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It is fairly common for someone to post a question with an easy-to-fix notational error, for example, writing an integral and forgetting to put $dx$ at the end. Some users will just edit the post and fix the notation, but others seem to prefer commenting something like, "I don't understand what you've written. Is there meant to be a $dx$ at then end of that integral?"

This strikes me as disingenuous and rude. The user commenting this way almost certainly does know what the OP means, and what they're really trying to say is, "hey, you forgot part of the notation." I understand that this particular form of disingenuousness is common enough in the mathematical community - certain teachers like to use it - but is it fair to say that it does not create the type of atmosphere we wish to maintain at a site such as this?

Thanks in advance for your thoughts on this matter.

EDIT: It's apparent this question has produced a good deal of misunderstanding. I'm not asking how to respond to a commenter who I think is "playing dumb". I'm not asking if, or suggesting that, I can distinguish it from honest questioning. I'm asking whether doing it is a good idea. Is it helpful, or does it do more harm than good? I know that it happens sometimes, and I wonder if it is sound pedagogy.

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    $\begingroup$ If you're eager to guess what an OP means, where's the problem? I find it rude if an OP lets me guess. Tastes are different, obviously. $\endgroup$ – Professor Vector Aug 30 '17 at 18:22
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    $\begingroup$ Simply sliding in and making a quick edit to include $dx$ when an integral sign is used, and disappearing may go unnoticed by the OP. I'd make such an edit, but also post a comment: "Don't forget to include $dx$ whenever you write an integral." I make such an explicit comment because on a text, an asker might integrate successfully a difficult integral, but $dx$ is missing, or in the case of an indefinite integral, $+C$ is missing, and that could undermine a user's test score for such errors. $\endgroup$ – Namaste Aug 30 '17 at 18:59
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    $\begingroup$ This comment seems to be based on a strange misunderstanding of my original question. Not sure what to say. $\endgroup$ – G Tony Jacobs Aug 30 '17 at 19:20
  • $\begingroup$ @amWhy, I was not referring to your comment in mine. Your comment makes perfect sense to me. $\endgroup$ – G Tony Jacobs Aug 30 '17 at 19:51
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    $\begingroup$ I really enjoy these ambiguous things$$\int_0^1t^x$$Option choices are $(t-1)\ln(t)$ or $\frac1{x+1}$. Please choose one $\ddot\smile$ $\endgroup$ – Simply Beautiful Art Aug 30 '17 at 19:52
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    $\begingroup$ GTonyJacobs No worries; I was really suggesting a better way commenting & editing, than the one you speak of, on which I agree with your concern. I agree, some users can be pretty "snarky" in their comments. $\endgroup$ – Namaste Aug 30 '17 at 19:55
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    $\begingroup$ Questions that are actually ambiguous are another matter, one I was not attempting to address with this question. $\endgroup$ – G Tony Jacobs Aug 30 '17 at 19:57
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    $\begingroup$ I think this is a particular type of snark that is peculiar to math education. I imagine it has its defenders; it is certainly common enough. I wonder if we'll hear from them. $\endgroup$ – G Tony Jacobs Aug 30 '17 at 19:59
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    $\begingroup$ @SimplyBeautifulArt: The answer is obviously $t^x$, since I'm integrating with respect to a third and independent variable $y$. :) I suspect you could get anything at all if you choose $y$ dependent on $t$ and $x$ in a clever way! $\endgroup$ – Hurkyl Aug 30 '17 at 23:20
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    $\begingroup$ One may also ask how to evaluate ∫<sub>0</sub><sup>1</sup>t<sup>x</sup>e<sup>-t</sup>dt, but the trailing part was lost during cut-and-paste and then someone familiar with MathJax edited the truncated expression to $\int_0^1 t^x$. Things like this occur from time to time. They don't occur frequently, but they are not rare either. I don't think it's fair to assume that the commenter was playing dumb. $\endgroup$ – user1551 Aug 31 '17 at 3:48
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    $\begingroup$ I'm not talking about assuming the commenter is playing dumb. I'm asking whether the commenter ever should play dumb. Is it a valid pedagogical tool, or does it do more harm than good? $\endgroup$ – G Tony Jacobs Aug 31 '17 at 3:57
  • $\begingroup$ To fully 'play dump' is IMO usually not a good idea for this site; but IMO the example you give does not fully 'play dump' as it give a clear indication of what commenter thinks the problem is. Would it be only the first sentence I'd say it is unhelpful. Whether "I don't understand what you've written. Is there meant to be a dx at then end of that integral?" or "hey, you forgot part of the notation." goes over better is a matter of personal taste. Personally I'd find the 'hey' a bit odd for example. $\endgroup$ – quid Aug 31 '17 at 18:51
  • $\begingroup$ I think it's clear that my example wasn't optimal to illustrate my question. :/ $\endgroup$ – G Tony Jacobs Aug 31 '17 at 18:54
  • $\begingroup$ I apologize: I wasn't aware at the time (before your edit) that you are speaking of "pedagogy" (rough translation from Greek: to guide children). People will be grateful to know how you see them, but I'm not interested, I'm a mathematician. If somebody gives me three ambiguous terms of a series and expects I should guess the general form and give them the sum in closed form, I find that rude, and I may tell that person, with or without your permission. Playing dumb I leave to others (and not all are just playing). $\endgroup$ – Professor Vector Aug 31 '17 at 19:16
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    $\begingroup$ @ProfessorVector, I have no idea why you're commenting here. Nothing you've written has been relevant or helpful. Your allusion to my "permission" is bizarre, and the example you cite is utterly irrelevant to this discussion. Your etymological "reasoning" is beneath anyone who would call himself or herself a mathematician. Why you feel the need to "contribute" to this discussion is utterly unclear. $\endgroup$ – G Tony Jacobs Aug 31 '17 at 19:28
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Having been on the Internet a while now, I know that no matter how genuinely confused I am, and no matter how politely I try to phrase my question, there can still be someone who thinks I am just trying to be a jerk. Wikipedia has a policy, not observed as universally as it should be, that one should assume that others are acting in good faith. I think this is a good policy, not just on Internet message boards but in life.

Here is one of many examples. The querent had used the symbol ≤ to compare two groups. I asked for clarification:

What do you mean by ≤ here? Does that mean that (group A) is a subgroup of (group B)?

I would have been very unhappy if the reply had been some variation on “of course it means that, stop being an ass”. (It wasn't; the reply was flawless: “Yes, that is what I meant”.)

Even if I had intended to be an ass, nothing would be gained from a rude or defensive response. Simply replying “Yes, that is what I meant”, as the querent did, is always superior. This was a successful interaction. I think we both got it right.

Summary: On the Internet, it can be hard to tell sometimes if people are trying to be jerks. Sometimes they are trying to be jerks. But it is nevertheless better to act, as much as possible, as though they are not. Haters gonna hate; we don't have to let them bring everyone else down too.

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    $\begingroup$ From the Be nice policy: "Be welcoming, be patient, and assume good intentions." $\endgroup$ – Simply Beautiful Art Aug 30 '17 at 19:48
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    $\begingroup$ Yes. But also, even if you suspect the intentions might be bad, it is often best to behave as if you thought they were good. Because, if you were mistaken, and they really were good, it is obviously better, and even if your suspicions were correct and the intentions were bad, at least only one person is acting like a jerk. $\endgroup$ – MJD Aug 30 '17 at 19:52
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    $\begingroup$ I am aware of the "assume good faith" principle, and have argued for it voluminously on Wikipedia. Unfortunately, that's not what I was asking about here. $\endgroup$ – G Tony Jacobs Aug 30 '17 at 20:00
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    $\begingroup$ Having now reread your question, I still think my answer addresses it directly. $\endgroup$ – MJD Aug 30 '17 at 20:02
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    $\begingroup$ Then it's apparent that I need to clarify my original question. $\endgroup$ – G Tony Jacobs Aug 30 '17 at 20:05
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    $\begingroup$ There's a difference between, "how should we respond to behavior X?", and on the other hand, "is behavior X considered helpful?" I am in complete agreement with you about the answer to the first question; I was asking the second one. $\endgroup$ – G Tony Jacobs Aug 30 '17 at 20:09
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    $\begingroup$ And my point is that neither you nor anyone else can be sure of recognizing behavior X when you see it, so there is little factual basis for any opinions about the behavior. $\endgroup$ – MJD Aug 30 '17 at 20:33
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    $\begingroup$ I'm not claiming I can be sure of recognizing it. I'm addressing the prior question, of whether one should engage in it in the first place. Maybe this behavior is good and helpful, and I should incorporate it into my technique? There are people who will cheerfully admit to doing it, and defend it, so there's no need to engage in forensics to recognize it in this context. You may find the behavior unhelpful, but that's not a universally shared view. $\endgroup$ – G Tony Jacobs Aug 30 '17 at 21:25
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    $\begingroup$ It's not about recognizing it. I was trying, with this question, to generate a conversation about the pros and cons of "playing dumb" as a pedagogical technique. $\endgroup$ – G Tony Jacobs Aug 30 '17 at 21:26
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I'd say it's completely down to the particular tone the user uses. Using "playing dumb" to point out user mistakes, on its own, is not bad in my opinion.

I think, so long as it isn't taken to the extreme of making fun of the OP, this is a good way to teach the OP to be exact when using mathematical language. Often, if a user learns how to properly use mathematical language, he has learnt a much more valuable lesson than just how to solve some particular integral - and after all, this site is here to help people be better at math moreso than solving their homework. Naturally, if the OP then edits and improves his question, the answer must either be deleted or edited - if not, it certainly is un-helpful.

I think it is related to providing "technically correct" answers, such as if a user asks "Prove there is no number $x$ such that $x^2=2$", and the first answer will be "We cannot prove that, because $x=\sqrt{2}$ solves that equation".


TL;DR:

No, I don't think the practice is bad in itself, however overdoing it can prove unhelpful. Going overboard and doing it when someone forgets a $dx$ is taking it too far, but that doesn't mean the whole concept is bad.

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    $\begingroup$ "Naturally, if the OP then edits and improves his question, the answer must either be deleted or edited - if not, it certainly is un-helpful." There is a problem there, because in general it is frowned upon to edit a question in such a way that it invalidates existing answer posts. It is thus better not to give actual answers to questions that one believes to be misstated (a comment is fine though). Except maybe if one also anticipates the correction. $\endgroup$ – quid Aug 30 '17 at 16:35
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    $\begingroup$ I prefer TL;DR to be up front, so I don't read the entire thing before getting to it. $\endgroup$ – Simply Beautiful Art Aug 30 '17 at 19:45
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    $\begingroup$ In the spirit of @quid's comment, I agree that questions or suggestions about clarifying the questions are better placed in comments than in answers. $\endgroup$ – G Tony Jacobs Aug 30 '17 at 21:32
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    $\begingroup$ @GTonyJacobs true but a long winded hint on specific cases can exceed the 599 character limit of a comment so without making multiple comments sometimes there may be no other easy options as well. $\endgroup$ – user451844 Aug 31 '17 at 1:59
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    $\begingroup$ I have never tried to leave a hint that exceeded 599 characters. One for the bucket list, eh? $\endgroup$ – G Tony Jacobs Aug 31 '17 at 4:56
  • $\begingroup$ @GTonyJacobs Hyperlinks are pretty long $\endgroup$ – Simply Beautiful Art Sep 12 '17 at 21:43
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Sometimes these things can be borderline as written, and it's necessary to ask for clarification. Because of the differences in our backgrounds, something like "Is there meant to be a $dx$ at then end of that integral?" could be intended in all good faith.

But also much hinges on presentation. Text on the internet is, in general, a notoriously ambiguous mode of communication.

As a matter of courtesy, one should try to soften such corrections. Actually, I don't think the example you gave is so very bad. It's certainly within the limits of slack which you cut people you don't know very well.

On the other hand, I have seen things where posters, who should have known better, have said things along the lines of "Your question about conditions on a set $X$ to be a group is utterly wrong because what if $X=\emptyset$?" when there was, in all likelihood, an innocent omission on the poster's part. That sort of obtuse comment is counterproductive, but it could be presented in a better way.

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    $\begingroup$ Just recently there was a question about the topological properties of a certain subset of $\Bbb R$, which neglected to specify the topology. Someone who should have known better posted a completely po-faced reply about the properties of the set in the discrete topology. I was happy to see this deliberately unhelpful answer downvoted into oblivion. $\endgroup$ – MJD Aug 30 '17 at 18:15
  • $\begingroup$ @MJD Exactly${}{}{}$ $\endgroup$ – rschwieb Aug 30 '17 at 18:29
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    $\begingroup$ I remember that question, about whether $(0,1)$ and $[0,1]$ were homeomorphic. Doing that stuff about the discrete topology is fine, if you also talk about why specifying the topology is important, and answer the question from the perspective of the usual topology on $\mathbb{R}$ as well. $\endgroup$ – G Tony Jacobs Aug 31 '17 at 14:45
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"Playing dumb", as you put it, is a principal and important method of teaching, not restricted to mathematics. I've found it works well when used correctly. I use it in my office hours, and I use it on math.stackexchange.

The situation where it applies is where a little error signifies to me a principle point of misunderstanding. In such a situation, I ask a simple question about the format or meaning of the original question, either to the student in my office hours or in a comment/answer here on math.stackexchange. My intent is to force the asker to ponder what they actually meant to ask, and sometimes this is all that it takes for them to reach understanding.

Now, this can be hard to judge, and sometimes it doesn't work. But often it does, as is proved on math.stackexchange when various answerers miss the point and post answers which go over the OP's head, whereas I "play dumb" and my comment/answer hits the point.

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    $\begingroup$ This is the kind of answer I was hoping for, even though I don't, a priori, agree with you. I asked this question to challenge my own preconceived notions. Can you please cite an example, preferably from Stack Exchange, where this strategy is used correctly and effectively? My personal experience with it has been negative, so that's why I ask. $\endgroup$ – G Tony Jacobs Sep 1 '17 at 15:03
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    $\begingroup$ I'll try to find one, though I admit that it doesn't come up often and it may be hard to find. $\endgroup$ – Lee Mosher Sep 1 '17 at 15:04
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I have very frequently added the $dx$ and done similar things. If I were to see $\displaystyle \int f(x,y)$ then I might ask whether that was intended to be $\displaystyle \int f(x,y) \, dx$ or $\displaystyle \int f(x,y)\, dy.$

There are actual cases where I don't know what is meant and I ask. If someone asks what is intended I would not start from the assumption that it's sarcasm. Once on Wikipedia someone said they objected to the existence of a certain Wikipedia article on the grounds that a mathematical equation should not be the subject of a Wikipedia article unless it's an earth-shaking new discovery. I expressed some objection to that position and he allowed that I had a point, but then added: "but you know what I meant." I didn't know what he meant. Further discussion revealed that he thought it was obvious that a mathematical equation should not be the topic of a Wikipedia article, and he assumed that would be obvious to me, and that he didn't know what an "equation" is. It would have been easy for me to think he was being sarcastic, and maybe he thought I was being sarcastic. Sometimes someone who claims not to understand what you meant does not understand what you meant.

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  • $\begingroup$ Michael, I remember you from Wikipedia. Are you still active there? I was GTBacchus. I hear what you're saying here, but I think I can generally tell the difference between genuine requests for clarification and this particular rhetorical technique. In any event, my question is about the rhetorical technique, not about honest questions. $\endgroup$ – G Tony Jacobs Aug 30 '17 at 14:59
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    $\begingroup$ "Sometimes someone who claims not to understand what you meant does not understand what you meant." You mean sometimes, people actually mean what they say?! This is mind blowing, we have to tell the world! $\endgroup$ – 5xum Aug 30 '17 at 14:59
  • $\begingroup$ I'm not sure how I came across as assuming all requests for clarification are sarcasm. I don't assume that at all. $\endgroup$ – G Tony Jacobs Aug 30 '17 at 15:00
  • $\begingroup$ @GTonyJacobs : I didn't think you thought that ALL such requests are sarcasm. $\endgroup$ – Michael Hardy Aug 30 '17 at 17:00
  • $\begingroup$ @GTonyJacobs : I still frequently edit Wikipedia articles but no longer often create new ones. $\endgroup$ – Michael Hardy Aug 30 '17 at 17:01
  • $\begingroup$ I don't think I phrased my initial question as well as I could have. I knew at the outset that many requests for clarification are simply that. I was trying to ask about a very specific rhetorical technique that many mathematicians use. I call it, "playing dumb". The answers I'm getting pointing out that sometimes requests for clarification are simply that indicates that I didn't phrase my question well. $\endgroup$ – G Tony Jacobs Aug 30 '17 at 17:03
  • $\begingroup$ @GTonyJacobs, even after reading your comments, I still don't know what you meant by "playing dumb" if you don't mean "requesting clarification when a question is ambiguously phrased and unclear." I suppose you will think that I'm playing dumb, though. $\endgroup$ – Wildcard Sep 6 '17 at 1:13
  • $\begingroup$ No, I don't think that. I mean situations where a commenter points out an error in notation, not by saying, "I think you mean X", nor by asking, "do you mean X", but by pretending to be confused or misled when they're really not. The OP means Y, but types X. The commenter knows what they meant, but just responds to X anyway, without letting on that they suspect an error. That's what I'm talking about. Some people do that, on purpose. $\endgroup$ – G Tony Jacobs Sep 6 '17 at 1:28
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I think some principles apply:

  1. It's incumbent on people seeking help to make their questions clear

  2. Careful use of notation is very important in mathematical questions. Sometimes even tiny changes can radically alter what is being asked.

  3. We have a role not just in answering questions but in helping people learn and understand, and in being able to ask better, more precise (well-formulated) questions.

  4. A better formulated question is often more readily answered by the asker. Numerous times I have been preparing to ask a question and have found that proper preparation in asking the question (care over notation and definitions, clearer expression of the issue etc) has quite a few times led to me answering it myself. Helping people improve their ability to do this -- to formulate questions properly, with all the benefits that brings -- is crucial to helping them get better, faster answers and with their own development as users of mathematics. That is, helping people to arrive at better questions is definitely part of helping them.

  5. There are numerous aspects of doing that; part of it will be editing (at least if it's obvious what the intent is), part will be commenting to explain the issue. Part of it can include "playing dumb" in that comment, as long as it's not done in a rude way - it's a form of instruction with a long history and is at least sometimes quite effective. It does, for example, make it clearer that the responsibility for the question is their own - they should not post any old nonsense and expect others to do all the lifting to make it work as a question.

So I think playing dumb - at least in some situations - is fine, as long as we keep in mind the point: firstly to help the user end up with a good question and secondly to help them write better questions in the future. If it's doing that without putting posters off, I think it's completely fine.

In terms of the original question, it's disingenuous by the ordinary dictionary definition of the word ("not candid or sincere, typically by pretending that one knows less about something than one really does") but I don't think it's automatically rude.

Sometimes it's actually useful to approach it that way because sometimes at least what it seems the user is asking is not what they actually wanted to ask, and presuming you know less than you think you do may - in some cases - be more accurate, and perhaps less rude.

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    $\begingroup$ This is a great answer. Too bad it's also a late answer, and so isn't likely to get the attention it deserves. $\endgroup$ – Wildcard Sep 6 '17 at 1:16
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    $\begingroup$ @Wildcard :-/ I want a bounty on meta. $\endgroup$ – Simply Beautiful Art Sep 12 '17 at 21:47
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In math, I know that there is a lot that I don't know. If I make an assumption about something, I could very well be wrong.

For example, I think I understand the basics of calculus, but I'm not secure enough in that knowledge to teach it to someone else nor even to correctly guess what is meant when something is omitted.

In your integral example, I wouldn't be sure whether $dx$ or $dt$ is meant. Without Michael Hardy's answer, I wouldn't have even thought of $dy$ as a possibility.

For basic arithmetic, I might be more confident if I think the asker is unaware of operator precedence, but I still would not assume that someone who writes a - b/c meant (a - b)/c.

On the other hand, I think it would really be playing dumb if I were to say I honestly think $$\prod_{i = 1}^n 1 - \frac{1}{p_i}$$ could possibly mean $$\left(\prod_{i = 1}^n 1\right) - \frac{1}{p_i}.$$

Although of course coming from someone else that could be a genuinely sincere query that is misunderstood as sarcastic.

Maybe instead of saying "I don't understand X" it would be better to say "I think you meant to write Y rather than X." Then hopefully the response is either "I really did mean X" or "You're right, I'll change it accordingly," not "What the hell is your problem?"

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    $\begingroup$ I'm really beginning to regret how I phrased this question. In my example, there was not meant to be a $t$ anywhere in sight. The point was to ask whether intentionally playing dumb, when you really do know what they meant, is more helpful or more harmful. A couple of people have answered saying that they think it's a good strategy. I wanted to know why. Personally, I agree with you that, "I think you meant Y rather than X, is that right?", is almost universally better. $\endgroup$ – G Tony Jacobs Sep 2 '17 at 22:24
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    $\begingroup$ I would say harmful. In the black and white of text, there are few cues to distinguish the helpful teacher from the jerk. $\endgroup$ – Robert Soupe Sep 2 '17 at 23:06
  • $\begingroup$ "...I might be more confident if I think the asker is unaware of operator precedence, but I still would not assume that someone who writes a - b/c meant (a - b)/c." - good grief, and just when I was starting to see that "90% of people will get this arithmetic question wrong" stupidity again in a number of other places. :o $\endgroup$ – J. M. is a poor mathematician Sep 3 '17 at 5:04
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Some people are not comfortable telling directly to others they are wrong. It can be because they are afraid to sound rude. Or simply because there is still a small possibility of they are the one that are wrong and are don't want to loose face. Then, "playing dumb" is not a snarky way to dismiss the OP and point out an obvious mistake, but a polite way to speak and a form of etiquette.

A real-life example: A highly reputed Japanese professor told me about his PhD student in that way: "He is really brilliant and very passionate. In life, he will always respect me and stay polite, but when we do maths together, he has no hesitation telling me directly when I am wrong".

A SE example: on another SE site about language with many non-native English users, someone answered one of my question starting by "I was trolling on the web to find an answer..." and I commented something like "There is probably a typo. You meant strolling I think". It appeared that I was wrong and the use of to troll here was correct. I would have felt embarassed if I had made a more direct comment like "Hey, you meant strolling on the web"

My opinion is that we should not think too much about people playing dumb. Most of the time, the OP will get the content of the comment, understand (s)he is wrong and correct the question. Or someone else will do it.

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  • $\begingroup$ Yeah, this question was not intended to be about others playing dumb. This question was intended to be about whether or not I should do it. Is it a good way to teach? Totally different thrust, you know? $\endgroup$ – G Tony Jacobs Sep 13 '17 at 3:19
  • $\begingroup$ Ah sorry, I understood the question as "Shall we do it or not?" as a collective. I would suggest to always give the other the benefit of the doubt and "playing dumb" a little will not hurt you and may make the other person more comfortable. $\endgroup$ – Taladris Sep 13 '17 at 3:31
  • $\begingroup$ In my experience as a student, it has made me more uncomfortable, but I wonder if that's just me, or just the way that teacher did it. Interesting. $\endgroup$ – G Tony Jacobs Sep 13 '17 at 3:32
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    $\begingroup$ I guess it is a problem of degree, personal taste and culture (starting a comment by "hey" sounds rude to my French ears). I tend to play dumb in my first comment, and become more direct afterwards if I feel it necessary. $\endgroup$ – Taladris Sep 13 '17 at 3:37

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