Obvious But Underappreciated Truths

The following observations relating primarily to exams, quizzes, problem sets and other assignments are obvious to most but often underappreciated. They are worth thinking about.

Most of these observations are based on experiences with mathematics classes but are also pertinent to other subject areas.

When in doubt, it's a good idea to write it out.

It's generally a good idea to answer the question that was asked, rather than a question you would have preferred had been asked.

With some exceptions, someone reading the answer to a question should be able to infer what the original question was, what the conclusion is and how that conclusion was arrived at. The reader should also be able to verify, without having to supply his own ideas, that the solution is correct.

If one reads a solution out loud, it should sound as if it was written in proper language, in complete sentences. It's worthwhile trying to read what one's written and ask oneself whether it makes sense.

Notation is important. The use of correct notation encourages correct reasoning; the use of sloppy notation often leads to sloppy and incorrect reasoning.

Written communication is more precise than oral communication. It is perfectly reasonable to say "the limit is 17" or "the limit as x approaches 8 is 17," but it is incorrect to write "lim = 17" or "limx-> 8=17."

An equal sign is neither a colon, a right arrow, a double right arrow, a comma, a semi-color or any punctuation mark.

If you write down a solution that makes sense and can be understood but make a minor error leading to an incorrect conclusion, you will probably earn almost full credit; if you write down the same incorrect conclusion without a clue regarding how it was obtained, you will probably earn little or no credit; if you write down a correct conclusion without a clue regarding how it was obtained, your are playing with fate and have no legitimate complaint if you receive little or no credit.

When taking an exam, it's a good idea to read the instructions.

It's also a good idea to look at all the questions.

Many sheets of paper have two sides.

If something is crossed out, it is interpreted as if it was meant to never have been written. One should generally not cross anything out during a calculation except to correct an error.

An answer to a question generally requires a conclusion, but a conclusion is generally only part of a complete solution.

Things happen in class even when one is not there. One is responsible for everything that is done regardless of whether or not one is there.