A cheating scandal has besmirched the U. S. Naval Academy and Virginia Military Academy and other institutions. Cheating is apparently widespread in precollege schools or in colleges and universities. Students have admitted this on TV and in the press. As a teacher of more than 30 years, I primarily blame this on the teachers. Women have a special responsibilty in STOPPING THE CHEATING, not only for their own sake, but as mothers, sisters, citizens.

Before explaining my "method", 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.

In 1955, I began teaching mathematics and physics at Inter American University of Puerto Rico, San Germ&aacut;n, PR. I soon discovered that many students depended upon little rolled-up cribs. Out of concern for their eyesight, I announced that I would, henceforth, give open-book exams with a different version for each student. (No! "Open-book" is not permissive! I'd want any person working for me to look up critical formulas and constants. Besides, by not depending upon memorization, I could give them more difficult problems than otherwise.)

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 -- even under my current system -- how RUBBER TESTS, hence, also RUBBER GRADES can exist. So I created a list of 200 STANDARD TASKS which students knew they must perform correctly, one or many at a time, whenever individually ready. If incorrect, it must be done over -- in different format. Completion resulted in a "P" ("Passing") grade. I gave "F" only when a student gave up. (Yale U. intoduced "P" in the 70's, under less rigorous conditions.)

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. 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 Statistics exam to 121 students -- same type of problem, different numbers on each paper.

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.

And that's another reason for doing this. AN IMPORTANT ITEM OF INFORMATION DOES NOT DEPEND UPON THE PARTICULAR FORM USED IN PRESENTING IT. ONLY IN MAGIC IS THE FORM AND THE WORDS USED CRITICAL! No wonder children go for books about magical events. It's simply different than the "magic" most teachers practise in teaching and testing in specific "golden words". And it's easy to show how arithmetic teachers seem to CHEAT or "go weird", and how this impression can and should be eliminated.

But I still haven't told you about THE BEST TESTING, which springs from the COMPUTING environment of all these present files. I call it "The Householder Test".

In 1942, mathematician Alton S. Householder established the Computing Bureau at Oak Ridge, TN, in "The Manhattan Project", which led to creation of the nuclear bomb. Householder said the best way to determine if a student knows "anything" -- math, English, etc. -- is to require the student "to make the computer do it". With a computer , you can't leave anything out, as teachers often do, leaving the student to fill in the gaps. And you can't intimidate a computer, as some teachers and parents do with their students or offspring.

So, join me in inducing our cheataholics to go "cold turkey" for a cure, and to seek support in staying so.

       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.