Understanding Mathematics by Peter Alfeld, Department of Mathematics, University of Utah

Do you find it difficult to prepare for an exam?

Some of the questions most frequently asked in a math class are: Will this be on the test?, or What will be on the test? Those are reasonable questions, but chances are that if you have to ask them you are not spending your time effectively.

Exams are artificial situations. You do not take a class to prepare for a particular contrived and transient situation. Rather you are most likely taking the class so that you can function better in the long term, for example in your career. Ideally, you should be taking the class at least partly because you like the subject. (If not, ask yourself if you set the right goals for yourself.)

So you should focus on the long term aspects of the class, and on the subject, and in the process, as a pleasant side effect, you will become well prepared for the test.

Specifically, I suggest you make a habit of doing the following:

Different Kinds of Test

Different kinds of tests have different kinds of strengths and weaknesses. Here's a brief summary:

Take Home Tests

One can ask more sophisticated and therefore more instructive questions. The test is more of a teaching tool than an assessment tool. Students can work together and learn in the process. Grading tends to be tedious and more difficult because of the amount of student writing and the larger scope for partial answers and partial credit.

In Class Tests - Closed Books and Notes

This is the standard sort of test. The learning effect comes from preparing for the test, not from taking it. Tests tend to be short and easy to grade. Students tend to dislike this kind of test because it makes their proper preparation more crucial.

In Class Tests - Open Books and Notes

Allowing open books and notes makes it possible to ask more sophisticated, and therefore more instructive, questions. Students tend to like this format since it allows them to think of their books and notes as a crutch. But actually at least some of the questions on the test are likely to be harder than in a closed books and notes test, and students sometimes waste significant amounts of time searching their materials for items that they actually could think of immediately if only they tried. Grading is similar to closed books tests.

Oral Exams

This in my opinion is by far the most effective form of a test. You can adjust your questions according to the student's answers, and find out better than in any other way what the student really knows. Often a side effect of an oral exam is that the student for the first time understands key issues that were previously not understood. The major impediment to using oral exams exclusively is the amount of time it takes if there is a large number of students. Students tend to be terrified of oral exams, but they should look at them as opportunities to prepare in a benign context for similar situations later in their lives and careers. Every interview (or conversation with a co-worker, client, or customer) is a form of oral exam, to various degrees, even though it is not called one.

Fine print, your comments, more links, Peter Alfeld, PA1UM