I recently talked to someone who hasn’t been in college for years, but was trying to help a current student at a respectable four-year school. My informant looked over the assigned homework and the tests in a course and came to the conclusion the teacher didn’t test on the same things he assigned homework on.
I teach to the tests, or more accurately, I test to what I teach. If I am given a common final, which I have been in one of the courses I’m teaching, I teach to that exam. Usually, I carefully word problems the same way they are worded in the homework. This semester, when designing a test, I checked the common final. Did it say to solve problems algebraically, analytically, or symbolically? It went with algebraically, and so did I. I don’t want my students to be confused by the wording when they are given the final exam.
There are other things than wording. If I ask for answers to be given to three significant digits, and the homework says to approximate solutions to three decimal places, I am being unfair to the students. These are asking two different things. I won’t give a mixture problem or a rate-time-distance problem on the final unless the students have both seen examples in class and been assigned homework on them.
This does not mean that the students aren’t challenged by my tests, they just shouldn’t be surprised by them.