Jump to content

Menu

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


Recommended Posts

  • Replies 213
  • Created
  • Last Reply

Top Posters In This Topic

Top Posters In This Topic

Popular Posts

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

2 minutes ago, Not_a_Number said:

It's being exposed to the model that makes them fluent.

Is this the same as "going over it"?  Giving the explanation and tieing it to whatever the activity is?  Then I totally agree.  It is easy to do things that are just "going through the motions."  

 

4 minutes ago, Not_a_Number said:

Usually, the time they need is measured in months and not days

Yes -- this is what I think with place value -- I think kids are exposed and exposed and practice and practice, so that when they get to 2nd grade, hopefully they are ready to make trades for addition and subtraction.  

  • Like 1
Link to post
Share on other sites
Just now, BaseballandHockey said:

@Cake and Pi Did you not teach counting on or did your kids not know it?  Are you saying that they weren’t using it when they got placevalue? 

I am not sure that teaching counting on is the right description.  I think that most kids just reach a point in their math understanding when it is there. 

I definitely teach counting on. I did with all my homeschool class kids. It was really helpful for them, because they didn't have to count everything from 1 after I taught it, which I think enhanced their understanding of numbers as being "all together," so to speak. 

  • Like 2
Link to post
Share on other sites
Just now, Lecka said:

Is this the same as "going over it"?  Giving the explanation and tieing it to whatever the activity is?  Then I totally agree.  It is easy to do things that are just "going through the motions."  

Yes -- this is what I think with place value -- I think kids are exposed and exposed and practice and practice, so that when they get to 2nd grade, hopefully they are ready to make trades for addition and subtraction.  

I think of making trades as the thing you're supposed to be exposed to. So, I expose my kids to the place value model by making them actually do trades for calculations. With my classes, I also have them make lots of trades up and down for games. 

  • Like 3
Link to post
Share on other sites
15 minutes ago, Cake and Pi said:

Okay. So just for fun, I decided to ask the numerate members of my immediate family about their mental models for numbers. 

DH:
He says he sees just the digits of a number, the way one would write the number, in his mind with an implicit understanding that the digits are multiplied by powers of ten, and that's it unless he is given context. With context he switches to visualizing quantities, quite accurately, so it sounds like he uses a quantity model. He gave me some examples that I'm not going to remember correctly. Something like one cubic foot of concrete is a cube *this* big (holds out hands). Ten cubic feet of concrete is a traffic barrier. Three hundred cubic feet of concrete is the foundation of our home, etc. He said if the context were stuffed animals, "one" would be a kid holding a stuffy. "Six" or "ten" might be a shelf with stuffies lined up on it for sale in a store. "Fifty" might be a claw machine full of stuffies, etc. 

For reference, he is a chemical engineer who does mostly process and controls engineering in mining, mineral processing, and water treatment. He also handles the budgets and cost estimates for enormous large-scale projects. He's sort of a Jack of all trades in the engineering world. He routinely works with very large numbers that represent large *physical* quantities, usually in the millions, of um, STUFF, lol. He doesn't remember early elementary or the process of learning place value.

Honestly, if you ask me to visualize a number, I'll probably do the digits, too. However, if you make me think about how I think about integers, I do think about counting and not measuring. So I have a quantity model of number even thought I don't see it in my head. 

 

15 minutes ago, Cake and Pi said:

DS 13:
Numbers were not automatically associated with any mental image, just sounds. He has great trouble visualizing in general. However, when pressed to "picture" a number in his head, he arrived at a length model. He said 27 is a vertical stack of 27 balls next to a measuring tape with the height of the stack equivalent to the quantity in the stack. When I asked about bigger numbers, like 1,123, he said he envisioned basically block letters of "1123" rotated 90 degrees counterclockwise and stretched until the height of a measuring tape at 1,123.

Background: DS 13 is 4ish years accelerated in math, ASD, PG, and NOT a visual thinker (unusual for ASD, but there you go). Compared to my other 2e kids, he had a relatively difficult time understanding place value. I think we worked on the idea of place value for a solid month when he was 4y 11m to 5y 0m old before it clicked. 

Interesting. 

 

15 minutes ago, Cake and Pi said:

DS 11:
For small numbers, under 10, he envisioned groups of cakes, lol. For slightly bigger numbers, his mental model was cookies lined up horizontally with groupings of 5. He described 27 as essentially OOOOO  OOOOO  OOOOO  OOOOO  OOOOO OO. 1,123 was a big pile of 1,000 cookies with a smaller pile of 100 cookies to the right of that and a line (again grouped in 5s) of 23 more cookies to the right of that.

Context: DS 11 is maybe 2 years accelerated in math, PG with a small army of other Es, and suspected ASD. He picked up on place value immediately the first time I introduced it at 4y 3m. As in, he was immediately able to do *all* of the skills I described in an earlier response to you that I hope to get DS#4 doing eventually. As soon as I explained that 1,000 was 10 hundreds, he could say that there must be 100 tens in 1,000, could build numbers with any of our manipulatives from a number said aloud or written down, could write and say a number based on a physical model of it, etc. After all the trouble DS#1 had, I was armed and ready to hunker down and focus on place value for a while, but he seriously got it the very first day I introduced it to him.

Cakes, lol! I love it. 

 

15 minutes ago, Cake and Pi said:

DS 9: 
DS 9's response basically blew my mind. I obviously don't operate on the same wavelength as him. I asked him what he saw in his mind when he thought of 27 and his response was "three cubed." Okay, new tactic needed. I figured he'd have some other model for non-square, non-cube numbers but figured composite numbers might elicit a similar response, and so I asked him what he envisioned with the first prime number that popped in my head, 31.
"Two to the fifth minus one."
Oooookaaaaaaaay...... "But what do you SEE in your mind for 31?" I asked.
"I see zeros and ones," he answered.
"Seventy two. What do you see for seventy-two?" 
"A seven and a two with a one and a two under them."
"Whaaaaat? What are the one and the two?"
"They're places for the hoppers. You can change the orders of the numbers and hoppers go with them so they're the same number."
Then he described putting apples into his "inventory" and using "block commands" and "burning up" 9 apples to "transfigure" 10 regular apples into a golden apple and having separate hoppers to put regular apples and golden apples in... but then he said his hoppers hold multiples of 64. Oh, but he doesn't always use hoppers. He also has buckets. The buckets can be empty or full of water, and those are all zeros and ones (binary). Or he can stack two buckets and add water to the inner bucket and have all zeros, ones, and twos (base 3, I guess). So I essentially have no idea what, if any, mental model he has for numbers, place value, anything. There seems to be an evolving complicated something going on in his head all the time.

Hahahaha, I do have opinions on basically all the numbers under 100, so I can imagine saying something like what he said for the first few numbers 😄 . Like, I do think of 27 as 3^3 and of 31 as 2^5 - 1. I don't have any hoppers in my head, though!! 

(On the other hand, 91 is just mean. It pretends to be a prime but it's NOT.) 

  • Like 1
Link to post
Share on other sites
3 minutes ago, Not_a_Number said:

I think of making trades as the thing you're supposed to be exposed to. So, I expose my kids to the place value model by making them actually do trades for calculations. With my classes, I also have them make lots of trades up and down for games. 

With an hto chart (for example) you don't have to make trades.  You can represent the number you have in the chart, and can do that without making trades.  

You can work on trades separately as "making trades."  With a game or something.  

 

 

  • Like 1
Link to post
Share on other sites
Just now, Lecka said:

With an hto chart (for example) you don't have to make trades.  You can represent the number you have in the chart, and can do that without making trades.  

You can work on trades separately as "making trades."  With a game or something.  

I know, but I personally think conceptually place value is about making trades. I don't think of the other things as actually being conceptually place value -- rather, they are about noticing patterns that come out of place value. 

To me, place value just means "different units in a number count different things." To get a feel for things counting different things, you trade. And then you trade. And you trade some more. 

  • Like 1
Link to post
Share on other sites

I have seen kids make trades in a very rote way.  I think if trades are done with just someone going "now you give me this one and I give you that one" kind of stuff, I don't expect much to come out of that.  

Very irritating.  

Of course that would be fine for many kids.  

But some people give less explanation and more rote "now do this, now do that" with kids with special needs.  It's a major pet peeve of mine.  

For my other two kids -- it would probably be fine if they were playing math games in a group while the teacher sat at her desk.  That would probably meet their needs.  Not to say -- that is all they would need.  But it would probably be effective/purposeful as practice.  

  • Like 1
Link to post
Share on other sites
2 minutes ago, Not_a_Number said:

I know, but I personally think conceptually place value is about making trades. I don't think of the other things as actually being conceptually place value -- rather, they are about noticing patterns that come out of place value. 

To me, place value just means "different units in a number count different things." To get a feel for things counting different things, you trade. And then you trade. And you trade some more. 

I don't think this would work with everyone.  I don't think everyone can pick up the "trades" concept and directly transfer that to the written numbers.  

If you think that is something fine to do but just not in the category of "place value" -- I could agree with that.  If you called that "writing numbers" or something.  

  • Like 1
Link to post
Share on other sites
3 minutes ago, Lecka said:

I have seen kids make trades in a very rote way.  I think if trades are done with just someone going "now you give me this one and I give you that one" kind of stuff, I don't expect much to come out of that.  

Well, if it's always the same rule, and you always use the same model, and you talk about how that doesn't change the number, it really does develop a sense of place value. 

It's OK for trading to be rote. There's no meaning in it, anyway. A green chip isn't worth 10 yellow chips for any profound reason -- it's just what we decided. The interesting thing is what we learn when we use that over and over and over again. 

Edited by Not_a_Number
  • Like 1
Link to post
Share on other sites
Just now, Lecka said:

I don't think this would work with everyone.  I don't think everyone can pick up the "trades" concept and directly transfer that to the written numbers.  

I don't think anything works with everyone, but I do think this is the concept you're trying to teach -- that you can trade a unit for 10 of another unit. There's really nothing else TO place value. 

  • Like 1
Link to post
Share on other sites
3 minutes ago, Not_a_Number said:

Well, if it's always the same rule, and you always use the same model, and you talk about how that doesn't change the number, it really does develop a sense of place value. 

It's OK for trading to be rote. There's no meaning in it, anyway. A green chip isn't worth 10 yellow chips for any profound reason -- it's just what we decided. The interesting thing is what we learn when we use that over and over and over again. 

This depends on a lot of things.  I do NOT think this is a great thing to say for special needs, especially possible memory issues.  

It is actually really easy to do things in a rote way, and not make the connection.  

Really, really easy.  

I have an impression this is especially the case for kids with autism who have very low working memory.  And a lot of kids who have ASD level 2 are going to have low working memory.  

With low working memory, it is really easy for kids to go "okay, I'll do this thing."  And then "okay, I'll do that thing."  But there is not a connection made, they are forgotten.  

Making the connection just by doing something over and over is just not something to expect.  

And if there is a language delay -- then any kind of self-talk kids might have where they are narrating to themselves what they are doing, and thinking to themselves "now I am doing this, now I am doing that," which REALLY helps in noticing patterns -- you just can't count on any of that self-talk being present in a way that can help kids to remember things.  

You have to say (or show) the things that you want them to be noticing, and not just think -- if they do it enough, they will notice on their own.  There are actually things that support that ability to notice and remember, that can be problems.  

Because literally just doing an action is not what is going to produce learning, unless the learning is just the action -- and the learning we would want is an understanding of place value.  

A lot of kids with autism also have trouble with sequencing, my impression is this goes along with low working memory and language delay, because it just makes it harder to remember things and the order they happen.  There is less self-narration of "I am doing x, I did x" and there is less ability to remember things as a cohesive sequence of events, instead of random actions.  

When this is the case -- it is just not going to be easy to do something over and over and make connections, because the ability to make the connections is not as good.  

But math activities can be great for working on sequencing, self-talk, etc, etc, all those things that can help kids to develop the skills of "learning to learn." 

Developing the skills of "learning to learn" are big things in autism.  You can't assume that kids are showing up with "learning to learn" skills and even when they have them, certain things tend to be harder for them if they have low scores in certain areas (like expressive language or working memory).  

 

  • Like 3
Link to post
Share on other sites
33 minutes ago, Not_a_Number said:

You're right that some concepts can absolutely be taught as lightbulbs being suddenly switched on. That generally works best with concepts that kids are naturally exposed to over and over again, and it also works best for naturally mathy kids. So, mathy kids have spent time reading numbers, and thinking about groups, and maybe using money, and maybe listening to you talk to older kids... so they are already primed for the concept. 

However, I teach LOTS of things most kids aren't in any way primed for. I teach kids vectors, and I teach kids variables, and I teach kids trig, and I teach kids parametrizations, and even advanced kids tend to need to have time with the concepts to have them really sink it. Usually, the time they need is measured in months and not days. And if you don't give the kids that time, they pretty much never figure out the concept, no matter how many times we try to USE the concept. Using it isn't the thing that gets kids fluent. It's being exposed to the model that makes them fluent. This was a serious epiphany for me, and it has vastly improved my teaching. 

So for me, the idea that place value would also require lots of time is just a natural outgrowth of other things I teach. I also teach my own kids quite young, which means I'm often teaching at the bottom end of when it's developmentally reasonable. That also extends the required exposure time (but also makes them fluent sooner, of course.) 

 

Oh, obviously you don't need to count on to do place value -- they are disjoint skills. But "counting on" can show awareness of a number as a concept, particularly if you use it in conjunction with subitising. And that makes it likelier that a kid will be able to accept that a differently-colored chip might genuinely mean a different quantity.

I think some kids need to be taught to apply counting on a strategy for formal symbolic addition, but I can’t think of a kid I know who got place value, and I’ve worked with a lot of kids, who didn’t show me in other ways that if they knew a quantity they could count up from that number to solve some kind of real life problem.

  • Like 2
Link to post
Share on other sites
Just now, BaseballandHockey said:

I think some kids need to be taught to apply counting on a strategy for formal symbolic addition, but I can’t think of a kid I know who got place value, and I’ve worked with a lot of kids, who didn’t show me in other ways that if they knew a quantity they could count up from that number to solve some kind of real life problem.

Oh, yeah, I believe that. I'm just saying it's also possible to teach it. Not that you have to, but you can. But I agree that a kid ought to be read to count on to "get" place value. 

  • Like 1
Link to post
Share on other sites
2 minutes ago, Lecka said:

This depends on a lot of things.  I do NOT think this is a great thing to say for special needs, especially possible memory issues.  

It is actually really easy to do things in a rote way, and not make the connection.  

I'm not saying the whole process is rote. I'm just saying the fact that a chip gets traded for 10 chips of another color, and not, say, 9 chips or whatever... that's rote, because there's nothing to understand. That's just something you remember. 

But there are lots of interesting observations to make when you trade. For instance, you can compare sizes. You can add. You can subtract. If a kid is able to, you can learn to associate those numbers with written numbers. You can keep score using poker chips and keep track of who's winning. 

I'm not saying place value learning is rote. I'm saying that the early stage of it -- which, for me, is the trading -- involves a rote procedure. But that procedure can lead to sophisticated understanding, in the same way that working with written numbers eventually leads to a sophisticated understanding of written numbers, even though when we simply learn to write them down, we do start by saying "this unit is worth a 10, and this unit is worth a 1." 

  • Like 1
Link to post
Share on other sites
2 minutes ago, Not_a_Number said:

Oh, yeah, I believe that. I'm just saying it's also possible to teach it. Not that you have to, but you can. But I agree that a kid ought to be read to count on to "get" place value. 

I am still not sure what it is here.  Are you saying that you can teach counting on, or teach it as a strategy in formal math.

  • Like 1
Link to post
Share on other sites
Just now, BaseballandHockey said:

I am still not sure what it is here.  Are you saying that you can teach counting on, or teach it as a strategy in formal math.

What is "formal math"? I mean, I teach kids to put numbers together using counting on -- I explain why it works so that kids stop counting from 1. 

  • Like 1
Link to post
Share on other sites
7 minutes ago, Lecka said:

When this is the case -- it is just not going to be easy to do something over and over and make connections, because the ability to make the connections is not as good.  

Right. I absolutely believe that. I'm sure some kids need more handholding than others. I'm not suggesting being hands-off with place value teaching. When I use poker chips, we have LOTS of conversations about what's going on with them and why things work and what's allowed and what's not. Just like one would have those conversations about written numbers. 

  • Like 2
Link to post
Share on other sites
4 minutes ago, Not_a_Number said:

What is "formal math"? I mean, I teach kids to put numbers together using counting on -- I explain why it works so that kids stop counting from 1. 

To me, formal math is math that involves symbols like numerals and plus signs in this case.  If a kid shows me elsewhere they can count from a number, then I can say, hey you can use that here in addition and they will understand.  

Like if a kid is cracking eggs into a bowl for scrambled eggs and we drop the one that should be 5, but they can go to the fridge and get another one and come back and put it in the bowl and count 5, then they get it.

Or if they can have 4 chicken nuggets and see that their brother had 5 and have a fit and then when you give them one more know they have 5 even before it’s on the plate, and either stop whining or, if they are my persistent youngest, tell you they really wanted six?  

Those kinds of things tell me that if I try to teach counting on as an addition strategy or place value it won’t work, other as as very brittle memorized algorithm.

  • Like 1
Link to post
Share on other sites
1 hour ago, Cake and Pi said:

DS 13:
Numbers were not automatically associated with any mental image, just sounds. He has great trouble visualizing in general.

Do you think he has a developmental vision problem (which would cause the poor visualization) or do you think it's an indication of synesthesia? It might be worth teasing apart. Both could be going on even. But the synesthesia can run in families and if present, yeah it could make things uber glitchy. I never realized till my dd was 20 and started talking about it that she was experiencing synesthesia. I've been realizing I need to investigate it for ds and just haven't gotten around to it.

1 hour ago, Cake and Pi said:

My only explanation is that he was paying attention to my conversations with older siblings as he played quietly in the same room 

That is a riot! I can see why this last dc is such a jolt!

1 hour ago, Cake and Pi said:

I *never* taught counting on to the older three boys, at all, ever -- so they obviously mastered place value without first having that skill.

I'm trying to ponder in my mind dyscalculia vs. some kind of seizure/damage. Did you say he had CP or some kind of oxygen deprivation? I don't know. It just seems odd to have ALL the other children be crazy ahead and then this one so radically different. Have they done genetics to see if he has a syndrome going on? Even within autism you can have mutations and syndromes. 

 

  • Like 2
Link to post
Share on other sites
5 minutes ago, BaseballandHockey said:

To me, formal math is math that involves symbols like numerals and plus signs in this case.  If a kid shows me elsewhere they can count from a number, then I can say, hey you can use that here in addition and they will understand.  

Like if a kid is cracking eggs into a bowl for scrambled eggs and we drop the one that should be 5, but they can go to the fridge and get another one and come back and put it in the bowl and count 5, then they get it.

Or if they can have 4 chicken nuggets and see that their brother had 5 and have a fit and then when you give them one more know they have 5 even before it’s on the plate, and either stop whining or, if they are my persistent youngest, tell you they really wanted six? 

Those kinds of things tell me that if I try to teach counting on as an addition strategy or place value it won’t work, other as as very brittle memorized algorithm.

I'm really sorry, but I'm not following! I'm not relating counting on to place value. But I've explained to kids how to do additions like 8 + 1 without counting them from 1. I generally build up on the kids' understanding of counting -- I've only worked with kids who understand quantity fairly well via counting, and I do think that's true on average. 

But anyway, I'd talk to a kid about why if you're doing 8+1, you don't have to count the 8, because if you counted it, you'd just end at 8, right? So can you keep going? And for kids who are comfortable counting, they do absorb that and stop counting from 1 in a way that doesn't seem at all brittle. Honestly, it was the opposite of brittle when I taught it -- practically all the kids I taught like this retained it despite seeing me for an hour once a week, which was REALLY not enough. 

ETA: I was often teaching this in the context of games, not written addition. Some of the kids who were being taught this couldn't write well and mostly needed this for games with dice or with Tiny Polka Dot cards or with normal cards for Addition War. 

Edited by Not_a_Number
  • Like 1
Link to post
Share on other sites

 

12 hours ago, Not_a_Number said:

But why do you expect all those understandings at once? My question was whether you could START with teaching him the names for numbers purely using place value chips. This could temporarily be his model for bigger numbers, while you worked on one-to-one correspondence, counting, and counting on with other items. As he keeps trading and playing games and naming the numbers, his understanding might increase. I understand that it won’t generalize to other manipulatives or to the concept of place value in general, but it’s a model. 

Oh, I don't. I would think that if he was going to get it any time soon, though, he would understand *some* portion of all of that, not all of it. I was just illustrating that that he doesn't have any understanding at all. None of the pieces are there. I think @Kanin might be right about DS 7 thinking the trading game is hilarious precisely because it makes no sense to him and he thinks it's funny that such an obviously unfair trade (to him) is being promoted by me.

12 hours ago, Not_a_Number said:

Do you think having him associate a 23 with 2 yellows and 3 greens will hamper him when you work with other manipulatives? 

No idea, really. Right now I can't even get him to associate 23 with 2 yellows and 3 greens, though, and I'm not sure I really want to put energy into trying to teach it to him to him anymore. I've really spent the last 4 months on this and the only progress we made was that he temporarily was able to name (or when he wasn't speaking, point out cards with the numbers written on them) some multiples of 10 represented on the abacus. That skill is gone now, so we're basically exactly where we were four months ago.

12 hours ago, Not_a_Number said:

I think that right now, you want him to LOOK at a ten (in a ten frame, in a hand, as a base-10 block, etc) and immediately grasp it as a single entity that ought to be categorized as such when you make up a number, and he's not ready for that. However, since he CAN trade, he could work on his association between 10 units and a single 10. The nice thing about a place value chip is that it's obviously a single entity and not 10 things. You don't get distracted into counting it, because there's nothing to count. So every time you trade up and down, you work on the idea that a 10 (at least in place value chips!) really is represented by a single thing. You work on it in a physical way with a specific object and you accept that having an easy model means that it won't be a widely applicable model. 

I agree. I think I will ditch the place-value chips though, in favor of using dimes and pennies since that doubles as an applicable life skill, and right now we're just hoping that he'll be able to live independently as an adult some day.

 

10 hours ago, Lecka said:

I really think he could just want his pizza in 3 pieces just because.

Have you done same/different?

If you have — you can line up 3 little pieces and 3 big pieces and ask him if he thinks they are the same or different.

I think he hasn't made the leap that total amount does not necessarily relate directly to number, that pieces with different sizes represent different quantities or that you can break something into pieces and still have the same amount. For example, he has a medication he takes each night. His dosage is 3.5 squares, which ends up being four pieces (three wholes plus a half square). I break the pieces off of a bigger block, and if I leave two squares joined, he asks for more because he only has three separate pieces. He'll say that I didn't give him enough.

We've done lots work with same/different. He likes worksheets where he is supposed to find the one picture in a group that is slightly different from all the others. It's just not translating to math or quantities. To use @PeterPan's analogy, I think it's getting filed in some other, non-math, non-quantity related folder. We need to work on it more.

10 hours ago, Lecka said:

Are you going down a list of these from speech therapy or something?

...

Have you done anything with sorting by feature, function, and class?  There is a lot out there for this with autism.

No for the first, but we probably should be.

Yes for the second, for years. It's obviously in need of more work, though!

Thanks pointing this out.  When we get private speech up and running again, I'll be sure to include this his goals.

9 hours ago, Lecka said:

I kind-of think making trades is probably more advanced than needed at this point.

Yes, I completely agree. We'll revisit trading, probably with dimes and pennies, in a while -- possibly a long while. I'm going to switch over to the Ronit Bird stuff for now.

8 hours ago, Not_a_Number said:

I'm actually not trying to make the abstract part of numbering as concrete as possible. What I'm trying to do is create an equivalent model that is possible to appreciate using lots of hands-on experimentation. And generally, I don't expect this model to be internalized in days or even in weeks. I expect it to be slowly internalized over the course of months. 

I haven't worked with students with a language disability, so I really can't claim that I have data that I do not. I'm really just chiming in because I know that the way I conceive of teaching place value isn't much like what I've seen anyone else do. But since I'm not finding myself able to explain why it works or how it's different, I probably should stop.

I think my DS 7 *needs* everything to be as concrete as possible. Honestly I'm not convinced that having such a model, other than in the context of money, is a gainful use of his time and limited mental energies. He's not going to just experiment with a model and discover things. He must be taught every. single. step. He must be pulled to every. single. conclusion. He has to be taught how to play with every. single. new toy. 

I like your idea for kids in general, maybe just not for kids like my DS 7.

  • Like 2
Link to post
Share on other sites
2 minutes ago, Cake and Pi said:

I think my DS 7 *needs* everything to be as concrete as possible. Honestly I'm not convinced that having such a model, other than in the context of money, is a gainful use of his time and limited mental energies. He's not going to just experiment with a model and discover things. He must be taught every. single. step. He must be pulled to every. single. conclusion. He has to be taught how to play with every. single. new toy. 

I like your idea for kids in general, maybe just not for kids like my DS 7.

Eh, then just use money 🙂 . But I wasn't arguing that he's going to experiment himself -- I was saying that you'd do the experimenting together. I'm not really a "discovery model" person, per se -- I like my discovery VERY guided. 

What I'm really saying is that place value chips (and dimes and pennies, because it's the same thing, anyway) ALLOW one to get more of a feel for what the quantities mean. You're already trying to introduce him to written numerals, right? Written numerals are much worse than place value chips or than dimes and pennies. There's no way to get a feel for anything unless you're already good at manipulating things in your head. 

 

5 minutes ago, Cake and Pi said:

No idea, really. Right now I can't even get him to associate 23 with 2 yellows and 3 greens, though, and I'm not sure I really want to put energy into trying to teach it to him to him anymore. I've really spent the last 4 months on this and the only progress we made was that he temporarily was able to name (or when he wasn't speaking, point out cards with the numbers written on them) some multiples of 10 represented on the abacus. That skill is gone now, so we're basically exactly where we were four months ago.

It really does sound like he isn't ready. I did have kids who weren't ready for place value in my homeschool classes. They were shaky on subitising and had trouble counting on. They seemed like they needed more experience with the idea of number before they could group numbers.
 

8 minutes ago, Cake and Pi said:

Yes, I completely agree. We'll revisit trading, probably with dimes and pennies, in a while -- possibly a long while. I'm going to switch over to the Ronit Bird stuff for now.

I think that makes a ton of sense. 

Part of the reason I was talking about a developing photograph is that I have the sense that you're used to things "clicking" as opposed to developing, because your kids are mathy and also enjoy math and play with it. And my experience with topics that kids aren't already playing with themselves is that developing is much more common than clicking, even with really accelerated kids like my DD8. 

Now, it sounds like this photograph isn't ready to develop at all, so may as well leave it. But maybe for later, thinking about what model you're trying to communicate is a good idea 🙂. Some kids can absorb lots of models at once. And some kids can barely figure out one. 

  • Like 1
Link to post
Share on other sites
2 minutes ago, Not_a_Number said:

I'm really sorry, but I'm not following! I'm not relating counting on to place value. But I've explained to kids how to do additions like 8 + 1 without counting them from 1. I generally build up on the kids' understanding of counting -- I've only worked with kids who understand quantity fairly well via counting, and I do think that's true on average. 

But anyway, I'd talk to a kid about why if you're doing 8+1, you don't have to count the 8, because if you counted it, you'd just end at 8, right? So can you keep going? And for kids who are comfortable counting, they do absorb that and stop counting from 1 in a way that doesn't seem at all brittle. Honestly, it was the opposite of brittle when I taught it -- practically all the kids I taught like this retained it despite seeing me for an hour once a week, which was REALLY not enough. 

So I think that your students are probably not coming in at the same point that I understand this kid to be at. I could be wrong, and I apologize to @Cake and Pi if I am misunderstanding.  My point is that there is a point at which kids can be taught counting on as a strategy for formal math like 8 + 1, and they can learn it easily.  But this kid isn’t there.

In order to understand place value you have to have an understanding that number is an attribute of a set, and that we can represent a number by organizing that set in various ways.  So we can show the concept of 5 by holding up all the fingers on one hand, or by drawing a picture of 3 ducks in a pond and 2 beside it, or by ordering 5 counters in a dot pattern, but that all 3 of those sets share this attribute of fiveness. 

Once a kid can get that, and has an understanding of five that goes beyond “the number I get if I count this set”, and can figure out by visualizing, for example, that if they have 4 fingers up and put up their thumb, or they have a dot pattern of 4 and add a counter in the middle and it will be 5, then they are ready to both count on as an addition strategy, and to begin to tackle place value.  Many kids who have rich experiences will get to that point without being taught, and so it can be easy to think that 8+1 is a starting point.  But it really isn’t, it’s just that the early learning happened naturally.  For some kids, like kids with dyscalculia, or kids with cognitive disabilities, or kids with severe deficits in executive functioning, we need to present those early concepts in a more intentional way and lead them to readiness.  It’s not exactly teaching, it’s more like providing them the experiences that will lead to the lightbulb moment, because these are really developmental concepts.

  • Like 2
Link to post
Share on other sites
1 minute ago, BaseballandHockey said:

Once a kid can get that, and has an understanding of five that goes beyond “the number I get if I count this set”, and can figure out by visualizing, for example, that if they have 4 fingers up and put up their thumb, or they have a dot pattern of 4 and add a counter in the middle and it will be 5, then they are ready to both count on as an addition strategy, and to begin to tackle place value.

Yeah, I agree with you. I was agreeing with you that those both show an understanding of number as a concept, and therefore, while you didn't technically need to be able to count on to do place value, they require the same skills. 

  • Like 1
Link to post
Share on other sites

So, @BaseballandHockey, how would you know if a kid has a good fundamental understanding of quantity? I don't personally visualize numbers at all. If you asked me to visualize what happens if I raise an extra finger after 4, I'd find that harder than just doing 4 + 1. So how can you tell when there's confusion? Would a kid have trouble extrapolating from 2 ducks and 2 ducks to 2 oranges and another 2 oranges? What are some definite symptoms of confusion? 

  • Like 1
Link to post
Share on other sites

Inconsistent or nonsensical answers.  
 

Just not being able to do it.

 

Being able to copy/repeat but that is all.  Edit:  when copying/repeating getting a detail wrong in a way that is just — nonsensical.  

Edited by Lecka
  • Like 2
Link to post
Share on other sites

Rapid guessing.

Saying the answer to the previous problem.

Always pointing to the left when there is a choice of left or right.  

Always saying the second choice when given a choice. 

  • Like 3
Link to post
Share on other sites
4 hours ago, ieta_cassiopeia said:

Alternative solution for the Ronit Bird issue: consider downloading (or downgrading) to version 12.6.5.3 of iTunes, which is the last version of iTunes to allow management of books. That should allow you to run the Ronit Bird eBooks on your computer. (But whatever you do, don't let iTunes update itself, and keep a backup of the installer file in case).

 

Old versions of iBooks can still get books, so in principle it should be possible for older versions of iTunes to do so (since it appears books are still classified as such at Apple's end, in a way that is backwards-compatible).

Unfortunately, this did not work. 😞 It was a great idea! I tried getting the sample on this version of iTunes and got "This book sample requires an iPad with the latest version of iOS and Apple Books installed and Automatic Downloads enabled."

Our charter funds roll over in April, after which I'll have a fresh $1,800 at my disposal for technology and curriculum for DS 7. I may end up just buying an iPad at that point. This is not the first time I've felt like we really needed one for something.

  • Like 1
Link to post
Share on other sites
Just now, Lecka said:

Rapid guessing.

Saying the answer to the previous problem.

Always pointing to the left when there is a choice of left or right.  

Always saying the second choice when given a choice. 

All these and “fishing”, extolling through answers and watching your face to see it they hit the right one.

  • Like 3
Link to post
Share on other sites

Really an example — just getting an obvious “more or less” problem incorrect.  
 

Like — if working on numbers and then they can’t say who has a bigger pile of chips when one pile is comically larger.  
 

It’s a 50-50 chance!  
 

We would have that.  
 

Edit:  this could make me think — he is memorizing a position but not understanding one number is more or less than another

With this also — randomly giving an answer two more instead of two less when that really would not make sense — like just guessing but also doing part of it right but in a way where it shows — they did not understand.  

Or doing 3 similar problems, then going back to a previous problem type, and it is done the same — no ability to tell apart two problem types 

Edited by Lecka
  • Like 1
Link to post
Share on other sites

I also think I see it more in what they do then in how they answer questions.

Like for example, if I ask a kid to put 5 of something on a table.  At school that would be “we’re going to need 5 whiteboards for this game, can you grab them?”

I have kids who would go get a couple put them on the table, count to 2, realize they need more. go back for a couple more, count get 4 realize they need more, and go back and get a couple more, count realize they have two many, make a set of 5 and put the other one back. I would not attempt to teach counting on to that kid.

I have other kids who might get 2, then 2 more, count and realize they need 1 more.  That kid might be ready for counting on.

Then I might have a kid who got 2, and then got 2 more and knew without counting that it was 4, either because they carried the first 2 in their head and thought 3,4 when they picked up 2 more, or because they combined the 2’s in their head, or because they automatically subitized when they put it on the table.  That kid I can say with confidence is ready.

Or a kid who I know can subitize 2 but when I go to move my piece in a board game and I skip a square and start counting from 2 (not skip counting, just jump to 2 and then count by 1’s) and is convinced I cheated?  That kid’s number sense is very young.

 

  • Like 4
Link to post
Share on other sites
13 minutes ago, Cake and Pi said:

Our charter funds roll over in April, after which I'll have a fresh $1,800 at my disposal for technology and curriculum for DS 7. I may end up just buying an iPad at that point. This is not the first time I've felt like we really needed one for something.

Yay!!! I'm glad you'll have some funding options. Also you could look at therapro, proedinc, super duper, and maybe consider an AAC app like LAMP. But an ipad could be huge. I'm glad you have that option coming!

  • Like 2
Link to post
Share on other sites
5 minutes ago, BaseballandHockey said:

I also think I see it more in what they do then in how they answer questions.

Like for example, if I ask a kid to put 5 of something on a table.  At school that would be “we’re going to need 5 whiteboards for this game, can you grab them?”

I have kids who would go get a couple put them on the table, count to 2, realize they need more. go back for a couple more, count get 4 realize they need more, and go back and get a couple more, count realize they have two many, make a set of 5 and put the other one back. I would not attempt to teach counting on to that kid.

Me neither.

 

5 minutes ago, BaseballandHockey said:

I have other kids who might get 2, then 2 more, count and realize they need 1 more.  That kid might be ready for counting on.

Yeah, I agree that you'd need understanding of at least "how many more?" for small numbers. I tend to do small additions with my kids and other number sense stuff before we do counting on. But I definitely have never worked with kids other than my kids when young who can't do this stuff. So I have zero experience. 

 

5 minutes ago, BaseballandHockey said:

Then I might have a kid who got 2, and then got 2 more and knew without counting that it was 4, either because they carried the first 2 in their head and thought 3,4 when they picked up 2 more, or because they combined the 2’s in their head, or because they automatically subitized when they put it on the table.  That kid I can say with confidence is ready.

Makes a lot of sense. 

 

5 minutes ago, BaseballandHockey said:

Or a kid who I know can subitize 2 but when I go to move my piece in a board game and I skip a square and start counting from 2 (not skip counting, just jump to 2 and then count by 1’s) and is convinced I cheated?  That kid’s number sense is very young.

Do kids associate numbers with board game moves relatively readily?  

  • Like 1
Link to post
Share on other sites

In my mind, place value is a way of organizing quantities to make them easier to wrap our mind around them and to manipulate them.  But organizing large quantities only makes sense if you have the basic principle that numbers can be thought of as made up of components.  That 7 IS 4 and 3.  Not just that if you count out 4 and then count out 3 and then count them together you will get 7, or that if you see 4 + 3 on Xtramath and press 7 you get a smiley.  I think it is way easier to teach a kid that numbers have components Ronit Bird style than it is to teach them in a context of 20 and 7 is 27.  

Although I also reread @Cake and Pi‘s original post and it’s possible I imagined the kids I’ve worked with and I am underestimating.  

  • Like 3
Link to post
Share on other sites
2 minutes ago, BaseballandHockey said:

Although I also reread @Cake and Pi‘s original post and it’s possible I imagined the kids I’ve worked with and I am underestimating.  

So, I had the impression that he was probably ready for counting on and probably not ready for place value. He sounded more like my weaker homeschool class kids than the kids you work with. But I'm not SURE about that or anything. 

Edited by Not_a_Number
  • Like 1
Link to post
Share on other sites
3 minutes ago, Not_a_Number said:

Me neither.

 

Yeah, I agree that you'd need understanding of at least "how many more?" for small numbers. I tend to do small additions with my kids and other number sense stuff before we do counting on. But I definitely have never worked with kids other than my kids when young who can't do this stuff. So I have zero experience. 

So when I say a kid needs to be able to count on that’s what I mean.  Not that they need to be able to or choose to apply counting on as an addition strategy.  It was why I questioned when  @Cake and Pi said her kids couldn’t count on.  

3 minutes ago, Not_a_Number said:

 

Makes a lot of sense. 

 

Do kids associate numbers with board game moves relatively readily?  

Some of them yes, some no.

I teach mostly much older kids.  Like I have kids working where this kid is now, but they are 16 not 7.  And many of them like board games.  I usually play monopoly for the first couple weeks of school, with pennies dimes and dollars, and a graphic organizer.  I switch up the dice and introduce a calculator half way through.  By the end of the first couple weeks I know what I need to know about each kid to teach.  

  • Like 1
Link to post
Share on other sites
3 hours ago, BaseballandHockey said:

Did you not teach counting on or did your kids not know it?  Are you saying that they weren’t using it when they got placevalue? 

I am not sure that teaching counting on is the right description.  I think that most kids just reach a point in their math understanding when it is there. 

3 hours ago, Not_a_Number said:

I definitely teach counting on. I did with all my homeschool class kids. It was really helpful for them, because they didn't have to count everything from 1 after I taught it, which I think enhanced their understanding of numbers as being "all together," so to speak. 

My older three kids never did counting on at all. They also never did the pre-skill to counting-on that counting-on replaces and is more effeciciant than: counting up from 1. So, when I gave them an expression like 4+3 or a group of 4 and 3 more objects, they never counted up from one like "I have 1, 2, 3, 4... 5, 6, 7" to get the sum and they also never counted on like "I already have 4, so 5, 6, 7." I taught them to subitize 0-10 as five-and-something first, absolutely no counting. Then they automatically regrouped with 5s instead of counting. So, 4+3 was "Move 1 from the 3 to the 4. Now I have 5 and 3, that's 8." They would do this with their fingers at first, but later just did it in their heads.

I straight up never taught them to count objects. We used counting to mark time. Like, we counted to 20 when washing hands. I made them count the number of seconds for their timeouts, so at 2yo they were counting to 50-120 (as they were able), at 3yo they counted to 100-200 (depending on how serious the crime, lol), and so on. We used counting to keep track of quantities that were not easy to see, such as cups of flour for a big batch of homemade bread or drops of a water clarifying solution put into the fish tank. I suppose they picked up 1-to-1 correspondence that way? I don't know. It was just never NOT there. As soon as they started saying and reading numbers, the numbers were associated with the corresponding quantities. It seemed automatic. 

When determining number of objects, I taught them to line things up into groups of 10 made of two 5s, which they could do without any counting. So I guess place value was built into everything we did anyway.

In kindergarten my DS#2 was asked to count in a group activity and he told the teacher no, announcing loudly that "counting is slow and inefficient and often inaccurate" and that he could figure out the number better by grouping. He got sent to the office and I got a phone call because the teacher felt like he was undermining her authority in front of the class. She insisted that he NEEDED to count and that if he didn't he would never understand numbers. She sent me studies showing that kids who could count to 20 when they entered kindergarten did better on math assessments in 4th or 6th grade or something than kids who couldn't count. I felt like she missed the point of those studies.

3 hours ago, Not_a_Number said:

I know, but I personally think conceptually place value is about making trades. I don't think of the other things as actually being conceptually place value -- rather, they are about noticing patterns that come out of place value. 

I generally don't do any trading in my mental arithmetic. For smaller numbers, I'm just going up the number line. There are hops up my number line going on in my head. I used to have something like an old-time car odometer in head. In fact, I'm pretty sure I learned to count by watching the way the separate wheels would spin on odometer of my mom's car. The next wheel to the left would catch and spin with the 9, bringing the wheel to the left up 1 while the wheel on the right came back to 0. But that was when I used counting to add. When my strategies got more efficient, my mental model shifted to a vertical number line.

  • Like 1
Link to post
Share on other sites
21 minutes ago, Cake and Pi said:

I generally don't do any trading in my mental arithmetic. For smaller numbers, I'm just going up the number line. There are hops up my number line going on in my head. I used to have something like an old-time car odometer in head. In fact, I'm pretty sure I learned to count by watching the way the separate wheels would spin on odometer of my mom's car. The next wheel to the left would catch and spin with the 9, bringing the wheel to the left up 1 while the wheel on the right came back to 0. But that was when I used counting to add. When my strategies got more efficient, my mental model shifted to a vertical number line.

I believe you that’s what you do, and it clearly works for you, but those are derived from the model. They aren’t primary. The primary model is that one unit is worth 10 of another.

Out of curiosity, can you do arithmetic in other bases? I don’t mean do them quickly, but you can use base 2, right? 
 

26 minutes ago, Cake and Pi said:

In kindergarten my DS#2 was asked to count in a group activity and he told the teacher no, announcing loudly that "counting is slow and inefficient and often inaccurate" and that he could figure out the number better by grouping. He got sent to the office and I got a phone call because the teacher felt like he was undermining her authority in front of the class. She insisted that he NEEDED to count and that if he didn't he would never understand numbers. She sent me studies showing that kids who could count to 20 when they entered kindergarten did better on math assessments in 4th or 6th grade or something than kids who couldn't count. I felt like she missed the point of those studies.

Lol! Yeah, kindergarten can be like that... 

I do teach my kids to group, but I find our life is easier if it’s easy for them to add 1 or 2 to a number. I don’t use counting on for bigger numbers — maybe 3 occasionally. Otherwise, I group. But I find that the addition facts come faster with counting on for small numbers. And I like them to be able to add a small number quickly to a larger number, too.

 

29 minutes ago, Cake and Pi said:

I suppose they picked up 1-to-1 correspondence that way? I don't know. It was just never NOT there.

I think most kids do understand quantity intuitively. Some things your kids do are definitely not standard, but this one is common. 

  • Like 1
Link to post
Share on other sites
3 hours ago, Lecka said:

This depends on a lot of things.  I do NOT think this is a great thing to say for special needs, especially possible memory issues.  

It is actually really easy to do things in a rote way, and not make the connection.  

Really, really easy.  

I have an impression this is especially the case for kids with autism who have very low working memory.  And a lot of kids who have ASD level 2 are going to have low working memory.  

With low working memory, it is really easy for kids to go "okay, I'll do this thing."  And then "okay, I'll do that thing."  But there is not a connection made, they are forgotten.  

Making the connection just by doing something over and over is just not something to expect.  

And if there is a language delay -- then any kind of self-talk kids might have where they are narrating to themselves what they are doing, and thinking to themselves "now I am doing this, now I am doing that," which REALLY helps in noticing patterns -- you just can't count on any of that self-talk being present in a way that can help kids to remember things.  

You have to say (or show) the things that you want them to be noticing, and not just think -- if they do it enough, they will notice on their own.  There are actually things that support that ability to notice and remember, that can be problems.  

Because literally just doing an action is not what is going to produce learning, unless the learning is just the action -- and the learning we would want is an understanding of place value.  

A lot of kids with autism also have trouble with sequencing, my impression is this goes along with low working memory and language delay, because it just makes it harder to remember things and the order they happen.  There is less self-narration of "I am doing x, I did x" and there is less ability to remember things as a cohesive sequence of events, instead of random actions.  

When this is the case -- it is just not going to be easy to do something over and over and make connections, because the ability to make the connections is not as good.  

But math activities can be great for working on sequencing, self-talk, etc, etc, all those things that can help kids to develop the skills of "learning to learn." 

Developing the skills of "learning to learn" are big things in autism.  You can't assume that kids are showing up with "learning to learn" skills and even when they have them, certain things tend to be harder for them if they have low scores in certain areas (like expressive language or working memory).  

All of this 100% fits my observations with DS 7. 

3 hours ago, PeterPan said:

I'm trying to ponder in my mind dyscalculia vs. some kind of seizure/damage. Did you say he had CP or some kind of oxygen deprivation? I don't know. It just seems odd to have ALL the other children be crazy ahead and then this one so radically different. Have they done genetics to see if he has a syndrome going on? Even within autism you can have mutations and syndromes.

Both, they're interrelated. Just google HIE. CP is a pretty misleading term for his condition, honestly. It's probably better to just stick with encephalopathy. Whole exome sequencing was clear. He has ASD and ADHD and probably SLDs, but so do some or all of the older three. The only difference between them and him is the encephalopathy.

4 hours ago, BaseballandHockey said:

My point is that there is a point at which kids can be taught counting on as a strategy for formal math like 8 + 1, and they can learn it easily.  But this kid isn’t there.

No, he's not really there yet. He's close, though. He can count on with with smaller quantities in context. Like he knows when his brothers have 3 slices of pizza and he only has 1 and can even tell you that he needs 2 more. Same with if he has 3 pieces of chocolate and thinks he should have 4. He can tell you he needs 1 more. He can add on his fingers up to 5 or so when it suits him. But he can't tell you how old he'll be on his next birthday, and when he gets tired basically anything bigger than 7 is "nine" or "twenty." It's coming though. We could use counting on within 5.

6 hours ago, Not_a_Number said:

you said your kiddo did have a sense of one-to-one correspondence, right? Am I remembering right? Or is his sense of quantity shaky? 

Yes! He usually has 1-to-1 correspondence when counting to about 12 when he's fresh and interested. His performance fluctuates dramatically though. On a really good day, he can get to 17 or 18. On a bad day he looses it around 8 or 9. Maybe it's an attention thing? It seems like 1-to-1 should be a concept that you either understand or you don't. It doesn't seem like it should be something you can do and then not do all in the same few minutes.

He can rote count to 23, perhaps missing or mixing up a number or two in the teens but just as often he can do it correctly. Why 23? Why not 24? I don't know. I've never heard him accurately count beyond 23. He knows number names, though, and will pull out counting words like twenty-nine, sixty-five, one hundred, a million, even infinity. 

5 hours ago, BaseballandHockey said:

 It was why I questioned when  @Cake and Pi said her kids couldn’t count on.

Sorry, I wasn't being clear. The older ones are absolutely able to count on, they just don't. It's not a strategy they've ever used.

3 hours ago, Not_a_Number said:

I believe you that’s what you do, and it clearly works for you, but those are derived from the model. They aren’t primary. The primary model is that one unit is worth 10 of another.

Out of curiosity, can you do arithmetic in other bases? I don’t mean do them quickly, but you can use base 2, right?

I can do arithmetic in other bases, but my mental model in other bases is always the odometer, even though I've physically modeled other bases with linked centimeter cubes arranged into place value chunks analogous to base-10 blocks. I'm pretty sure the odometer model is my primary model. It's what I revert to when I'm tired. It's the first thing I remember using as a child. 

Counting on is *my* default, btw. I taught myself addition with my own personally contrived version of the touch points in Touch Math (a bit different of course, since I was making it up myself as a kid). I was stellar with complex math concepts, but I was pretty horrible with arithmetic. I relied pretty heavily on my calculator. I didn't master addition or multiplication facts until I'd drilled three kids to fluency.

What is your mental model for other bases?

7 hours ago, BaseballandHockey said:

@Cake and Pi was my first list helpful?  Do you want another one?  

It was super duper extremely helpful! Yes, please!

  • Like 1
Link to post
Share on other sites
8 hours ago, Cake and Pi said:

I can do arithmetic in other bases, but my mental model in other bases is always the odometer, even though I've physically modeled other bases with linked centimeter cubes arranged into place value chunks analogous to base-10 blocks. I'm pretty sure the odometer model is my primary model. It's what I revert to when I'm tired. It's the first thing I remember using as a child. 

Counting on is *my* default, btw. I taught myself addition with my own personally contrived version of the touch points in Touch Math (a bit different of course, since I was making it up myself as a kid). I was stellar with complex math concepts, but I was pretty horrible with arithmetic. I relied pretty heavily on my calculator. I didn't master addition or multiplication facts until I'd drilled three kids to fluency.

Interesting! Yeah, I don’t teach counting on for numbers larger than 3, although I’d certainly rather my kids count on than they count from 1. But for larger numbers, we’ll group and do trades.

My default stance is to work with what my kids are already doing, and my kids do tend to count objects. So I try to spin off from counting.

I don’t remember exactly what I did with DD8... we just kind of used her intuition. So we probably did lots of comparisons to additions she could already do via counting on (that was the other reason I wanted counting on: I wanted “this sum is 1 more than another one I know” to be easy.) Eventually, after I thought she got all the ideas, I drilled her on all of them

 

Quote

What is your mental model for other bases?

I tend to use the “odometer” thing for counting, but I add by trading. I’d probably use the traditional algorithm with a table for digit addition for bigger numbers, since the traditional algorithm makes perfect sense to me and I can extend it. 

Do you know what I mean about trading being the definition and everything else flowing out of it? It’s definitely the mathematician in my speaking 😉 . I tend to like working from definitions and find that it works well for the kids I’ve worked with (although that might very well not work for kids like your son, since I have no experience at all — I hope you don’t mind me chiming in.)

 

8 hours ago, Cake and Pi said:

No, he's not really there yet. He's close, though. He can count on with with smaller quantities in context. Like he knows when his brothers have 3 slices of pizza and he only has 1 and can even tell you that he needs 2 more. Same with if he has 3 pieces of chocolate and thinks he should have 4. He can tell you he needs 1 more. He can add on his fingers up to 5 or so when it suits him. But he can't tell you how old he'll be on his next birthday, and when he gets tired basically anything bigger than 7 is "nine" or "twenty." It's coming though. We could use counting on within 5.

That’s a helpful description 🙂 . 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. I did lots of subitising, small additions, games, and counting on for small numbers. (They were counting, anyway, and I certainly didn’t want them to count from 1!) When counting on seemed established (not that one HAS to count on, but it showed comfort with grouping), I was going to do teen numbers with a single place value 10 poker chip and see if that worked, but then COVID hit. So I don’t know how it was going to go. But I definitely remember feeling that we’d need to see whether trading worked with one chip first. 

With my own kids, I do jump into all of place value when we start on it, but my kids can generally count to 100 and are otherwise much more comfortable with numbers than the kids I was teaching. 

 

 

8 hours ago, Cake and Pi said:

Sorry, I wasn't being clear. The older ones are absolutely able to count on, they just don't. It's not a strategy they've ever used.

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.

Edited by Not_a_Number
  • Like 1
Link to post
Share on other sites
15 hours ago, Cake and Pi said:

Unfortunately, this did not work. 😞 It was a great idea! I tried getting the sample on this version of iTunes and got "This book sample requires an iPad with the latest version of iOS and Apple Books installed and Automatic Downloads enabled."

Our charter funds roll over in April, after which I'll have a fresh $1,800 at my disposal for technology and curriculum for DS 7. I may end up just buying an iPad at that point. This is not the first time I've felt like we really needed one for something.

That is a big shame 😞 It's not good when a book (or ebook) so useful is tied to one specific vendor and one specific level of updating.

  • Like 2
Link to post
Share on other sites
18 hours ago, PeterPan said:

Do you think he has a developmental vision problem (which would cause the poor visualization) or do you think it's an indication of synesthesia? It might be worth teasing apart. Both could be going on even. But the synesthesia can run in families and if present, yeah it could make things uber glitchy. I never realized till my dd was 20 and started talking about it that she was experiencing synesthesia. I've been realizing I need to investigate it for ds and just haven't gotten around to it.

That is a riot! I can see why this last dc is such a jolt!

I'm trying to ponder in my mind dyscalculia vs. some kind of seizure/damage. Did you say he had CP or some kind of oxygen deprivation? I don't know. It just seems odd to have ALL the other children be crazy ahead and then this one so radically different. Have they done genetics to see if he has a syndrome going on? Even within autism you can have mutations and syndromes. 

 

On the genetics side, I won't highjack this thread, but have you checked which variant of MTHFR your child has?  Both my son and husband have the worst form of this problem.  Interferes with B6 and B12 uptake (and other issues), which results in behavioral problems, learning issues, as the person's cells don't have the proper vitamins to function properly.  Doctor (MD) has said no enriched flours (the laboratory form of folic acid/folate is like a key that jams into your cells' "locks" and doesn't give them a vitamin, it just jams the lock).  I can only use organic flour.  No commercial flour products, usu.  Just thought I'd mention it.

  • Like 2
Link to post
Share on other sites

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. 

  • Like 1
Link to post
Share on other sites
1 hour ago, Clickie said:

On the genetics side, I won't highjack this thread, but have you checked which variant of MTHFR your child has?  Both my son and husband have the worst form of this problem.  Interferes with B6 and B12 uptake (and other issues), which results in behavioral problems, learning issues, as the person's cells don't have the proper vitamins to function properly.  Doctor (MD) has said no enriched flours (the laboratory form of folic acid/folate is like a key that jams into your cells' "locks" and doesn't give them a vitamin, it just jams the lock).  I can only use organic flour.  No commercial flour products, usu.  Just thought I'd mention it.

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. 

  • Like 1
Link to post
Share on other sites
  • Cake and Pi changed the title to Math Woes (and some reading/language discussion beginning on p.4)

Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

Guest
Reply to this topic...

×   Pasted as rich text.   Paste as plain text instead

  Only 75 emoji are allowed.

×   Your link has been automatically embedded.   Display as a link instead

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.


×
×
  • Create New...