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.
My Math Homework
After scouring the internet, reading tons of books, and using my own bag of tricks, Calendarwas born. And, if you follow my blog, you know I LOVE Calendar. But it just wasn't enough. The kids needed more practice then even Calendar could provide. Word problems, higher level computation....
So I decided that their homework was what needed to change. I took a complete departure from everyone at my school and created a spiral homework. It was 10 problems a day, not of what we just learned, but of EVERYTHING that we learned. The kids were constantly seeing the same style problem over and over and over. Their skills were always being refreshed....and it worked like MAGIC!
So when I moved to 4th, and then to 5th, I took this style homework with me. And every year I create sheets like this, my students math scores soar. Because nothing is being forgotten, the kids are always practicing those basic skills they need. I can honestly say that because of this homework (and Calendar) if I don't get to a lesson in math that day...I STILL FEEL OK! I know all of the standards are covered and I simply DO NOT EVER stress about math. Ever.
Doing homework this way has the added bonus of freeing up some time to do all of those concept lessons that I like to do. I get the kids thinking about math processes, instead of always worrying about the rote memory of it all. It really is amazing what one little 10 problem page can do.
However, doing the work isn't enough. The key to this is that every.single.day, without fail, we go over the homework. I have it worked into my math block (just 10 minutes) to go over the problems. I don't teach during this time, I just show the students how to do the work, with their help at times, on the ELMO and then they take it home to study for later. This review of the problems is what makes this homework better than anything I have done before. If they kids didn't get it at home the night before, they get it when we go over it. Then, when they see a similar problem on a homework that week (or the next or the next) they *do* get it.
Another thing I add into my week are weekly spiral quizzes. These are where I get my data for small groups, intervention, and mastery from. Here is the form I use to break all the information down...and the post explaining it. It is also test prep (and you all know how I love test prep).
I really just love this whole part of my classroom. I think...KNOW it works and it helps me room to run so smoothly.
I know at this point you are probably sold (I seriously love this...it is my favorite thing I have ever created. Ever. Simply because of the value it holds in my classroom.) If you are interested in having it in your own room, I have sets for 3rd, 4th, and 5th grade.
I realize this isn't super cheap, but it is worth every.single.penny that you spend. I honestly and truly believe that. It will help you to run your math block smoothly and keep you on target. (oh and it comes with an answer key too :)
So there you have it....my sales pitch ;) How do you structure your math homework?