Question 1: For me, I hope that my high school graduates understand the historical background and significance of the mathematics that they have been introduced to. I wish for my students to be problem solvers, to be able to look at a situation, decide the mathematics that would best model or solve the situation, then successfully solve the situation. As a secondary understanding, students need to realize that the text is a resource, not the bible for the course. A text is to be read and utilized, but the teacher is the professional in the classroom. The NCTM Standards has created a wonderful and complete list of mathematics that should be covered in the high school--unfortunately, no one can ever complete the recommendations with today's curriculum.

Question 2: One of the most essential features of every high school mathematics curriculum should be relativity and application. When you teach mathematics in isolation the entire time, students see no practical need for the subject, and therefore they have no strong and deep interest in the subject. When mathematics is taught with practical and some not-so-practical applications, students get a feeling of the power of mathematical modeling and its relativity, thereby enabling some students to acquire a strong and deep interest in mathematics.

Question 3: High school mathematics education is working well when students stay in mathematics programs for more than what is required. If students begin taking three and four years of mathematics in high school, something is working. In looking at external assessments, such as SAT and ACT, you will begin to see a change in the assessment tool, because students will become stronger, and then the tool will be reassessed. Wouldn't it be great to have students scoring strong enough to make assessors reevaluate their tools?

Question 4: I believe that high school mathematics teachers should have degrees in mathematics or an equivalent degree, with supplementary work in areas that utilize mathematics extensively: i.e., physics, biology, chemistry, computer programming, business, etc. As a district mathematics mentor teacher I am always amazed at how few of the mathematics teachers have actual degrees in mathematics, and of those with degrees in mathematics, how little they can apply mathematics. I know mathematics teachers with degrees in mathematics who have never seen a vector or a reason for teaching this concept. It surprises and bothers me that colleges/universities do not require courses to be taken that utilize mathematics even for the high school student. Science and mathematics teachers should work hand in hand to create the strongest students. Mathematics teachers should enjoy children as well as mathematics. With this attitude the pedagogical approach to teaching would become student centered and extremely interactive.

When the focus of the classroom becomes "the student", we find that teachers, for the most part, are taken out of their comfort zone. Teachers of today were taught in a teacher-centered classroom, with university learning also in a teacher-centered classroom. The only models they have had are not what is being asked of them in today's classroom. So teachers must learn on their own, through trial and error, what makes the student-centered classroom work best. Unfortunately, in today's education, high school teachers who utilize a student-centered classroom get little or no support from universities, and with no support from the university level the parents of the students no longer support the student-centered classroom.

Question 5: I entered mathematics because of a positive experience in mathematics at the junior high school level. I had the pleasure of having a teacher who believed in and successfully used the SMSG [School Mathematics Study Group] mathematics program. My enjoyment of mathematics was strengthened in high school by a mathematics teacher who had been an engineer, and thus he always gave us applications of what we were doing. It was not until college that I discovered being female was not an advantage or even a level playing field. I was told by many a professor that maybe I should think of a more ``lady-like'' major. But the enjoyment from seventh and eighth grade was enough to allow me to continue through a master's degree in mathematics.

Question 6: My expectation of higher education in mathematics is that it be supportive and not the course to ``teach those kids what they do not know'' and ``to weed them out'' of any major. Many of my students come back and tell me that their mathematics instructor is hard to understand because of their English skills, or that their instructor only does the examples from the text, or that their professor is really smart but they cannot teach what they know. Not once in my high school teaching have I heard of a college/university mathematics teacher that made mathematics interesting and applicable for my graduates. This saddens me very much.

For prospective mathematics teacher I expect to see a well-rounded curriculum that emphasizes not only mathematics but the applications of mathematics. Education courses are important, but so is the commitment of the university to keep their education teachers in touch with what is going on in the high school mathematics community. Some education teachers have not been in a high school mathematics classroom for five or more years. Why can't education teachers make the commitment to either teach a class at a local high school or at least volunteer to be an assistant in a high school classroom to really see what is going on in those classrooms that they are preparing teachers for. College/university professors should model what they expect from their students in the classroom.