"One effect is that it is much easier to cheat at math than cheat at writing an essay."
Interesting point, but the context is people failing algebra, and I don't immediately see how the ability to cheat contributes to that problem. Can you elaborate?
"Graders look at how you got to an answer, what techniques you used..."
And although free-form answers do make it a little "softer" of a subject than it may seem at first glance, there are good objective standards to go by. The fact is, a good multiple-choice test can tell you a lot about how well a student understands algebra; it's hard to devise such a test for subjects like writing.
The point about cheating is this: what makes cheating possible? It's because there is a gap between answers written on a piece of paper, and what is inside someone's head. This is true of all kinds of tests, but it is more true of answers that are identical for every student. If the names on the tests were somehow mixed, this would be undetectable by graders, where it would be immediately apparent for a written exam.
The significance of that has nothing to do with preventing cheating. It just means that the gap between right answers and real knowledge is greater when the answers are all identical. A concrete example: in my college physics classes, I studied with a friend who solved problems by memorizing which type of problem required which formulas. I figured out which formula to use by visualizing the problem, which is a much more efficient way of doing it and leads to a better general understanding of physics.
These important differences are undetectable just by looking at whether we both got the right answers on a test. You can account for this indirectly, by limiting the amount of time, so that my study partner would never be able to finish the whole test by using his method. But the information he gets about the incorrectness of his answers does nothing to help him fix his inefficient method. He did very well on the homework, the issue was only revealed at the midterm.
Physics education would be improved if taught people how to visualize problems, which means making it more qualitative and less quantitative.
Interesting point, but the context is people failing algebra, and I don't immediately see how the ability to cheat contributes to that problem. Can you elaborate?
"Graders look at how you got to an answer, what techniques you used..."
And although free-form answers do make it a little "softer" of a subject than it may seem at first glance, there are good objective standards to go by. The fact is, a good multiple-choice test can tell you a lot about how well a student understands algebra; it's hard to devise such a test for subjects like writing.