Question 1: (a) All students should able to work with numbers and be reasonably adept at arithmetic. Many years in the classroom show me that students who have mastered the multiplication tables have a much easier time mastering algebra techniques because they "see" the arithmetic relationships present in the problem. Students without good arithmetic skills are forced to do algebra as a rigid set of rules applied in an arbitrary manner. These arithmetic skills of the students should include fractions, decimals, percents, and the ability to move between forms with ease and accuracy. I would want all students to have a well developed number sense.

(b) High school work should reinforce these number skills while building algebra skills. There are certain skills (lists vary from teacher to teacher) that all students with a high school diploma should have. In addition to being able to perform various algebraic techniques, the student should understand what he/she is doing and why?

(c) The arithmetic and algebra skills listed in (a) and (b) are the minimum ALL high school students should have. Those students with the resources to continue their education should be able to THINK logically and, to some degree, abstractly. They should appreciate that mathematics is a tool that can be applied in a wide variety of areas (even some real life situations).

Question 2: Regardless of the particular course, algebra to calculus, I want my students to be able to THINK. I want them to realize that mathematics is logically based and most topics are related to one another in a many ways. They should be able to analyze a situation algebraically or graphically or both. They should understand when technology might help then investigate something and when it would be better or faster to do it themselves. I want them to understand that not all questions/problems can be answered quickly or immediately, but most can be done with perseverance and thought.

Question 3: High school mathematics education will be working well when we have more students taking higher level math classes in high school, and colleges and universities no longer have to offer remedial classes for vast numbers of students.

Question 4: (a) It is critical that high school teachers have a good understanding of mathematics above what they are teaching. This requires that they have a degree in mathematics, not math ed. It is important that they love and enjoy mathematics and can pass on their enthusiasm for what they are teaching. They should see multiple ways to teaching a topic and be able to show how it fits with topics studied earlier and topics still to come. Since really good students will see what they think are other ways to do a problem, often correctly, it is important for the teacher to be able see other ways also and convince the students that this is natural and valuable. A good teacher has many ways of teaching and gets students involved in the development of new material. New material should, whenever possible, be taught as a natural consequence of earlier topics. This will help reduce the students' notion that mathematics is nothing but rigid rules and techniques totally unrelated to anything they have ever or will ever do. A good teacher sets high expectations for the students, is consistent and fair in evaluations, and always pushes the students just a little farther than they want to go.

Question 5: I always enjoyed mathematics in high school and college. As I tried other areas in college, I found none quite as interesting as my math classes. The fact that I didn't have to write papers was as added bonus.

Question 6: (a) I would like my students to have college professors who are enthusiastic about what they are teaching and can find good ways to convey their enthusiasm and knowledge. I would like my students to have classes where the expectations are high and reasonable. Since technology, often the graphing calculator and sometimes the computer, have become so common in the high school classroom, I would like my students to encounter professors who can find effective ways to use this technology in their classes.

(b) I would like prospective mathematics teachers to be: well educated, well rounded in areas other that mathematics, above average, full mathematics majors with a wide understanding of the mathematics they might have to teach, well-spoken, and able to communicate well to students, parents, and colleagues what they are thinking or teaching. It is critically important that the community at large view teachers as intelligent, caring, thoughtful people.