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Your post was a good top to bottom on the subject. I am also of the class of '63, got into one of the good schools, and have had two careers, one in aerospace as an engineer, the other as a high school teacher.

I did not permit open cheating, (copy other's work, pass notes, etc. Calculators were invented while I was teaching, but were not large storage devices for many years later. (I remember my slide rule had a set of formulas on the back, eventually I knew them by heart, but it was always reassuring to have the law of sines and cosines available. I don't know if the teacher knew or not.

My point is that a good teacher is all that is required to turn this situation around. As you indicated, when group work is required, the lesson should be in doing the work well, so that everyone benefits. It should not be the primary mode of a classe's learning. My son experienced too much of this "support your fellow student" approach to learning, and I believe it supports Ayn Rand's form of mooching. In one class, a student who was artistically inclined always volunteered to do the display board, as long as others did the research and typing. What Cr*p.

When I wanted a clean test, I asked to see the students work. Level of dificulty can change, and required detail can become too comples to copy easily. I taught math and science but the same could be applicable anywhere. No detailed solution, (less score). I have used the device of multiple tests, and even once made each student's problem unique. If all use calculators, the simple math solution would not be enough, students would need to show intermediate steps. This means many scan type tests could not be used, but I enjoyed the job well enough to stay up late grading the papers so I could get them back the next class meeting. ( I did schedule tests so I could do this.)

The bottom line, is that if the students are cheating, they are only learning to cheat. If the teacher is charged with teaching, they must step in and ensure students are doing the work. Lazy teaching facilitates cheating.

Thanks. I agree with you.

You mentioned showing work: I don't ever remember taking a math or science test (other than the standardized tests like the SAT, GRE, LSAT and GMAT) where I wasn't required to show work. Starting in 8th grade with Algebra, we had to show virtually all our steps for full credit. (Sometimes if we were right and skipped one or two levels of simplification but it was clear how we'd proceeded, it would be OK) Same in high school and college. When I was in graduate school in economics, taking mathematical economics and graduate mathematics courses like topology and measure theory, we spend most of our time proving theorems. In seminar, we took turns each week presenting sections with half a dozen theorems or so. Any other seminar member could ask for any part of any proof, even the theorems listed among the assumptions -- talk about have to have all your work laid out!

As I worked with my kids doing math homework, I found it very curious that they were not expected to show their work. But, when I would work through stuff with them, I found that they were being taught different methods than I had been. Surprisingly, very cook-book-y, emphasizing whichever special cases they were studying, whereas my training was all aimed at moving quickly to the general cases and the most mathematically rigorous and powerful theorems. Harder 'til you get used to it, but much better training for further work. Of course, at that level, cheating is virtually impossible: some of the proofs are published (usually in outline), and you're welcome to use them if you understand them and can work out the steps. Then, of course, you're working on problems of your own devising or new applications. Fun stuff.

The new calculators are a problem. The teaching of analytic geometry and calculus today emphasizes the use of graphing calculators which have significant memory. The result is the kids can visualze better than we could quickly, but they have more trouble manipulating equations and 'seeing through' to the ultimate solution. (You remember, when you knew the answer, but it would take ten minutes or so to go back and actually work the problem out step by step).

Oh, well. Happy Thanksgiving!