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This is the first time I post a question here, but sometimes I do read posts here. My question is concerned (again) with homework questions. My objectives in this site has been always the followings:

I - Learn Mathematics,

II - Teach Mathematics to whom want to know it.

In general I don't answer homework problems, because in general they only seek for a solution, not for a better understanding of the problem, but sometimes, I leave a comment to OP, to improve the question, to show efforts, etc...

But all of this seems to me a waste of time, because in most part of the cases, another user answer the question, even if the question is only a "Prove it" or "Prove that". Now, we can close questions of this kind, but the questions is put "On Hold" and if a answer was given, anyone can read the answer. Today I get angry with a question and instead of help, I have posted a ironic answer which I have deleted.

My question is: Why even after the question was closed, we can still see the answer? Is it not better to turn the answer invisible or something like that?

Remark: sorry about my English.

Thank you

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The opposition to fully answering homework questions roughly amounts to:

The OP will get away with cheating on their homework, or at least without learning anything from it. MSE shouldn't facilitate this.

Usually, any other visitors will not be hampered by such considerations. So as soon as a full answer has been there for 10 minutes, the OP will likely have what they wanted. (I won't go into the answer/close wars that this realisation sometimes provokes.)

If the answers are hidden from view after closing, two things happen:

  1. OP cannot request clarification from answers, closing the opportunity to still learn something;
  2. Nobody else can benefit from, or admire (or dislike, for that matter), the work of the answerer.

Moreover, any proper hints that were given as answers are also hidden from view, while they would normally be admissible as answers.

A further thing to consider is duplicates, for which it is certainly not beneficial or even justifiable (in most cases) to hide the answers -- stronger, it can be downright harmful, as the new answer may be better than all existing answers at the duplicate.

In summary, while it is understandable that some would like no full answers to appear under homework questions, the solution proposed by you does not seem a good one to me.

It would be better to try and convince those who give full answers to homework questions to reconsider their actions. (Although, given the amount of times this has been attempted in the past, the success rate of such nudges will likely be far from stellar.) To me, this seems the only road to a long-term viable resolution of the matter.

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    $\begingroup$ +1 for the final paragraph. It works well in an environment where the leadership is on board with that philosophy and has the capability to curtail violations. Given how surreal some of the discussions on this meta have been, it seems inconceivable that things could actually be moved in that direction. $\endgroup$ – user14972 Sep 27 '13 at 22:08
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    $\begingroup$ To comment on the last paragraph, the only reason why people will give full answers is because those answers will get lots of votes. The problem is that anyone can vote, and from my experience an answer to an easy homework question will bring much more votes than a nice deep answer to a complex self study Question. $\endgroup$ – N. S. Sep 27 '13 at 22:47
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    $\begingroup$ Also, some people probably started giving answers instead of hints to homework questions because of the following phenomena, which I saw pretty often: User A gives some good hints to a homework question, which makes the problem easy but the OP still needs to do some work. Minutes/hours later, User B gives a complete answer by filling in the missing details between User A's hints.... User's B answer then gets much more votes and gets accepted... And while I understand why the OP accepts the answer which requires no work for him, it is the community which votes UserB's answer as "best one"... $\endgroup$ – N. S. Sep 27 '13 at 22:52
  • $\begingroup$ @N.S. To say that people only give full answers for the votes isn't true -- at least if we look at all the PSQs instead of only homework ones. One may just want to sharing a nice argument with the community, have extra information about the OP, or just "like the sound of their own voice" as some user recently put it. In some sense one could argue the rep system is skewed towards favouring the simple Q&As. But (at least in my mind) anyone having a reasonable amount of rep will care more about the occasional nice comment by a colleague or an esteemed user. That's how it works for me, at least. $\endgroup$ – Lord_Farin Sep 28 '13 at 0:09
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    $\begingroup$ @N.S.: I’m pleasantly surprised by how often a good hint is accepted even when there’s also a complete answer (which may have got more votes). $\endgroup$ – Brian M. Scott Sep 28 '13 at 9:39
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    $\begingroup$ @Lord_Farin: All of those reasons, and a few more besides. Sometimes there really doesn’t seem to be any way to give a hint that isn’t essentially the solution; this seems to happen most often with very easy and very hard problems. And when the asker seems to be just getting started on a topic or to have some serious misconception, I sometimes judge that a complete solution with explanation of how to think about such problems will do the asker more good than anything else. $\endgroup$ – Brian M. Scott Sep 28 '13 at 9:45
  • $\begingroup$ @BrianM.Scott I might be wrong, but it is my impression that typically that happens on harder/higher level homework questions. $\endgroup$ – N. S. Sep 28 '13 at 15:10
  • $\begingroup$ @N.S.: I was thinking specifically of low-level problems when I made the comment. $\endgroup$ – Brian M. Scott Sep 28 '13 at 18:23
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In general I don't answer homework problems, because in general they only seek for a solution, not for a better understanding of the problem

I don't think this statement is true. I have asked a lot of homework questions here, and I do appreciate it to get a really good hint, but getting a good (full) solution, I do appreciate as well. I think there is a general misconception that students won't learn anything from full solutions (complete proofs).

The process of 1) reading a proof, 2) trying to understand every step, and then 3) rewriting it in your own style, (or bonus step 4) explaining it to someone else), is in my experience one of the most effective ways of understanding math.

In some books/readers I feel that the author just didn't give enough examples in the text. Reading the solutions of some exercises works the same way, as having some more examples in the text. And I'm really glad that I can use MSE as a source of such worked example exercises.

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    $\begingroup$ You is just a (good) example in the middle of a thousand of homework questions which just seek the answer. My argument does not apply to you, but it does apply to the other part (which is a thousand). $\endgroup$ – Tomás Sep 26 '13 at 19:35
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    $\begingroup$ I believe there are a lot of people who honestly believe that the way to learn something is to keep staring at other peoples' solutions until it sinks in. Furthermore, there is a snowball effect -- the more people see others questions saying "do this problem", the more that confirms that the way to learn is to ask others to do their problems. There are certainly some people who are here just to get other people to do their homework or exams for them (some even say so themselves!). $\endgroup$ – user14972 Sep 26 '13 at 19:47
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    $\begingroup$ @Thomas I don't really see why a student would seek for just an answer, unless it's homework that gets graded in some way. And I find it hard to believe that the majority of the homework questions here fall in this category of cheating. In all other cases, I think a student asks for an answer because he hopes he is going learn from it. I mean, every student wants to pass the exam. If you are not going to learn from the homework questions you get, you're chance of passing the exam are close to zero. $\endgroup$ – Kasper Sep 26 '13 at 23:46
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    $\begingroup$ One other point I want to make, because people think so bad of PSQ questions. Sometimes, you have spend hours in an exercise. You asked your teacher for a hint, but still you don't get it. You think again and again, but it's just one of those concepts that won't fit in your brain. You get tired, and after some time, you give up, but you still want to know how the F can you solve this. At this point of time, I would like to go to MSE, state the exercise, say I surrender, I can't do it, please help me with a full solution in a detail. $\endgroup$ – Kasper Sep 27 '13 at 0:02
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    $\begingroup$ For example, this question: math.stackexchange.com/questions/259563/… I don't state much more than the exercise, I had thought about it for hours, I was tired, and I just hoped that someone could enlighten me. And luckily it worked :) $\endgroup$ – Kasper Sep 27 '13 at 0:11
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    $\begingroup$ Most of the time, when I need to spend a few days working through someone else's proof, I end up with only a shallow understanding—I can understand each step, and maybe some larger units, but the entirety remains beyond me. I have said before that I think it's better to offer some suggestions for somewhat similar problems and/or lemmas than to give a full solution to the specific problem. $\endgroup$ – dfeuer Sep 27 '13 at 3:27
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    $\begingroup$ @Kasper And how are we to discern the case you discuss from just another PSQ? By adding a (short) paragraph on what you have tried. Full details are not always required. If you say you've been thinking about it for hours, asked for a hint, which didn't help, then I don't think your post will accrue (m)any close votes. At least, it wouldn't get mine. $\endgroup$ – Lord_Farin Sep 27 '13 at 8:19
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    $\begingroup$ What I think is that the most part of people do not like mathematics, and because in modern times, mathematics is a obstacle for a lot of things we have to do in life, people just come here, seeking a easy answer, so they can have a easy way to avoid this obstacle. $\endgroup$ – Tomás Sep 27 '13 at 12:21
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    $\begingroup$ About @Hurkyl and dfeuer . You guys think the exact same way as most of the teacher at my university. They even came up with a new idea. They have made a reader. With no proofs at all. Only definitions and theorems. Then they have bunch of exercises where they gave some hints to solve the theorems, and some other exercises. I'm getting completely frustrated from this. Even if I think I solved it myself, I want to know if it is correct. I can't ask my teacher to look at all my work. I just want a solution manual to see if what I do is correct, and understand the exercises I couldn't finish. $\endgroup$ – Kasper Sep 27 '13 at 21:46
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    $\begingroup$ Luckily, I found out, that my teacher almost literally copied a book (and a very good book goo.gl/YeEZEe ) and translated it in dutch. In the original book, the theorems are proved, and I really think that reading all those theorems and understanding every bit of it, makes me a much better mathematicians. From getting only frustrated about hearing the word multidimensional real analysis, I now think about the beauty of some of the proofs I've read there. What is so bad about having a solution? You always can try it yourself if you think it doesn't help you. $\endgroup$ – Kasper Sep 27 '13 at 21:55
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    $\begingroup$ @Kasper: Unfortunately, the real world is grey, and facts like [$\exists$ PSQ: $\neg$ PSQ $\implies$ Lazy student seeking for just an answer] aren't actually useful at all for making real world decisions. PSQ, however, is much less grey than the typical question. $\endgroup$ – user14972 Sep 27 '13 at 22:11
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    $\begingroup$ Okay this is getting completely off-topic. Don't understand me wrong. I'm not against giving hints, or suggestion for similar problems. Especially because a hints can make you feel like you were almost able to do it yourself. But I just don't get the general concensus that full solution are of such poor educational value. $\endgroup$ – Kasper Sep 27 '13 at 22:13
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    $\begingroup$ @Kasper: They're not. What is poor educational value is when students get in their head that "to learn, I have to read other peoples' solutions", not "to learn, I have to work through problems, and sometimes peek at other peoples' solutions to get ideas". When they think "I need help to solve $x^2 - 3x + 2 = 0$" rather than "I need help learning how to solve quadratic equations". Or the absolutely crippling "I could solve the problem myself if you tell me what to do" instead of "I could try to figure out on my own what to do". $\endgroup$ – user14972 Sep 27 '13 at 22:21
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    $\begingroup$ Maybe your are right, maybe not @BrianM.Scott. Last week I saw at least five peoples, who ask for the first time a question. A question like this: Prove this is true... Then, do you know what they do? They never more enter again with the same account. If you ask something like: give us your thoughts, or what have you done so far? What we get? Nothing, because the only thing they want is the answer. Some of them has the courage to delete the account after the answer is posted... $\endgroup$ – Tomás Sep 28 '13 at 12:08
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    $\begingroup$ Now, I think @BrianM.Scott, that you are trying to read my mind. If I posted this question, is because I saw a lot of guys which only seek the answer. If you post a question, what is the problem to give a minimum of information? The most of people I am treating here, is people of this kind, which is the big majority here. It is sad but it is the truth. $\endgroup$ – Tomás Sep 28 '13 at 12:14

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