Question 1: Can reason qualitatively about ideas which are essentially quantitative

Can use analytic methods to reason logically from assumptions to conclusions

Appreciate mathematical ideas and approaches without necessarily able to symbolically analyze them

Willing to use mathematical reasoning

Have the curiosity to explore new mathematical ideas with varied approaches

Understand the difference between analysis and synthesis of ideas

Are interested in and willing to use technology to explore mathematical ideas and compute mathematical conclusions

Question 2: Exploration of mathematical ideas

Geometric reasoning

A core of symbolic manipulation by hand

The ability to do extended symbolic manipulation using technology

Experience with visualization

Conceptual reasoning at a basic level

A core understanding of a function

A basic understanding of the reals and R^2 both algebraically and geometrically

Question 3: When graduates are interested and willing to use mathematics after high school

When overall student mathematical knowledge is commensurate with the student's own ability and a standards based curriculum

Question 4: Most important aspect for teachers

To love the subject and able to convey that feeling

To enjoy watching others learn

To know enough that when you can't answer a question, you can explore other ways to make progress

To be able to communicate math ideas to diverse audiences

To inspire students to learn

To motivate students to seek their own interpretations and descriptions

To be enthusiastic

Question 5: I was good at computation and symbolic reasoning

I was struck by its power to analyze ideas

I liked numbers and manipulating them