Administration Kills My Soul

Almost everyone who teaches a 100-level math class needs to submit copies of all their exams as part of a quality control measure. For most people, the exam gets a brief glance to ensure that the difficulty is not too far out of whack and that non-mathematical bonus questions don't generate non-trivial amounts of credit. (Did you catch my triple-negative?) Some instructors are invited to come and discuss their classes' exams with me. We talk about what makes a good question, how to phrase questions in less confusing ways, and other suggestions that may lead to improved student achievement. We would like for more students successfully complete their required math classes.

One instructor's first exam resulted in a very low average in the class; the students also scored poorly on the second exam. The instructor met with me to discuss the exams and the scores. We came to this question:

Simplify the following expression to obtain a single irreducible fraction. Show all intermediate steps.

The students had, as a group, done fairly poorly on this question.

And I found myself saying, "This question is not appropriate for this class. We don't teach fractions in this class, and you shouldn't test on any material that is not in the syllabus."

What I really meant to say was: The students who take this course tend to be so poorly prepared for college-level math, that you should not assume that they know anything unless you have spent several class periods teaching it.