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Check AMS Mathematics Subject Classification, you will find the 2 digit classification "97" for mathematics education. Thus it seems that It is allowed to ask mathematics education research questions on MO. But, such questions often find the following problems on MO:

They could hardly remain open since basically they haven't got one correct answer.

Since they haven't got one correct answer people often Judges them as CW or "soft". Of course, this is not a problem if the question remains open.

Asking them in way that is suitable for MO is too difficult. Of course, this is a nice challenge for the OP if he or she has a slim belief that the question has a chance to remain open.

Let me give an example. Here is my last question on MO. For me, it is indeed a "hard" serious research problem. Respecting MO rules, I couldn't ask for peoples' opinion about the possible effects of teaching wordy heuristic strategies on different thinking styles. I couldn't ask for references, since I am a mathematics educator and it is my job to know and to find them. And I couldn't ask such and such questions for different reasons. Thus, I did try to set my question in a way that the answers remain based on facts rather than opinions. And I hoped to shed some light on my research problem. But the question is now [on hold]. And I am holding this question:

Is mathematics education research question allowed on MO?

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    $\begingroup$ I slightly changed the title, on the one hand as you seem to ask for the general problem and not the individual question only and also since ' "97" research question ' did not make any sense to me as I could not make sense what the 97 should be. I hope you do not mind the change, of course you can always roll back or choose something still different. $\endgroup$
    – user9072
    Commented Jun 29, 2013 at 13:29
  • $\begingroup$ @quid You made it better indeed. Thanks $\endgroup$
    – Amir Asghari
    Commented Jun 29, 2013 at 13:32
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    $\begingroup$ There's something wrong with the premise of the first paragraph. Check the MSC and you will also find 2-digit classifications for, e.g., "astronomy and astrophysics", "geophysics", and "biology and other natural sciences". The issues with asking questions in those fields on MO may be different from the issues with mathematics education, but I think this at least demonstrates that MSC codes shouldn't be taken as the definition of appropriate topics for MO. $\endgroup$
    – Mark Meckes
    Commented Jun 29, 2013 at 17:20
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    $\begingroup$ As a side note, the general attitude to subjective questions has changed on Stack Exchange. Subjective questions can be fine questions. See Good Subjective, Bad Subjective. $\endgroup$
    – Kaveh
    Commented Jun 29, 2013 at 18:53
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    $\begingroup$ When this question and its answers were first posted, the site Mathematics Educators Stack Exchange did not yet exist. But now that it does, I suggest that questions about mathematics education be asked there. $\endgroup$
    – JRN
    Commented Jan 28, 2019 at 1:29

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In my opinion, math education research questions are mostly off topic. Although they're important questions, our userbase doesn't have many math education researchers, and as a result most questions about math ed research would result in speculation and argument rather than precise expert answers.

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  • $\begingroup$ I upvoted this while superficially it seems to rather contradict my own answer. But, also to me the main divide is: is this a question for experts, or at least people well-informed in the subject, or rather likely to generate some general exchange of vague opinion, personal experience and recollection and so on. $\endgroup$
    – user9072
    Commented Jun 29, 2013 at 14:50
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    $\begingroup$ I think the user-base argument is not so strong: Suppose it included very few researchers in $p$-adic dynamics; would you suggest questions in this area not be asked? If the questions result in speculation/argument, then they should be closed down. I do agree that Mathematics Education questions are important; thus, I would be happy to see them raised here (if phrased properly). I think it quite reasonable to try to use MO as a vehicle for exploring questions about Mathematics Education, and that these concerns are relevant to many of the users (even those who do not research them directly). $\endgroup$
    – Benjamin Dickman
    Commented Jun 29, 2013 at 17:52
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    $\begingroup$ Most people don't have strong but half-baked opinions on p-adic dynamics. $\endgroup$
    – Noah Snyder
    Commented Jun 29, 2013 at 17:57
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    $\begingroup$ You have missed the intended point of my hypothetical: Namely, that "number of relevant researchers in the MO user-base" is not, on its own, a good decider for question admissibility. Separately, in response to your later comment, if the issue is that people are posting "strong but half-baked opinions," then those responses should be down-voted. $\endgroup$
    – Benjamin Dickman
    Commented Jun 29, 2013 at 18:36
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    $\begingroup$ @BenjaminDickman in practise it does not helpo much to downvote these answers. The "noise" is still around via permanent bumps. In addition to often causing annoyance on my part for various reasons, mainly abstract ones. Not math-ed specificallty but most thing of the type where people have half-baked opinions. The better solution in my opinion is to enforce rather higher standards for these types of questions than for others (not the oppsite, since it is vague anyway) for questions of this type. $\endgroup$
    – user9072
    Commented Jun 29, 2013 at 19:20
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There is a certain amount of uniformity that is necessary for a Q&A site like MO to work well. The aspects that make good/poor math questions are pretty uniform across major fields. There are already substantial differences between math and statistics, for example, enough to warrant a separate site. I think math ed is similarly substantially different. (Note that there is already a proposal for an education site where math ed might fit better.) This may be disappointing but it appears to be the nature of Q&A sites like MO that guides these divisions.

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    $\begingroup$ On the surface, this seems a rather convincing argument. But then, having that in mind, you should exclude all the questions of "what is the idea behind" type, historical questions, philosophical questions, career advice type question, most CW questions and so on. $\endgroup$
    – Amir Asghari
    Commented Jun 29, 2013 at 16:35
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    $\begingroup$ @AmirAsghari: Yes, sadly, most of these also tend to be less successful on MO. $\endgroup$
    – François G. Dorais Mod
    Commented Jun 29, 2013 at 16:41
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There is a mathematics-education tag with $187$ questions asked; more strikingly, there is a soft-question tag with $931$ questions asked, and the wiki-description of this latter tag is: "Questions that ask about some aspect of mathematical research or study which doesn't involve the actual mathematics. In general, soft questions can be answered without using mathematical reasoning." My feeling is that Mathematics Education questions are about an aspect of mathematical study, and often don't involve (research-level) mathematics, nor do they require the sort of reasoning common to graduate programs in pure mathematics.

Perhaps also of interest is searching for the word favorite: there are $802$ results. The results vary from What are you favorite instructional counterexamples? to What are your favorite puzzles/toys for introducing new mathematical concepts to students?. (The latter includes the teaching tag, for which there are $137$ questions asked.)

It seems to me, then, that a question such as "When did you first encounter the idea of problem-solving heuristics (cf. Polya) and has it affected you in your own problem-solving?" is quite reasonable. Answers to these questions from experts (i.e., professional mathematicians) are valuable, at the least, to Mathematics Educations researchers (some of whom include professional mathematicians). I should think that mathematicians would be interested in improving the state of Mathematics Education, and that MO is an excellent place to get the sort of expert answers one could not find elsewhere. I realize that the italicized portion in my previous sentence does not in and of itself justify Math-Ed questions; nevertheless, I am quite confident that an education-overflow site would not do justice to Mathematics Education in particular.

Finally, I agree with a remark made by G. Kuperberg (though I don't mean to imply he would support my position here) within the highly-voted post on the Philosophy behind Mochizuki's work on the ABC conjecture. In a comment, he observes: "I think that people are working way, way too hard to define MathOverflow by what it isn't. Although I still like MO, too many babies have been thrown out with various bathwater." Pure Mathematics is different from Mathematics Education; it is also different from Applied Mathematics, History of Mathematics, Mathematical Modeling, Statistics, and so forth. Which of these should stay and which of these should go? Here I respond only to the MSC $97$ query, and say: If others wish to define MathOverflow by its avoidance of Mathematics Education questions, then I am disappointed. I think that pedagogical questions - like historical questions, etc. - can be phrased in a way to make them appropriate for MO.

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  • $\begingroup$ I never tagged one of my question "soft" apart from my second question ever on MO that was not a "research" question. To emphasize one of your points (the sort of expert answers one could not find elsewhere), I like to say that It was true for nearly all the questions I asked, and more interestingly, in two cases, after reading the answers I felt I was quite off-road in my earlier thinking :) $\endgroup$
    – Amir Asghari
    Commented Jun 29, 2013 at 19:19
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    $\begingroup$ To answer you question, which should stay and which should go: in my opinion, all should stay but with high standards for the questions, higher than those in other subjects (not lower, which is what happens often). $\endgroup$
    – user9072
    Commented Jun 29, 2013 at 19:28
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Added: The answer focuses on Mathematics Education, since this was what was asked about. I hold the same opinion mutatis mutandis for History of Mathematics, Foundations of Mathematics (when to the philosophical end) and some other subjects that are also likely to generate many half-informed or even mis-informed replies.

In brief, my answer would be yes research-level questions on the subject Mathematics Education are, or at least should be (if the perception is that this is not so), allowed on MO.

However, while not being a firm in this subject myself, I would say that your question is not a research-level question on Mathematics Education. Rather, you seem to want to do a survey that is, or could be, part of some research-activity in this field.

This does not seem like a good fit for MO, not unlike it does not feel like a good fit for MO to ask people to proof-read preprints or other things that are more crowd-sourcing some legwork of research, as opposed to asking a precise question.

For example, had you asked about existing research-papers on this subject or existing data on it, this would be a question more in the spirit of the general MO-model and more generally SE Q&A sites.

Put differently, I think research-questions on Mathematics Education should be allowed, carrying out surveys as part of Mathematics Education research should not be allowed, and this goes, possibly with rare exception, for any other survey- or polling-type questions.

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    $\begingroup$ You are somehow right about my current MO question. It took me about three days to write down the question in a way that I thought it could reach the audience. I tried different versions but none could satisfy MO rule. What you see now at the question seems like a survey, but it wasn't designed to do a survey. If you see one of my older question (mathoverflow.net/questions/130883/…), you will find that $\endgroup$
    – Amir Asghari
    Commented Jun 29, 2013 at 14:11
  • $\begingroup$ there are just 13 answers. Thus it is not even a "big list" type question. But the answers indeed completely changed my understanding of the issue of proof comprehension. After all, as I mentioned above, asking a Suitable-for-MO Mathematics education question is too difficult. And, I am experimenting different versions. $\endgroup$
    – Amir Asghari
    Commented Jun 29, 2013 at 14:21
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    $\begingroup$ @AmirAsghari: you say "just 13 answers" but 13 is really alot compared to the typical question; I have no data handy but for me 4 are already many answers. (This does not mean everything with many answers is "bad" but just to show that 13 is a huge number of answers, IMO). Also, I share the concern of Noah Snyder at the end of his answer. Put differently: I consider expert-discussion of the subject on-topic but I am worried about questions designed in a way that everybody can say something. $\endgroup$
    – user9072
    Commented Jun 29, 2013 at 14:40
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    $\begingroup$ @AmirAsghari: to clarify my point, I think question that are likely to (only) generate the type of answer Benjamin Dickman gave would be good. (But also note he says the question is vague.) The other answer are sort of interesting, but then not answers to a research-level question in math ed (but responses to some sort of survey). $\endgroup$
    – user9072
    Commented Jun 29, 2013 at 14:54
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    $\begingroup$ I mentioned "just 13 answers" meaning that we cannot do a survey with that number of answers. What matters is the quality of answers that was indeed amazing in that case. Another example is mathoverflow.net/questions/128016/… where I had just one answer that was yours. I learned a lot from that, and also from the comments. For years, I was interested in students' understanding of definitions, and now I could see it through the eyes of mathematicians. $\endgroup$
    – Amir Asghari
    Commented Jun 29, 2013 at 14:58
  • $\begingroup$ @AmirAsghari: I see the point regarding 13 answers better now, thank you. Also, I am pleased you found useful my answer on the question you mention. $\endgroup$
    – user9072
    Commented Jun 29, 2013 at 15:04
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    $\begingroup$ You might want to have a look at "Checking if your question is on-topic" of Is my question suitable for cstheory? sometime ago in reply to a user who asked if he can post interdisciplinary questions on cstheory. $\endgroup$
    – Kaveh
    Commented Jun 29, 2013 at 22:33

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