We have said before that history of mathematics courses are different than mathematics courses and must be taught differently. Likewise, the exams in history of mathematics courses must be different than the exams given in mathematics courses. The reason for this is that there are two things you want to test: the students' knowledge of history and their knowledge of the associated mathematics.
However, it can make for a very hard exams if all of the mathematics discussed in a course is fair game on the exams. A question where the student has to apply the method of exhaustion, Descartes' method of tangents, or even the Egyptian method of multiplication to a novel situation will be challenging indeed. Such questions are appropriate for a take home exam, but hardly for an hour in-class exam.
Most people give a variety of types of questions that test the students' knowledge of both mathematics and history, while not demanding mastery of fine detail, and which are possible for the instructor to score objectively in a finite length of time. Here are some of the types of questions that can be asked. Some sample questions have been linked:
True-False Fill in the blank Multiple choice Matching Chronological order Short answer Essay Take home Some of these questions have objective answers that are either correct or not. It is good to have some of these on an exam, for the student cannot argue that his grade was adversely effected by the way you grade. I particulrly like the short answer questions for they are questions that the student cannot bluff his way through; you will get some really creative wrong answers when you ask what prosthaphaeresis is. In addition essay questions provide a good way to show mastery of the material. I like to have a mix of questions.
Also available are an actual midterm exam and final exam that I have given in the past.
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If you have comments, send email to V. Frederick Rickey at fred-rickey@usma.edu .
Posted 19 January 1998. Revised July 2005.