Well, they'd better get learning how to draw information out of a lecture if they ever want to amount to anything. Because no one's going to hold their hand in college. Maybe I'm biased because in the private schools I attended from 5th to 8th grade there were no group projects or 'hands on' learning, we sat at our desks every day, listened to lectures, and took notes for every subject from Latin to Mathematics. It seemed to work fairly well.
As a returning college student who admittedly stinks at Math and is going to school with the intent of becoming a History teacher, I'd like to offer my two cents.
In observing your conversation, your comments seem especially biased to your particular method of learning and for your particularly high level of Mathematics.
Based on your comments, you're obviously well versed in Mathematics and have no difficulty performing advanced calculations that most of the population would never dream of attempting.
Papist teaches High School Freshmen. They are no where near your level of achievement. Their brains have not finished fully developing, nor have they had the years of education and experience you have. Furthermore, everyone has different styles of learning that work best for them. A good teacher is cognisant of this, and tries to meet his students needs to the best of his ability. Some students (such as yourself) do very well with nothing more than a lecture. Others need more hands on work, and large amounts of homework is required for them to really "get" the concept.
I can understand what you are saying about lectures, as this is how I learn best when it comes to History. I can listen to a lecture or read a book once, and my mind absorbs it like a sponge. I can see the events play out like a movie in my mind. For me, History just "clicks" and I don't understand why anyone else wouldn't find it fascinating.
When it comes to math however, my mind turns to concrete. It took me five hours to complete one stupid Algebra homework assignment today! (I'm sure you think I'm an idiot, but at least I'm willing to admit my faults.) I listen to the lectures, I take copious notes, but until I sit down to try to work out the problems, I just don't get the concept. (I hate myself for it!)
There is much to be said about Papist's comments about the quality of a College Professor versus a High School teacher.
My college professor has his doctorate in Mathematics and has 27 years experience at Bell Labs. He's obviously a bright man. He has a firm grasp of the material, and begins every lesson with "If you understand this, this is easy, but if you don't, this is hard."
Well no kidding! (If we understood it, we wouldn't be in the class!)
Although as a person he is a very nice man, he is a HORRIBLE teacher. For the first 4 weeks he used nothing but power point presentations until the class yelled at him enough for him to stop.
He can't understand why anyone would have any difficulty with mathematics, and is completely opposed to explain alternative methods to solving problems.
Maybe I'm just being a "baby" and need to suck it up and deal with it, but as someone who is paying for her education herself, I want a teacher who actually is interested in teaching the material, not just repeating what is written in the book.
The point of all this is, that it is great that you understand math so easily, but you should be aware that others are not as fortunate as yourself when it comes to comprehending mathematics.