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My Maths Homework Cheats 2012 Dodge

Bill Fulton informs me that there is a user on math.SE whose questions are almost entirely copies of homework questions from Math 592 (Algebraic Topology) and 597 (Real Analysis) here at Michigan. In the case of the analysis course, almost every question which had been assigned appeared on math.SE. These courses do not have their problem sets online, so it is extremely unlikely that this is someone self-studying the material at a different location. I am sure this is not the only case.

There is an interesting discussion to be had (and which has been had before) about how the math.SE community, and we professors, should deal with this new situation. But for tonight, I want to try persuasion. This is really extraordinarily dumb behavior on the student’s part.

I think it is safe to assume that someone who enrolls in graduate school at UMich is aiming to produce a thesis, and most likely to get a tenure track position at a research institution. Some of our students are aiming to teach at a Liberal Arts or Community College, but these positions require research too. Your future career success depends on your ability to understand the mathematics you are learning in your courses, and apply it to produce new results. There is no way to learn math without working tons of hard problems. Every bit of time you put into problem solving is a slight increase in the odds that you can get the job you are dreaming of. Why on earth would you waste that opportunity?

Moreover, you are planning to work in a closely-knit field, where personal recommendations from your senior colleagues are crucial to success. Why on earth would you take the risk of ruining your reputation in this way? And, yes, academics will view this sort of behavior very negatively — are you surprised?

Finally, you are dramatically harming the instructors ability to teach the class. When I teach advanced courses, I grade all the homework myself, and I use it to adjust my teaching. When no one solves a problem, or when the solutions all miss a basic insight, I add lectures on the relevant background. If the homework is actually being done by posters on math.SE, I lose all ability to calibrate my instruction.

ADDED: I have had a number of people raise the concern with me that I do not make clear enough that I do not know whether the student in question was a graduate student or an undergraduate. Indeed, I don’t. I believe that the professors of the effected courses know who the person is, but I don’t and I’d rather not. I assume that most students in such courses, either graduate or undergraduate, are dedicated and work tremendously hard. I’ve had several people assure me that, in particular, this is true for the students in the topology course, and I am glad to hear it.

Perhaps the student plans to work in some field very far from topology and real analysis, and thinks of the course as a waste of time. In this case, it is unfortunate that the student did not receive better advice especially because, at UMich, a student can only enroll in a limited number of courses. But, in fact, experience in any form of mathematical thinking strengthens ones overall mathematical ability. Moreover, learning fields outside one’s concentration is an excellent investment in the future. It makes you more able to participate in cross-disciplinary research (which is more and more of research). It also makes you a more valuable teacher if you can cover more topics.

Perhaps the student wants to experience listening to excellent lectures on algebraic topology, but doesn’t want to do problem sets. Maybe because the student doesn’t have enough time, or maybe he believes himself to be one of the rare people who learns best by passively listening. (I doubt that such people exist, but I’m willing to grant the possibility.) Well, good news! This is exactly what auditing a course is for! I have never known a math professor to refuse to let someone sit in on his or her course. As a grad student, you are only required to enroll in one course a term; I encourage you to audit two or three more if that is your interest. But you should be able to find one course a term where it makes sense for you to do the homework.

Perhaps the student was having a personal crises and simply couldn’t work on some particular week? Well, in this case, that isn’t true — the questions appear at a steady rate over the last two months. But, if it were true, it would make much more sense to ask for an extension, or to simply omit a problem set. In my experience, professors at the graduate level are generally very flexible. (I have some sympathy here. My senior year of undergrad, I had a major paper due the same week I started seeing an amazing lady, and I briefly considered buying a paper online to spend more time with her. What I did instead was to turn out some of the worst writing I have ever produced, collect a well deserved D+, and keep my integrity. Professor West, would you feel better to know that I married her?)

Perhaps the student was badly over his head in the course? This could be a serious problem, or just a sign that the particular teaching style/subject matter was a bad fit for him. It’s an excellent issue to bring up with the professors, or with one’s advisor. Again, faculty at this level are usually extremely helpful and flexible.

Perhaps the student is an undergrad? Well, if the student plans to go on to graduate school, all of the same issues apply. In fact, the concern about recommendation letters would be extremely pressing in this case. It’s also especially unfortunate, as I know that I, and I expect most faculty, are rather sympathetic to undergrads who take graduate courses beyond their level.

Perhaps the student is an undergrad who plans to continue in some non-academic path? In that case, it may be a good strategy to get the transcript boost of some graduate courses and not worry about learning the material. (Or it may not. I have a friend who, after majoring in Classics, went on to work at D.E. Shaw. When a job applicant mentioned ancient Greek fluency on her resume, he was called out to grill her. There are a lot of mathematicians working in hedge funds, so you might want to be careful what you claim to know.) But, if that’s your plan, I’ll let you on to a poorly kept secret. Graduate courses are usually graded very leniently. If you just want that line on your transcript and never want to think about the course again, you could probably just do a bad job on the problem sets and get your line.

Cheating is always wrong. But I understand why my calculus students cheat — they think of the course as a formal hurdle in the way of their diploma. In a graduate course, this is the knowledge you need to begin your career. It makes no, no, no, no sense.

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David Speyer

What this points to more than ever for me is that the teaching of rote learned facts – event X was on this date, person Y was the king, math problem Z resolves to such and such – has rapidly decreasing value in the 21st Century as the time taken for anyone to discover factual data has approached zero.

Facts are now a near-zero cost commodity.

Rather, what needs to be taught is critical thinking, idea creation, questioning of dogma, creativity (as much as such a thing can be taught) and most of all, context. Students should be taught to ask, “How does this apply to my world? If event X was on this date, what predeterminants caused it, and what was the post-event sequence of events caused by the event? Why did those things happen? What was in place that made it so? Who were the actors, if any and why?” You get where I’m headed.

Technology is a given in learning today, so teaching the skills of the 21st Century, underpinned by technical literacy and good digital citizenship are key.

So, not cheating at all, in any circumstance. Simply intelligent use of the available tools to access commoditised information. 21st Century skills applied.