WRITING UP MATHEMATICAL CONVERSATIONS

T. M. Thompson


Ideally, creating the homework write-up is the place where several kinds of learning is demonstrated.

First, it is a place where learning of mathematics is demonstrated.  You are presenting evidence of your understanding of the material presented in class and your reading in the textbook.  So make your presentation clear and complete.  Never, EVER, include only a one-word answer, or just a numerical quantity.  Your job is to convince the reader that you understand the question and have a solution.  If a numerical answer is sought, show ALL the steps necessary to justify that solution.

Second, it is a place where learning how to communicate is demonstrated.  You wish to convey CLEARLY, SUCCINCTLY, and CONVINCINGLY to the reader that you have answered the given question.  This will involve the use of WORDS, PHRASES, as well as appropriate SYMBOLS.  Remember, mathematical symbols are just shorthand for conveying certain words.  They need to appear in a context.  For example, the equation

2x + 3y - 5 = 0

is really the sentence:  "Two times ex (x) plus three times wye (y) minus five equals zero."  Notice that there is a subject and a predicate.

Third, it is a place where each student shows their OWN thinking.  Homework is not a group effort.  I expect that students will help each other.  But do not give answers.  Give hints.  Certainly, some of you may compare answers.  And by helping guide another student in the class, your own understanding will usually also be enhanced.  But copying helps no one's learning.  And if my reader suspects that copying is taking place...

Finally, presentation is also very important.  You are "selling" your solution to the reader.  So make it NEAT.  That is why pencil is required.  If you find yourself erasing, and erasing, and erasing, get out a new piece of paper and start over.  Leave your work uncrowded.  Do not use a two-column approach to save paper.  It is simply too hard for the reader to follow.  Make your work FLOW.  I am not asking you to rewrite the question or problem statement, but make sure that you have solved or answered COMPLETELY.

Oh, yes, one more thing.  I have found that for my own reference, listing the problem number with a slash or fraction bar and then the page number underneath, is very helpful for future reference.  E.g., problem number 63 on page 396 would be given as 63/396.  (Vertical or enlarged format would even make it clearer.)

Good luck.  If you have questions, ask, call, e-mail, stop by.  I will be glad to help.

Examples:  The good, the bad, and the ugly.