Question 1: Graduates should have a general understanding of what their mathematics knowledge will be used for. Few people go on to be mathematicians on a strictly theoretical level; therefore, it seems to me that students should know the purpose of the mathematics they are learning. They should see the use of mathematics as a tool to solve certain types of problems and that many types of mathematical tools can often be used to solve the same problem, depending on the level of user expertise, and precision desired.

Question 2: a. Development of critical thinking skills

b. Development of technological skills as an aid in increasing problem-solving precision at a higher level.

c. Connection to real-world problems and careers.

d. Opportunity for enrichment for accelerated students.

Question 3: a) At the college level: Survey college professors. The problem here is that if a college offers only a "traditional" approach curriculum and a student comes from a "nontraditional" high school (e.g., integrated, spiral-learning curriculum), the student will not seem as well prepared, and vice-versa. The same goes for entrance testing. For college mathematics, then, I think any type of assessment will be difficult until we are all in alignment.

b) The work/career arena: Survey business. They will know if their work force is prepared or not.

Question 4: I'm a good one to answer this one, in my humble opinion! My math background consists of one year of calculus before I switched majors to accounting. I have a clear math credential because I passed the NTE in math. Despite my lack of college math courses, however, I feel I do a good job in my teaching, the reason being I have good MATH SENSE. I can often think through a problem better than some of my colleagues who have math degrees. I also have an intense interest in what math to use for solving which type of problem, and I try to develop that same interest in my students. A good math teacher should try to get his or her students excited about solving complex problems using the math they have learned. That will not happen unless the teacher is excited about it in the first place. The high school math teacher, however, also needs to realize that math is an extremely difficult subject for most kids, so there needs to be a lot of patience on the teacher's part and willingness to try other approaches in teaching a concept.

Question 5: I have always loved math, more specifically, the beauty of logical process. My father and grandfather were both math whizzes and always encouraged me in that area. I applied to enter college many moons ago as a math major. When I struggled in calculus, however, I switched majors, thinking a math major shouldn't be struggling in a math class (I never did before!). I ended up teaching math because I love the high school level, and yet had only an elementary credential. Math was the only subject I felt I could pass the NTE in and the only one I really enjoyed. That was six years ago--the love has returned! I wish I had never left.

Question 6: Students: I expect my students to not be afraid of higher mathematics; rather, I hope they will understand that, as the problems of their chosen field become more complex, they will need to learn more complex tools to solve. This might be in statistics for the social sciences or calculus for the sciences. I expect them to face that challenge without fear.

Prospective (and current?!) mathematics teachers: I will answer this question with a personal reflection. One area I know I am weak in that I feel is extremely important in the teaching of mathematics is background knowledge of real-life applications of the various concepts I am teaching, hence my interest in it as mentioned above. From what I have seen, though, math majors do not necessarily have this knowledge base either. I think it would be wonderful to require some sort of work experience for credit, so that math might be seen at work, literally. I would also like to see it happen for current teachers as some sort of professional development. How, I don't know, beyond school-business partnerships.