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Recently I was a bit disappointed by the closure as off-topic various questions on teaching and applications of mathematics, e.g. today: this question on why the Fundamental Theorem of Algebra is not taught in high-school, and this question on the applications of complex numbers. Math.SE is supposed to be a general purpose site to handle questions about all aspects of mathematics. We do have members here who enjoy answering such questions and who possess the expertise to do so. To properly answer such questions does require significant mathematical expertise. As such, this is currently the best SE site to handle such questions.

I suspect that some of those who voted to close as off-topic these and similar questions may have chosen "off-topic" for lack of a better choice. I think one should choose "off-topic" only for topics where there is a clear community consensus that such topics are considered to be off-topic, so that one doesn't relay false impresssion of community standards to newcomers. If memory serves correct, there is no concensus here that such topics are off-topic.

Are there any compelling reasons why we should exclude questions on topics like those above? If the site was overloaded by such questions then we might have to draw some sharp boundaries to keep the site more focused. But such questions are so rare that I don't think that is anything to worry about currently. Even on analogous general level math sites (e.g. sci.math) such questions are relatively rare. I see no reason to believe that it would be much different here. Thoughts?

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Personally I voted to close the question on "applications of complex numbers" because 1) the person asking the question put about 1/2 second into composing the question. 2) I'm fairly certain it is a duplicate but was too lazy to hunt down what it was a duplicate of [referring back to 1), why should I invest 1 min to find a duplicate when the author spent 1 second asking his (poorly composed) question?] – Bill Cook Mar 21 '12 at 21:37
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@Bill Thanks for replying. Yes, no doubt the question is weak, but closing it as "off-topic" may send the wrong message if there is no consensus that such topics are indeed off-topic. If you don't have the time to improve the question, why not downvote with an explanation, or something else constructive? – Gone Mar 21 '12 at 21:40
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Sure. I'm glad you brought this up. In retrospect, voting to close "off topic" was probably not the right choice. I still think it deserved to be closed, but again because it's a duplicate. – Bill Cook Mar 21 '12 at 21:43
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I was hesitating between not a real question, not constructive and off-topic in the second example which looked like this when I cast the last close vote. As it stands now I think it would be a question that could have generated very interesting and on-topic answers and it is a pity that the first version was asked the way it was. I would definitely see such a question with a little bit of thought invested (and maybe a prior perusal of the corresponding Wikipedia page) as on topic. – t.b. Mar 21 '12 at 21:46
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I agree that off topic was not the ideal reason. The question is very poorly put, no effort has been shown by the asker, but perhaps that was not a reason for closing it. If @BillCook or someone else wants to reopen it just to close it as a duplicate, with the proper reference, it'd be fine by me. Possibly this one: math.stackexchange.com/questions/154/… – lhf Mar 21 '12 at 21:58
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@lhf My primary point was to help raise awareness of the issue that one may be inadvertantly sending incorrect strong messages on topicality by doing so. Surely when a newcomer sees a handful of high-rep folks closing a post as off-topic that sends a strong message. While experienced members may easily infer that off-topic wasn't the real closure reason, a newbie may not realize such and, as a result, might never ask another question on such topics, incorrectly inferring that they are strictly off-topic. We could lose interesting members and/or content for no good reason. – Gone Mar 21 '12 at 22:07
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@BillDubuque The question has been edited but in its original form was too vague. Perhaps, closing as off-topic was not the right choice, though. – azarel Mar 21 '12 at 23:09
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@BillDubuque I thought the Fundamental Theorem of Algebra question was actually a good question. However, I voted to close for two reasons: 1) (this was a small factor) It was not a question about mathematics qua mathematics, but rather mathematics qua the discipline, which I view as barely on-topic. 2) (main reason) I see no way to give this an even remotely mathematical answer, and any answer would consist of speculation as to the motives of various individuals, especially politicians. To me, this seems reason enough to close. – Alex Becker♦ Mar 21 '12 at 23:51
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The FTA question contained three questions: Why don't they teach FTA in US high schools? Do they teach FTA in US high schools? Do they teach FTA in high school elsewhere? I hold that the 2nd and 3rd of these questions are off-topic on m.se; Bill, do you disagree? It's not clear to me whether the 1st question was meant as "why don't they teach the statement?" or "why don't they teach the proof?" Under the 1st interpretation, I go with Alex Becker's comment above. Under the 2nd interpretation, it's a good m.se question. Perhaps I was hasty in voting to close. – Gerry Myerson Mar 22 '12 at 0:29
@GerryMyerson I indeed interpreted it the first way. Upon further reflection, I think that it could be edited along the lines of the second interpretation so that I would vote to reopen. – Alex Becker♦ Mar 22 '12 at 0:44
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@BillDubuque I voted to close the question on complex numbers since the question was very vague and I believe the author of the post put in little effort to ask the question. I voted to close it as not constructive. – user17762 Mar 22 '12 at 2:06
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For a question like "Why is the mathematical object X taught like this in the US and like that in France?", the answer might very well be an expansion of "Because of Bourbaki.". This is not "pure", context-free mathematics, but it is certainly a questions for mathematicians and not for politicians. If someone has to "speculate as to the motives of various individuals", this just means that he does not know the answer to the question which does not imply that the answer does not exist. – Phira Mar 22 '12 at 10:59
@Phira Discussions on how to teach topics, or why they are taught in a certain order, etc, can often lead to interesting pedagogical considerations. See for example Pierre Samuel, Sur l'organisation d'un cous d'arithmetique, L'Enseignement Math., 13, (1967), 223-231, where Samuel shows that one can organize a course in elementary theory based on any possible ordering of the major themes. – Gone Mar 22 '12 at 16:19
@Alex I think that pedagogical-related questions about how or why certain mathematical topics are taught should certainly be on-topic here. See for example the paper of Pierre Samuel that I linked to immediately above. Such questions have valid (and interesting) mathematical answers, having nothing to do with politics. – Gone Mar 22 '12 at 16:28

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