Student's guide to Good Problems

Many students, especially those in science and engineering, believe that writing has nothing to do with mathematics. This is false. In any field, it is important to be able to communicate your ideas and results to others. Exactly how you communicate them varies from field to field, but in nearly all fields it is through writing. Mathematical writing, however, has its own particular style. The emphasis is on clarity and precision, and not on the clever turn of phrase.

The ``Good Problems'' program is designed to teach you how to write about mathematics coherently. It provides you a set of specific writing skills and gives you enough practice through regular assignments so that writing well will become a habit. It is also designed to be as painless as possible.

Throughout the term, some homework problems will be designated ``good problems''. You need to write the solution to this problem carefully, in good ``presentation'' format. It will be graded partly for correctness, but with emphasis on presentation.

During the term you will receive six handouts, each addressing a particular writing skill. The good problem is graded only on those skills already covered, with greater emphasis on the newest skill. By the end of the term you will have acquired the basic skills of mathematical writing. The handouts are:

Each handout consists of a description of a particular writing skill, motivation for the importance of this skill, whatever explicit rules can be given, and examples of good and bad presentation emphasizing that skill.

If you already have these basic writing skills, then it should only take you ten extra minutes to write up a good problem. If you do not have these skills, then you will have to spend extra effort in the short term to acquire them. In the long term, however, these skills will save you much time and effort. Besides making future writing assignments easier, these skills will help you with problem-solving (by encouraging organization and logic) and with reading mathematics. These skills should be carried into future mathematics courses, and become a useful life skill.

Teachers wishing to use this method can download instructions and all the materials (.pdf).
Martin J. Mohlenkamp
Last modified: Fri Sep 3 13:53:44 EDT 2010