I can run."  "I can swim."  "I can dance."   Over time, I might connect the words to science.  For example, I might get a picture of a favorite animal, and zoo in on various body parts and take screen shots, and make a book that says "I see a foot."  "I see a tail". "I see an ear."  and in the end "I see a kangaroo!"

I'd then practice reading the sentence a few times, and then I'd take the sentence, give it to the child, and ask them to cut the words apart (or ask them to point to where they want me to cut if that's where they are motorically).  After each cut, I'd check.  If the child accidentally cut in the middle of the word, I'd point out that they accidentally cut "can" in half, and tape it back together before trying again.  Correcting and talking about errors will probably yields more learning than getting it right.  While I do this, I'm reinforcing the idea that these are words, they start here, and stop here, and they're separated this way.  I'm also reinforcing the repeated words, which are likely high frequency words.

Then we take the words from the sentence, shuffle them up, and then problem solve how to put them back together.  This is a time for lots of conversation and problem solving.  "OK here we have Johnny.  Now we're writing Johnny can swim.  We have Johnny, now we need can so it will say Johnny can.  Which word is can?"  Again, let the kid make mistakes.  Then read the mistakes, laugh at the mistakes "Ooops we made Johnny swim can.  Swim can?  That's not right.  Let's try again."  While you're doing this you're going over the sight words over and over again.  You can also reinforce other strategies, like using first sounds.  "Can  cccaaaaannn /k/ an. I need a word that starts with /k/.  Remember /k/ looks like this (shows them the hand shape for the ASL sign for C, or write a c with your finger on the table, or point to a C somewhere around.  Hmmm, which of these words starts with C.  Oh you're so clever!" or referring to a mentor text (teacher speak for the last sentence you wrote).  "Johnny can. . . " Hey wasn't "can" in our last sentence, let's look back there. Oh yeah, we wrote "Johnny can run.  So, this says Johnny can run.  Johnny  . . . can  . . . yep that word's can, let's look back at our (2) word cards, which one looks like can.  Those match!  OK, put that here.

Then take the words, tape them back together and put them in some kind of book form, and add the book you've made to your reading rotation, as a text to review sight words and to practice fluency.  Have your kid call Grandma and read the book on Zoom.  

Here's an online training on Predictable Chart Writing.  Note that this training was written with a grant that's specific for kids with significant cognitive impairment.  So, it references it a lot.  But, it's also a strategy I use with kids, like yours, who don't fall into that category.  It's also written for a classroom with multiple kids.  

https://unc.az1.qualtrics.com/jfe/form/SV_06NLeVyP59uQ5Y9?Q_JFE=qdg

 

Independent writing with an Alternative Pencil

This is my other favorite activity.   

I strongly believe that every kid over the age of 5 needs a way to write all the letters of the alphabet, and to explore with them, and try them out, and practice being readers and writers.  Too often, or kids with disabilities, we delay this.  So, the other kids are playing with writing, or making cards for Grandma, etc . . . , and the kid with disabilities is instead either dictating, with the adult controlling the pencil, or they are copying out handwriting, or they're doing some fine motor task that leads to handwriting, but we (by which I mean the special education community as a whole) treat writing like it's about the fine motor piece, when in reality three are other critical pieces that kids need to practice like having ideas, and holding them our heads while we write, and connecting sounds in words, and kids with disabilities whose disabilities impact their motor skills or their letter learning, often miss all of those.  

An alternative pencil, which is just another way to make letters, is a way around that.  For most kids that I teach, and I'm guessing for yours, I would suggest a keyboard, but some kids will use a letter board, or an alphabet flip book, or stamps, or stickers.   You can also use more than one thing, e.g. a keyboard sometimes, and pointing at letters on a letter board for you to write sometimes, and using stamps at other times.  

Once you figure out how he's going to write, then I usually provide two types of experiences:

1) Experiences where kids use their alternate keyboard to write things in real context, or in the context of play that imitates real context.  This could be using stamps to "write their name" on a card to Grandma, or using a letter board to dictate letters for you to add something to the shopping list, or using a keyboard and a printer to make a sign for a block construction building, or scribbling to pretend to take orders when you play restaurant. 

2) Formal writing experiences where you find or take a picture, or he draws one if he's got some representational skills, or he tells you what to draw, and then he writes words to go with it.

In both cases, I'd spend as much time as I needed picking a topic, and a purpose, and then I'd let him write using all the letters of the alphabet however he accesses them.  

After he writes, I'd have him tell you what he wrote and write those words underneath.  Then I'd make connections between what he wrote, and what he told you he said.  So, if he tells you he's writing about cars and trucks, and there's a c in his writing, I might circle it and say "I see you used the letter c to write about the cars you saw today.  Let me show you how I write car".  If he can't tell you what he wrote, then i would still look for letters that you can comment on.  

Here's a training about this process.  Like the Predictable Chart Writing above, it is from DLM, and is written to highlight the work of the most complex kids, kids who have more needs than your son.  I think they do that intentionally to show that they really do mean every child. But their work is applicable to much wider range of kids than who they highlight. 

https://unc.az1.qualtrics.com/jfe/form/SV_es4fZVSDnrafgpv?Q_JFE=qdg


Here's a piece of writing I love about the way that one parent uses an alternative pencil with her son, who his about your son's age.  

https://www.kimrankin.com/new-blog/2019/3/14/encouraging-emerging-independent-writing-in-a-young-aac-user?rq=pencil

Using Letters and Sounds Across Contexts

I would work on using the letter knowledge he does have, in contexts, and on building recognition of more letters in the context of meaningful activities.  

One activity that I really like is "voting by letter".    This relates to the math activity I described above in the math activity where you makes graphs of various information.  Think of a question with two or three answers like "Which animal do you like best? Dogs or Cats or Fish", or "Where should we go this weekend Hiking or the Zoo".  Ideally some of the time it should be an activity where you can actually make the decision happen (e.g. what should we make, cookies or brownies?").  Have each person write the first letter of the thing they vote for, or you write them, and then sort the letters, and make a little graph to see which one wins.  Then act on it!

Also encourage him to use letters to solve problems (easier not in a pandemic, I know) so in the grocery store, let him know you're looking for pinto beans, and write a P on a post it note and then have him help you find the beans that start with P.  
 

Note: here is a Jolly Phonics video for your enjoyment.  I started to write about phonics for a kid like this, and realized that is a whole different post, but somehow I can not erase the video.  So, please, enjoy it!  It has some catchy tunes.  

And note, I'm not anti phonics.  Phonics is just a "conventional strategy" although it's one I would start now, and I decided to divide this into a post about emergent strategies, and a post about conventional strategies.  So, it's coming, but maybe tomorrow or Friday. 

 

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23 minutes ago, BaseballandHockey said:

Phonics is just a "conventional strategy" although it's one I would start now, and I decided to divide this into a post about emergent strategies, and a post about conventional strategies.

Is an "emergent strategy" sort of a pre-reading strategy? 

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  • Cake and Pi changed the title to Math Woes (and some reading/language discussion beginning on p.4)

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