re: Thomas H. Foregger (firstname.lastname@example.org) Content of high school geometry courses
I am a high school math teacher in Southern California. In our high school a student may take high school geometry if they qualify. Last year we had a 6th grader taking honors geometry and usually have about six eighth graders taking honors or regular geometry.
Honors geometry is very rigorous, old-style, proof-based geometry. This year, for the first time, we have 6 classes of geometry emphasizing problems solving, integrating other areas of math with the study of geometry, and one class of traditional geometry. In the 9 years I have been teaching high school math, none of the teachers have been able to get into solid geometry. Except in honors classes, students don't put enough effort into the proofs at home to be able to move at a normal pace through the simpler proofs. Hence more time is spent in class on even the simplest proofs.
I am one of the teachers teaching geometry using a problem-solving investigative approach. We had hoped to have greater numbers of students having success in geometry -- doesn't seem to be happening -- and to have students much better grounded in thinking logically through problems while using their expanding knowledge of geometrical relationships. I do see growth in problem-solving. But there is a difficulty with students of today with the perception of what is required as they do homework. If one gives 1 problem that requires a half hour of thought and a paragraph detailing those thoughts, the majority of students give it 5 minutes. But if I gave them a page of problems requiring a little work on each problem, many more students would accomplish that work. They are not used to a short assignment that requires a lot of work!