Question 1: Considering the range of students abilities, interests, and plans for post high school activities I suppose it would have to be "problem-solving." I think all students, whatever their level, should be able to solve problems. I am not referring to the traditional method of students mimicking a method for types of problems that a teacher has shown them "how to do." I'm talking about a systematic approach used to solve problems that you have not seen before.

Question 2: Considering content, I think every high school should offer students everything from Pre-Algebra to Calculus. Within each of these classes the following should be required:

- problem-solving activities

- use of technology

- cooperative learning (probably best using projects or labs)

- communication skills (written and oral)

- work ethic (organizational skills, study skills, etc.)

Question 3: This a tough and slow process, but "feedback" is the only answer. Traditional feedback would be quizzes and tests but these are pretty superficial. We need feedback from our students 2, 5, 10 years after they graduate. We also need feedback from colleges and employers.

Question 4: I think teachers of mathematics must have a passion for mathematics. They must be inquisitive lifelong learners to inspire their students to be the same. We use the "essential elements of instruction" in our district and I think they are sound. I am sure that there are other pedagogical models that also are successful. A teacher needs to use a model that he/she are comfortable with, but they do need some structure. "Flying (teaching) by the seat of your pants" has never worked.

Question 5: I loved mathematics as a student and I wanted to be a teacher. At the time I did not realize the complexity of the teaching profession, but that just makes it more interesting. This is my 25th year of teaching and I have learned something new every year to make me more effective in the classroom.

Question 6: (a) Traditionally many (most) college professors of mathematics have failed their students. They need to be more caring and inspirational in their approach to teaching. These are two adjectives that most college math students would not think to use when describing their professors.

(b) Part (a), of course, would apply even more to future teachers, because we tend to teach as we learned. Prospective teachers also need a structured pedagogy for their classroom. Education classes tend to be somewhat philosophical and, therefore, do not always meet pedagogical needs.