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This supports what I thought, after reading that study I wrote about -- that very young children might actually relate to manipulatives as toys, and no more. I think you might need to have a certain comfort level with abstraction in general, and the concept being 'manipulated' in particular, before you can relate to manipulatives as anything other than toys.

-- CarolynJohnston - 28 Jul 2005

You nailed it EXACTLY.

I'm impressed.

I'm going to go read the article in full now...

-- CatherineJohnson - 28 Jul 2005

I don't think it is that they relate to them as toys per se, but yes, I agree about the ideas that small children might not understand the abstraction.

All sorts of child development courses discuss issues like object permanence and concepts of volume. You know that famous Seymour Papert example? You have two transparent cups, one short, and one tall. The short one is filled with juice. You pour the juice out of the short cup and into the tall cup (in its entirety.) You ask the child "which cup has more" , and children under a certain age say "the taller cup", even though it's the same amount of liquid.

Papert or Minsky tells a famous story about some grad student trying this test on Minsky's kids--and one of them tells the grad student "oh, you should try that on my brother; I don't understand the concept of volumes(or whatever it was called) yet" and the grad student is dumbfounded. (the details of the story are probably apocryphal...)

Another reason might simply be that abstraction is possible--but not this kind of open ended abstraction. Usually, with manipulatives, kids are supposed to play on their own undirectly, and somehow derive these rules. But that's a really big leap--even if they weren't seen as toys, they might be seen as building materials, or abstractions representing people, etc.

Imagine telling a high school student: "here's a curve; here's a bunch of very thin tiles; derive something" and expecting them to derive integration is the area under the curve. Bit of a leap, no?

-- KtmGuest - 29 Jul 2005

I don't think it is that they relate to them as toys per se, but yes, I agree about the ideas that small children might not understand the abstraction.

But I think preschoolers relate to almost everything as toys. It's either food, or it's a toy. (Everything else you said, I agree with).

But here's another angle on it: manipulatives, played with independently, form the basis of almost all learning in Montessori schools, or so I've heard (no personal experience here). Presumably it works to some degree, or we couldn't have Montessori public schools, as they do in some places, including here. When do Montessori-schooled kids make the move to pencil and paper?

-- CarolynJohnston - 29 Jul 2005

Well...I think in the study they used direct instruction with the manipulatives. That's the impression they gave (and given that it was a peer-reviewed study I would imagine they kept the teaching method consistent across the two conditions).

One thing that interests me about this is the fact that parents find skinnies & bits confusing.

We're told that that's because 'we aren't used to the way math is taught now' or 'we expect to see children sitting in rows doing worksheets' or 'parents don't like change' & blah, blah, blah.

But what if the answer is much simpler?

What if the reason we see skinnies & bits as confusing is that:

skinnies & bits are confusing?

-- CatherineJohnson - 29 Jul 2005

Presumably it works to some degree, or we couldn't have Montessori public schools, as they do in some places, including here. When do Montessori-schooled kids make the move to pencil and paper?

Good question.

I still want to know why paper and pencil is easier.

I absolutely agree that it IS easier, based on personal experience.

But why?????

-- CatherineJohnson - 29 Jul 2005