Chapter 4



Home Work



                There was a time at my university when all mathematics classes were small, less than thirty, and the professor would assign "homework" exercises to be handed in to him from time to time.  For purposes of discipline, to protect lazy students against themselves, we would usually say that some part of the course grade, maybe twenty percent, depended on the homework.  Actually, we didn't really want to base any of the grade on homework, which represents diligence more than accomplishment, whereas accomplishment is more easily and fairly measured on examinations; but experi­ence has shown that young students will often neglect to keep up with the work if there isn't some element of compulsion.  There are also other values in our reading what students write at home:  We thereby keep track of the kind of thing that is or is not being under­stood, we enter small notes of correction where it might do some good, we get to know the class.  Students work better if there is some feedback.


                Feedback alone would be sufficient, and using the homework for grading purposes would be unnecessary even as a discipline, if the professor really did read everything the student wrote, and really did know the student.  A student who knows his work will be read and appreciated has a powerful incentive to performance, and no incentive whatever to copy a paper surreptitiously to hand in as his own; the professor would soon know those papers to be false if after a couple of weeks the purported author manifestly did not know what those papers had earlier proclaimed he did.  Any conversation with the pro­fessor would give it away.  One can hardly imagine John Stuart Mill cribbing a translation, or lying to his father about having read his assignment.


                This is the way it is in many advanced classes in mathe­matics, engineering, and so on, even for technical exercises where there is in essence only one correct way to do each problem, and where finding out from a neighbor how to do it would not neces­sarily lead to detection.  The professor knows the student, and could grade him A, B, C, or whatever without looking at the homework scores in the classbook, or even the examination papers.  The student, knowing this, is not only disinclined to deceive, but is actually unable to deceive.  In such a class, it is unnecessary to tell the students not to consult each other in the preparation of home­work problems and labora­tory reports, or diaries of the kind kept by students of theater or literature for showing to the professor at stated periods.  On the contrary, since learning is best accomplished when there is some inter­action between people interes­ted in the same thing, a professor who knows his class can and should encourage them to collaborate and discuss their assignments with each other as much as possible.


                The ideal situation requires small classes and energetic professors; professors, moreover, who really enjoy giving that much time to instruction.  Doubtless it depends on other things, too.  But so long as there are any students who are hiding out, as it were, anony­mous, known mainly by their names and scores in a class book, there is the possibility that some of them will be trying to gain those scores falsely.  Therefore professors in many college classes, especially in elementary mathematics and science, and especially in large and middle-size uni­versities, will, when they assign credit to daily or weekly exercises, caution the students to do them without outside help. Then they are angered or saddened to discover cheating from time to time.


                There seems to be a dilemma here.  On the one hand the exercises are important; everyone must do them.  Giving "credit" is the disciplinary device without which it appears some students will grow lazy and find themselves in trouble at the end of the term.  But then, this very "credit" leads some students into cheating.


                It is easy to take a pessimistic view, and say that deviant behavior is a fact of life, and that in all domains of human endeavor, wherever rewards exist, there are rewards to be had by theft as well as by honest toil; and that we keep this down to a tolerable level by police and the courts.  This is true in a university too, and there is no way entirely around having a law, a police, and a court for academic dishonesty.  But the level of equilibrium of crime is not a constant of nature, and it is worth knowing if there are any pre­ventive measures that could reduce academic crime before it reaches the stage of arrest and trial.


                In the case of burglary in the outside world, the locking of windows and doors has an effect on the overall crime rate, as the police never tire of telling us.  Why else do policemen routinely check doors of business properties every night?  One might argue to the contrary, that a burglar frustrated by locked windows or an alarm system will simply go off to another house instead, and that the rate of burglary depends on sociological variables unrelated to locks and sirens: unem­ployment perhaps, peer-group pressure, or an unresolved Oedipus complex. 

                An economist will answer that whatever the other variables might be, the cost of burglary operat­ions must be a factor.  If a burglar must try ten houses where in pre-lock and pre-alarm times he only needed to try one, he is working ten times as hard for his money, and taking ten times the chance of getting caught.  Since raising the price of anything will reduce the demand, the locks and sirens are bound to reduce burglary, no matter how numerous and assiduous a cadre of would-be burglars there is in the city.


                Then there are those who despise economists, and will not allow the analogy between the price of corn and the price of burglary, much less the analogy between the price of corn and of plagiarism.  They will say that we do not want to live in a world where locks and sirens are the only things that keep men from being burglars.  We would rather live in a world of trust and honor, where everyone is taught civilized behavior and respect for others and their property. 


                There are those who talk this way, but it is hard to see what they mean us to do about it, lockwise and sirenwise.  Would they have us eschew locks as demeaning to our neighbors?  Do they believe that where a man sees no lock he is therefore prevented by shame from stealing?  That where he does see a lock he is so insulted ("Oh, so that's the way you're going to be...") that he feels entitled to steal?  Yet there are those who believe that these are the student reactions in the face of the monitoring or non-monitoring of homework assign­ments; and there are professors who act on this belief by blandly distributing home­work assignments and then, without exactly reading the results, giving the 10% or whatever to all students who hand in enough pages.


                Well, this is convenient, but it does not do the job.  I have participated in freshman calculus courses where the lectures were large, and the weekly homework papers overflowed the hallway pigeon-holes we had set up to receive them.  They were graded in a cursory sort of way by teaching assistants, who kept a score sheet.  The cheating was rampant.  Papers that were handed in early were sometimes stolen, apparently so the thief could copy and hand in the result as his own.  The amount of copying that went on in the dormi­tories was of course unfathomable.  Also, the very ubiquity of the copying caused students who would not otherwise have cheated to feel that they had to follow suit or be unfairly disadvantaged, as indeed they were in any case. 


                If we are to take the world as it is, we must recognize that there will certainly be cheating, and therefore both a corruption of the record and a loss of learning, if we hand out unsupervised problem sets with a promise of reward in the form of grades.  If we promise nothing at all in the way of reward there will of course be no cheating, but there might be so little home­work done that we will again have accom­plished too little in the way of teaching.  In the case of elemen­tary mathematics and science, how­ever, there are a couple of devices that can get around this apparent dilemma, even in classes so large that the professor doesn't know many of the students, and even by professors who do not care to pay a lot of personal at­tention to their students.


                In calculus we prescribe something like thirty exercises a week, "from the book."  Our students come to rather large lecture sections three times a week, and then in smaller groups once a week to a problem section with a teaching assistant.  At that weekly class they are subjected to a tiny examination ("homework quiz") that takes only five or ten minutes of the class time: it consists of one of the assigned homework problems verbatim.  Any student, therefore, who has written (and understood!) all his home­work for the week is bound to get the question right.  A student who has done less than his week's work has a cor­responding proba­bility of not getting the answer, though if he under­stands the subject he will get it right even without having "done" all the homework.  The weekly quiz scores then add up to ten percent of the term grade in calculus.


                It is not that we think students should be scored on whether they knew how to do a certain problem on a certain Tuesday in February.  Many of us, if we had our way, would prefer the Oxford or Cambridge examination system, where the exercises done during term have no bearing whatever on the grades at the end of the year, which are assigned on the basis of a several days' worth of written examina­tions each May (cf. Chapter 9, Grades and Examinations).  But as long as we have the American college system of four or five courses per term, with every student's program unique to himself, and the American system of discipline by numerous small examinations and so on, this quiz system of homework incentive works better than the earlier alternatives of (a) exhortation to honesty in graded but unmoni­tored homework, and (b) ungraded assignments.  I know; I have tried both myself: (a) leads to cheating and (b) leads to sloth.


                Not only does (a) lead to cheating, it has a second, even more serious defect.  To the degree that the homework is done "hon­estly," the student is deprived of the benefit of collaboration with his colleagues.  There is much to be learned in the dormitories; students spend more hours teaching each other, if they are given the chance, than any professor can possibly spend talking to them in his office.  What a pity to convert these educational conversations about how to do the homework problems into "cheating."  It doesn't merely rename what is happening, it corrupts the process.  When the collaboration among classmates is done for a direct "homework grade," it too often turns into copying without understanding; whereas if the consultation is in prepara­tion for tomorrow's "homework quiz," it is real understanding that will be sought, not just an "answer."


                The same principle applies to laboratory exercises in elementary classes in the sciences, including computer science.  Students are told to "turn in their own work," sometimes even when they are working in pairs, and when they are necessarily in consultation in many parts of the work.  It isn't surprising that many times the duller member of the team ends up copying from the one who knows what's going on; and he does it without attempting to understand it, because the grading is done on sole evidence of the document (the "lab report," or the computer program), which is produced out of the sight of the professor. 


                It would be much better if the professor demanded that these exercises be done, but that the reports, not graded directly, be kept in a journal, nicely rewritten so that he could glance at them once or twice during the term, and also so they could be used by their authors during the periodic "laboratory quizzes."  Such a quiz should be designed so that with the use of his own (well-written) lab notebook a student can describe in a very short time what he had actually done at this or that point in the experiment.  Let him have collaborated with the class genius as much as he liked: a copied lab report will do him little good if he doesn't understand what he was supposed to have accom­plished.  If his journal was based on a beneficial collaboration, it will both have taught him something about the subject and gained him points on the quiz.


                The quiz, by the way, should be nothing so crude as a request for data.  For so primitive a form of questioning a copied lab report will serve as well as an honest one, and it is not data the professor wants to ask about anyhow.  The questioning should be definite and par­ticular in asking what that student actually did.  By "definite and par­ticular," I mean to include questions such as "From whom, or in what cupboard, did you get the voltmeter?"  We want the student to get all the help he can during his laboratory work, or other homework exercises, but if we want to be sure he did it "hands on," why not just ask?


                A note on non-elementary classes:  When it comes to third-and fourth-year courses in mathematics, engineering and some of the sciences, I would modify my stand concerning unsupervised homework.  Here, unlike courses in (say) history or literature, daily or at least weekly written exercises do make sense.  The problems are typically fewer and longer than the sort of thing that makes up a calculus assignment, but they are still a necessary part of learning and a neces­sary discipline for every student.  The nature of the material in the more advanced courses does not permit the use of the kind of 'homework quizzes' we give to calculus students, since a typical exercise cannot be done in five or ten minutes; therefore the device of using the quiz rather than grading the homework in the raw will not work.


                Yet it is even more valuable in advanced technical courses than in the elementary ones for students to talk over their work with one another, or to get help when a problem seems intractable.  Converting this behavior into dishonesty would be a pedagogical mistake, while removing the discipline that results from giving formal credit for homework would be a psychological mistake:  even students of good will would find other things taking priority, to where by midterm they might find themselves hopelessly lost.  Unless we revise our system of examinations entirely (See Chapter 9, Grades and Examinations), I see no way out of this dilemma, and therefore recommend grasping it firmly by both its horns:


                I announce to the class that the homework exercises count 20% (or whatever) of the term grade, that they will be assigned well in advance and collected weekly.  They will be graded (typically by Teaching Assistants here at Rochester, though professors do it too) weekly by a spot-check, that is, by careful grading of a certain number -- not announced in advance -- of the assigned problems.  Students are nonetheless encouraged to talk about the problems with their neighbors, to ask advice on how to do problems, and are even permitted to read each others' work if that should be convenient.  The only prohibition on collaboration is wholesale copying, which is plagiarism and easily provable if detected.  Thus students have a golden opportunity to amass 20% of the possible hundred simply by attending to their work, without pressure or fear; and they will, unless they make extremely unwise use of their freedom, keep up with the course at the same time, making things easier for themselves at final examination time.


                One might call this policy the decriminalization of homework.  If we were to decriminalize everything this way, homework, exams, term papers and the lot, we would of course have nothing reliable to base our grades on, and I advocate no such thing.  Even this much decriminalization applied to freshmen might prove too heady; I prefer the 'homework quiz' for them.  But for math students in a partial differential equations course, for physics students in a classical electricity and magnetism course, the other 80% is plenty for security purposes, while these 'free' twenty percent can still focus the weekly energies of almost all students.  Those who use it unwisely will soon discover their error without our having to scour their papers for elusive evidence of cheating.


                It appears to me, in summary, that the analysis of the temp­tations to student dishonesty in unsupervised out-of-class exercises, and the search for preventive measures, thus turns up a valuable by-product:  It leads the way to a structure of assignments and examinations that make those exercises more valuable even for those who would under no system have been tempted to violate the rules, while it brings into the fold those marginal others who might otherwise have taken a cheap way around learning anything.  This is not the only domain in which the systematic reduc­tion of the occasions for academic dishonesty calls for something more fundamental than a locked door, and something of more positive value.