This has the following consequences for Math 12:

**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. A 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 well-organized indications of what you are doing and why. I will try to provide examples of this as we go.

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; look at it as an integral part of the
learning process. It's one of the things you can do far better than a
computer.

Comments to: dpvc@union.edu

Created: Mar 24 1998 --- Last modified: Mar 24, 1998 4:59:19 PM