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Topic: Progressive Education at Its Best
Replies: 64   Last Post: Jul 5, 2007 9:13 PM

 Messages: [ Previous | Next ]
 Michael Paul Goldenberg Posts: 7,041 From: Ann Arbor, MI Registered: 12/3/04
Re: Progressive Education at Its Best
Posted: Jul 1, 2007 9:24 AM

On Jul 1, 2007, at 12:30 AM, Edmond David wrote:

> MPG Posted: Jun 30, 2007 11:53 PM
>> ...when Wayne volunteers he knows a method for doing
>> square roots and asserts essentially that it's THE way
>> to do this by hand, is it unreasonable to expect him to
>> explain it?

>
> Sorry, I missed that. Can you point me to it?
>

<http://mathforum.org/kb/message.jspa?messageID=5782367&tstart=0>

> Don't know about Dom but when I was teaching high school mathematics
> 40 years ago, the time spent teaching the "long-division style"
> square root algorithm was approximately zero; the only way to change
> would be to increase the time, a situation you probably do not
> intend. One caveat is that I did take time to explain why the
> algorithm works in terms of algebraic expression, a fact that is not
> obvious when applying the algorithm itself. I was taught the
> algorithm in, maybe, sixth grade as an interesting phenomenon, not
> with any hope for comprehension as to why it worked nor even to be
> tested later. My conviction is that the teacher had no idea why it
> worked. When I had algebra in high school, I was able to figure out
> on my own the basis for its validity and was truly impressed with the
> power of algebra to clarify a phenomenon that is less obvious in
> strictly numerical form. I enjoyed sharing that experience with my
> own classes years later but knowing full well that most of the
> students had never seen the algorithm nor was I expecting them to
> know it thereafter.
>
> An aspect of the algorithm that I've always liked is that it teaches
> estimation in the only way that it can be taught, by estimating
> stuff. That is an important plus for the traditional long-division
> algorithm, but the square root algorithm is even better for the
> purpose.
>
> Interpolation is a different matter entirely. We have lost a lot by
> avoiding the subject just because we no longer need to use table
> lookup. The underlying concept of linear interpolation - and how to
> reasonably adjust if the situation is obviously not linear - remains
> just as important as it ever was. Not from a computational
> standpoint, obviously, but for mathematical understanding, the goal
> we all seek.
>
> Wayne

Date Subject Author
6/30/07 Bishop, Wayne
6/30/07 Michael Paul Goldenberg
6/30/07 Bishop, Wayne
6/30/07 Michael Paul Goldenberg
6/30/07 Haim
6/30/07 Michael Paul Goldenberg
6/30/07 Haim
6/30/07 Michael Paul Goldenberg
7/1/07 Haim
7/1/07 Michael Paul Goldenberg
7/1/07 Haim
7/1/07 Michael Paul Goldenberg
7/1/07 Greg Goodknight
7/1/07 Bishop, Wayne
7/1/07 Michael Paul Goldenberg
7/1/07 Michael Paul Goldenberg
7/2/07 Haim
7/1/07 Haim
7/1/07 Michael Paul Goldenberg
7/1/07 Greg Matheson
7/1/07 Haim
7/1/07 Michael Paul Goldenberg
7/1/07 Greg Goodknight
7/1/07 Michael Paul Goldenberg
7/2/07 Greg Goodknight
7/2/07 Michael Paul Goldenberg
7/2/07 Bishop, Wayne
7/2/07 Michael Paul Goldenberg
7/2/07 Greg Goodknight
7/2/07 Michael Paul Goldenberg
7/2/07 Greg Goodknight
7/2/07 Michael Paul Goldenberg
7/3/07 Greg Goodknight
7/3/07 Haim
7/3/07 Michael Paul Goldenberg
7/3/07 Greg Goodknight
7/3/07 Michael Paul Goldenberg
7/3/07 Greg Goodknight
7/3/07 Michael Paul Goldenberg
7/3/07 Haim
7/3/07 Michael Paul Goldenberg
7/3/07 Haim
7/3/07 Haim
7/3/07 Haim
7/3/07 Michael Paul Goldenberg
7/4/07 Haim
7/4/07 Michael Paul Goldenberg
7/4/07 Haim
7/4/07 Michael Paul Goldenberg
7/4/07 Haim
7/4/07 Richard Strausz
7/4/07 Michael Paul Goldenberg
7/4/07 Anna Roys
7/4/07 Jim Wysocki
7/4/07 Anna Roys
7/4/07 Michael Paul Goldenberg
7/5/07 Anna Roys
7/4/07 Michael Paul Goldenberg
7/4/07 Haim
7/4/07 Michael Paul Goldenberg
7/3/07 Greg Goodknight
7/3/07 Haim
7/3/07 Michael Paul Goldenberg
7/2/07 Haim
7/2/07 Michael Paul Goldenberg