Place Value

[Not_a_Number]

So I think what I'm hearing is mostly that people need to see way more example and way less theorizing and I can fill in the theory as we go. 

Would it be worthwhile to post earlier lessons? I have transcripts recorded. 

[NorthernBeth]

Yes, that would absolutely be helpful!!  

I am not just arguing.   I really do want to understand how you are thinking, because I know you understand math on a much deeper level.  I don't expect to understand it at the same level.  But I would like to understand your thinking in this, if I could , in order to help my students.

Because I would rather teach conceptually than procedurally, and even when I understand the concepts myself, it is so much easier to show kids a series of steps to do, rather than to help them understand a concept.   Especially if they hate math and school and don't particularly want to be there in the first place. 

So if you show me what you do and say and I can compare that to what I already do and say, then I can see the difference and understand what you are getting at.

[UHP]

14 minutes ago, Not_a_Number said:

Right, and that's obviously not what you should be seeing, lol. But I don't know how to demonstrate. I don't want to post videos of my kids, and anyway, I'm not sure that would be helpful... 

If I post a few lesson transcripts a week for a few years, would that do?

A video would explain a lot but I share your pessimism about bad outcomes from posting videos that involve your kids. Don't do it.

I don't think you should make a years-long plan about how to communicate your ideas. Write up a lesson transcript and maybe write some comments on it. You might inspire yourself to write something else, you might inspire someone else, or you might get inspiring feedback. If instead you wind of disheartening yourself and you don't get any good feedback, I hope you wouldn't give up right away but you wouldn't have to continue for years.

The kind of transcript I'd like to see at least once: not just one thing that happened in the lesson but how you prepared it, how you introduced it, how your pupil reacted to your introduction, how you reacted to that reaction, on and on till you tell how you closed the lesson. Think of Jane Goodall's field notes.

[Not_a_Number]

1 minute ago, UHP said:

A video would explain a lot but I share your pessimism about bad outcomes from posting videos that involve your kids. Don't do it.

I don't think you should make a years-long plan about how to communicate your ideas. Write up a lesson transcript and maybe write some comments on it. You might inspire yourself to write something else, you might inspire someone else, or you might get inspiring feedback. If instead you wind of disheartening yourself and you don't get any good feedback, I hope you wouldn't give up right away but you wouldn't have to continue for years.

The kind of transcript I'd like to see at least once: not just one thing that happened in the lesson but how you prepared it, how you introduced it, how your pupil reacted to your introduction, how you reacted to that reaction, on and on till you tell how you closed the lesson. Think of Jane Goodall's field notes.

A lot of the lessons I post I don't even introduce. I just say "DD5, go work." Occasionally, I'll tell her not to use poker chips and to do it mentally. Occasionally, she'll ask if she should use poker chips. She's slowly getting more and more able to do things mentally at this point.

I feel like to explain the lesson, I'd have to explain WHY I'm doing these kinds of lessons and what we did before them, otherwise they just seem... random? I'm not too bothered about what we're doing in them exactly, you see. I'm working on some specific mental models, and lots of things help with those. Really any exposure does. 

[NorthernBeth]

Okay, so you say "DD5, go work."  And she pulls out .... what?   her notebook?  a textbook?  some handwritten problems?  some manipulatives?   Is she making up her own work? Is she reading the directions and things  independently?  Is it a mixture of different types of problems?   At some point , you must be teaching concepts, right?  What do those lessons look like?   If she brings her work back and everything was wrong, what do you do?   If she gets confused , and doesn't understand what the problems are expecting,  what do you say?  My impression is you are not following a pre-made curriculum, but maybe I am wrong?  If it is kind of all your own stuff, do you have a scope and sequence in mind?  

I don't think you need to write an entire year's worth of lessons, unless you are really dying to.

It would be nice to see the occasional transcript, and some of your thought process. 

For example:  I have noticed recently that DD5 understands how to add to 10, but is having difficulty adding beyond 10.  It seems like she is getting confused about ________________________. So today, we are going to try _______________ using   ______________________ manipulatives.   I am just going to do some oral problems with her.   I am hopng she will see_______________.  I will be on the lookout for any confusion regarding the concept of ________________. 

And then any actual dialogue back and forth on the concept. 

I am probably using too easy as example, but that is the kind of thing I am wondering about.  

[Not_a_Number]

19 minutes ago, NorthernBeth said:

Okay, so you say "DD5, go work."  And she pulls out .... what?   her notebook?  a textbook?  some handwritten problems?  some manipulatives?   Is she making up her own work? Is she reading the directions and things  independently?  Is it a mixture of different types of problems?   At some point , you must be teaching concepts, right?  What do those lessons look like?   If she brings her work back and everything was wrong, what do you do?   If she gets confused , and doesn't understand what the problems are expecting,  what do you say?  My impression is you are not following a pre-made curriculum, but maybe I am wrong?  If it is kind of all your own stuff, do you have a scope and sequence in mind?  

I don't think you need to write an entire year's worth of lessons, unless you are really dying to.

It would be nice to see the occasional transcript, and some of your thought process. 

For example:  I have noticed recently that DD5 understands how to add to 10, but is having difficulty adding beyond 10.  It seems like she is getting confused about ________________________. So today, we are going to try _______________ using   ______________________ manipulatives.   I am just going to do some oral problems with her.   I am hopng she will see_______________.  I will be on the lookout for any confusion regarding the concept of ________________. 

And then any actual dialogue back and forth on the concept. 

I am probably using too easy as example, but that is the kind of thing I am wondering about.  

I teach very rarely. I introduce operations and I sometimes suggest new methods/shortcuts.

[JazzyMom]

I'm interested in knowing how much time you spend per lesson and how many lessons per week.  Also, how much time do you spend on self-directed exploration with manipulatives vs. instruction where you explain things with manipulatives vs. work on paper?  Are you always closely observing their self-directed work?  And if so, what specifically are you looking for?

I think that you, being mathy, probably have a clear picture of where you're headed.  However, one concern I would have as a mom who was a strong enough math student but is not mathy (hope that makes sense) is whether or not you have a road map that is easy to follow?  For example, I'd like my students to grasp this, then this, then this, and then we'll be ready for X.  And if the ultimate goal is X, what is that X that you're preparing them for? 

Have you ever encountered students who did not want to work with manipulatives?  (Only asking this last question because I tried to show my 11 year old something with manipulatives yesterday, and he went along with it for a bit but had a look like, "Umm...  No thanks, I got it."  I tended to be that way, too, as a kid - not wanting a lot of exploration and just wanting to get on with it.  I wonder if some kids are just like that or if my older kids are just like that because of the way I've taught them.)

Edited June 29, 2021 by JazzyMom

[NorthernBeth]

Does she always just get it?

Because honestly, the 6 year olds I teach really don't.   Not most of them anyways. 

Any concept needs to be taught and retaught, for a really long time before they can do any of it independently. 

And we have to constantly review what the adding sign means, and the subtraction sign means, and the equals sign too

If I just handed them poker chips, they would pretty much just build towers with the poker chips. 🤣

And truthfully, the curriculum is so full, most times they just don't get the time they need to really grasp a concept before it is time to go on to the next thing.  Which means I am constantly reviewing adding , while introducing subtraction and trying to gradually extend their number recognition.

It is just not the kind of thing where except for a couple of my strongest students, could I say:  "Here, just go do your work." and expect anything worthwhile.  

Possibly you have been working with stronger students than you realize? 

Anyways,  I am off to go do some laundry.   

[sweet2ndchance]

1 hour ago, Not_a_Number said:

Right, and that's obviously not what you should be seeing, lol. But I don't know how to demonstrate. I don't want to post videos of my kids, and anyway, I'm not sure that would be helpful... 

If I post a few lesson transcripts a week for a few years, would that do? 

Obviously, it is obvious to you but not your audience. You just talk so much about poker chips in your many math posts on this forum that people have generalized poker chips when you talk about manipulatives. Does that make sense?

Personally, I think that you are trying to get across that your teaching method is in the box and can be applied to any manipulative. But you're trying to teach theory when your audience is looking for advice on and examples of practical application of that theory. Then you get frustrated that people are not separating the theory from the practical application as these are two separate things in your mind. But your audience doesn't necessarily think that way. Yes, I think interspersing theory into examples of practical application would possibly get your point across better.

There is a reason that Youtube videos are insanely more popular than blogs. If a picture is worth a thousand words then a moving picture that can show how it is done is invaluable. Which is why you made a babywearing channel, at least in part, I'm sure. But you don't have to record yourself teaching your actual children. You could record yourself teaching an imaginary student and annotate your lesson with theory and reasoning. Nicole the Math Lady teaches in her lessons on Youtube this way. You could record yourself demonstrating concepts at a whiteboard similar to how Maria from Math Mammoth does in her videos or use an animated whiteboard video maker like Animatron. You could make completely animated videos with something like Animaker or Vyond as well. There are many alternatives to recording your own children's lessons.

[sweet2ndchance]

10 minutes ago, NorthernBeth said:

If I just handed them poker chips, they would pretty much just build towers with the poker chips.

Lol, yup same here. Especially boys for some reason. Every manipulative becomes a building toy no matter what it is lol.

[Not_a_Number]

9 minutes ago, NorthernBeth said:

Does she always just get it?

No. Not always. But I try not to introduce new stuff too often.
 

9 minutes ago, NorthernBeth said:

Because honestly, the 6 year olds I teach really don't.   Not most of them anyways. 

Any concept needs to be taught and retaught, for a really long time before they can do any of it independently. 

And we have to constantly review what the adding sign means, and the subtraction sign means, and the equals sign too.

Yes, we have to review the symbols quite a lot. Absorbing operations is a big goal here.

 

9 minutes ago, NorthernBeth said:

If I just handed them poker chips, they would pretty much just build towers with the poker chips. 🤣

And truthfully, the curriculum is so full, most times they just don't get the time they need to really grasp a concept before it is time to go on to the next thing.  Which means I am constantly reviewing adding , while introducing subtraction and trying to gradually extend their number recognition.

It is just not the kind of thing where except for a couple of my strongest students, could I say:  "Here, just go do your work." and expect anything worthwhile.  

Possibly you have been working with stronger students than you realize? 

No, I have a wide range of students. I just tend to be pretty laser-focused on operations and symbols and their relationships. 

[Not_a_Number]

2 minutes ago, sweet2ndchance said:

Lol, yup same here. Especially boys for some reason. Every manipulative becomes a building toy no matter what it is lol.

I do teach them how to use them. I don’t insist on them, but most kids I’ve taught that were having trouble appreciated them being available. 

[sweet2ndchance]

1 minute ago, Not_a_Number said:

I do teach them how to use them. I don’t insist on them, but most kids I’ve taught that were having trouble appreciated them being available. 

I never said you didn't. But my boys, and boys in general that I've taught, know how to use them but will use them as building toys rather than manipulatives given the chance. Especially those with ADHD or ADHD tendencies. Girls will do it too but with boys it is almost a guarantee if you look away for 5 seconds, there will be a tower or a pyramid of manipulatives when you look back lol. 😛 

 

[daijobu]

1 hour ago, Not_a_Number said:

Right, and that's obviously not what you should be seeing, lol. But I don't know how to demonstrate. I don't want to post videos of my kids, and anyway, I'm not sure that would be helpful... 

 

Okay, so now you sound like a troll, no offense.  It isn't obvious to me.  Because you haven't stated what's in the box.  Even now and the thread is on its second page.  You are telling me that the cardboard box does not contain poker chips.  What does it contain?  

[Not_a_Number]

27 minutes ago, sweet2ndchance said:

I never said you didn't. But my boys, and boys in general that I've taught, know how to use them but will use them as building toys rather than manipulatives given the chance. Especially those with ADHD or ADHD tendencies. Girls will do it too but with boys it is almost a guarantee if you look away for 5 seconds, there will be a tower or a pyramid of manipulatives when you look back lol. 😛 

 

I had an ADHD boy in my class and that wasn’t my experience. At least, manipulatives weren’t any worse than anything else. They did play with them, but it didn’t detract from the usefulness.

 

12 minutes ago, daijobu said:

Okay, so now you sound like a troll, no offense.  It isn't obvious to me.  Because you haven't stated what's in the box.  Even now and the thread is on its second page.  You are telling me that the cardboard box does not contain poker chips.  What does it contain?  

I don’t know how to explain 😕 . That’s why I’m asking what would be helpful. I see that demos are helpful. I’ll try to focus on those.

Edited June 29, 2021 by Not_a_Number

[Not_a_Number]

So, don’t your kids appreciate the manipulatives? It’s a lot easier to take away 9 blues from 3 greens and 5 blues, if you know the trading rules, than it is to do 35 - 9, if you aren’t good with place value yet.

[sweet2ndchance]

13 minutes ago, Not_a_Number said:

I had an ADHD boy in my class and that wasn’t my experience. At least, manipulatives weren’t any worse than anything else. They did play with them, but it didn’t detract from the usefulness.

No one said that playing with them detracted from their usefulness. It was just a general comment that given the opportunity, such as just giving a child some manipulatives and telling them to go work with them, can often lead to everything but productive work on the task at hand.

[UHP]

20 minutes ago, Not_a_Number said:

I don’t know how to explain 😕 . That’s why I’m asking what would be helpful. I see that demos are helpful. I’ll try to focus on those.

I hope you don't feel ganged up on. It sounds like many people are interested in learning more about what you're doing. So how should you explain it? I think among all of us here giving you grief — and I don't mean to boast! — I have the best advice for you. Just write down what happens over the course of one session, not a "typical" or an "ideal" session but one that really happened and that you have a fresh memory of.

Go into way more detail than feels natural. This might be a sticking point for you: you think we surely understand well enough to fill in the blanks, we'd be bored to tears by the details. I don't think so.

1 hour ago, Not_a_Number said:

1 hour ago, UHP said:

The kind of transcript I'd like to see at least once: not just one thing that happened in the lesson but how you prepared it, how you introduced it, how your pupil reacted to your introduction, how you reacted to that reaction, on and on till you tell how you closed the lesson. Think of Jane Goodall's field notes.

A lot of the lessons I post I don't even introduce. I just say "DD5, go work." Occasionally, I'll tell her not to use poker chips and to do it mentally. Occasionally, she'll ask if she should use poker chips. She's slowly getting more and more able to do things mentally at this point

"Go work" counts as an introduction, and new information to me. What goes on in the 60 seconds after you say that? What goes on in the 60 seconds after that? I don't have a good guess.

"Occasionally X and occasionally Y" is too cloudy of a description, for me. What specifically happened today?

1 hour ago, Not_a_Number said:

I feel like to explain the lesson, I'd have to explain WHY I'm doing these kinds of lessons and what we did before them, otherwise they just seem... random?

I don't think so.

Edited June 29, 2021 by UHP

[sweet2ndchance]

46 minutes ago, Not_a_Number said:

So, don’t your kids appreciate the manipulatives? It’s a lot easier to take away 9 blues from 3 greens and 5 blues, if you know the trading rules, than it is to do 35 - 9, if you aren’t good with place value yet.

I don't know what you mean by appreciate exactly but I usually have to tell them to use the manipulatives because they try to do it without them first because they think it is quicker but it becomes obvious that they are not fluent in the idea of place value. Those that are fluent, can do it  in their head because they can visualize it, or as you say have a good mental model, and don't need the manipulatives any more.

Most kids I've taught just want to get it done so they can move on to a subject they like better or do what they want to do rather than do school. The ones that actually enjoy math and enjoy the challenge rarely need the manipulatives after a few tries at it because they can quickly and easily visualize the idea in their head and then generalize the concept.

[lulalu]

I think the confusion comes in the fact that you (Not_a_Number) haven't looked at or know what people are using. So you keep implying that what you do is different. There is a lot of there that does a really deep job of working with place value- RightStart, Miquon, Singapore, Gattegno are all ones that do a great job of building a foundation for place value. There are more I am sure, but these are the ones I have looked through. Without knowing how and what people are using to teach place value, you are confusing (at least me) when you keep saying that what you do is different. Because what you describe sounds just like RightStart to me just using poker chips instead of their abacus. 

If you were to look at several curriculum, I think you could then understand how place value is taught. Then you would more easily be able to talk about what you do differently. 

For me personally a video is needed. Maybe just get the back of your kid's head, or block their faces. But reading what you say isn't enough for me to see that it is different. And really only a few lessons here or there are needed. It doesn't have to be an overview of it all to follow along with what you do. 

[goldenecho]

10 hours ago, Not_a_Number said:

Why wouldn’t it work? It’s not arbitrary, it’s fixed. I’m not against writing the numbers on them, but I haven’t had to — same as with the C-rods, kids get used to what each color is worth. I can imagine kids not being able to do it, but I didn’t have that happen with any of the 30 kids I had in my classes.

My son picked it up pretty quickly, and the boy I'm tutoring is picking it up just by letting him play with them and without any explicit instruction on the colors.  I imagine in any class there will be some children who are color blind, though.   Two of my boys (but not my youngest, who is the only one I homeschooled) are partially color blind but they can usually tell shades of things.  I haven't tried with the blocks to see if they can tell the color differences between say, light blue (#5) and light purple (#6).

[daijobu]

3 hours ago, Not_a_Number said:

Right, and that's obviously not what you should be seeing, lol. But I don't know how to demonstrate. I don't want to post videos of my kids, and anyway, I'm not sure that would be helpful... 

 

What's funny is I just now ordered a set of poker chips from Amazon because with my young nieces visiting later this summer, I'll want to teach them some place value for fun.  

IOW, I see poker chips in the cardboard box...  🙂

[Not_a_Number]

1 hour ago, lulalu said:

I think the confusion comes in the fact that you (Not_a_Number) haven't looked at or know what people are using. So you keep implying that what you do is different. There is a lot of there that does a really deep job of working with place value- RightStart, Miquon, Singapore, Gattegno are all ones that do a great job of building a foundation for place value. There are more I am sure, but these are the ones I have looked through. Without knowing how and what people are using to teach place value, you are confusing (at least me) when you keep saying that what you do is different. Because what you describe sounds just like RightStart to me just using poker chips instead of their abacus. 

If you were to look at several curriculum, I think you could then understand how place value is taught. Then you would more easily be able to talk about what you do differently. 

I've looked at lots of curriculum, I swear -- I just don't use it myself. I think NorthernBeth summarized it pretty well -- I tend to think of place value as a theme that runs throughout arithmetic instruction and not simply as a unit you finish early on in your schooling. 

I'm sure that what I do is much like what RightStart and Singapore and most conceptual curricula do. It's just that I have a different expectation for what progression through the skill looks like. 

 

1 hour ago, lulalu said:

For me personally a video is needed. Maybe just get the back of your kid's head, or block their faces. But reading what you say isn't enough for me to see that it is different. And really only a few lessons here or there are needed. It doesn't have to be an overview of it all to follow along with what you do. 

Interesting. I'll have to think about making a YouTube channel where I just lecture in front of a piece of paper or something, I guess. 

[Not_a_Number]

1 hour ago, sweet2ndchance said:

I don't know what you mean by appreciate exactly but I usually have to tell them to use the manipulatives because they try to do it without them first because they think it is quicker but it becomes obvious that they are not fluent in the idea of place value. Those that are fluent, can do it  in their head because they can visualize it, or as you say have a good mental model, and don't need the manipulatives any more.

I think what I mean is that they like the fact that they can keep working on the question without me helping? At least, that has happened with all the kids in my homeschooling classes -- if they were stuck and I reminded them about poker chips, they'd use them. You're right that some kids do prefer to start in their head even if they don't know what they are doing! 

 

Quote

Most kids I've taught just want to get it done so they can move on to a subject they like better or do what they want to do rather than do school. The ones that actually enjoy math and enjoy the challenge rarely need the manipulatives after a few tries at it because they can quickly and easily visualize the idea in their head and then generalize the concept.

I haven't found that the kids I've taught who like math find place value intuitive very quickly. I mean, they can NAME the columns and they'd be able to tell me how to trade between them, but they would still get stuck if we have to go "backwards" or if we have to use place value for new operations. 

Basically, I think there are different levels of comfort with concepts. Would describing the different levels be helpful? Would watching DD5 move through those levels be useful? So far, I've found that all the kids who consistently use the model do move through the levels, although the speeds and the reliance on the physical manipulatives REALLY vary. DD8 only took a year or two, I think, whereas I have kids in my homeschooling classes who will clearly need the physical manipulatives for a long time -- possibly into decimals. It really depends on the facility with building models in one's head, which varies a lot. 

Edited June 29, 2021 by Not_a_Number

[lulalu]

5 minutes ago, Not_a_Number said:

I've looked at lots of curriculum, I swear -- I just don't use it myself. I think NorthernBeth summarized it pretty well -- I tend to think of place value as a theme that runs throughout arithmetic instruction and not simply as a unit you finish early on in your schooling. 

Yes, but that is what I am saying RightStart and Gattegno and Miquon do this too. 

RS has place value work for a long time because of the abacus. 

I think that is where I get confused with what you say. It just doesn't sound different to me than the good conceptual curriculum I have used. It just sounds like you use a different manipulative. 

 

That's why I think a video would be useful. Because from what you write (and I have read all your posts on lessons) I can't see the difference. 

[Not_a_Number]

Just now, lulalu said:

Yes, but that is what I am saying RightStart and Gattegno and Miquon do this too. 

I haven't seen the curricula focused on C-rods like Gattegno and Miquon work nearly as much as I do with trading, although it's possible that I'm missing something due to not having actually gone through the curriculum. What I tend to like from Gattegno and Miquon is the early work with all the operations -- I do that, too. 

 

Just now, lulalu said:

RS has place value work for a long time because of the abacus. 

Is that work integrated with all the operations? Do the kids spend a long time exploring how place value interacts with all the operations? Is there an expectation of slow development of the model and how it works with everything else? Is there a focus on different levels of understanding and different levels of comfort with abstraction? 

 

Just now, lulalu said:

I think that is where I get confused with what you say. It just doesn't sound different to me than the good conceptual curriculum I have used. It just sounds like you use a different manipulative. 

I think the biggest difference is that I expect a different sequential progression of skills. In some sense, I have a lot of sympathy for Benezet and his experiment... what I want math to be is an immersion into a world of logic and numbers. All I give to kids is common-sense meanings of the things they see, and then we use them as best we can. 

 

Just now, lulalu said:

That's why I think a video would be useful. Because from what you write (and I have read all your posts on lessons) I can't see the difference. 

If the posts don't sound different from anyone else, then probably the video wouldn't solve the problem, either! I feel like it looks different zoomed out, not zoomed in... 

[Not_a_Number]

By the way, you all ought to give me a bit more credit for exposure to standard curricula 😉 . We do own Beast Academy and use it occasionally, and I've taught all the AoPS classes, and I've glanced at lots of other curriculum, and I've rewritten a whole AoPS class... I do know what standard sequences look like! And I don't like 'em. I don't think they grapple successfully with what makes math hard. 

Edited June 29, 2021 by Not_a_Number

[Not_a_Number]

49 minutes ago, daijobu said:

What's funny is I just now ordered a set of poker chips from Amazon because with my young nieces visiting later this summer, I'll want to teach them some place value for fun.  

IOW, I see poker chips in the cardboard box...  🙂

You should totally teach them some place value!! You'll have to report back. 

So do you need some lesson plans? 😄 

[daijobu]

40 minutes ago, Not_a_Number said:

 

So do you need some lesson plans? 😄 

Yes, please!  

[Not_a_Number]

Just now, daijobu said:

Yes, please!  

Perhaps I'll make one more post about how I introduce place value as theoretical thing, then do a data dump of a bunch of lessons? DD5 has only been learning for less than a year... I have all the records. 

[Porridge]

1 hour ago, Not_a_Number said:

By the way, you all ought to give me a bit more credit for exposure to standard curricula 😉 . We do own Beast Academy and use it occasionally, and I've taught all the AoPS classes, and I've glanced at lots of other curriculum, and I've rewritten a whole AoPS class... I do know what standard sequences look like! And I don't like 'em. I don't think they grapple successfully with what makes math hard. 

You have tons of respect from me. I couldn’t do what you do in a million years 🙂. But I think the other boardie’s point may that “glancing” at the other curricula doesn’t necessarily give you an in depth feel for how they teach or present or weave in the concepts. And I wouldn’t consider Right Start to be “standard curricula.” You might learn a lot from how Joan Cotter presents the concepts.  If not the concepts, then the method of presenting the concepts in a way that the teacher / parent can readily understand and put into practice.  But take my POV with a large grain of hypertension inducing Na CL because I only used 2 levels of Right Start.

[Not_a_Number]

6 minutes ago, WTM said:

You have tons of respect from me. I couldn’t do what you do in a million years 🙂. But I think the other boardie’s point may that “glancing” at the other curricula doesn’t necessarily give you an in depth feel for how they teach or present or weave in the concepts. And I wouldn’t consider Right Start to be “standard curricula.” You might learn a lot from how Joan Cotter presents the concepts.  If not the concepts, then the method of presenting the concepts in a way that the teacher / parent can readily understand and put into practice.  But take my POV with a large grain of hypertension inducing Na CL because I only used 2 levels of Right Start.

Well, what am I supposed to do?? I've taught lots of curricula at higher levels, and NONE of them seemed to do what I wanted them to. From teaching them, I've made certain generalizations about things I want and don't want in a curriculum and I haven't found an elementary curriculum that matches those constraints or goes in anything like the order I would like them to. Plus, I've taught many kids who use a variety of curricula and I haven't on average been impressed. SOME kids are impressive, but that's mostly been about their parents being good, responsive teachers.

I can probably figure out how to present the concepts in a way that a parent can put into practice, but I'm still not sure if I want to actually write a curriculum. For one thing, I don't know if anyone would want to do what I do, because it's extremely stripped down -- it's basically mostly interacting with arithmetic. I don't go into early geometry and we don't work hard on time or money or most of anything else. 

For now, I'm curious what it would take to communicate the ideas to people who are interested. I suppose it's possible that the only way to communicate them is to write a curriculum, though... What do you think? 

[Not_a_Number]

13 minutes ago, WTM said:

But I think the other boardie’s point may that “glancing” at the other curricula doesn’t necessarily give you an in depth feel for how they teach or present or weave in the concepts.

I think I'll also note that I don't tend to think that concepts like place value need to be "weaved in." I tend to think they need to be pretty primary. 

[NorthernBeth]

I wish we could just focus on the arithmetic.  Unfortunately we also have to teach time, and fractions, measurement, and money, and probability and graphing, and patterns.  They just added coding, multiplication and division to our Grade 1 curriculum this year, so that should be interesting, as well.  

Even if you didn't write a whole curriculum, it might be helpful to see a unit of lessons on adding or subtracting.  Where do you start? How do you build it up? That kind of thing.  What does a week of math look like when you are introducing a new topic and you are doing a lot of teaching and explaining?

 

[Not_a_Number]

1 minute ago, NorthernBeth said:

I wish we could just focus on the arithmetic.  Unfortunately we also have to teach time, and fractions, measurement, and money, and probability and graphing, and patterns.  They just added coding, multiplication and division to our Grade 1 curriculum this year, so that should be interesting, as well.  

I do do multiplication and division early on. And that's basically all I do -- addition, subtraction, multiplication, division and place value 😛 . At some point, I teach all the other stuff, but I really want to get the fundamentals down. Plus, all the rest of it makes WAY more sense if you can already do arithmetic!! Money and time and fractions all kind of follow naturally from getting the operations and place value down... 

I really hate the "everything but the kitchen sink" thing that's happening with elementary curricula 😕 . That's actually a big complaint of mine. 

 

1 minute ago, NorthernBeth said:

Even if you didn't write a whole curriculum, it might be helpful to see a unit of lessons on adding or subtracting.  Where do you start? How do you build it up? That kind of thing.  What does a week of math look like when you are introducing a new topic and you are doing a lot of teaching and explaining?

Yes... I'll definitely try to explain! Thank you very much for your suggestions -- they've been extremely helpful and definitely help me visualize what I need to do. 

[Clarita]

18 hours ago, Not_a_Number said:

Interesting. I'll have to think about making a YouTube channel where I just lecture in front of a piece of paper or something, I guess. 

The Montessori math curriculum that I had purchased for my kids, the lady sometimes just does the demonstration with her there. She just pretends like the camera is the child and presents the lesson to it. She does do a mix of videos with kid and without kid (she'll fast forward and skip sometimes if her daughter is super distracted). Some parents says that the ones with her daughter does help, in terms of not feeling like the only one who's kid that is suddenly building towers with the manipulatives and actually knowing how much engagement we expect from a child (# of problems done and time). The parents (when she surveyed) thought the solo presentations were enough, coupled with some suggestions on things to say or ways to address a child who is not engaged in an ideal way.

If videos are too difficult . Pictures of the lesson/manipulative setup and showing how those change throughout the lesson (where they move to or whatever) along with the descriptions are also good enough.

I know this is super early in your blog launch (and it is not necessary to be one of the first things you do); however I find a general scope and sequence map really useful. This does not have to be linear in any way just a which things are kind of parallel to other lessons and which ones need to be sequential. 

PS I'm now demonstrating counting on to my son. I just supplemented that detail into the adding lesson we were doing in his current curriculum.

[Clarita]

16 hours ago, Not_a_Number said:

I can probably figure out how to present the concepts in a way that a parent can put into practice, but I'm still not sure if I want to actually write a curriculum. For one thing, I don't know if anyone would want to do what I do, because it's extremely stripped down -- it's basically mostly interacting with arithmetic. I don't go into early geometry and we don't work hard on time or money or most of anything else. 

I think there is value in what you are doing, even if it's tidbits on how to interact with your kids with arithmetic. Perhaps we all just wish you wrote a curriculum, because your method seems so successful.

[Not_a_Number]

37 minutes ago, Clarita said:

I think there is value in what you are doing, even if it's tidbits on how to interact with your kids with arithmetic. Perhaps we all just wish you wrote a curriculum, because your method seems so successful.

I always do wonder if it's replicable, I have to admit. Which is maybe a good reason to write a few lessons and have people test-drive them?? Because it's so much easier for someone to run THEIR OWN program than it is for them to communicate it. 

[amiesmom]

19 hours ago, Not_a_Number said:

Would describing the different levels be helpful? Would watching DD5 move through those levels be useful?

 

23 minutes ago, Not_a_Number said:

I always do wonder if it's replicable, I have to admit. Which is maybe a good reason to write a few lessons and have people test-drive them??

Yes to all of this.

[Not_a_Number]

Just posted the next one in the series: 

https://mentalmodelmath.com/2021/07/02/lesson-plan-introducing-place-value/

I don't know if this explains much of anything, but it felt necessary to post before launching into examples of early lessons. I'll try to dig through DD5's lessons and find a representative one. 

Is this helpful in any way? 

Edited July 2, 2021 by Not_a_Number

[daijobu]

2 hours ago, Not_a_Number said:

Just posted the next one in the series: 

https://mentalmodelmath.com/2021/07/02/lesson-plan-introducing-place-value/

I don't know if this explains much of anything, but it felt necessary to post before launching into examples of early lessons. I'll try to dig through DD5's lessons and find a representative one. 

Is this helpful in any way? 

Yes, this is very helpful.  I was inspired by this thread to return to the fairly unreadable Garlikov (?) blog post...and try again to reread it.  And, since I mainly use a Chromebook, I went to the trouble to get some sort of powerpoint extension so I could view his A/V powerpoint.  (Did he create this before youtube was invented.)

And...genius.  The blog post is terrific.  (Too bad all the good stuff is buried in the middle of a bunch of useless boring stuff, so you really have to search for it.  But the powerpoint is terrific.  It could have been a video, but as a ppt, it was nice to be able to step through each slide.  

It all reminds me of what I did with the algorithms in Singapore Math, but his approach is slower and gentler.  For me it's like I didn't even both introducing place value until we studied the major algorithms.  

Garlov (??) didn't extend it to long division, but that's and easy enough extension.  

I think the big loss is his powerpoint isn't really accessible.  Is the author still alive?   

[Not_a_Number]

3 minutes ago, daijobu said:

Yes, this is very helpful.  I was inspired by this thread to return to the fairly unreadable Garlikov (?) blog post...and try again to reread it.  And, since I mainly use a Chromebook, I went to the trouble to get some sort of powerpoint extension so I could view his A/V powerpoint.  (Did he create this before youtube was invented.)

And...genius.  The blog post is terrific.  (Too bad all the good stuff is buried in the middle of a bunch of useless boring stuff, so you really have to search for it.  But the powerpoint is terrific.  It could have been a video, but as a ppt, it was nice to be able to step through each slide.  

Yes. It's a great blog post. I always feel hesitant linking to it, because it's SO sprawling and hard to follow. But he makes a lot of excellent points in that post. I'm very much of the same mind as him about almost all the things he says, which is rare. 

 

3 minutes ago, daijobu said:

It all reminds me of what I did with the algorithms in Singapore Math, but his approach is slower and gentler.  For me it's like I didn't even both introducing place value until we studied the major algorithms.  

Garlov (??) didn't extend it to long division, but that's and easy enough extension.  

I think the big loss is his powerpoint isn't really accessible.  Is the author still alive?   

Yeah, he seems to be around and still posting, as far as I can tell. By the way, the spelling Garlikov is correct, I believe. 

I'm going to try to provide walkthroughs of the same kind of thing as he does in the PowerPoint, of course, but it'll take me some number of weeks/months. 

[Eilonwy]

On 6/29/2021 at 4:18 PM, Not_a_Number said:

I feel like to explain the lesson, I'd have to explain WHY I'm doing these kinds of lessons and what we did before them, otherwise they just seem... random? I'm not too bothered about what we're doing in them exactly, you see. I'm working on some specific mental models, and lots of things help with those. Really any exposure does. 

I agree that they need some context, an introduction to what the goals of the lesson or group of lessons are.  This could be something you don’t tell the kids, but adults would need to know more to be able to write effective questions, and to work through them.

Three things that stand out to me from trying a similar approach for the past several months are:

1. Experience is key, both for the kids and for myself.  I’ve copied lots of your questions, and lots of examples have been great to explore how it works (and what doesn’t work).  The puzzles are great, but I don’t get the impression that they are your everyday questions. To gain that experience, we need examples of math questions of this type to try, and later to adapt ourselves, to give everyone the experience of trying out playing with place value. 
 

2. Alongside place value, specific definitions of operations are used and I think these are just as important.  I know this isn’t the main point of the thread, but I don’t think it can actually be separated, and this provides most of the ways to develop exposure to place value.  It’s also where people might notice the biggest differences from other methods (that I’ve come across). 
 

3. How to respond with useful, constructive follow-up questions to the various ways kids might react is also a challenge, and for this, transcripts of what everyone said would be so useful, to develop strategies. I’d love to see videos, but I completely understand why you wouldn’t want to video your kids. 

For me, a mix of theory and questions to try and lesson transcripts would be most helpful, along with a list of what order to develop the concepts in. 

[Not_a_Number]

1 hour ago, Eilonwy said:

I agree that they need some context, an introduction to what the goals of the lesson or group of lessons are.  This could be something you don’t tell the kids, but adults would need to know more to be able to write effective questions, and to work through them.

Three things that stand out to me from trying a similar approach for the past several months are:

1. Experience is key, both for the kids and for myself.  I’ve copied lots of your questions, and lots of examples have been great to explore how it works (and what doesn’t work).  The puzzles are great, but I don’t get the impression that they are your everyday questions. To gain that experience, we need examples of math questions of this type to try, and later to adapt ourselves, to give everyone the experience of trying out playing with place value. 

They are my weekly questions with my Zoom class kids but I don't actually do puzzles with my own kids except in the context of classes, no. For one thing, my kids aren't all that motivated by puzzles, and given the way I teach, they find questions like 17 + square = 81 tricky enough, anyway, since they don't have an algorithm to use... 

I did puzzles for the classes since I figured they'd be motivating to kids who aren't used to interesting math. So you're right that it's not my main thing -- it's just something I've been working on, and it seems only fair to share it. 

 

1 hour ago, Eilonwy said:

2. Alongside place value, specific definitions of operations are used and I think these are just as important.  I know this isn’t the main point of the thread, but I don’t think it can actually be separated, and this provides most of the ways to develop exposure to place value.  It’s also where people might notice the biggest differences from other methods (that I’ve come across). 

You're right about that, too. Would you like a post about subtraction before I move on to specific examples? I was debating what to do first... that, and I need a post on the equals sign, I think, since I try to work on models of those very early as well and have been very pleased with the result. (DD8 is, as you know, solidly working on algebra, so I can evaluate.) 

Oh, and I need a post on "shapes" as variables. Hmmm. Quite a lot of theory before I can do useful examples, eh? 😕 But otherwise things kind of don't make sense. 

 

1 hour ago, Eilonwy said:

3. How to respond with useful, constructive follow-up questions to the various ways kids might react is also a challenge, and for this, transcripts of what everyone said would be so useful, to develop strategies. I’d love to see videos, but I completely understand why you wouldn’t want to video your kids. 

Yes, I'll try to take transcripts down 🙂 . I had some in the other thread... were those detailed enough? Unfortunately, I don't have transcripts recorded for the earliest of lessons, which is where I'll probably start. 

 

1 hour ago, Eilonwy said:

For me, a mix of theory and questions to try and lesson transcripts would be most helpful, along with a list of what order to develop the concepts in. 

I am actually not super fussed about the order of concepts, as long as it's relatively logical. Like, I don't remember if I did division or negative numbers with DD8 first, you know? 😛 I genuinely don't remember. On the other hand, my sense of what's logical is probably not shared by all... 

[Eilonwy]

22 hours ago, Not_a_Number said:

You're right about that, too. Would you like a post about subtraction before I move on to specific examples? I was debating what to do first... that, and I need a post on the equals sign, I think, since I try to work on models of those very early as well and have been very pleased with the result. (DD8 is, as you know, solidly working on algebra, so I can evaluate.) 

Oh, and I need a post on "shapes" as variables. Hmmm. Quite a lot of theory before I can do useful examples, eh? 😕 But otherwise things kind of don't make sense. 

You don’t need more theory before you can do useful examples, I think.  Examples that are then discussed as you come to key points would probably be easier to understand.   I think you could do examples next and then mix in the related theory in the same post or after.  

Edited July 3, 2021 by Eilonwy

[daijobu]

Honestly I don't need any theory.  If a gold medal IMO winner says, "This is how I teach math," then I'm listening.    

[Not_a_Number]

1 minute ago, daijobu said:

Honestly I don't need any theory.  If a gold medal IMO winner says, "This is how I teach math," then I'm listening.    

I think it's less "theory" and more "big picture"? 

That being said, I know plenty of brilliant mathematicians who are atrocious teachers. So I wouldn't listen to me for that reason 😛 . 

[daijobu]

4 minutes ago, Not_a_Number said:

I think it's less "theory" and more "big picture"? 

That being said, I know plenty of brilliant mathematicians who are atrocious teachers. So I wouldn't listen to me for that reason 😛 . 

Okay, then let me describe you this way:  "A gold medal IMO winner who also has experience teaching young children over average ability AND poorly prepared Stanford undergraduates AND is currently teaching her own 2 daughters."  

I think you are truly unique in this respect, and as Cal Newport says, you are the best person to write this book.  

[daijobu]

Just now, daijobu said:

Okay, then let me describe you this way:  "A gold medal IMO winner who also has experience teaching young children over of average ability AND poorly prepared Stanford undergraduates AND is currently teaching her own 2 daughters."  

I think you are truly unique in this respect, and as Cal Newport says, you are the best person to write this book.  

 

[Eilonwy]

2 hours ago, Not_a_Number said:

2 hours ago, daijobu said:

Honestly I don't need any theory.  If a gold medal IMO winner says, "This is how I teach math," then I'm listening.    

I think it's less "theory" and more "big picture"? 

The sort of theory I think would be helpful to people trying to use your ideas is probably not really theory at all, but rather discussion of things like how do you think about subtraction/ multiplication/ equations/ division/ variables etc., and why, and how you talk about them with students. I don’t think all of these would be obvious from just reading examples & transcripts, but they should be combined with examples & transcripts to illustrate what it looks like in practice. 
 

23 hours ago, Not_a_Number said:

I am actually not super fussed about the order of concepts, as long as it's relatively logical. Like, I don't remember if I did division or negative numbers with DD8 first, you know? 😛 I genuinely don't remember. On the other hand, my sense of what's logical is probably not shared by all... 

It’s not so much a difference in what is logical as that what is logical is more obvious in hindsight rather than in advance, for people without experience.  Like where you’ll hit sudden jumps in difficulty.  

Edited July 3, 2021 by Eilonwy