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We've all seen them: posts that ask the community members for help regarding a homework problem, lacking in any previously attempted work. Sometimes you can't blame the asker for not knowing where to start- most, if not all of us, have ran into these issues often enough at some point.

Having said that, I do suspect that there's a good deal of posters who have simply copied and pasted their assignments (sometimes in the form of an image file) to the post, without putting much- if any at all- effort into solving the problem. I think it's pretty reasonable to make this claim; however, it can be tricky to differentiate who really didn't know where to begin than who is just trying to dump a homework assignment on the community.

Thus, I write this post to pose a suggestion: Math.SE could petition its askers to at least write out a definition or two pertinent to the problem if they really don't know where to begin. After all, knowledge of the terms' definitions are (usually) a great starting point to understand just what the homework problem has given you, and what the homework problem wants back. If the asker doesn't know the definition (at times, it's just too obvious that's the case) then the help one offers isn't really enriching the asker's knowledge of mathematics. All one ends up doing is making the asker a poorer student.

If the asker did know the definitions, it would be easier for the community to highlight a proof or computation strategy, and would imply that at least the asker is learning something.

What do you think?

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    $\begingroup$ So you're saying that you don't know where to begin when answering questions of the form "I don't know where to begin"? :-P $\endgroup$ – Asaf Karagila Oct 28 '14 at 3:56
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    $\begingroup$ I think it is a very good suggestion, not universal in its applicability, but then what is? $\endgroup$ – André Nicolas Oct 28 '14 at 4:20
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    $\begingroup$ I like this suggestion, and also that of writing down the problem itself rather than uploading it as an image (those tend to be shortlived, too). $\endgroup$ – darij grinberg Oct 30 '14 at 6:28
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    $\begingroup$ @AndréNicolas I hear you. The one instance I could think of where such a suggestion might not make a difference is with contest-style problems that without some obscure algebraic trick, might seem impossible to solve. In that case, asking for a definition might just frustrate the asker or something. However, for the homework questions people post up, I think (normally) asking for a definition is a good enough starting point $\endgroup$ – daOnlyBG Oct 31 '14 at 16:03
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Tim Gowers has a series of blog posts on this topic and related topics. In one, he says:

Let me introduce a notion of fake difficulty. Every pure maths supervisor at Cambridge has had conversations like this:

Supervisee: I found this question rather difficult.

Supervisor: Well, what were your thoughts?

Supervisee: Erm … I don’t know really, I just looked at the question and didn’t know where to start. [By the way, never say that. Ever.]

He goes on to say:

This is a fake difficulty because it is not a legitimate reason to get stuck on a question. If you don’t know a definition, you can look it up. “I didn’t know where to start” is a well-known euphemism for “I was too lazy even to work out what the question was asking.”

That's how I read it too; I find the remark intensely annoying. Unfortunately, I don't think we are well-equipped to help these people, except perhaps by doing their homework for them. Someone who is faced with a question asking if $[0,1]$ is compact, and who is too lazy or disorganized to look up the definition of compactness, or even to ask a sensible question along the lines of “how can I understand compactness better?” is probably not going to benefit from gentle prodding or helpful suggestions.

If I had one of these three people in my office, I would ask them to write down the definitions, and we could proceed from there to have a discussion about it. On this web site, the users most in need of this kind of back-and-forth discussion are those least likely to participate in one, so I don't think we can usually help them. In the past I have often left comments 1 2 3 4 suggesting that the writer should start by writing down the definition of compactness; these comments are almost never answered. (Item 3 is a happy counterexample.) My current practice is usually to downvote the question (as a warning to other readers) and move on quickly.

I wish I could be more optimistic.

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    $\begingroup$ MJD, I would literally do the exact same as what you've just said: ask for a definition, down vote for no responses/further attempts. Unfortunately, due to the ease of creating multiple account, one could simply ask a "b.s."-quality question, see it downvoted, and then ask another one... and after enough times, one could just open a new account and post more homework questions. It's a numbers game, really: eventually, at least a few of those questions would be answered by an well-meaning MSE user. $\endgroup$ – daOnlyBG Oct 31 '14 at 1:01
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    $\begingroup$ A user saying "I have no idea where to start" is very likely admitting to asking the wrong question. (Of course, the questions they need to ask are probably not part of a homework set.) $\endgroup$ – user642796 Oct 31 '14 at 13:12
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    $\begingroup$ Suggestion, I hope not too cynical: the answer to "I don't know where to start" is "in that case, start again at the beginning of the course". Faced with that option, most students will manage to find somewhere a bit more recent to start. $\endgroup$ – David Oct 31 '14 at 23:20
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    $\begingroup$ I could post that, or I could post nothing. Posting nothing seems equally helpful, and is less trouble for me. $\endgroup$ – MJD Oct 31 '14 at 23:22
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    $\begingroup$ Tim Gowers is flat wrong. While ‘I don’t know where to start’ is often a euphemism for ‘I’ve not actually thought about it’, this is by no means always the case. (By the way, if downvotes of a question have any effect at all on me, they increase the likelihood that I’ll look at the question and possibly give a compensatory upvote: I’ve seen far too many questions downvoted even when the asker provided some context, apparently only because the question was deemed too elementary.) $\endgroup$ – Brian M. Scott Nov 3 '14 at 22:46
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    $\begingroup$ maybe this is not exactly this case in this question, but what has happened to me is that even after applying the definitions, or maybe, tried 4 or 10 ideas, now I don't know what else to do. What would you suggested in that case? $\endgroup$ – Pinocchio Nov 7 '14 at 15:27
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    $\begingroup$ @Pinocchio: Give an indication that you have done these things. I find that often when I write an email to a colleague, to my supervisor, or even just a question online, writing down what I've tried and where I got stuck will often have the effect of showing me the path for finding my own answer. I think that if anything else, that should be the reason why we have to encourage users to post better questions. It will cut the number of new questions by causing many people understand their own problems. $\endgroup$ – Asaf Karagila Nov 10 '14 at 22:17
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I think that one of the issues here is that we (professors, teaching assistants, private tutors) sometimes expect that by solving one problem, the student could deal with the same type of problems immediately.

But we forget that the underlying approach to a problem is something that have to be taught as well. Especially with abstract problems. This is why I always tell my students to work with the class notes near by, to begin by writing down the definitions, etc. and then see what exactly you have to do.

Back to the website. Depending on whether or not I can feel confident in my ability to assess the OP's difficulty, I might post a hint suggesting to verify the definitions with or without an additional hint as to how to proceed. If I'm less certain about how much the OP understands I might just leave a comment.

Sometimes, however, when I have the time and energy, I might write a longer answer showing how to verify the definitions and so on. You know, the sort of thing that in order to "copy-paste the answer" you'd have to work in order to extract a submittable answer, so you end up writing your own.

Of course it can be expected that other people have asked the OP in the comments what seems to be the issue, and this may affect the outcome. I could decide to vote to close, or I could better understand the difficulties of the OP.

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    $\begingroup$ And that's how I improve my teaching abilities with the help of MSE. $\endgroup$ – Asaf Karagila Oct 28 '14 at 4:13
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    $\begingroup$ I would at least sugest the OP of the question to name his sources, some OP's seem to think there is only one book on a certain subject and symbols always mean what their book says they mean. , haven given them time to write down the definitiuons, sometimes the light of knowledge starts to glow and no other action of us is needed :) $\endgroup$ – Willemien Oct 28 '14 at 9:41
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This idea is emphatically not new. And has been repeated. This is why sometimes questions are closed as off-topic with the reason "Missing context": the prompt specifically directs the OP to visit the second link above to find out how to improve the question.

Its success, however, is debatable.

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I (like Asaf, it seems) try to base my behaviour on the site the way I teach in classrooms - this can be more or less straightforward depending on the situation.

One thing I stress in my classes is that it is a standard situation to be given a problem and not know where to begin, and I encourage students to tell me when this is the case. So I certainly don't want to discourage these kinds of questions on the site. However, rather than simply stating the problem, the question should ask specifically for help getting started, and the answers should provide this kick-start, rather than a complete solution. (I still maintain, although I know some other users disagree, that in most cases where the question is about an exercise from a book or a class, that the asker will learn more from answers that leave them something to do.) I guess I can't avoid talking about the "no-context" controversy, so I'll mention it briefly - I'm in favour of this close reason existing, and use it, but my requirements for context are fairly minimal, and can be met by the OP merely saying how much of the problem they could do before they got stuck, even if it was nothing.

Usually the first thing I ask in this situation, as you suggest, is whether the student knows the definitions - so I also tend to do this in a comment on the site. This also helps to establish the conventions being used in the asker's book/course (which one of several equivalent definitions are being used as a starting point, do rings have units, etc.) and adds more context to the question.

Once the definitions are established, I would usually give a hint on how to get started, and nothing more, so that the student has a chance to try something out and see if the problem clicks for them - they are always invited to come back to me for more help if they need it. This is a little harder to do on MSE, and can occasionally result in long threads of comments with the OP getting increasingly confused - particularly if my hint wasn't as good as I thought, as sometimes happens - but usually I think it works well.

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