Math manipulatives: tool or crutch?

[talk2ham.1]

O.k., so I know it's a tool. A necessary tool. What I'm really getting at is, how can I be sure our math manipulatives are being used as a tool to build/reinforce concrete ideas and not just a complicated form of a calculator that saves the student the trouble of actually thinking?

 

And how do I draw a young student (the kind that prefers caveman communication skills to actual conversation) into a discussion that might reveal whether he is actually thinking through the problems with the manipulative or whether he is just looking for the fastest, most thoughtless way of getting his math homework done?

[UrbanSue]

So, you are using manipulatives all the time for all math?

 

We use them to teach a subject concretely but then move on from there. We use Singapore and manipulatives are the first stop. If we need to use them for more than a few of the textbook problems, we stop and work with them more and then go back to the textbook. We don't use them at all for independent workbook stuff. At that point, I want my dc to demonstrate they can handle the abstract math.

 

So, they're an important tool and I would absolutely spend as much time as necessary with them to get a concept down. But I would be concerned if they were needed for all or most computation.

[kitten18]

It's not a crutch.

 

At some point they will stop using the manipulatives because they will find it much faster to do it in their heads.

[2squared]

We use a variety of manipulatives with RightStart, but none of them are thoughtless or used in lieu of thinking. Once my kids are faster without the manips, they switch and don't look back. What manips and math program are you using? Is the math too easy if your son can complete it without thinking?

[dbmamaz]

i think in singapore you are supposed to go from physical representation (manipulatives) to drawn representation, to in your head. i think kids progress at different speeds and really, its faster to do without the manipulatives so they will probably quit at some point, but you could try taking them away and asking him to do a few problems. if he gets stuck, suggest he draw it.

 

but to me, the more they do the hands-on, the more intuitive it will become . . i dont see the harm.

[charcat13]

If my daughter understands a problem when I write it down she will get annoyed if I use manipulatives. I usually only break them out to explain something new or review something she's having trouble with. She doesn't use them when she does her workbook.

[In The Great White North]

Ds's first grade teacher (in a Waldorf school where they kept the same teacher for 8 years) said her last class had students still counting on their fingers for multiplication when they left 8th grade. And she didn't have a problem with it.

 

I'd put that in the "crutch" category.

[K&Rs Mom]

It's not a crutch.

 

At some point they will stop using the manipulatives because they will find it much faster to do it in their heads.

 

:iagree: Especially if laziness is the problem, it won't take long to figure out the easiest way, which is without manipulatives.

[Samiam]

I've found my boys only use the manipulatives when they really need to...ie can't figure it out and ask me for help and I in turn, asked if they tried to work it out with the math cubes first (which are always on their desk). Once they've got a grasp on a type of problem, they don't want to use the cubes, they've said they are "annoying". If a much older student was still using manipulatives, ie fingers in 8th grade, that speaks to me that the students didn't master the facts when they needed to...I'd be stopping right there and focusing on the basic facts at that point.

[Ellie]

O.k., so I know it's a tool. A necessary tool. What I'm really getting at is, how can I be sure our math manipulatives are being used as a tool to build/reinforce concrete ideas and not just a complicated form of a calculator that saves the student the trouble of actually thinking?

 

And how do I draw a young student (the kind that prefers caveman communication skills to actual conversation) into a discussion that might reveal whether he is actually thinking through the problems with the manipulative or whether he is just looking for the fastest, most thoughtless way of getting his math homework done?

 

 

Not all children need manipulatives, so, no, I wouldn't say they are "necessary." Neither my children nor I would have needed them. I think there's an overemphasis on "thinking through" math problems, to the extent that children are dependent on them instead of being able to figure out how much wallpaper they need in the kitchen without pulling out the C-rods, KWIM?

 

Not sure I can answer your question, though. Not sure what your question actually is, or rather, what the problem is?

[RoundAbout]

O.k., so I know it's a tool. A necessary tool. What I'm really getting at is, how can I be sure our math manipulatives are being used as a tool to build/reinforce concrete ideas and not just a complicated form of a calculator that saves the student the trouble of actually thinking?

 

And how do I draw a young student (the kind that prefers caveman communication skills to actual conversation) into a discussion that might reveal whether he is actually thinking through the problems with the manipulative or whether he is just looking for the fastest, most thoughtless way of getting his math homework done?

 

 

I've never considered them a crutch because my son makes it abundantly clear when he no longer wants to use a manipulative. Almost always its when using the tool becomes more bothersome or slow than doing it in his head. Some manipulatives are brilliant at demonstrating concepts - particularly c-rods and the AL abacus - depending on the problem, but there should be a very natural transition away from them.

[laundrycrisis]

They are a tool until the concept is understood. After that they are a crutch. Our son with LD issues had to be forced off them, because he was using them to avoid having to deal with numerals as symbols, at all.

[happypamama]

I don't think of manipulatives as being a crutch, and both of my kids have quit using them when they were ready. I still pull them out for my 8yo occasionally, especially when introducing a new concept. Just this week, we talked about cups, pints, quarts, and gallons; the c-rods made it really easy for him to see the relationships between each unit of measurement. He tells me when he no longer needs them because he can visualize in his mind. After I introduce a concept, I won't pull the rods out unless he seems to need them.

[Dmmetler]

I think manipulatives become a crutch when they're the only way a child can solve a problem long-term. For example, I caution parents AGAINST using Touch Math for anything but children with serious learning challenges for which all other approaches to get basic, life-skills math have failed, because

while it can be quite successful in teaching a way to find an answer for basic operations, it's too easy for that to become the only problem solving strategy kids know how to use-and if a child is going to go on into fractions, or worse yet, into algebra, those touch points don't work so well.

 

I have to say, though, I've never seen this as a problem with physical manipulatives, simply because you CAN take them away. I do like the way Singapore (and, I'm sure other approaches) specifically move from the physical to the visual to internalizing the same strategy so the connection is obvious. And for the kids who really don't need the manipulatives much if at all, it still gives them exposure to the concrete, whether they want it or not ;).

[Dana]

Ds's first grade teacher (in a Waldorf school where they kept the same teacher for 8 years) said her last class had students still counting on their fingers for multiplication when they left 8th grade. And she didn't have a problem with it.

 

I'd put that in the "crutch" category.

 

 

I used my fingers for the "trick" for the 9's times tables all through my undergrad math degree. I finally got my 9s memorized during grad school (math & education). So yes...crutch in some ways...but doesn't necessarily prevent one from progressing. I do feel that it slowed me down, so I covered the pages in Singapore that showed the trick for 9s when my son was learning it and have done my best to be sure he knows his times tables (drill, drill, and more drill... separate from math).

 

I have to say, though, I've never seen this as a problem with physical manipulatives, simply because you CAN take them away. I do like the way Singapore (and, I'm sure other approaches) specifically move from the physical to the visual to internalizing the same strategy so the connection is obvious. And for the kids who really don't need the manipulatives much if at all, it still gives them exposure to the concrete, whether they want it or not ;).

 

 

I love algebra tiles, base 10 blocks, and Cuisinaire rods.

I think seeing algebra tiles would have helped me. I didn't see the difference between x^2 and x because they both had x's! I did get it... but I think algebra tiles would have led to an "ah-ha" a lot faster.

Base 10 blocks really show why our algorithms work for standard arithmetic.

I made my son show long division with base 10 blocks for a couple of days. He really didn't like it quickly...took too long. But it helped him see what was going on with the standard algorithm much more clearly.

 

I would encourage manipulatives for a while when learning a new concept. Then I'd start pulling away once I thought the concept was there, unless the child really wanted to continue using them. In our case, I had to yell at my son to use the manipulatives after getting a problem wrong with pencil & paper :)