I give my Intermediate Algebra students a practice test. The practice test is problem-by-problem similar to the test. I reorder the problems, change the numbers, a few irrelevant details, and the word problem, but the test requires the same skills as the practice test. If I want them to be able to isolate the radical and square both sides of the equation, I don’t care that they know that is what they will have to do.
I tell them that I have a better idea of what to study than they do. Rather than make them guess what to study, I tell them. For some students, this works out very well. They learn what I tell them to learn and get A’s. Other students persist in disbelieving me and either don’t study, or study the wrong things.
I just handed back the second test where three students scored more than 25 points higher than on the first test. All of them studied harder, because they believed what I told them this time. But I still have to ask, why didn’t they study for the first test?