In three words, high school mathematics should strive for clarity, correctness and accuracy. We find that the biggest obstacle to most students doing well in calculus is their inability to express themselves. Students need to work on thinking through problems. Working on problems that are not given in standard form, perhaps even with incomplete data, is more like what people will need in life. If we can train people to competently deal with such questions we will have given them a good lesson in how to organize their thoughts.
Students learn by doing.
The key to good teaching is to persuade the student that they are capable of figuring out how to do the problem and then getting them to do it. Students must study for themselves. Thus the precise content of material is much less important than the teacher's ability to inspire the student to think about it, and to recognize that this is worth doing. This is no longer the case, so we need to make the material seem worthwhile. We believe this is best done by having teachers that are better mathematicians, and better trained to be teachers.