Course Responsibilities:
One of the biggest differences between working at the highschool level and
at the college level is the following:
Clear writing is a reflection of clear
thinking.


in high school, frequently it is
enough to demonstrate a knowledge of the appropriate material; in college,
you will be expected not only to know the appropriate material, but
also to be able to articulate that knowledge, through speaking and
writing, to an intelligent, but slightly lesswell informed, listener or
reader. Most people find that the process of organizing material well
enough to express it clearly is a tremendous help in solidifying their own
understanding of the material.
This has the following consequences for this course:
 You must know the definitions precisely. Typically, a quick
restatement in your own words, while fine at an intuitive level, will lack
the precision necessary for a correct use of the concept. You are
responsible for all definitions from class, and you may be asked to
reproduce these on exams and quizzes. For example, an exam question might
begin: "Give the precise definition of ..."
 You are responsible for understanding the theorems and proofs from
class; it is not sufficient simply to know how to apply them. Your
statement of a theorem should include all the hypotheses that were present
in the statement of the theorem in class. An exam question might be:
"State and prove the Fundamental Theorem of Calculus".
 You must explain your work using words. Written explanation is
a crucial part of the learning process, and it is not sufficient simply to
write down a series of equations and circle a number or formula at the end.
It is important that you be able to give clear and wellorganized
indications of what you are doing and why. I will try to provide examples
of this as we go, and will put copies of the best student answers in
the notebook outside my office.
Note that the goal is to explain why you are doing what you are
doing, not what you are doing. Saying something like "I took the
derivative" usually is insufficient; I can see that you took the
derivative, the question is why? How do you know that the
derivative is the right thing to use? What differentiation rules did you
use?
It is important to realize that writing explanations, while it helps me to
grade your work, is mostly for your benefit. It is the best way to
make sure for yourself that you fully understand the material. If you do
understand the material, it should not be a hardship to write a brief
explanation of what you are doing. On the other hand, if you are not
entirely sure about the process, trying to write an explanation of what you
have done is one of the best ways to recognize that you are not completely
clear on the subject. Even if you are right, the organization required in
writing about what you have done will help you draw the connections
necessary for a full understanding of the material. Don't look at writing
as just another hoop to jump through; view at it as an integral part of the
learning process. It's one of the things you can do far better than a
computer.

Math 15 (Fall 2000) web pages
Created: 26 Aug 2000
Last modified: 27 Aug 2000 14:32:32
Comments to: dpvc@union.edu



 