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Some questions are so ill-defined that one has no idea what the questioner is asking, and it is reasonable to close such questions. In other cases, although the question is ill-defined, it reveals a muddle or misconception in the questioner's mind that can potentially be put right by careful explanation. In two recent cases, the question was of this latter type, and it was clear that the OP, although confused, was genuinely trying to resolve an imagined contradiction. I think that my answer, on each occasion, was a reasonable attempt to resolve the muddle. So it was disappointing to see that the questions were closed because "it isn't clear what you are asking". Of course the questions were not clear; what was clear was the misconception underlying them.

There is more to teaching mathematics than solving well-defined problems. Sometimes what is needed is to dissolve false assumptions and wrongly conceived ideas. We should not smack down people who are genuinely trying to understand just because their presentation is, necessarily from their inadequate state of knowledge, confused.

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    $\begingroup$ I looked at one of those questions. Personally I find the answers rather might augment the confusion. I would answer something quite different in style. This shows, the site is not well suited for this. There is no doubt that there is more to teaching mathematics than well-defined problems. But this site is still for well-defined problems. It is not that end all and be all of teaching mathematics. It cannot be this. Over-stretching it is harmful. $\endgroup$ – quid Nov 13 '15 at 22:58
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    $\begingroup$ In specific instances when this happens, you should feel free to post the question to this thread to help get it reopened. $\endgroup$ – Eric Wofsey Nov 13 '15 at 22:59
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    $\begingroup$ Could you provide examples of what sort of questions you're addressing? $\endgroup$ – Milo Brandt Nov 13 '15 at 23:35
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    $\begingroup$ @quid: On the webpage describing what this site is for, the first listed item that the user is invited to ask about is "understanding mathematical concepts". The style of answers will always vary; it is up to the OP to pick the one that is most helpful. Perhaps your answer would best have resolved the OP's confusion. IMHO, it may be more useful to clear up a misconception than to supply the details of a calculation that the OP cannot do. $\endgroup$ – John Bentin Nov 13 '15 at 23:47
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    $\begingroup$ Yes, I agree, that conceptual questions can be better than computational ones. I still feel the sin(1/x) question is rather too vague. It would be good if OP included a bit more information what they understand and do not understand around the general matter. For example, do they understand that/why |x| is not diff'able at 0, do they not know any non diff'able function. Etc. The question is on hold, so that it can be improved. The right way to 'consider "unclear" questions' is to help clarify them, not to add answers until one fits. $\endgroup$ – quid Nov 13 '15 at 23:59
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    $\begingroup$ A problem with sin(1/x) qis not OP's math confusion, but the question is "lazy" and thus unclear. "I've read in textbooks that sin(1/x) can't be differentiated because it oscillates too rapidly,[...]" No matter how confused about differentiability they ought to be able to give the textbooks and/or an exact reference or quote. Chances are it did not really say just this, or not even this at all (indeed sin(1/x) is a peculiar example for a non-differentiable funct). Just rereading what it actually says might clear up the matter, and if not will result in a more clear question. $\endgroup$ – quid Nov 14 '15 at 9:40
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    $\begingroup$ People who vote to close a question as "unclear" ought to first ask themselves whether the question might conceivably be more clear to someone with a different background. I answer a lot of questions about the mathematics of computer graphics. This is a fairly narrow niche, and is probably not familiar to the average math prof. In numerous cases, I see questions in this area branded as "unclear" when I'm pretty sure what they're asking. Annoying. $\endgroup$ – bubba Nov 15 '15 at 3:17
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    $\begingroup$ @JerryGuern I don't know that it is fair to describe people who do this as "trolls". The question should be clarified, either by the poster, or as an edit if it is 100% obvious what it should say. The question and answer are taken as a pair when deciding how to vote, so if you have to make big assumptions in order to make the question "answerable", it is not a good answer to the question that is posted. $\endgroup$ – Morgan Rodgers Nov 15 '15 at 7:45
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    $\begingroup$ @MorganRodgers So you're saying that if some student didn't know enough to specify EVERYTHING that should have been specified, we should refuse to attempt to help? And if we make some reasonable assumptions about student-level problems so we can help, we should be down-voted and lose reputation points? I don't buy that. There's no good reason to down-vote a helpful answer to a poorly-asked question, particularly when doing so gets the helpful answer deleted. $\endgroup$ – Jerry Guern Nov 15 '15 at 9:19
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    $\begingroup$ @JerryGuern No, I'm saying we should engage them in the comments to clarify what they are asking, and get those changes edited into the actual question so that the pairing of the question/answer makes sense. Reputation points are minor. It's not about taking away your reputation, it's about downvoting answers that are not likely to be useful to the community at large. And of course, sometimes the point is for the low-valued question/answer pair to be deleted, if it cannot be edited or clarified to be of value. $\endgroup$ – Morgan Rodgers Nov 15 '15 at 9:48
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    $\begingroup$ As a teacher/tutor of many years, my inclination is to help, not nitpick. If I refused help until students asked their questions with perfect clarity, we'd never get anywhere and they'd never learn anything. Math SE exists so people can get help. $\endgroup$ – Jerry Guern Nov 15 '15 at 11:39
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    $\begingroup$ @JerryGuern Sorry to be blunt. But your answers there were quite poor. You might consider that you were a bit out of your depth there. The down-votes were justified and it is a good thing those answers are deleted. Trying to help, is not always helping. $\endgroup$ – quid Nov 15 '15 at 13:47
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    $\begingroup$ @BrianM.Scott you might be annoyed by this somewhat less often when you start taking into account that for some "clear" and "I guess I know what is meant" are not the same. It annoys me when some users blur this distinction, especially when they do so with an attitude of superiority, implying that due to their expertise they understand the question while others do not. Indeed, sometimes it might just be the other way round, if all one knows is a hammer etc. $\endgroup$ – quid Nov 15 '15 at 14:02
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    $\begingroup$ @quid: I might add that clear versus I guess I know what is meant is far from being a binary distinction. $\endgroup$ – Brian M. Scott Nov 15 '15 at 21:02
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    $\begingroup$ " There is more to teaching mathematics than solving well-defined problems. " Amen. $\endgroup$ – nilo de roock Nov 21 '15 at 12:55
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Who's to say that closing as "unclear what you're asking" isn't educational? Even if it's a bit...harsh, sometimes the message of "this is nonsensical" is important and educational. One of the biggest issues in learning mathematics is learning how to think precisely and clearly. It is easy to adopt "not even wrong" ideas at first, and sometimes it is necessary to correct this.

"On hold" isn't the worst thing that can happen to a question. Once the asker realizes that their question is nonsensical, and tries to reformulate it in an answerable way, it is not hard to take if "off hold".

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    $\begingroup$ I think that it is more helpful to say "The way to understand this is ..." than "You are confused; come back when you are not confused". $\endgroup$ – John Bentin Nov 14 '15 at 8:46
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    $\begingroup$ I agree. In the specific case linked it is mainly about "this is not precise and detailed enough." (not really nonsensical) OP scribbles a half-remembered sentence as something it says in textbooks. They should give the textbooks and an exact quote. (Or, not make claims about what it supposedly says in textbooks.) $\endgroup$ – quid Nov 14 '15 at 9:47
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    $\begingroup$ Are we supposed to answer people's confusion on questions or just answer their question? It is ok to put on hold questions that demonstrate no effort on the part of the OP, but how is it helpful to just not answer a question if it is a valid point of confusion? I feel like this question is asking how to control "Tumble Weeds" in some sense, and not to just write off the generic OP as not being clear enough. $\endgroup$ – theREALyumdub Nov 14 '15 at 15:10
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When a question is tagged for deletion, we are given a list of reasons from which to choose to explain why it should be deleted. I think that, sometimes, we choose the unclear option because there is no "I think that this question indicates a lack of understanding so deep that there is no way I can help this person out" button.

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    $\begingroup$ While putting on hold/closure can lead to deletion it is not a necessity. The expressions "tagged for deletion" and "choose to explain why it should be deleted" thus could be confusing, especially as there actually is a separate process to delete question that however does not involve giving a reason. $\endgroup$ – quid Nov 14 '15 at 17:46
  • $\begingroup$ It looks as though the OP for the "sin(1/x)" question is turning out to be like that. $\endgroup$ – John Bentin Nov 14 '15 at 18:01
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    $\begingroup$ @JohnBentin it is never to late to vote to close :-) $\endgroup$ – quid Nov 14 '15 at 20:57
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    $\begingroup$ "I think that this question indicates a lack of understanding so deep that there is no way I can help this person out." In that case, I feel like it might often be good to leave the question open in case someone else feels they can help the person out. Voting to close makes it harder for someone else to have the chance to help. $\endgroup$ – Mark S. Nov 26 '15 at 18:05
  • $\begingroup$ @MarkS. Of course you are right. I stand corrected. $\endgroup$ – steven gregory Dec 29 '15 at 2:00
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I totally agree with John Bentin. More precisely,

  1. An analysis as to what are the cost-benefit of censorship on stack exchange might be interesting: Deleting an unclear question might make it easier to search but certainly discourages people from asking questions, particularly first time askers. Improving such search engine as there might be would seem to be a better alternative inasmuch as, whether clear or unclear, a question always proceeds from a need or desire to understand.
  2. Given that even perfectly clear questions are often misread, the grounds on which a question is closed are not always … clear. (E.g. compare the first sentences in the OP and in the avid19 answer.)

  3. More generally, censorship is always dangerous, if only because power corrupts even censors. If only for that reason, I have never accepted to censor anybody, not even my own students.

Obviously, I am a first amendment absolutist.

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    $\begingroup$ You seem to have a very strange definition of "censorship" $\endgroup$ – mrf Nov 18 '15 at 15:52
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    $\begingroup$ @mrf he didn't read the PSA $\endgroup$ – Braiam Nov 19 '15 at 2:02
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    $\begingroup$ I have no idea where first amendment is coming into this. This is a private website that can do whatever they want. They can remove your posts solely because they don't like you and it won't be "censorship". $\endgroup$ – user223391 Nov 27 '15 at 8:05

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