People who don't learn or understand this material probably won't use it, but people who do may be surprised to find where it is useful. This applies not just to the content of the course, but to its association with careful, creative thinking. It will probably be up to you to find places where you can use this mathematics. But depending on your career, you may find that things that are now obvious to you are not known to others; or on the other hand, you may find it taken for granted that you know this material and much more. But most likely, you may actually use the subject of this course and the skills you've gained, without even realizing it.
In reality, the questions and complaints mentioned above are all too frequently tacit, and it may be that much more difficult to bring these issues to a point of real discussion. Sometimes these complaints only show up on teachers' end-of-term evaluations. There are certainly more useful responses for individual students in individual situations than those offered here. The key point, however, is for the teacher to be able to listen to these kinds of questions and implicit challenges as having serious substance in them, that strike to the root of the problems of teaching and learning mathematics.
The authors are grateful to the editor for his very useful suggestions.
Sandra Keith is a professor of mathematics at St. Cloud State University MN. Just as Einstein allegedly wanted to ride on a ``beam of light'', she has been interested in getting into the minds of students to understand how they think! She has worked with exploratory writing assignments and other interactive teaching methods. She served as director and edited Proceedings for the National Conference of Women in Mathematics and Sciences and was assistant editor of Winning Women (MAA). Her interests include better public relations for mathematics, improving the mathematical environment for women and minorities, better advising, and mathematical networking.
Jan Cimperman is an assistant professor at the same school. Her interests include mathematics education, particularly, teaching elementary teachers. She frequently gives workshops on the MCTM Standards and the use of manipulatives to explore mathematical concepts at the K-6 level. She is interested in the variety of ways in which students learn.