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Topic: Re: To K-12 teachers here: Another enjoyable post from Dan Meyer
Replies: 1   Last Post: Jun 4, 2013 8:14 AM

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Richard Strausz

Posts: 4,621
Registered: 12/4/04
Re: To K-12 teachers here: Another enjoyable post from Dan Meyer
Posted: Jun 3, 2013 9:25 PM
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> On Jun 1, 2013, at 4:06 AM, Richard Strausz
> <> wrote:

> > The link below is to an interesting discussion,
> coincidentally about volume of cylinders, that deals
> with how teachers deal with misconceptions.

> >
> >

> That's funny, not just the teacher's original
> mistake, but posters' responses as well. A couple
> come close but the majority look like they have just
> saw a radio for the first time and are trying to
> figure out how it works.
> First off, thinking that Tuesday comes after
> Wednesday is a misconception. This is a mistake in
> mathematical reasoning. Ultimately, this is a poor
> understanding of algebra and the ability to apply it.
> And naturally, I am not surprised since this is
> essentially an anti-algebra site. I make the point
> about "misconceptions" because labeling this a
> misconception is like thinking that algebra and
> mathematics is all about knowing the right facts or
> formulas.
> I like #23's response, it says it all ...
> "Is this not a delightful case of letting the algebra
> getting in the way of the understanding."
> How does algebra get in the way of understanding when
> the understanding in this case is algebra?
> In any event, Lou already addressed the crux of these
> comparison problems previously, using algebra. Lou
> showed that if you are making a comparison between
> two cases then you introduce a multiplicative
> constant "k" and then describe k, which is the ratio
> of the two cases. The same gist applies here except
> that you will show (algebraically) that the ratio of
> r1^2*h1/r2^2*h2 does not equal r1*h1/r2*h2. In fact,
> it is different by a factor of r1/r2 which destroys
> the idea that one comparison can imply the other.
> What is ironic is that every teacher that saw the
> mistake in the original teacher's algebra did so
> because they have been exposed to algebra. No one,
> including myself, Dan or anyone here, would have ever
> tested that conjecture using trial and error or
> pouring popcorn into cylinders except for the fact
> that the ALGEBRA LOOKED WRONG. Yet, do they proceed
> to devise lessons to teach algebra? No.
> Bob Hansen

Bob, if you were leading such a workshop and someone made that mistake how would you respond?


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