>What if this idea was used in med schools for new surgeons? After thinking >of all these interesting problems he's ready to perform surgery.
Dan why are you comparing learning mathematics with a highly skilled-specialized-payed professional. The mental differences between an highly educated adult(o.k. there are a few Doogy Howsers out there) and the adolescent barely out of childhood. I find these comparisons rediculous and boring. Sure the doctor had to learn the basics(whatever that is) but as anyone who does surgery knows there is one very important thing that makes a good surgeon and that is experience. She must be able to think on her feet and problem solve. No amount of basics learning can really prepare her for things that come up. Learning by doing that is what may occur. Sometimes there is more than one way of doing it. That is what makes any problem interesting.(My father is a surgeon). I went with what you said but I refer to what I said before. There is no comparison.
>How about a carpenter?
Not quite as bad as the first example but still I don't think this applies.
>I don't know about you people but I had to practice, practice, practice to >learn to tie my shoes with proficiency.
I just ware slippers!!! Have you seen how many young people don't tie there shoes? Is it because they didn't practice? I don't think so. Dan I really see no validity in this argument. Could you try again?
Is not math the same way?
In your case maybe. In the majority of my students not at all!!!! Dan I hope you allow your students to make mistakes. I hope you allow your students to be creative and come up with different maybe even crazy ideas that will help them create a firm base of knowledge free from the narrow veiwpoints of those in authority.
I hope this gives you something to think about on a friday afternoon. Have a great weekend. Aloha!!!