Question 1: My answer to this question has changed over the past two years. I now believe that problem-solving skills are most important. I find that I am putting less emphasis on memorizing formulas and facts, and more on developing strategies and using technology. Also, good guessing and estimation skills compliment problem-solving skills.

Question 2: We are struggling with this at our school. We have a solid "core" curriculum (Algebra I, II, Geometry, Trig, Analytic Geo) plus AP Calculus I, II and AP Statistics. With Algebra reform, and integrated/interdisciplinary movement, some of us are beginning to think about whether our curriculum meets the needs of our students and our society.

Question 3: Right now, we judge our effectiveness by looking at math contest results, and results on ACT, SAT, AP tests. These tests reflect what math educators think are important, and we believe that if our students earn good scores, we have been effective in our teaching.

Question 4: First, the teacher has to have a solid background in higher math - an analogy would be that a bookkeeper and an accountant can both do the same job, but the accountant has the "big picture." Second, teaching is a skill that either comes naturally, or must be learned - you have to know what questions to ask during class, and when to ask them. You have to invent creative approaches in teaching, or the students "tune out." Third, a teacher must go to class with excitement every day, no matter how he/she feels - excitement about math IS contagious. Fourth, you have to be alert to students who are "lost" and know how to help them understand - this country is run by "C students."

Question 5: In high school, I had a couple of very good math teachers - what else!

Question 6: I wish college teachers/professors had the same pressure that high school and elementary teachers have in thinking about how to teach. The image of college professors is totally "teacher-centered" (lecture, explain, prove, test on details) with sleepy students sitting quietly writing notes for an hour. No wonder prospective math teachers often have so much trouble - they are just teaching as they were taught!