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Consider three examples currently visible on the active questions page:

I use these questions as references, but I have no thoughts to share here about my own personal beliefs on them specifically. Instead, what I wish to ask is the following:

Question: If an MESE user posts a site-appropriate question about how to achieve something, then is it appropriate to respond with a justified-post about why one believes doing this particular thing is inadvisable?

On the one hand, stating why not for a how to post simply does not constitute an answer to the question; on the other hand, I am sure that we do not want to promote poor practices in mathematics education (in fact, I would go so far as to say such behavior is antithetical to the goal of this site).

My view is that the latter point is more important than the former, so that a response of this nature ("don't do XYZ, because ABC") would be both appropriate and desirable. But I readily concede that I may be missing subtleties in this matter, and have tagged this meta-question with discussion in the hope that it can be discussed.

More generally: What is the appropriate response to a how to XYZ question when one feels XYZ is a bad idea? Some options (which I neither declare to be "good" nor complete) are:

  1. Down-voting the post, and adding a comment explaining why.

  2. Adding a comment stating briefly why one feels this is a bad idea, and asking the OP for further justification as to why such a practice would be advisable.

  3. Posting an answer that says XYZ is a bad idea because of reasons ABC.

  4. Posting an answer that attempts to explain the how to, but including a disclaimer as to why this might be inadvisable in practice.

  5. Only posting if one has something concrete with regard to how XYZ could actually be achieved.

  6. "Your goal seems to involve PQR, which I prefer to XYZ, and you may get to PQR by trying ABC."

Discussion of related questions would be welcomed as well, e.g., surrounding votes/comments on others' answers for posts of this ilk.

Expanding momentarily on my comment above:

I am sure that we do not want to promote poor practices in mathematics education (in fact, I would go so far as to say such behavior is antithetical to the goal of this site).

I think that this must not be applied only to questions, but also to answers. In particular, I mention this answer (cf. my comments there) as an example in which I would argue it is not only enough to down-vote the post, but that the post should be removed (I flagged it for deletion, but the moderator opted instead to comment). From my perspective, an answer that promotes poor practices pedagogically may be commented on, questioned, even down-voted if necessary; but one that suggests e.g. sexual misconduct has no place on a site for educators of any sort.

Image anonymized and preserved for posterity:

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    $\begingroup$ This is an important point. Thank you for raising it. $\endgroup$ – quid♦ Jun 25 '14 at 11:53
  • $\begingroup$ I'm quite against doing (a) and (b). But (c) is a quite reasonable endeavour, which is (unfortunately) hard to push forward. $\endgroup$ – vonbrand Jun 30 '14 at 1:37
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    $\begingroup$ @vonbrand It seems that you are responding to the reference examples, rather than discussing the actual question/topic. Or perhaps I have misunderstood your comment? $\endgroup$ – Benjamin Dickman Jul 2 '14 at 8:24
  • $\begingroup$ Perhaps I should have said something along the lines of "Don't even think to do that" on (a) and (b), while (c) would be "interesting idea, hard to do". And yes, I'd answer that way (and I believe I did). $\endgroup$ – vonbrand Jul 6 '14 at 20:03
  • $\begingroup$ @quid Feel free to create a separate meta post (and use anything from here, e.g., the anonymized image) for community input. I agree that it is important to discuss precedent-setting activity on the meta site, and I stand firmly by my belief that a post encouraging e.g. sexual harassment/misconduct in the classroom should be subject to immediate deletion. (And possibly removal of the user, though this may be more circumstantial, e.g., if it was intended as a "joke" -- but I will not remark further in that direction here.) $\endgroup$ – Benjamin Dickman Aug 28 '14 at 21:28
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    $\begingroup$ By a self-deletion the specific problem seems resolved. It should be a good idea to discuss the general question "Under which circumstances should something be deleted?" I plan to start this in a couple of days. $\endgroup$ – quid♦ Aug 30 '14 at 13:59
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I prefer that posted answers be constructive.

So I have avoided answering questions a and b above, where my answer would be roughly "don't." I use techniques 1 and 2 instead, with negative comments as comments.

Another approach is:

$\;\;\;\;$6. Your goal seems to involve PQR, which I prefer to XYZ, and you may get to PQR by trying ABC.

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    $\begingroup$ First: I've added in your approach 6 to the main post. Second: One of the features of approach 2 is that it could be applied to a lot of questions. As an example (rhetorically here): "Why do you think it is a good idea to start a math circle in a small rural university town?" Perhaps this might seem like a hassle if applied to many questions -- but I think it would really strengthen queries if how to posters generally included in their questions some justification for why such-and-such is (potentially) a good idea. $\endgroup$ – Benjamin Dickman Jun 25 '14 at 19:23
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I'll second Matt F's idea that answers be as constructive as possible, and add some of my thoughts about your list of suggested responses.

  1. If you feel that strongly about the question, then I think downvoting is not proper. I'd only downvote a genuinely bad question, be it poorly-written or not really meant for this site or otherwise ill-formed. If it spurred you to come up with a response of some kind, then surely it's a good question, eh? Just cancel it all out and neither up- nor downvote.
  2. Adding a comment to prompt the OP into describing their motivation can be very effective. I suggest doing this first to allow the full context of the question to be properly understood. If it has already been done, or if OP does not provide more details, then proceed with other avenues.
  3. This feels a tad aggressive. I suggest only doing this in extreme cases where you truly don't have any further suggestions (e.g. "do PQR instead", "try doing it this way, but I recommend against it because of ABC") and feel quite strongly that the idea proposed is ill-advised. Be prepared, though, to see that other answers which do provide alternatives and further explanations have more upvotes than yours. I have not seen any questions posed on the site that have spurred in me a response of this form. And you can see that an example answer of this form has been surpassed by other, more thorough explanations.
  4. This feels like a great approach, depending on your knowledge of the situation. This approach will work particularly well if you your description of what to do takes into consideration your justification of why not. That is, if you can illustrate why OP's idea is bad by describing a potentially good way of enacting it and showing where it will do students harm, then this can constitute a good answer. (Indeed, this would be a much better answer than just saying, "You could do it via XYZ But I'd suggest to not bother.") I did not find any examples like this on the site, but I suppose this could occur at some point.
  5. This feels like part of #4, just with more reasoning behind the answer. But I think this raises my main point about answers being constructive: If you don't have anything to say beyond "I suggest not doing this", don't bother posting. Surely, someone can provide some reasoning for why not, or else someone can suggest alternatives.
  6. This seems to be the most common approach so far. Here is a great answer of this form. (You could argue that it's actually a direct answer to the question, but I think it feels more like "here are some ways to show probabilistic intuition to students".) I suggest using this whenever possible, but try to be sure that you're reading into OP's motivations properly. (That is, if you say "It looks like you want the students to get at PQR..." and that's not really the goal ... well, oops.) See point #2: leave a comment to get the true context/motivation of the post before addressing it in this way.

Overall, depending on the exact situation and your knowledge, I think an ideal approach is this:

  • Apply #2 to understand what's going on and what OP is looking for
  • If you have something constructive to say, answer with some combination of #4,5,6: suggest some possibilities, maybe explain why the overall idea might be harmful (or whatever), and if possible suggest some alternative routes to the fundamental motivation of the idea.
  • If it's truly an awful idea, use #3 (and provide evidence/reasoning!) but I think this will be quite rare.
  • In general, only downvote a post if it is a poor question, not because you disagree with the motivation/content of the question.
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  • $\begingroup$ Clarify and be constructive; I agree. One point of divergence: When, for 3, I listed XYZ is bad for reasons ABC, I was not suggesting a one sentence answer (similar to the to which you linked - which I think is closer to a comment, and certainly not an answer). Rather, I was thinking of a well-reasoned response with links to the literature on why some-such approach might be expected to lead to negative learning outcomes. $\endgroup$ – Benjamin Dickman Jul 9 '14 at 21:16
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    $\begingroup$ @Benjamindickman Ah yes. I suppose I addressed that more in point 4. The distinctions aren't all that important; seems like we agree on the overall ideas! $\endgroup$ – Brendan W. Sullivan Jul 9 '14 at 21:19
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Many of those questions are really XY problems. Others probably more in the line of "I stumbled upon this <extremely cool way> to approach <problem>, I must teach this!" while forgetting that understanding the <cool way> requires a lot in the way of mathematical prerequisites or even just plain maturity handling abstractions, which aren't to considered granted. A form of the expert curse (can't understand that non-experts don't "get" stuff that is bread-and-butter for you), much of the time. Perhaps telling someone they are cursed isn't considered polite, but sometimes necessary...

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No. It's not. The first question you cited has a highly rated answer. It wasn't a question I read, but I'd be inclined to DV this answer as 'not an answer.'

There are many cases of this phenomenon, Proving trigonometric identities among them, although in this case the nay-sayer was -3 DVed.

I think it wrong to DV the question (your 1 suggestion) as the question itself may be valid even if a member feels the problem should be solved another way. "Have you considered XYZ" might be an appropriate comment, but it runs the risk of going off on a tangent.

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    $\begingroup$ Passing to an extreme case (cf. mathoverflow.net/a/74710/22971) consider the following question: How can I formally explain Martin's Axiom and its implications for ZFC to my first-grade students, especially since most of them are still having trouble counting past 10? What do you think is an appropriate response? $\endgroup$ – Benjamin Dickman Jul 2 '14 at 19:43
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    $\begingroup$ Ben - point well taken. Yes, there's a point of absurdity that I need to acknowledge. In general, I believe one should answer the question as posed, but in your example, an "are you kidding me" comment and DV seem appropriate. $\endgroup$ – JTP - Apologise to Monica Mar 22 '15 at 13:35

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