This sounds reasonable enough until one ponders the underlying presumptions and misconceptions.
There is an undercurrent that the amount of material to be taken from a given subject (Calculus II, Linear Algebra, etc.) for a mathematics course, and the depth of understanding aspired for, are fixed. If so, we must pay attention to the way in which these are determined. It is fair to demand that the premises of higher education be upheld to the extent possible. By that, I mean that the student is expected to do much of the learning outside of class, and is the one who is responsible for his or her achievement in the course. Then, what the instructor does in the classroom matters less than most people think, and to the extent that it does matter is usually different from the expected way. I have seen in courses taught simultaneously by more than one instructor with common exams, that student performance is nearly independent of the instructor. This holds even when the instructors are rated very differently by the students.
In actuality, it is next to impossible to control the level of a course, unless the course is always taught by the same person, and he or she decides to maintain a fixed level and succeeds at doing so. There are simply too many factors that enter into said level, including intangible ones.
It is customary to leave the level of aspirations--within bounds--as the prerogative of the instructor. For instance, one must decide whether to remind the students that it is a normal aspect of this stage of their education to read the textbook for both concept and examples, as opposed to allowing the students to expect to "get" almost everything in the classroom; when, if a topic on the syllabus has, say, five subtopics within a general heading (e.g., in Calculus, applications of the integral or techniques of integration), the instructor must decide whether to hold the class responsible for all five; whether to aspire that the students be able to handle questions of moderate difficulty on exams, as opposed to only easier ones; whether to inform the students what kind of problems will be on the exams, or to insist on command of the material by withholding detailed information about the exams. And surely it is reasonable to place the bounds for the level of instruction at a "prestige" college, where the students are very talented (and ambitious), higher than at a college where the students are less so.
All too often, the level of the course ends up low. Suppose that one has ample evidence that the students are capable of doing fairly well at a given level of aspiration, and without excessive exertion. Is there any justification for running the course at a lower level? Without trying hard, I can come up with several common reasons or excuses for that; see if you can imagine what some of these are .... All right, here's one reason: the instructor wants to be liked by the class; asking students to exert themselves is far more likely to make students unhappy than letting them off easy. A variant of that with social and political overtones: the instructor does not want to risk poor evaluations by the students.
Many students: If the instructor presents the material the right way, I won't have to struggle to learn it. And a good teacher doesn't expect too much from me!
In other words, if the teacher puts in more effort in explaining the material,---which may include more time per topic or reduced depth (hence covering less in the course)---the student will have less work to do.
We should never forget that it is impossible to get beyond the surface of a subject without a certain amount of struggle. The student attitude above is saying, in effect, that they should be held accountable only for easy things.
Committed instructor: If I put in more work to find good ways of explaining the material, I expect it to be matched by effort by the students. Then, they will learn more.
As one of my colleagues once put it: "Overall, students don't want more; they want less."
One thing should be obvious: most freshmen are not capable of judging their own level, for they have grown accustomed to being taught below their level. A competent instructor will help by guiding the students in their learning in higher doses, but the students still have to do it. The only way that students will learn better is if they try harder and more effectively to learn outside of class.
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Steven Zucker
July 19, 1999