Question 1: High school graduates should be able to apply the mathematics that they have learned to the solution of problems. Even at this date, more than five years after the publication of the NCTM Standards, many students still think that algebra is mathematics. Students should be able to solve problems algebraically, graphically, numerically and verbally. They should understand that a problem does not solve itself at a glance and that they must think through a solution, applying all the mathematics that they have learned. Most important, they should be encouraged to collaborate with other students in the solution of problems and the creation and completion of projects.

Question 2: I think that all students who are bound for some sort of post-secondary experience should study mathematics for their entire four year high school experience. Probability and statistics should be part of this study. Problem solving should be emphasized at all levels. The mathematics courses should be integrated so that the traditional algebra, geometry, algebra is eliminated. I know that this is a common trend today, but it is not happening quickly enough. Most important, again, is the continuous study of mathematics throughout high school.

Question 3: We know that high school mathematics education is working well when students can analyze and solve problems in different ways. Assessment must be done differently. When students are asked to interpret and apply the mathematics that they have learned to a problem situation, then they should have more time to solve the problem. Last May on the AP Calculus exam, my own students had difficulty in starting some problems in the allotted time. Yet, given more time, they were easily able to think through the solution, too late to be counted.

Question 4: Some high school mathematics teachers of today are still teaching rote algebraic manipulations. Staff development is an essential part of mathematics education reform. We are entering a new century and some teachers are still teaching like they were taught. I spent my entire summer conducting institutes for mathematics teachers where we worked on curriculum, assessment and teaching strategies. These are the committed teachers and I learned from them as much as they learned from me. Every math teacher today must constantly continue learning.

Question 5: I always knew that I wanted to be a teacher so first and foremost I am a teacher. I was a good student in almost every subject and I chose mathematics because I had a math teacher for most of my high school career who loved mathematics and communicated her enthusiasm to the class. I really did not appreciate all that she saw but I somehow knew that one day I would understand her excitement. I did, but it took me years to do so.

Question 6: I expect that my students will continue to learn in college as they have been taught by me in high school and that they will be expected to solve problems graphically, numerically and verbally as well as algebraically. As I write this, there are still freshman math courses in college that are taught in the same way that I learned. Assessment is still often composed of students performing rote algorithms and cooperative learning and assessment are not there.

It is vital that prospective mathematics teachers be taught in the spirit of the NCTM standards and calculus reform. I recently had a student in a graduate course finishing her last course for her masters degree in mathematics education. She had never touched a graphing calculator in any of her courses until she took my course. I was an adjunct for the summer. I do not know what is happening at that university in math education, but it seems to me that she should have been better prepared for her entry into the teaching profession.