A cheating scandal has besmirched the U. S. Naval Academy and Virginia Military Academy and other institutions. As a teacher of more than 30 years, I primarily blame this on the teachers.

For I early learned how to formulate cheat-proof tests. (Later, how to construct and give non-rubber tests, with non-rubber grades.)

Before explaining, I recall three anecdotes about this "addiction".

The Dean said, "Professor Hays, I don't understand this student's complaint. He said he had most of the same answers on that math exam as the student in front of him. But that student got an 'A', while he got a 'C'. Can you explain that?"

"Yes, Sir. You see, that student had a different exam than the other student. Oh, the same type of problems; but different numbers written into the blanks. Right answers for the wrong problems."

Another time, the Dean said, "This student complains that you graded him unfairly on a make-up final. What I don't understand is his saying that, if he's wrong, this means you're ignorant of math also. What does he mean by that?"

"Sir, he missed the final because of illness and presented a doctor's excuse. You asked me to give him a make-up. I would have, anyway. However, to prepare him, I gave him a take-home practice-exam -- essentially the same problems that would appear on the exam. When he had trouble with it, I further tutored him, and gave him a new copy of the problems with the answers completely worked out. I examined him only when he said he was ready. The new exam had the same problems, but different numbers than in either of the previous cases. He worked some of the presented problems. But, mostly, he crossed out the numbers on his paper and inserted numbers he'd memorized from the practice-exam, along with the associated solutions. Now, Sir, I did that practice-exam. So, I gave myself an 'A' and gave him a 'C'."

On another occasion, a noticeably pregnant young woman observed during the exam period that exams around her had different numbers. So she spent the period filing her nails and writing letters. Her exam paper contained only her name and the statement, "You have to pass me so I can get the government to pay for my hospital!" I'm afraid she brought up her child to curse my name.

I not only gave different exams to each student, but, during a trial period, I gave different homework assignments.

Some colleagues complained that homework was optional in my class (for reasons soon disclosed). I was assigned an assistant to help grade papers, so I embarked upon a five-week experiment.

Each student in an "Elementary Algebra" class received five different homework problems each class session. After four weeks, my two best students begged for mercy.

"Sir, we've been doing the homework for most of the students. And it's killing us! Our girls friends are mad because we never have time for them. And our parents are mad because we never come home weekends. Please, Sir, can you stop this?"

"I thought so. Some of these students don't even know how to copy correctly. I've proven my point. So I'm stopping required homework. And I'm not punishing you any more. I think you've had your punishment."

(In October, 1997, a controversy developed in Fairfax County, where we lived, when a GRADING SYSTEM was introduced which was based purely on tests, ignoring HOMEWORK partially or totally. Parents -- many of whom had, no doubt, done some of the homework -- objected this is "unfair". My example above suggests that CHEATING ON HOMEWORK MAY BE GREATER THAN ON TESTS! Even if to a LESSER DEGREE, it could contribute AS MUCH OR MORE because of the LARGE HOMEWORK TO TESTS RATIO.)

Two years of exposing CHEATING on TESTS and HOMEWORK made me realize how RUBBER TESTS, even under my current system, hence, how RUBBER GRADES turn out to be. So I changed these!

However, back when I gave a scheduled (RUBBER) final to all students, I used a "tracer".

Physicians inject radioactive tracers into the bloodstream of patients, following the tracer's progress through the body by detectors. As tracer, I used a very difficult problem, which was the same on each exam, but appeared in a different position on each paper. (An example appears as Madster Initiation Problem #1.) All other problems differed from paper to paper.

A colleague would help me proctor. We'd walk up and down the aisles, alertly checking behavior of the students. Afterwards, I'd explain about the tracer problem. Usually my colleague would say, "Wow! I couldn't solve that one!"

"Well, either no one correctly solves that tracer problem or they all do. It's the only problem some students solved correctly. Hey! Do you suppose this is evidence for telepathy?"

I knew the students were somehow signaling the answer. But I didn't care, since I didn't include the "tracer" problem in my grading.

Once, at the University of Maine (Orono), I gave a different statistic exam to 121 students.

I accomplished this with only typewriter and mimeograph machine. It would be much easier with today's technology. It's easy to insert a formula in a computer program which generates hundreds of sets of different numbers, placing them in blanks on an exam template. For non-numerical variation, a computer program could select different synonyms or different sentence forms to make each version unique.

       If you join us in Cheaters Anonymous,
       We won't make your misdeeds eponymous.
       We trust you're ashamed.
       All names will be changed.
       Jump forth in sunlight!  Geronimous!
       Don't take it untowards.
       Not joining you in cards.
       We're magnanimous.  But not quite gullonymous.