Once upon a time not too long ago, when factoring was a formal and formidable part of elementary mathematics courses, we all learned a definition for prime number. Perhaps you as well as I can remember someone who could recite or write, “A prime number is a whole number greater than one which has no factors other than it self and one,” but who could not find answers to such questions as: “What is the smallest prime number greater than 100?” or “What is the largest prime number less than 125?” Some of our teachers thought they were preventing superficial memorizing of the definition when, instead of asking us to quote it, t hey asked for five examples of prime number, but again the question fails as a valid test for the concept. To be sure, the question exposes one who can remember only four of the examples he once memorized, but one who can remember as many as five is as well off on that test question as he would be if he really had the concept. The problem is, how can we direct learning so that such superficiality, waste of time, and intellectual dishonesty are prevented rather than promoted.