Question 1: For those high school students who plan a career in mathematics or engineering or the like, I feel they should have a very good background in algebra, geometry, trigonometry, and functional analysis. Also I feel they should have an understanding of the methods of mathematical proofs.

For those students who are not as technically oriented, a good understanding of algebra, mathematical modeling, basic geometry and basic statistical ideas and applications. (These topics should also be included in the education of technically oriented students.)

Question 2: Basic algebra, basic geometry, basic statistics, and methods of mathematical modeling and problem solving.

Question 3: I wish I knew the answer to this question. Traditional testing seems inadequate to measure this. I would think that a student's enthusiasm to elect mathematics courses when entering college would reflect a level of competence, comfort, and interest which would indicate high school mathematics is working well. When my daughter recently went to college, various tables were set up with members of academic departments available for questions. The mathematics table with faculty at the ready was empty. No one asked a question. For no one to inquire about mathematics is such a shame. We high school teachers seem to be discouraging our students. Of course, those very students have been, in some cases, subjected to 18 years of their parents saying how much they hated mathematics and how poorly they did. That is one horrible obstacle which other subjects seem not to have to overcome.

Question 4: Mathematics teachers must have an excellent background in mathematics. They must be able to tie-in the subjects of high school mathematics so that students see and understand the relationships among them. They must be enthusiastic and willing to use new and different approaches to involve their students in the thrill of the subject. Group work and work with technology must be incorporated into the curriculum, and teachers must be educated in new and different methods.

Question 5: I, personally, found mathematics to be exciting and intriguing. Working out a problem, finding a mathematical model, seeing a proof, developing my own proof-these were all things I found wonderful and totally involving. Mathematics was the one subject which consistently held my interest and excitement and still does.

Question 6: I wish that my own students would develop a small fraction of my enthusiasm for mathematics. I hope they will find a college professor who could act on this and draw out even more enthusiasm. For prospective mathematics teachers I expect a wide base of mathematical knowledge, enough depth to understand the beauty of the subject, and enough enthusiasm to bring the subject to life for the students.