>You endorse the statement: > Only problem I have is that I don't think working >from the specific problem to the general skill works as well.
>What am I missing? How can one develop a general "skill" without >experiencing specific, particular situations and problems from which a >generalization can be drawn?
Gary...I guess what I meant was....how can you find the volume of the following rectangular solid (having w=3, l=4, h=5.3) if you don't first know how to multiply? I'm sure most of us agree that in the second grade we were taught the multiplication tables before any need to know such knowledge was ever introduced. Later....applications were developed to show us why we needed to know multiplication (as in the volume of a solid etc). I like to teach my trigonometry kids what the definition of sine is BEFORE I ask them to find the sine of 30 degrees and certainly prior to asking them to solve any triangular problems involving sun's shadows and heights of trees etc. I do understand the desire at times to introduce an interesting problem that get the kids interested....and then you show them the basic skills needed to solve the interesting problem....however, I don't really believe we are using our time most beneficially when we throw out a difficult (challenging, interesting) problem and then let the kids "work" on it. Yes, discovery MAY happen and this would be very nice....but since I have my students for 90 days during the entire year, I have to think that teaching a skill and then letting the kids use that skill on an interesting, challenging problem is the best policy given the educational constraints most of us are under.