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In this thread, Alex Bartel asks what I consider to be a question that is extremely important for our site.

"...here people are more than willing to solve homework questions completely, even if they see that an experienced mathematician has already posted a comment with the obvious aim to get the poster to think about the question. I think that this is extremely counterproductive, especially because the answers will be easy to google in the future. People who do this are actively playing against the lecturers and teachers, who often put a lot of effort into coming up with good exercises for their students. At the moment, I feel that this site is doing what AOPS has been doing for a long time - only worse!"

I would like to propose the following policy for math-SE which is something of a compromise between allowing users to post HW problems and not spoiling the student by giving them the answers too easily. To be clear, I think it can be very damaging for the development of a student if the teacher gives away the answers to HW problems the way that Alex identifies.

1) If a user posts a HW problem, they should understand that they are expected to type up their solution as an answer to their own post, and then after working with the community and responding to all comments (with edits to the answer) to everyone's satisfaction, they will then accept their own answer.

2) It should be expected of the community that no user will give away the answer to any HW problem under any circumstances, and that all hints should be based on a community agreed upon standard which depends on the attitude and level of knowledge of the student.

This way the entire thought process which the student has gone through to learn the solution will be laid bare for all to see. At a certain level there must be trust in the student-teacher relationship. A student who is determined to cheat cannot be stopped from doing so; however once a student has put sufficient effort to try and solve a problem on their own, it would be a tremendously valuable resource to have these kinds of detailed and thorough solutions available.

Once an honest student has put a lot of work into a problem, but is stuck, I think this policy will encourage the user to go through a learning process themselves. Perhaps mathematical issues and confusing things which are not so obvious to experts will be well explained by the OP who has now completely understood how to get past whatever was getting them stuck. Furthermore, in the future other students who get stuck for similar reasons will be able to much more quickly make progress in their studies.

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    $\begingroup$ I like this idea a lot in theory, and this has been discussed quite a bit, the problem is getting everyone to agree to it, and getting them to follow through with it. Also, this issue extends beyond HW questions. Many users(even high rep users) often answer questions after another user has adequately answered. Sometimes the new answer adds some extra details, sometimes not. In general, I would prefer if there was more commenting on answers. In my opinion, these issues are very similar and stem from the same root: Reputation Hoarding. $\endgroup$ – BBischof Dec 5 '10 at 21:41
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    $\begingroup$ I think full solutions are great. I have learned a ton from them. In one of our classes in college this year we have a lecturer who is very 'anti-solutions' leading to hours spent digging through books/internet trying to find out how to even approach the problem in the first place, we were learning nothing. It wasn't until found a great problems/solutions style book on the subject and I went and wrote out dozens of problems and solutions and made sure I understood them that I got to grips with the subject. After working through so many solutions I now no longer even need to attend tutorials. $\endgroup$ – Jim_CS Nov 23 '12 at 11:10
  • $\begingroup$ While I think it's a good idea for users to write up their own thoughts, I think you'll have a really hard time getting everyone to agree in practice, even if it's a good idea. That being said, I think that full solutions given by someone who has read the OP's post and solution can still be quite helpful, as a well thought-out post will guide the OP from their attempt to a full solution anyway. $\endgroup$ – Alfred Yerger Apr 3 '14 at 15:28
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I'm the high school math teacher referenced by Alex Bartel in his answer. I answered a question with an answer that was both on-topic and correct. He downvoted it, as is his right, and moreover, I agree with his reasons for downvoting it---except that I don't agree that his reasons applied to the actual question and OP.

In that question, the OP asked how many characters from a set of sixteen symbols is necessary for 16,777,216 distinct combinations. Is this a homework question being asked by a student? Perhaps. The thing is, though, perhaps not. Perhaps instead it's a graphic designer trying to understand the six-digit hexadecimal representation of colors used by HTML and CSS. Who knows? The OP didn't say who he was or why he wanted to know, and his reasons are none of my business.

So I chose to treat him as an adult in need of an answer to a question, not in need of a math lesson. Maybe it's because I came to math.SE after over a year of active involvement on Stack Overflow. On SO, people ask questions, and often times they get direct, complete answers to their questions. In general, the tone of SO seems to assume that, unless obviously otherwise, original posters are fellow working professionals---colleagues---struggling with some aspect of their code and trying to get some help with it.

It seems as though this isn't necessarily the assumption on math.SE. When an OP asks a question deemed basic, it seems as though responders assume the OP is a student trying to cheat on his homework. Of course, if it's true that the OP is a student simply looking for answers to his homework, then I agree that hints are more appropriate than complete answers.

But I do not make this assumption about the OP, even when he asks a very basic question. I believe that there is a significant population of non-student, non-mathematicians who are merely looking for answers to math questions that they aren't equipped to answer themselves. I understand that some people are like my wife when she asks me to compute the tip at a restaurant: she's just looking for an answer, not a lesson on percentages, and she resents my attempts to teach her---after all, she's a bright woman and a successful lawyer, she's just not very good at math. And I don't have a problem with that; in fact, if math.SE can serve that population of non-mathematicians, I believe it will be doing a great service to the world at large.

I don't claim to have an answer to the question of how to distinguish between students looking for homework help and non-student, non-mathematicians simply needing answers for their own reasons. And I agree that we shouldn't do students' homework for them, and towards that end it would be helpful if math.SE had some way to make that distinction.

But, and this is important, I also believe that if we get in the habit of downvoting correct, on-topic answers because they might be too helpful, we risk damaging the math.SE community, indeed the whole point of math.SE.

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    $\begingroup$ Dear Alex, I am glad that we agree on the principle of not solving students' homework. As for this particular instance, maybe it can be explained by our different backgrounds. My students at university are grown-ups and I treat them as such. Still, I teach them mathematics and I don't think that that's a condescending thing to do. My wife is also a bright woman and as non-mathematical as a person can be, but she doesn't at all resent my attempts to teach her mathematics and she knows that she would never get me to just tell her the tip without telling her how to arrive at it. In return... $\endgroup$ – Alex B. Dec 11 '10 at 3:12
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    $\begingroup$ ...she gets to tell me all sorts of interesting things about Leonardo da Vinci, about African art and so on. I don't think that that's condescending of her to teach me about things that are very well known to her. In the particular post in question, I downvoted it because I didn't in fact think that it was helpful. Being correct and on topic are certainly necessary criteria for being a good answer, but not nearly sufficient. The mathematics we are talking about is very easy high school maths and if the OP was a programmer, then he really ought to learn the combinatorics involved... $\endgroup$ – Alex B. Dec 11 '10 at 3:16
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    $\begingroup$ ...ideally by arriving at the method himself. This way he would know that he doesn't have to memorise anything, because he can always re-derive it. Moreover, if next time he faced a slightly different combinatorial problem, he would know that he could solve it himself. Please don't take the downvote personally, it is our freedom to judge what we think of as good or bad answers. I have had my answers with hints downvoted, too. There are plenty of people who think "he asked for a number, stop waffling and give him the number for god's sake". I just don't think that that's the right thing to do. $\endgroup$ – Alex B. Dec 11 '10 at 3:19
  • $\begingroup$ The way that people on this site treat askers of relatively basic questions changes over time. Experienced answerers do bring certain assumptions about the questioners: but (i) we have to -- it is in the nature of a site like this that questions show up mostly isolated from the actual context in which they arise -- and (ii) these assumptions are (largely) not prejudices: they are based on lots of experience. $\endgroup$ – Pete L. Clark Dec 5 '13 at 4:49
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    $\begingroup$ I think there are significant cultural differences between this site and SO: the latter was designed to be for working programmers and seems to be largely populated by such people. Our site really does seem to be largely populated by university students studying mathematics. There is a rather distinctive unpracticality to most math homework questions at this level.... $\endgroup$ – Pete L. Clark Dec 5 '13 at 4:57
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    $\begingroup$ ...E.g. if I ask "Why is every group of order $p^2$ abelian?" then how likely is it that I am a working professional and this question is part of my work? There's a huge difference here: people who have an undergraduate level of programming knowledge are very often paid to program, so lots of not especially advanced programming questions come from working people. Who is getting paid to do undergraduate level pure group theory? Anyone?? It seems overwhelmingly likely that such questions come from students taking classes. $\endgroup$ – Pete L. Clark Dec 5 '13 at 5:10
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Thank you Matt for bringing this up. Your suggestions sound interesting, but they don't address the most difficult issue in the whole debate: how will the policy, whatever we agree it to be, be enforced on the main site? BBischof in his comment highlights the main difficulty: the SE-system encourages giving complete solutions and it encourages playing the parrot and repeating other answers.

Here is an example: in this question, the poster clearly betrayed complete lack of understanding for (and possibly even ignorance of existence of) a very simple combinatorial identity, by asking a specific numerical question. Instead of explaining the mathematics to him, a high school maths teacher (of all professions!) just gave him the number. I downvoted his answer and left a comment. Now, his net score for the answer is 2 and the answer was accepted, which results in at least 15 + 30 - 2 = 43 reputation points. Even if now 20 people go and downvote his answer, he will be left with a positive reputation gain - as a reward for performing a trivial calculation and effectively preventing the student from learning a very basic technique. In fact, if only the asker upvotes the answer and accepts it, it will be almost impossible to offset the reputation gain by downvotes.

I am sure you don't need examples for the "parrot-phenomenon", since you will find it on every other question.

More to the point of this question, let me address the most common criticism voiced against an "anti-complete-solutions-policy": that it is presumptuous to decide for the poster what is good for them. Here is a very basic question addressed to all critics: why do you answers questions on math.SE, the reputation aside? Do you want to help the poster? Do you want to help disseminating mathematical knowledge? Now here is another question: which one of these aims is furthered by giving somebody the number he is asking for? How exactly have you helped him? If somebody asks you for a good sturdy rope because he wants to hang himself, will you also find it presumptuous to not just give him what he is asking for? Less dramatically, if somebody who doesn't know the country you are in asks you for running boots because he needs to quickly get to a town that you happen to know to be 500km away, will you just tacitly give him the boots, because you don't want to decide for him what is good for him? So how is this last example different from that of a student, who has no idea what it takes to succeed in life (how would he, he has barely lived)? I decide all the time, what is good for my (3 year old) daughter. This is completely analogous to the students: you just have much more experience in what it takes to learn mathematics than they do. What's wrong with deciding for them, what's good for them?

I will finish this tirade with an example: the way this student phrased his question, it was pretty clear that he was just expecting an answer on the silver plate (namely he didn't phrase the question at all, he just copied it verbatim from his exercise sheet). Instead of handing it to him, I only gave him small hints, one at a time, until one hour later he had the solution. Luckily, he played along and didn't decide "this forum sucks, I will go elsewhere, where they answer the questions properly". Now I claim that at the end, he learned something, he was much more appreciative of the very nice question his lecturer came up with and - possibly most surprisingly to the critics I am addressing - he felt much more content with himself and happy that I didn't give him a complete answer. I claim that I did know what was better for him, even if you think that that's a presumptuous thing to say.

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  • $\begingroup$ @Alex Bartel: Why I answer questions here? Well, I do want to help people and learn something myself in the process. The other examples are a bit too extreme to compare them with this in my opinion. Also, people that want complete answers know that what they do is not the correct way, that is different with your example of the runner to a city 500km away. Further, I cannot smell that it is a homework question, it could as well be a problem from a book. If they don't tell, I think it is their fault if they learn nothing from it. $\endgroup$ – Jonas Teuwen Dec 6 '10 at 13:25
  • $\begingroup$ Anyway, I also almost never give complete answers to any question. If people tag it as "homework" I will even give less (assuming that I know the answer of course) information to solve it. If I would really know it is homework, I wouldn't give a complete solution, but how can I know? My answer below this is based on that idea and the fact that I don't want to decide for someone else how to study, after all, I still am a student myself. $\endgroup$ – Jonas Teuwen Dec 6 '10 at 13:33
  • $\begingroup$ I'm sorry if my reply is too unstructured. I also wonder why other people upvoted my answer. $\endgroup$ – Jonas Teuwen Dec 6 '10 at 13:42
  • $\begingroup$ Alex, the lack of a 5-to-1 majority favoring one user's opinions on how the question should have been answered, is not a flaw in the reputation system. In fact, when I looked at the question just now there was rather the opposite ratio: 4 upvotes to 1 downvote (I might add another upvote eventually). Instead of allowing the reputation system to reflect the users' views, however imperfectly and noisily, you say we are supposed to over-ride those views though an "enforced consensus" and regard questioners as analogous to 3-year-old children. It does not sound like a promising approach. $\endgroup$ – T.. Dec 6 '10 at 14:21
  • $\begingroup$ I recommend to anyone interested in this discussion, to follow the first link (math.stackexchange.com/questions/12992). There one can read a short discussion in the comments, in which the author of the answer (also named Alex) responds to Alex's criticisms. $\endgroup$ – T.. Dec 6 '10 at 14:38
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    $\begingroup$ @T.. If you look carefully at the question you are talking about, you will see that my comment about the -1 got 6 upvotes. But those same 6 people didn't downvote the answer itself. I can think of several reasons for that. They might have felt that they will be punished almost as much as the poster, or they may be good-natured people who don't give downvotes lightly. So your attempt to portrait me as arguing a tiny minority view, if that's what it was, is counter-factual. Clearly, I am not advocating to "override the users' views", but rather to establish a consensus on what those views are. $\endgroup$ – Alex B. Dec 6 '10 at 14:45
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    $\begingroup$ As for the term "enforced consensus", the whole faq is full of "enforced consensus". It is a fact that there are lots of policies in life that can easily be scuppered by a minority, if not properly enforced. Giving full solutions to homework problems is a typical example, I am sure you can think of many others. The policies on this site are to a large extent shaped by the community. If a sizeable majority of the community should decide that they don't want to see complete solutions to homework problems, then it is perfectly reasonable to think about how to enforce this policy. $\endgroup$ – Alex B. Dec 6 '10 at 14:50
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    $\begingroup$ I looked at the OP's profile in the question linked to by Alex in his post and by @T.. in his comment above, and it seems more likely, based on the commentary that appears in the other two questions that he has asked, that he is teaching himself from a text rather than that he is a student in a class. Of course, one can't be sure with information given, but this underlies the point that if one presumes that every basic question (e.g. writing 16777216 as a power of 16) is automatically a homework question, then it will be very easy to generate false positives. $\endgroup$ – Matt E Dec 6 '10 at 16:50
  • $\begingroup$ dear Alex, of course I am well aware of the 6+ upvotes in a comment thread that I just urged everyone to read, as well as the vote counts on postings in the meta. I agree that a group of approximately 6 meta users may specifically support your views, but there are many other views and approaches, with the support not concentrated so strongly around any one to justify a declaration of "consensus", much less its enforcement. The FAQs are generally advisory and not restrictive like the policy you describe, and I see no objection to rules per se, only to gratuitous or harmful ones. $\endgroup$ – T.. Dec 6 '10 at 16:53
  • $\begingroup$ It should also be noted that those 6 upvotes could have been agreeing with Alex' comments that a different type of answer is better, and not agreeing with the "-1" that begins the remark, or with the sentiment that posting complete answers is undermining teachers, learners, academia, etc as expressed in the meta. This is not including the downvotes that would have accrued to the same comment had the software allowed it. What is clear is that across the site, the vote count on complete answers is generally non-negative, and reaching a 5-to-1 majority punishing answerers is unlikely. $\endgroup$ – T.. Dec 6 '10 at 17:31
  • $\begingroup$ Dear Matt, actually, I am not too bothered about the distinction "homework" vs "self-study" or "real life problem". In this particular case, the question concerned a piece of mathematics that people usually learn fairly early on in high school. My reasoning was that if this person failed to learn this in high school, then the best help he could receive here would have been a decent explanation of the mathematics involved, so that when he has the same question with slightly different numbers or a slightly different question in two days time, he doesn't have to come here to ask for the new no. $\endgroup$ – Alex B. Dec 7 '10 at 5:01
  • $\begingroup$ It is true that sometimes it's not so easy to tell what the motivation behind a question is, but firstly, there are cases where the wording completely betrays the origin of the question, so it still makes sense to know what to do when the case is clear cut. And secondly, even when that's not the case, it is often easy to tell what will help the poster most. E.g. what is more useful, a number as a solution for a particular numerical problem or a general procedure for solving such types of problems? $\endgroup$ – Alex B. Dec 7 '10 at 5:04
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I think it is the responsibility of the user itself to say that it is homework and only request a hint. If they get the complete answer on their plate they will learn nothing from it and in the end they will not succeed.

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    $\begingroup$ @Jonas The issue is more complicated than that. In many places, homework is graded and the score contributes to the final mark. Therefore, to solve questions completely for the poster is not only detrimental to their own development, but also unfair on their fellow students. Further, the extent to which this is detrimental to the students' development is often not realised by the students themselves. Profs, teachers and students who have worked hard themselves should know better than the shortsighted students who think that they will be best served by being given a number or a comlete proof. $\endgroup$ – Alex B. Dec 5 '10 at 10:56
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    $\begingroup$ @Alex Bartel: Yes, I see that, but then we decide for the student what is good for them. Even if they get good grades they might not succeed in the end because of "cheating". We just seem to have a different opinion, that is no problem, since I do agree that there should be a policy about homework questions. $\endgroup$ – Jonas Teuwen Dec 5 '10 at 14:17
  • $\begingroup$ Unless you edit the question so the answer will teach him how to find it out himself next time. Teach a man to fish, rather than handing them over to him $\endgroup$ – Ivo Flipse Dec 5 '10 at 21:16
  • $\begingroup$ @Jonas I don't regard it as a problem that we have different opinions, I just see it as a problem (my problem) that I don't understand your point of view. Maybe you could comment underneath my answer, addressing the questions I raise there, some of which are specifically aimed at you and at the people who upvoted your answer. $\endgroup$ – Alex B. Dec 6 '10 at 5:15
  • $\begingroup$ When I choose to give a student special attention by helping them with their HW, I demand an extremely high level of mathematical maturity from them. If I did not believe a student was capable of this maturity, I would not give them special attention. I consider it very disrespectful to me and to themselves for these students to give anything less than their full devotion and attention to any problems I assigned them. I consider their performance to be a reflection on me as their teacher. If a student handed me a solution he copied from the internet, I would be upset and discipline them. $\endgroup$ – Matt Calhoun Dec 6 '10 at 23:21
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    $\begingroup$ I don't see why we should expect anything less from users who post HW on math-SE. I consider it a sign of good faith on the part of these users to post their solutions, so that we can verify that they have really learned something; and I do not consider asking a student to do their own HW to be inappropriate, if they don't know that then they don't know what is good for them. In my mind, giving away the solutions to HW completely defeats the purpose of assigning HW in the first place; and along with Alex, I fail to understand your point of view Jonas. $\endgroup$ – Matt Calhoun Dec 6 '10 at 23:22
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Split up the answer, with a hint first, and then use the markdown technique for hiding spoilers.

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I would like to add two points for consideration.

1) What teacher only assigns 1 homework question? If a student posts several questions, then certainly providing a detailed answer for all of them may be counterproductive, but one question with one complete answer is often more instructive than hints.

2) With many of these questions, it's probably more effort to post a properly formatted well stated question, and then read the answers, than it is to just scratch some half attempt down on a sheet of paper.

In my opinion, it is just best to give the most instructive answer possible. Sometimes that might be a hint, but assuming that all students asking questions about homework shouldn't get full answers is a very very frustrating policy for the students that actually want to learn, and who cares about the others?

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    $\begingroup$ A little frustration is a good thing. "The most instructive answer possible" is the one the student comes up with herself. $\endgroup$ – Gerry Myerson Dec 5 '13 at 2:58
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    $\begingroup$ I agree, but if we were limited to what we teach ourselves, then we'd all still be counting on our fingers, if even that much. I agree that "just giving the final answer" should be discouraged, and that sometimes a hint is the best (if you take into account how much a student should be expected to know at their level of education), but I also think there is a great deal of education that can come from showing a complete reasoning. $\endgroup$ – DanielV Dec 5 '13 at 4:40
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    $\begingroup$ A possible compromise is to show complete reasoning on a related problem, and encourage the student to apply the method to the actual problem. $\endgroup$ – Gerry Myerson Dec 5 '13 at 23:02
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    $\begingroup$ In my limited ability, when I see a question with actual numbers involved, I will sometimes simply replace those actual numbers with variables and show the reasoning for the solution that way. I think what you are suggesting is a generalized approach of that. $\endgroup$ – DanielV Dec 6 '13 at 0:20

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