Question 1: High school students with AP calculus, some basic linear algebra and some basic probability are well prepared. Most high schools offer such courses. However, very few students take them. They have lost interest in math somewhere in the 6th to 9th grade.

Question 2: Algebra, trigonometry, geometry, analytic geometry, calculus plus basic probability and statistics. It is important that the students see some uses of mathematics in other than physical applications and statistics, which is hard to teach except in a routine way, could be good for this.

Question 3: I think the problems with high-school math start much earlier. By the 9th grade very few students care for a math education. There is a lot of confusion about how to teach math in junior high and a lot of kids drop out.

Question 4: What is lacking in the educational culture today, more so than in my time (late 1950s), is the belief that mathematics is indeed basic in one's education and that it need not be relevant to everyday experience at every step in the learning process. Mathematical skills, like verbal skills pay off handsomely. Continuity and emphasis on basic skills is, in the early stages of math education, as important as a fresh and exciting presentation.

Question 5: I was attracted to mathematics because I had a good teacher in high school (he was much better than my physics teacher). Then I realized that I was good at it ...