Question 1: High school students should understand that mathematics is an essential tool for understanding the modern world. They should be able to use elementary forms of the basic methods of mathematics, including arithmetic, algebraic, and geometric manipulations, and the construction of sequential logical arguments.

Students should realize whether or not they learn mathematics will depend most of all on their own efforts. They must be aware that learning mathematics requires the same type of self discipline that one sees in athletics. If students have not had the experience of doing much of their learning outside of the classroom, through the medium of consistent and rigorous homework assignments, it is very unlikely that they will be able to attain a minimal level of ability in the classroom environment.

Students should understand that the most important reason for learning mathematics is as an investment in their future. Although the "toy problems" that one encounters in elementary math provide motivation and serve to deepen one's understanding, they are not the primary purpose of mathematics. Students should be aware that mathematics is a coherent language, not a grab bag of tricks. A subject like trigonometry is an essential part of the curriculum because it is crucial in understanding physics and calculus, not because it can be used to solve surveying problems.

One of my favorite New Yorker cartoons shows a teacher addressing her first grade students with the statement "I am sure that some of you are wondering why it is important to learn how to read and write". Students should be aware that as in all of education, each time we decide not to learn a subject, a door is closed. The possibilities of our future largely depend upon how many doors we have left open.

Question 5: The notion that it provided an almost "magical" tool for understanding the workings of the physical world.