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Topic: If you really want math reform....
Replies: 117   Last Post: Jan 27, 2007 5:24 AM

 Messages: [ Previous | Next ]
 Michael Paul Goldenberg Posts: 7,041 From: Ann Arbor, MI Registered: 12/3/04
Re: If you really want math reform....
Posted: Jan 7, 2007 2:27 AM

On Jan 6, 2007, at 9:37 PM, Adrian wrote:

> theory class could, say, prove that every group of prime order is
> cyclic or that a cyclic group is abelian? Of course, I don't mean
> give an example of an abeliean cyclic group or something like
> that. Can they put together a coherent and sufficiently formal
> argument that proves these assertions or an assertion like it? If
> that is indeed what you are doing, then perhaps there is more to it
> than you at first let on. If not, then I think we are back to
> teaching them some particular fact without teaching them the real
> justification for that fact. Instead what you are doing is giving
> them a rationale for why someone might think the fact is true, not
> the actual justification for the fact that *proves* that it is
> true. Something like that is little more than a mnemonic device to
> remember the fact by.

Don't let Paul hear you disparaging anything to do with memorization!
>
> It's really much deeper even than math education -- a fact without
> justification is not knowledge.

Really? Gosh, we mathematics educators would NEVER advocate actual
knowledge. We're all about rote memorization and regurgitation, don't
you know?

> What do your students *know* when they are done? Have they
> acquired any knowledge? Or, do they just have vague rationales for
> facts that they believe without justification?

Hmm. You mean that at some point, we have to look at what students
can DO with what they've learned, and mere recitation isn't enough?
How radical. Watch out, Adrian: someone is going to shoot you for
being too fuzzy.

Date Subject Author
1/5/07 Kirby Urner
1/8/07 Kirby Urner
1/5/07 Dave L. Renfro
1/5/07 Kirby Urner
1/6/07 Kirby Urner
1/6/07 Kirby Urner
1/6/07 Kirby Urner
1/6/07 Kirby Urner
1/7/07 Bishop, Wayne
1/7/07 Michael Paul Goldenberg
1/7/07 Kirby Urner
1/7/07 Kirby Urner
1/7/07 Kirby Urner
1/7/07 Kirby Urner
1/8/07 Michael Paul Goldenberg
1/8/07 Kirby Urner
1/8/07 Michael Paul Goldenberg
1/8/07 Kirby Urner
1/8/07 Michael Paul Goldenberg
1/8/07 Paul A. Tanner III
1/8/07 Michael Paul Goldenberg
1/9/07 Louis Talman
1/8/07 Kirby Urner
1/8/07 Michael Paul Goldenberg
1/14/07 Dave L. Renfro
1/14/07 Michael Paul Goldenberg
1/14/07 Louis Talman
1/15/07 Bishop, Wayne
1/15/07 Haim
1/15/07 Louis Talman
1/15/07 Louis Talman
1/16/07 Michael Paul Goldenberg
1/18/07 Greg Matheson
1/15/07 Kirby Urner
1/15/07 Kirby Urner
1/15/07 Dave L. Renfro
1/15/07 Kirby Urner
1/16/07 Dave L. Renfro
1/15/07 Dave L. Renfro
1/23/07 Kirby Urner
1/26/07 Greg Matheson
1/27/07 Kirby Urner
1/27/07 Greg Matheson
1/7/07 Michael Paul Goldenberg
1/8/07 Paul A. Tanner III
1/8/07 Jim Wysocki
1/8/07 Jim Wysocki
1/8/07 Michael Paul Goldenberg
1/8/07 Kirby Urner
1/8/07 Michael Paul Goldenberg
1/9/07 Kirby Urner
1/9/07 Michael Paul Goldenberg
1/8/07 Haim
1/8/07 Michael Paul Goldenberg
1/8/07 Haim
1/8/07 Jim Wysocki
1/8/07 Michael Paul Goldenberg
1/8/07 Jim Wysocki
1/8/07 Michael Paul Goldenberg
1/8/07 Michael Paul Goldenberg
1/8/07 Michael Paul Goldenberg
1/8/07 Michael Paul Goldenberg
1/8/07 Jim Wysocki
1/8/07 Michael Paul Goldenberg
1/8/07 Paul A. Tanner III
1/8/07 Michael Paul Goldenberg
1/9/07 Haim
1/9/07 Jim Wysocki
1/9/07 Kirby Urner
1/9/07 Michael Paul Goldenberg
1/9/07 Jim Wysocki
1/8/07 Paul A. Tanner III
1/8/07 Michael Paul Goldenberg
1/8/07 Kirby Urner
1/8/07 Kirby Urner
1/9/07 Michael Paul Goldenberg
1/9/07 Kirby Urner
1/9/07 Michael Paul Goldenberg
1/9/07 Kirby Urner
1/9/07 Richard Strausz
1/9/07 Kirby Urner
1/9/07 Michael Paul Goldenberg
1/9/07 Kirby Urner
1/9/07 Paul A. Tanner III
1/9/07 Michael Paul Goldenberg
1/9/07 Kirby Urner
1/9/07 Richard Strausz
1/9/07 Kirby Urner
1/9/07 Paul A. Tanner III
1/10/07 Kirby Urner
1/8/07 Michael Paul Goldenberg