Question 1: I think I want students to understand the process of problem solving. Of seeing a problem for the first time and understanding how to take a step in the right direction (or at least some direction) towards its solution. I guess I'm trying to say the essence of what I think it means to do mathematics. That is, this is new, but it's somewhat like this other thing that I do know and do understand. So I am going to see how it is like that and how it is unlike that, and therefore apply what I already understand to something brand new.

Question 2: Appropriate technology; teachers who know, value, and enjoy learning, doing, and teaching mathematics; a curriculum that prepares students for the next phase of their lives, either work or college.

Question 3: Good question...when university professors say "Wow, these students are brilliant; I can't believe how much they know..." Just kidding... An accumulation of evidence, I suppose; test scores, universities stop doing remediation, employers no longer have to re-train the workforce.

Question 4: "Most important" is not really the right question, I don't believe, because the question is more complicated than that. But if I have to pick out one thing to say is most important, I'd say teachers have to have a strong knowledge of mathematics. But see, that's not nearly enough. It has to be coupled with the ability to engage students in the learning of it. So I have to say those two things are most important.

Question 5: I found mathematics to be challenging. I didn't know there was any other career option. I didn't know there was anyone living that did research. Please do not misunderstand; I'm glad I chose this even if it was out of ignorance. I love it, although it's the hardest job in the world---the best and the hardest.

Question 6: a) My expectations are that some students will have excellent professors and excellent instruction (I had an awesome calculus teacher that inspired me), and some will have awful teachers with rotten instruction, and some will have middle values between those two extremes. So we try to prepare them for any of those possibilities.

b) Prospective mathematics teachers need more mathematics courses. Education courses were pretty useless. More time needs to be spent on practice teaching with a mentor, because that's where you learn the education stuff, not from a textbook. Oops---that doesn't answer the question, but I'm going to say it anyway. Now the answer to the question: This varies so much state-to-state, school-to-school, that it's hard to say what you expect.