Question 1: I wish that H.S. graduates would retain the Big Picture of what they have studied, and be able to look up how to do things they've forgotten. For example, I would hope they would remember that a parabola is the graph of a quadratic function, whether or not they remember the quadratic formula.

Question 2: Algebra, geometry, functions, sensible use of technology.

Question 3: When we don't have to offer remedial high-school level classes in college. At my university, one-third of the teaching in the math department is courses which don't qualify for college credit. Of course, with more and more older people returning to college, or attending for the first time, we will be dealing with the effects of high school teaching in the 50s, 60s, 70s, and 80s for years to come.

Question 4: Unfortunately, many high school teachers are high school teachers because they were always good at getting the right answer and enjoyed the neat and orderly aspects of algebra. These people often do well in calculus, but "lose it" in the more abstract courses, and retreat to teaching material they feel comfortable with.

I wish that all high school teachers would convey that mathematics is a large, interconnected field, with many paths running through it; that there are unanswered questions; that mathematics is a powerful tool for solving real-world problems (and be able to give some real examples), and that mathematics is also an art, to be enjoyed for its own sake.

Question 5: Being put in an "accelerated" math class in algebra in the 8th grade. Before that, math was deadly--2, at most 3 new ideas per year, lots of review, lots of drill. In algebra, there was something new every week!