Confused by manipulatives

[skueppers]

I'm being forced to accept that my child is confused by math manipulatives. It's possible for her to learn to use them, but generally speaking, she gets distracted by the procedure of using the manipulative and stops being able to think about the math.

 

Math Mammoth is working well for her right now, and she's fine with pictures of objects. It's just the physical objects that throw her off.

 

Today she wanted to try Miquon again after a hiatus of two months. That was fine with me, since I was interested to see if things had changed. At the beginning of the page, she could add and subtract, using the rods, and make intelligent remarks about what she was doing. At the end of the page, she could no longer figure out a subtraction problem because she was using the rods wrong and not thinking about the actual math problem. It was clear to me that the problem wasn't that she was tired, but that at the beginning, she was using the rods to model the problem based on her understanding of the math, and by the end, she had stopped thinking about the actual math and was instead worrying about the right way to use the rods.

 

If you've been there with a kid like this, I'd love to hear how it went for you. Did you just stop trying to use manipulatives? Any words of wisdom?

[Ellie]

Lots and lots of children do NOT need manipulatives. I didn't. My two dds didn't. If your dd doesn't, why force them on her??

[abbeyej]

One of my kids definitely did better without manipulatives. There were a few times when we found them helpful, but generally he leapt easily to the abstract and found the manipulatives merely a distraction. Most of them got plenty of use in other ways though, lol, as building materials or happy little participants in creative play... I remember our multi-link cubes being turned into a heart and a feather and weighed in our bucket balance. If the heart was heavier, it was fed into the waiting crocodile mouth of the box for the balance (all based on Egyptian stories of the after life). ;)

 

My daughter has benefited more from manipulatives. Interestingly, she's the one who struggles with math, while he works several years ahead of grade level with ease.

[KrissiK]

Manipulatives are a tool and if you don't need them, don't use them. I don't use many, but the one I've found invaluable for Singapore Math 1B is unifix cubes. Couldn't have taught that book without them!

[ReidFamily]

I am finding my daughter does better without manipulatives as well. She is 5 and was doing abstract addition and subtraction before we bought math-u-see. She finds them cumbersome and too time consuming to model a problem with manipulatives when she can easily do it in her head. So we are backing off of using them and doing the math alone instead.

 

We did find the manipulatives very helpful for teaching place value but so far that has been the major help. We keep them around for particular problems when they are useful or to help solidify a concept if it is apparent she is a little confused but other than that we are not using them on a regular basis anymore.

 

For example she didn't like using blocks to show that 4 + 2 = 6. It more than triples the time to build the problem first than to simply say 2, which she can easily figure out in her head.

[skueppers]

Lots and lots of children do NOT need manipulatives. I didn't. My two dds didn't. If your dd doesn't, why force them on her??

 

I think I have this idea that it ought to help her understand things she's having trouble with, but what seems to help instead is to build the concept up slowly, which is what Math Mammoth is doing for her. Which would be why I started using it. I'm glad it's working, I was more just looking for been there stories, suggestions for the future, that kind of thing.

 

I would describe her as pretty good with math, but not exceptionally so.

[TracyP]

I think I have this idea that it ought to help her understand things she's having trouble with, but what seems to help instead is to build the concept up slowly, which is what Math Mammoth is doing for her. Which would be why I started using it. I'm glad it's working, I was more just looking for been there stories, suggestions for the future, that kind of thing.

 

I would describe her as pretty good with math, but not exceptionally so.

 

This describes my dd exactly. We have been extremely happy with MM too. I may pull out manips at some point to help illustrate a concept but I think *I* have to get over the fact that she will never use Miquon. I say this because I have wanted Miquon and may use it with youngers but this makes me realize that it is not her thing.

 

I don't know if it is related but AAS was also not for her. She is an awesome natural speller and the more I made her think about spelling the worse she spelled and got annoyed/frustrated/etc.

[boscopup]

I think I have this idea that it ought to help her understand things she's having trouble with, but what seems to help instead is to build the concept up slowly, which is what Math Mammoth is doing for her. Which would be why I started using it. I'm glad it's working, I was more just looking for been there stories, suggestions for the future, that kind of thing.

 

 

My oldest son doesn't need manipulatives for math either. He does great with Math Mammoth, and also doesn't need to draw all the dots or carrots or whatever in order to figure out how to add. He's pretty good with doing this stuff in his head. If he needed a manipulative, I'd use one, but so far, he just hasn't needed them.

 

Now we sometimes use objects for math facts games, like the "Some went hiding" in Math Mammoth 1A for helping do the math facts. He likes the game, because I usually use chocolate chips or candy corn (hey, it's Halloween!) or something else edible, then we get to eat the objects when we're done! He also enjoys the card games listed in the text.

 

But as far as rods and other manipulatives everyone just "has to have", I just haven't needed to use them for him as of yet. He catches onto concepts without them, and so did I when I was young.

 

So don't worry about it. If your child needs manipulatives to learn math, by all means, use them! If they don't need them, why complicate things? Some kids will need them and some kids won't. And there's nothing wrong with either method, as long as you're using the method that works for that kid, right?

[abbeyej]

...I'm glad it's working, I was more just looking for been there stories, suggestions for the future, that kind of thing.

 

I would describe her as pretty good with math, but not exceptionally so.

As I said, my oldest didn't really benefit from using manipulatives for math work. He *is* exceptionally good at math, though, lol, I don't think it had anything to do with my teaching or whether or not we used manipulatives. :) We just kept going with what worked. ... And pretty much the same for my dd, who is much less mathematically inclined. We just keep working day after day, trying to stick with what works. :)

 

Oldest went through Horizons 1-6 and Singapore (3-5 or 6 -- can't remember now!), various supplements along the way, then Dolciani Algebra 1 and now Jacobs Geometry. Younger one is finishing up Horizons 3 and has done some Singapore off and on. Oddly, while she benefits more from manipulatives than he did, he's the one who *gets* abstract concepts and can apply them in various ways. She's convinced I'm constantly changing the rules of arithmetic on her. ;)

[MerryAtHope]

My son didn't do well with manipulatives, so I only used them when I really needed to demonstrate a concept. But then it was different from how Miquon works. With Miquon, the child is learning by discovery-oriented methods. That's different than using manipulatives to teach a concept, where you are walking them through step by step what to do.

 

For my son, it was both the process of using manipulatives (he just wanted to "get done,") and the discovery-oriented method of Miquon that made it a no-go. (He didn't like that the book didn't "teach" him. Discovery oriented programs of all kinds make him feel like someone is holding back information to keep him from learning, rather than just being up front and logical!).

 

Interestingly, we are using Math-U-See right now (we used Horizons for years but it only goes up to Level 6). Suddenly he likes manipulatives! He doesn't love them--he doesn't reach for them first--but because the video demo shows how to use them, and makes concepts clear, he at least appreciates and uses them. Maybe they just make more sense to him now at 13 than they did at 7?

 

Merry :-)

[Dmmetler]

My DD doesn't need manipulatives to learn a concept, and does better with visual representations on paper, like in Singapore. Saxon drove her nuts for this reason-just way, way, too much reliance on manipulatives.

 

Having said that, I think part of the reason she doesn't is that the manipulatives are available for play, and she ends up discovering concepts that way, so that when she sees them in the book, they click. So I'm not getting rid of that Saxon kit yet!

[Tabrett]

This is an interesting thread. I have never tried Miquon. We did try RS and it was a flop. She could use the manipulatives, but she had a hard time transferring what she did with a manipulative to what was written on a piece of paper.

 

We are using SP 1a right now and she understands the pictures, but if I try to demonstrate the pictures with the abacus or unfix cubes it confuses her. She is getting better, but manipulatives make the math problems more confusing than just using the pictures in SP.

:lurk5:

[Spy Car]

With Miquon, the child is learning by discovery-oriented methods. That's different than using manipulatives to teach a concept, where you are walking them through step by step what to do.

 

This is not so. Using Miquon as written includes both following up on "discoveries" (that the child is lead to making) with the "explicit" mathematical laws they have "learned by doing", and it also includes direct step-by-step walk throughs of laws and concepts.

 

Recently I took my 6 year old though the Distributive Law as it relates to Multiplication as outlined in the Lab Annotations book. The instruction was direct, manipulative based, and highly effective?

 

The next week when multiplying two numbers (mentally) in Singapore he was able to take 7x3 and solve for 5x3 + 2x3 while envying the Distributive Law" as the reason his re-grouped method was valid. This understanding came directly out of a directed demonstration in the Miquon Lab Annotations book.

 

For my son, it was both the process of using manipulatives (he just wanted to "get done,") and the discovery-oriented method of Miquon that made it a no-go. (He didn't like that the book didn't "teach" him. Discovery oriented programs of all kinds make him feel like someone is holding back information to keep him from learning, rather than just being up front and logical!).

 

 

 

A parent has to actually read the teachers books. There is more mathematical information to be shared with young people than in any other early math program I have seen. It is very direct and comprehensible. It sounds like you have treated Miquon like it is a work-sheet math program and have missed out on the critical teaching components which impart great wisdom and information. It is all therein the teachers materials, but you do need to teach it.

 

Bill

[Ellie]

This is an interesting thread. I have never tried Miquon. We did try RS and it was a flop. She could use the manipulatives, but she had a hard time transferring what she did with a manipulative to what was written on a piece of paper.

 

We are using SP 1a right now and she understands the pictures, but if I try to demonstrate the pictures with the abacus or unfix cubes it confuses her. She is getting better, but manipulatives make the math problems more confusing than just using the pictures in SP.

:lurk5:

Here's my theory:

 

Public schools went off-track back in the 50s and 60s, discarding math instruction that worked--traditional math--for what they thought would work better--new math, group math, etc. Of course, it didn't. So then they decided that they could fix things by using manipulatives. Scores of schools jumped on the band wagon. Publishers jumped on the band wagon. That mentality crept into private schools, and eventually, when hsing became an official Movement, many hsers were sucked into manipulatives, too, even though it turns out that not all children *must* manipulate things in order to learn math.

 

I understand Cuisenaire rods and base 10 blocks. I had some manipulatives for teaching fractions that were very helpful as far as understanding how 1/2 and 4/8 were the same thing. But I can't figure out how pattern blocks and those other block thingies actually help a child learn his times tables or how to balance a check book. I know that some children really do better with a process math (one based on manipulatives, such as Miquon or MUS), but not all of them do. In fact, I'd bet that most children don't need them on a regular basis.

 

So that's my story and I'm sticking to it.

 

::wonders if she should put on the Zena Warrior Princess flame-proof armor::

[Spy Car]

Today she wanted to try Miquon again after a hiatus of two months. That was fine with me, since I was interested to see if things had changed. At the beginning of the page, she could add and subtract, using the rods, and make intelligent remarks about what she was doing.

 

What sort of intelligent things was she saying about what she was doing? It makes my ears stand-up (in a positive way) if the child can explain what they are doing, using manipulates or not.

 

What sort of values was she dealing with in her addition and subtraction problems?

 

Do you and she discuss the procedures in terms of having "wholes" and "parts" and finding sums or differences from those wholes and parts?

 

At the end of the page, she could no longer figure out a subtraction problem because she was using the rods wrong and not thinking about the actual math problem. It was clear to me that the problem wasn't that she was tired, but that at the beginning, she was using the rods to model the problem based on her understanding of the math, and by the end, she had stopped thinking about the actual math and was instead worrying about the right way to use the rods.

 

But why did it break down? If she explained and understands what she is doing and is developmentally past the stage in the concrete>pictorial>abstract learning progression she may (rightly) find the C Rods an unnecessary tool or crutch. If that is the case, move past them for these types of problems, but reserve them for teaching increasingly difficult concepts.

 

I am thinking about introducing decimals soon (at least tenths). And the Orange Rods value (ordinary 10 in the past) will shift to being 1-Unit and White Rods will be 1-Tenth each.

 

The Rods should not be a "calculator" for children who can add and subtract abstractly. They are to help "turn on the lights" and aid children who need them developmentally. When they are not needed for a particular operation, put them aside. But do remember there are other operations forthcoming that might be very well taught with C Rods. Read the Lab Annotations by topic when a new operation is introduced. There is a wealth of information that can be taught to children using manipulatives that would be hard to teach in any other fashion.

 

And if she is getting "messed up" doing addition and subtraction problems with the rods, I'd still want to know why. And I would have her narrate the reasons she is doing what she is doing. And make sure she knows what is the whole and what are the parts and how those things interrelate.

 

If you've been there with a kid like this, I'd love to hear how it went for you. Did you just stop trying to use manipulatives? Any words of wisdom?

 

We use the manipulatives when there is any lack of clarity, or when I want to teach something new in the most simple and easy understand means I can devise. Otherwise, we don't use them ordinarily. But will continue to bring them out whenever they might prove helpful.

 

Bill

Edited October 26, 2010 by Spy Car

[skueppers]

What sort of intelligent things was she saying about what she was doing? It makes my ears stand-up (in a positive way) if the child can explain what they are doing, using manipulates or not.

 

Things like, "if you know that 5 is made up of 3 and 2, it's easy to see that the answer needs to be 2." This would have been for a problem like 5 - 3= ?, for which she didn't use the Cuisenaire rods; she just knew that 5 = 3 + 2.

 

What sort of values was she dealing with in her addition and subtraction problems?

Things within 10, most of which she has memorized. Sometimes she forgets and needs to think about it, though.

 

Do you and she discuss the procedures in terms of having "wholes" and "parts" and finding sums or differences from those wholes and parts?

Yes. Though for the most part, she doesn't like it when I explain things to her and work with her to help her figure things out. She prefers for the book to explain things, which is one of several reasons why we've had trouble with Miquon and are using Math Mammoth instead.

 

But why did it break down? If she explained and understands what she is doing and is developmentally past the stage in the concrete>pictorial>abstract learning progression she may (rightly) find the C Rods an unnecessary tool or crutch. If that is the case, move past them for these types of problems, but reserve them for teaching increasingly difficult concepts.

It broke down because she wanted to use the Cuisenaire rods, and successfully used them at the beginning, but then lost track of the main point (the math) and focused on rote procedures with the rods. Come to think of it, it's not just math -- there are occasionally other kinds of hands-on things where she gets derailed by the hands-on aspect. For example, she deals much better with writing words down on paper than with forming them out of magnetic letters.

 

I don't know if she could have done the particular subtraction problem she got hung up on without the rods, as we haven't been working with subtraction in the last couple of months. It was her choice to use them.

 

In order for this to work successfully, she would have needed to:

 

1) Think about the problem.

2) Figure out how the rods could help her solve the problem.

3) Use the rods to solve the problem.

4) Write down the answer.

 

She skipped steps 1 and 2 because she got distracted by using the rods.

 

But do remember there are other operations forthcoming that might be very well taught with C Rods. Read the Lab Annotations by topic when a new operation is introduced. There is a wealth of information that can be taught to children using manipulatives that would be hard to teach in any other fashion.

Oh, don't worry, I will continue to read the Lab Annotations and see if there is anything useful to our study. But I also don't want to fight with her about math. I want her to be enjoying math, and if what she needs in order to enjoy math is to have Math Mammoth build up the ideas for her slowly, then that's what we're going to do.

 

And if she is getting "messed up" doing addition and subtraction problems with the rods, I'd still want to know why. And I would have her narrate the reasons she is doing what she is doing.

 

Yeah, she screams at me when I try to get her to talk about what she's thinking and doing, which is why I spend more time listening to what she volunteers. I'm working on encouraging her to be more receptive to teaching, but we're not there yet.

 

But I know what the problem was in this case. She was using the rods as you would for an addition problem even though it was a subtraction problem, because she was not thinking about what the rods represent. It wasn't that she misread the problem -- she knew it was a subtraction problem -- she just lost track of the connection between what subtraction is and how you would represent that with Cuisenaire rods.

 

She also volunteered, after the fact, that the rods make things more confusing.

 

And yes, Bill, I have read all the Miquon teacher's materials, we spent a lot of time playing games with the rods, building things out of the rods, etc. She's definitely sufficiently familiar with the rods and how they work.

[skueppers]

Since I seem to have gotten myself embroiled in a tangential discussion with Bill, I just wanted to say to the rest of you who have shared your experiences:

 

Thanks! I appreciated hearing about your children's responses to manipulatives, and what worked better for you. It is helpful to hear other people's stories!