Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

This is a soft question that I have been struggling with lately.

My professor sets tough questions for homework (around 10 per week).

The difficulty is such that if I attempt the questions entirely on my own, I usually get stuck for over 2 hours per question, with no guarantee of succeeding.

Some of the questions are in fact theorems proved by famous mathematicians like Gauss, or results from research papers.

As much as I dislike to search for answers on the internet, I am often forced to by time constraints if I even expect to complete the homework in time for submission. (I am taking 2 other modules and writing an undergraduate thesis too).

My school does not have explicit rules against googling for homework, so I guess it is not a legal issue.

However, it often goes against my conscience, and I wonder if this practice is counterproductive for my mathematical development.

Any suggestions and experience dealing with this?

share|improve this question

closed as not constructive by Andres Caicedo, Carl Mummert, William, Austin Mohr, Michael Greinecker Sep 4 '12 at 14:33

As it currently stands, this question is not a good fit for our Q&A format. We expect answers to be supported by facts, references, or expertise, but this question will likely solicit debate, arguments, polling, or extended discussion. If you feel that this question can be improved and possibly reopened, visit the help center for guidance.If this question can be reworded to fit the rules in the help center, please edit the question.

33  
Of course you should ASK THE PROFESSOR if you have doubts about what outside help is allowed or expected. Also: if stuck you can go and see the professor for help. That should be FAR MORE useful to you than getting something on the Internet. –  GEdgar Sep 3 '12 at 13:46
8  
In the real world, no one cares how you come up with answers to questions, so long as the answers are found soon enough to be useful, and that any outside sources are reasonably compensated and or attributed. Why systems of education fail to pass on this information is beyond me. –  zzzzBov Sep 3 '12 at 18:36
8  
@zzzzBov: Being able to do things by yourself is considered valuable, otherwise noone can be expected to do new things. In the Tour de France, you not only need to reahc the finish line, you are expected to do it without doping. And even I could win the Tour if I were allowed to go by car. –  Hagen von Eitzen Sep 3 '12 at 18:41
8  
Well, this isn't a mathematical question. It's more like a moral one. Shall I suggest it to be migrated? Meta, maybe. –  jmendeth Sep 3 '12 at 18:43
4  
@zzzzBov The problem is that students which google the assignments often submit dubious work, and many times understand nothing from what they submit. In real life, no matter how fast you can get the answer, if you do this your boss will definitely be not pleased. In school, the instructor can usually see the mistakes, and explain to the students, in real life, you are usually the "expert"..... The goal of the assignments is not for the student to solve the problem, it is to help the student understand the concept.In real life the goal is to solve the problem. Google cannot help in the first –  N. S. Sep 3 '12 at 21:17

12 Answers 12

up vote 45 down vote accepted

Personal anecdote. In the late 1970's i was taking topology from Munkres, Topology: a first course. The professor was Joel Spencer, a wonderful teacher, who is up for an AMS Trustee position, see the current Notices. In particular, he made up his own assignments that might not be questions in the book, which takes extra care and work. We had gone through compactness and the more intuitive sequential compactness and limit point compactness. We did most of the proof in class, that the product of just two compact spaces was also compact. the homework was to complete the proof for compactness, and throw in proofs that the product of two sequentially compact spaces was also sequentially compact, and the product of two limit point compact spaces was also limit point compact. Two of them were easy enough, but i struggled with the limit point one for at least a couple of days. Eventually I handed in a paper saying just that "I couldn't do this one." It came back from the grader with "Excellent" written on top, because the supposed fact is false. I was mystified, I asked Prof. Spencer what was so great about it. It took years for me to understand that not being able to prove something false was exactly right.

I still have the book. I see on page 182, problem 5(e) that Munkres was well aware of this, referring to Counterexamples in Topology by Steen and Seebach.

Putting it together, two hours on a mathematics problem does not seem very much to me. Oh, meanwhile, I am not in favor of cheating, or asking (anonymously) for others to support cheating.

share|improve this answer
3  
+1 and pity I can't make it +5 –  Old John Sep 3 '12 at 19:40
2  
(+1) This is certainly an interesting twist on the Prove or disprove... style of questioning. There is an inherent bias when one is told that a certain statement is true from the outset which tends to make such questions easier and, in my opinion, less useful for training towards mathematical research. This flips that bias completely on its head. –  cardinal Sep 4 '12 at 0:00
1  
You have to have a life outside of mathematics. I had a class where I spent days each on several problems and as I look back, my only thought is, I wish I could have that part of my life back. Yes, there will be problems that take 2 hours or even more. But, if you have 10 of them that take 2 hours each, do you expect a student to spend 20 hours a week outside of class doing homework? I'm not advocating cheating. I'm just saying spending that much time on one class is probably too much. Either the professor is asking too much, or the student isn't bright prepared, or something else. –  Graphth Sep 4 '12 at 14:18
1  
"Do you expect a student to spend 20 hours a week outside of class doing homework?" Yes. A typical undergraduate where I went to school takes 4 classes per term. At average of 3 hours per class that is 12 hours of class time per week. Compare to my contracted work hours, the students have at least 30 hours left in the week that they should fill with school work and related activities. –  Willie Wong Sep 4 '12 at 14:33
2  
@WillieWong: I think Graphth means 20 hours a week for each course. –  Jesse Madnick Sep 4 '12 at 15:46

Firstly, you should always appropriately reference any information you find out in this way.

Secondly, I think this process can actually be helpful to your learning, provided you spend a reasonable amount of time thinking about the problem first, as you are likely to collaterally learn other things while looking for the information you want. I would also recommend talking to other people on your course (and/or the professor) about the problem before you search the net.

Thirdly, if you don't understand what you read online, then don't hand it in as a solution. It's usually better to give whoever is reading your homework assignments an accurate idea of what you do and don't understand.

As an aside, there are a number of classical theorems proved by mathematicians like Gauss that are not unreasonable to set as homework exercises. You will likely have been presented with a completely different theoretical framework to the one that existed historically, which can make these results much easier to prove than they would have been at the time.

share|improve this answer
5  
Why do you have to reference information in homework when the instructor didn't reference the exercises? –  Michael Greinecker Sep 3 '12 at 13:36
5  
This was advice given to me as an undergraduate which I think is worth following. For what it's worth, I think the instructor should reference the exercises as well, so you might as well lead by example! –  Matt Pressland Sep 3 '12 at 13:37
1  
@Michael: Because you have some integrity (in this regard)...? :-) –  cardinal Sep 3 '12 at 13:38
2  
@cardinal I think using something on homework is very different from taking credit for something publicly, i.e. plagiarism. One can certainly ask an instructor whether using other sources is okay. An instructor can actually design exercises to get students to read papers... –  Michael Greinecker Sep 3 '12 at 13:42
2  
The following question is related to the comments above: academia.stackexchange.com/questions/1744/… –  Joel Reyes Noche Sep 3 '12 at 13:43

Write up your homework solutions in tex and cite your sources. Soon the professor will want you to help with research.

share|improve this answer
21  
No, please don't use TeX :) Spend your time with solving the problems, not with typing up their solutions. Among dozens of beginning students I had who tried their hands at TeX, most of the time they spent on typing was completely wasted because crappy solutions were written up in crappy TeX... Only a handful of students did a good job both with solving a problem and typing it up. –  t.b. Sep 3 '12 at 16:20
1  
@t.b.: You are right, in fact we should actively discourage math beginners from using tex, so that its usage lets us quickly discriminate math ability. –  binn Sep 3 '12 at 17:32
9  
While I agree that typing homework problems in (La)TeX doesn't particularly help with what the OP is asking, I wouldn't be so quick to dismiss its value. I learned to use LaTeX precisely by typing up homework solutions, and it has turned out to be an invaluable skill for other projects. Besides, it means I still have access to all those homework solutions without having to worry about losing the papers, and on a number of occasions it's been helpful to go back and read them again to remind myself of something. –  David Z Sep 3 '12 at 18:12
1  
Yes, I also used to TeX my solutions in some courses. But only because a) my handwriting is horrible for outsiders (which is still better than one of the profs who had invented the "universel letter" $i=\iota=1=\ell$), b) it was a fun experience ot learn TeX in non-contrived exercises, c) it encourages to write legible texts with argumentation instead of wild heaps of uncommented formulas, d) I had time enough to do so because I found all solutions by myself instead of spending fruitless hours in google (which didn't even exist) –  Hagen von Eitzen Sep 3 '12 at 18:36
1  
At this point, TeX is faster than hand-writing for me, especially because I usually go through multiple drafts while writing in pen. –  Potato Sep 3 '12 at 19:13

First of all, be relax and take things easier. If some problems are hard and you cannot solve them then I see no problem to ask for help as long as you want to understand and learn the tackling ways of the problems, not only to hand in a solution. The real fact is that some teachers do really poor at their classes and expect a lot from their students. I don't know how things in your
case are, but if you like mathematics you may learn a lot on your own. Moreover, if you study the problems and the solutions posted on this site you'll learn a lot!

share|improve this answer

Let me explain why I, and almost all faculty members I know, do not want students searching for homework problems online.

  • It destroys our ability to calibrate the course difficulty. Twenty hours of homework a week is very high for a math course; higher than I would expect from any course that was not promoted as a "boot camp" style course. Either you are falling behind the rest of the class, or other people are turning in much scantier work than you are, or everyone is googling the problems. The first two situations are obvious, and your professor should be adjusting to it. The last situation is invisible. We had an analysis course at MI last year pedagogically ruined because everyone kept solving the homework problems, so the professor kept increasing his pace, until an in class test revealed that no one was actually doing the homework themselves.

  • It forces us to use more obscure, and often not as good, problems. There are some fields where there are computations every student should do -- and, as a result, they are written up in books and online sources everywhere. It hurts my ability to design good problem sets if I can't put this fundamental problems on the problem set. Even in fields where there are not such key problems, there are often only so many ways to set up an example so that it is doable in a reasonable amount of time. If I can't use the examples which are already online, then I need to pick larger and stranger values for my parameters, which makes the problem set harder.

  • I do not believe that students will learn as much from reading a solution as finding it themselves; this is probably uncontroversial. Moreover, I think that hearing a solution from a classmate with whom you have been discussing the problem together is better than hearing it from a classmate who solved it separately; hearing it from a classmate is better than hearing it from a faculty member; and hearing it from a faculty member is better than reading it in a textbook or here on math.SE. I think that the more interactive and the less polished the presentation, the more you have to engage your own understanding to process and take in the answer. This is why I almost never leave full answers to questions that look like homework here; I think it is harmful.

Let me quote the policy I will have for the combinatorial representation theory course I will be teaching this Fall:

Homework Policy: You are welcome to consult each other provided (1) you list all people and sources who aided you, or whom you aided and (2) you write-up the solutions independently, in your own language. If you seek help from other mathematicians/math students, you should be seeking general advice, not specific solutions, and must disclose this help. I am, of course, glad to provide help!

I don't intend for you to need to consult books and papers outside your notes. If you do consult such, you should be looking for better/other understanding of the definitions and concepts, not solutions to the problems.

You MAY NOT post homework problems to internet fora seeking solutions. Although I know of cases where such fora are valuable, and I participate in some, I feel that they have a major tendency to be too explicit in their help. You may post questions asking for clarification and alternate perspectives on concepts and results we have covered.

You should ask your professor for his or her policy, but I think that this is on the permissive side of what most math professors would write if they thought about a policy.

share|improve this answer
2  
It is less permissive than mine was. I was teaching undergraduates, and it was generally pretty obvious, even in the more advanced courses, whether they understood the solutions that they were offering. Besides, the longer I taught, the more I came to think that it was more the students’ problem than mine: they’re the ones who fail to benefit if they misuse resources. –  Brian M. Scott Sep 3 '12 at 18:09
6  
A telling approach I have used on more than one occasion is to include verbatim a question (or two) from the homeworks on the test. This is usually a very strong gauge on whether the work is being done and understood outside of class. –  cardinal Sep 3 '12 at 18:58

In my opinion, restricting study materials is counterproductive (particularly if no computer-searchable version of the course textbooks exist.) I realize that blindly copying answers is bad, but cheating on coursework has always been a problem and it is an issue that is independent of the Internet.

One common complaint is that students will learn less by Googling than they will by reading the textbook. This may or may not be true, but being able to search gives the learner access to much more targeted information. The difference between needing to skim through fifty pages you already understand in hopes of finding a paragraph you didn't, and being able to immediately enrich yourself on the topic desired, is phenomenal.

The thing is, the anti-Google teachers are right about one thing - you aren't going to remember how to use it practically if you don't actually use it. One answer here said that the degree of the problem became apparent when an in-class test revealed that the students, who up until then had been passing relentlessly difficult questions with ease, knew next to nothing.

This is actually a really useful thing to know, because armed with that knowledge the real problem becomes apparent - the students aren't using their research, which is why it isn't 'sticking.' A great option would be to hold a brief, three- or five-question test before each class - placing numerous, smaller checkpoints along the way will teach the students how to learn the material and retain it for use far better than either cramming or Googling together a paper.

I'm going to go one step further, though, and say that this also illustrates a deeper need for education to evolve. We don't live in the dark anymore - we live in an age of effulgence, where learning of any sort is a phrase away. To educate successfully, it will become necessary to embrace this by teaching more applied mathematics and asking more questions. To wit, if the course itself demands knowledge, the students will learn.

That said, I do not at all approve of students asking for (or receiving) verbatim solutions, either online or from classmates. This is cheating no matter where it takes place.

share|improve this answer

The aim of doing homework is practicing what you theoretically learned at school. When you do your homework, you gain experience in the subject. If you are having difficulties on doing your homework, that is the sign of your lack of comprehension in the subject.

If every homework question is taking your two hours, then that means that you seriously are lacking theoretical background on the subject. I suggest you repeat it before rushing into homework. Or first try solving easier questions, and gain experience in the progress.

Don't leave your homework on your difficult courses to the last night before the dead-line. If you do so, when you realize that it won't finish in time, you will most probably give up doing it, or try to make it solved on the internet. Start doing your homework a few days earlier than the dead-line. If you start earlier, you will have enough time to overcome any hindrances on your path.

If you think won't be able to solve a problem, don't ask the problem itself to the other people. Ask the part of the problem in which you are stuck. If you ask the whole question to someone else, the solution won't be your original work and you won't get much benefit from that homework.

If you had no choice and made your question solved to someone else, at least try to solve a similar question (e.g.; change the numbers in the original question) yourself.

Remember that homework is for your own benefit. If you want to succeed, don't cheat.

share|improve this answer

The following excerpt from an answer JDH gave on a thread on meta might serve as a useful standard of comparison. It is much more permissive than the approach of David Speyer:

My opinion is that there is nothing wrong at all with posting homework questions here, particularly interesting ones, and I find much of the negative reaction to homework-question posters to be somewhat strange, alien to my way of learning mathematics in a give-and-take exchange of mathematical ideas. Surely posting questions here and studying the answers is not much different than studying hard in the library, talking mathematics with one's colleagues at math tea or talking to one's professor, which are all excellent ways to learn mathematics. In particular, I expect that students who post questions here might learn just as much if not more from the resulting answers as from their professors---we have a number of talented mathematicians, who are very good at explaining things---and that math.SE provides a valuable service to students having unapproachable professors, having professors who do not explain well, or who have few colleagues able to help them. Furthermore, the math.SE community strongly benefits from the questions and the insightful answers that might be posted.

(...)In particular, I hereby give all of my own students complete permission to post any and all their homework problems here, and indeed I encourage them to post their questions here and to study the answers well and thereby to learn some mathematics. I will be testing them on their understanding at the exam.

I would also encourage all mathematics professors to adopt a policy of encouraging collaboration on homework among their students, as talking about mathematics with one's colleagues is assuredly one of the best ways to learn mathematics. Indeed, I recommend that all professors should actively encourage their students to form study groups in order to work on their homework problems together. Learning as a group, they will go very far.

share|improve this answer
    
Michael, do we vote on this to indicate the value of your answer, or our agreement or otherwise with JDH? –  user16299 Sep 4 '12 at 11:44
    
@YemonChoi I guess voting about agreement. I think this question is actually a bit too soft, to fit the Q&A format. –  Michael Greinecker Sep 4 '12 at 11:46

I remember a class from graduate school. Microbial Physiology. There was one exam that we all had two weeks to work on and we were told it was fine to collaborate with others. The answers to the questions were not multiple choice or fill in the blank rather they were answers that required detailed explanations. The exam was also very difficult. I remember working with other grad students throughout those two weeks trying to help each other research the answers. We would gather periodically in someones lab or perhaps get together for lunch to go over what we had figured out so far. We divided up tasks so different people would look at different aspects of the problem. The end result was that we all learned a lot about the physiologic structures we were studying. I will always remember that exam as being very difficult but one of the most enjoyable and challenging to complete.

If the intent of the homework is to research and discover an answer, then by all means do so by seeking out advice from others, but if the intent was to give a student practice in learning a particular subject then it should be done by that student on their own.

share|improve this answer

In the end, the real danger in googling the answer is that in the end your understanding won't be good enough. You are in school to learn and you want to make darned sure, given tuition rates today, that you are getting your money's worth. From this perspective, the goal isn't to get the right answer so much as to understand the problem. If you can't understand the work well enough to do it now, then what happens the next time?

So I don't know about the moral issues. After all is it morally wrong to cheat yourself? I think the pedagogical issues are very real and you want to be careful about what you are doing. The thing your question says to me though is that you already are somewhat lost in the class in which case meeting with your professor is a very good idea and seeing what sort of help is recommended. A second thing is I would recommend getting a study buddy you can bounce thoughts and ideas off. That's a good way to develop understanding too.

Personally I don't have any problem with doing methodology research for homework (I am not a professor though). But googling for how to solve a specific kind of problem is not the same thing as googling the answer. With the first at least you can hold out hope that you will understand the process better at the end. The latter, not so much.

share|improve this answer

You go to a University to learn something. At first it's your decision. Noone forced you.

There are many ways to obtain a degree. What matters is if you gain what you require for your planned future ahead.

For example, if your plan is to become a maths professor and you chose a maths degree as a step of the journey towards your goal, then it is useless to go around and Google for the answer because you will have a hard-time when you actually become a professor which will be the time your ability to fix those will matter.

But if your goal is to become an analytical engineer then googling may not harm you as much. Because you can use the time you save to learn something else that matters. It doesn't have to be reading a textbook.

For example, the skill of finding the answer for a tough maths question from the Internet can become handy in your future carrier as it may improve your ability to deliver in short time spans and think out of the box.

After all what matters is not how you learn. What matters is how you use what you learnt and use it to make money.

Weather we like to accept or not, we do everything like learning to earn money. So ideally everything and practically at least most of the things we do must increase our value in the targetted future job market. If you keep that end in mind then you will not get lost. ever.

share|improve this answer
3  
What kind of point of view is this? –  timur Sep 4 '12 at 15:43

Be your own book, create your own. You have a free mind to explore. Discover your potentials, if you resort to googling, you will not be complete and you will be missing the fun of failures as it breeds success..

share|improve this answer

Not the answer you're looking for? Browse other questions tagged or ask your own question.