The value of manipulatives
(Note: I'm "resurrecting" an old post, with added information and a video. The topic is still very much valid.)
Manipulatives are IN, in math education. But do they TRULY facilitate learning to such an extent as people promoting them claim?
The entry at Text Savvy, Hands-on, Brains-Off, explains some of the pitfalls in manipulative use. Very enlightening!
Quoting from an article at Education Week (Studies Find That Use of Learning Toys Can Backfire):
The video below also illustrates how manipulative use can lead to problems.
The girl solves an addition problem involving thousands by drawing thousand-blocks, hundred-sheets, etc. on the board, taking 8 minutes. Then she says that at home she has been taught to stack the numbers and add. She solves it that way, too, taking 1 minute. But she gets two different answers.
(Hat tip to Denise)
Clearly, manipulatives aren't the best way to solve such problems, and children shouldn't be led to believe so. Not that this girl believed that way... she seems to understand which way is easier and quicker.
My take is that manipulatives aren't the ultimate answer to math teaching.
They're a reasonable starting point. But children should NOT be taught to rely on them. Children need to be taught and shown how to transfer all of that concrete play into the abstract.
In my books, I often instruct concepts with pictures, which essentially take the place of manipulatives. Then the student does a bunch of problems that have the same pictorial representation in them, including having to draw those same pictorial models to illustrate the math problems. THEN after that, the student goes on to totally abstract representation.
Here's one example from my book Add & Subtract 2-B: Adding with Whole Tens. The student first adds using the pictorial model, and then with numbers only.
I don't know if that approach suffers from the drawbacks mentioned in the article above. I hope not; from the feedback I get, it seems to work well.
Manipulatives are IN, in math education. But do they TRULY facilitate learning to such an extent as people promoting them claim?
The entry at Text Savvy, Hands-on, Brains-Off, explains some of the pitfalls in manipulative use. Very enlightening!
Quoting from an article at Education Week (Studies Find That Use of Learning Toys Can Backfire):
In a similar series of experiments at the elementary-school level, the researchers found that children taught to do two-digit subtraction by the traditional written method performed just as well as children who used a commercially available set of manipulatives made up of individual blocks that could be interlocked to form units of 10.
Later on, though, the children who used the toys had trouble transferring their knowledge to paper-and-pencil representations. Mr. Uttal and his colleagues also found that the hands-on lessons took three times as long as the traditional teaching methods did.
The video below also illustrates how manipulative use can lead to problems.
The girl solves an addition problem involving thousands by drawing thousand-blocks, hundred-sheets, etc. on the board, taking 8 minutes. Then she says that at home she has been taught to stack the numbers and add. She solves it that way, too, taking 1 minute. But she gets two different answers.
(Hat tip to Denise)
Clearly, manipulatives aren't the best way to solve such problems, and children shouldn't be led to believe so. Not that this girl believed that way... she seems to understand which way is easier and quicker.
My take is that manipulatives aren't the ultimate answer to math teaching.
They're a reasonable starting point. But children should NOT be taught to rely on them. Children need to be taught and shown how to transfer all of that concrete play into the abstract.
In my books, I often instruct concepts with pictures, which essentially take the place of manipulatives. Then the student does a bunch of problems that have the same pictorial representation in them, including having to draw those same pictorial models to illustrate the math problems. THEN after that, the student goes on to totally abstract representation.
Here's one example from my book Add & Subtract 2-B: Adding with Whole Tens. The student first adds using the pictorial model, and then with numbers only.
I don't know if that approach suffers from the drawbacks mentioned in the article above. I hope not; from the feedback I get, it seems to work well.
Comments
Further, the notion that there's some "best" way to teach math that trumps all others is intriguing, but I don't find it very convincing, regardless of what way is being touted as "best."
I have no doubt there are some ineffective ways, confusing ways, ways that suppress student thinking, etc. And I don't recommend doing those, but they tend to dominate US math teaching in school.
Models, with or without manipulatives, are part of how good teachers try to open up possibilities for students and how students construct their own understanding. If they make mistakes or construct 'inefficient' models on the way to grasping key mathematical ideas, I'm not sure how that's a bad thing. But then, I really AM a progressive educator.