It has been along time since Dolciani taught 15 year olds, if ever. And the ones she taught did not grow up with video games like tetras where the object is to arrange congruent shapes to fit in the appropriate slots. Today's kids are quite comfortable with the notion of transformations.
Math is the second most exciting thing
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From: NealAgMan@aol.com [mailto:NealAgMan@aol.com] Sent: Saturday, November 26, 2005 7:41 PM To: firstname.lastname@example.org; email@example.com Cc: firstname.lastname@example.org; email@example.com Subject: Re: Proving the base angles theorem w/out constructing anything
Lou----at least for Prof. Mary Dolciani's take on your question, look at the response I posted. She states expressly that that proof "seems elusive to many students." It seems to me that she is absolutely right. If I have trouble with it, after studying quite a bit of geometry and spending years pouring over geometry books to see various approaches to different problems, I can't help but think that the average 15 year old will be somewhat lost.