Nothing could be a bigger waste of time, right?
I know we all though it was a huge waste of time then, and I wouldn't disagree. Most of Geometry and Trigonometry I never used again. There have been some things which I use regularly and enjoyably, but a good chunk of it I haven't touched since, and I'm a 'Mathematician' of sorts. It seems odd to me that I learned more useless stuff in High School Math than I did in College.
If we took out most of the crap that's currently in the courses, time could be spent much more productively. One thing that I most enjoyed in college was that Moore Method of teaching. Basically, lecture, instruction, and text are kept to a minimum, and the bulk of the course actually comes from the students working problems, proving theorems, doing the work themselves. The teacher assigns theorems and problems, and the students have to prove them. This places the students so deeply in the material that they can't forget it, making you learn much better, and forming a closer community in the classroom.
I had several classes that were all taught in this method to some degree, all advanced classes, and I loved each and every one of them.
Furthermore, applying this type of teaching to High School Mathematics classes would more successfully accomplish what the courses are trying to do anyway: Make the students think. Geometry, in particular, is about fostering and improving a student's ability to think rationally and deductively; promoting analysis of problems instead of just hazarding guesses at everything, and it's about time it started to do that.
Someday I hope to teach Geometry just to get to do this.
-Henry out.
