A Brief Diatribe From My Previous Life
(or “r u a student?”)

We all know about students who claim they don’t do homework. Indeed,  some of us have—occasionally, though not often successfully—tried to join their ranks.  When problem-solving is required, however (physics and mathematics both spring to mind but they are by no means alone), it is virtually impossible to learn the material without a certain amount of drill, because the number of concepts that must be mastered is too large to retain without an excess of confusion unless drill has reinforced the learning process.  Besides this general circumstance, there are courses where applications (think, “word-problems” if you like) are important, and where the principles used for them are also so complex that no mastery at all has ever been obtained by anybody who has not worked a good many!.

In any class for which drill is essential, it may be possible for a student to furnish his or her own self-discipline in order to do an adequate amount of homework.  Students who are unable to do this, are likely to fail.  So, for these subjects, failure is the only alternative to homework.  In order to help students who are not very good at self-discipline, the best schools may hire graders to check the papers that have been turned in, so as to make sure the students are doing the work correctly.  At some schools, the funding sources may regard graders as a reckless extravagance, contributing very little to the athletic program. When that happens,   relatively undisciplined students are left on their own, though such devices as frequent quizzes can help them with their weakness.  Also, sometimes an instructor may sacrifice some or all of his or her (presumed) research time for this sort of discipline-enforcement.

Naturally, students who don’t need the discipline resent this sort of treatment.  Surprisingly enough, so do many of the students who do need it.  As a result, when an instructor collects homework papers, there is a tendency for the students to regard that action as an arbitrary hurdle, to be “got around” by any means available.

However, there is also another role for homework checking.  In certain courses the hard problems can’t be done at all until the easy ones have produced familiarity with the material, yet many of the easy ones can be done without explicit use of the principles under discussion.  An instructor who does not have time to check the problems can only learn about the resulting lack of knowledge by giving formal examinations, by which time it is rather late for the student to undo any damage that may have been done by mis-estimating the difficulty of the material.  For that reason, an instructor who does have time to check at least a few of the problems may very well  decide to do so.  The intention, when this is done, is not to see who has written down the right answer (which may sometimes be copied from  an answer book anyway); nor to see who is unethical but not clever, and can be “caught,” nor to praise the brilliance of a student who can do the problem by a method not under discussion at that time in that course; nor even to give the instructor something to do to fill in time that he or she might otherwise waste watching television,  going to basketball games, or attempting  to find a new way to deal with Schroedinger’s cat.  Of course, any of these may sound very much like a motive for paper-checking, but usually none of them is.  Rather, the intention is more mundane: merely to ascertain whether the students are really mastering the principles the instructor is trying to teach.  The main purpose is to observe who has and who has not managed to master the methods under discussion at the time enough to use them on—especially—the easier problems.

Most instructors are not particularly fast at careful grading, and most instructors are quite short of time.  (Some instructors waste a lot of time.  See if you can figure out why this fact doesn’t result in their having lots of free time in which to take care of homework and other important matters.)  The result is that it may be unusual for all the homework problems to be checked, and it may even be rare that the problems that are checked will be the ones requiring the most ingenuity.  Students who understand all this will write answers, even to “easy” problems, in sufficient detail that the instructor can tell whether they understand the material he/she is trying to tell whether they understand.  In fact, there is no reason for the instructor to look at the papers of students who do not do this: those students can’t be helped by homework checking.

Students who need the reassurance of a daily intelligence test will not usually find that having part of the homework graded will fulfill that need.  It is not even likely that filling that need is any of the instructor’s business.  The educational system has a different purpose.

The moral for students:  Have the homework ready daily to turn in if called for.  Be sure to “show your work” unless circumstances clearly indicate that this is unnecessary.  If you can see a way to do the homework that does not involve the material of the course, make a note to yourself so you don’t forget it.  It is also permissible to boast of the fact through a note to the instructor.  But then do the homework in such a way as to utilize the material of the course, and write each problem up in such a way that the basis of your solution can be seen.  Do not be confused by the fact that some instructors (including the writer) sometimes let you “get away with” exceptions to these precepts.  Turn in the work on time because that not only reduces the number of hours checking it may take but, usually, will also increase the benefit you receive by having the work checked,  when it is checked.

(There is probably also a moral for teachers—and maybe even one for mystery writers—but finding it is left as an exercise.)

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