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I am asking in regards to this question: What are questions from students that improved the teachers understanding of mathematics?

The first comment says it's a call for discussion, and therefore not appropriate for this site.

I think it might be very fruitful, and would not like it to be considered off-topic. It is not asking for opinions only, but for experiences (if that matters).

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To some extent I agree with mentioned comment in that the question seems a bit like starting a conversation, rather than asking a focused question. However, this question might also create a nice resource of examples of positive student-teacher interaction.

Generally speaking, I am of the opinion that the site is still small enough that we can and should be somewhat open for more discursive and open-ended questions such as that one.

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Asking for experiences should not be off-topic. Sharing practical experience is (to me at least) one of the most important forms of help a teacher could get from a colleague. Such questions do not have a definite answer but I would like to see them here, so I would propose making them community wiki — as far as I understand, that is what CW is meant for. (This proposition was a misunderstanding stemming from the usage of CW on MO. After reading quid's comment below, I see no reason to make discussions CW.)

I think some forms of discussions are ok here, but they should be focused and about mathematics education. I think the question in question is sufficiently focused and could provide useful material for future readers. Making useful and findable material should be an important goal, not only satisfying the needs of the OP.

From a different point of view (also mentioned by quid), I think we shouldn't be too trigger-happy when rejecting off-topic questions. I think we still need to experiment what works and what doesn't. We are not getting too many new questions at the moment, so I would welcome almost any kind of questions about teaching and learning mathematics if their potential answers could be useful for future readers.

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  • $\begingroup$ I agree with the general point, just on CW a remark: The usage of CW you describe is common on MO (and I think math.SE too), however, it is not really the intended usecase for CW and we do not use it here in this way, at least we did not up to know. (The intended usecase for CW is: when having a post that is edited by many then it is CW.) $\endgroup$ – quid Oct 19 '14 at 11:46
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    $\begingroup$ @quid, ah, I see. I'm mostly used to CW on MO (and maybe M.SE). If that is the general SE idea about CW, my CW remark is unnecessary. $\endgroup$ – Joonas Ilmavirta Oct 19 '14 at 12:22
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As I've said in my comment, the question looks interesting. However, the way it is currently written, it feels to me like a call for discussion.

A possible rewrite is "can you share examples of how a student question helped direction your research?" I believe it keeps the main spirit intact while turning into a fruitful question.

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  • $\begingroup$ The "most" in OP is not optimal, I agree. $\endgroup$ – quid Oct 19 '14 at 11:50
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Comments copied from main (they can be restored if we want).

  1. This looks like a call for discussion. It may be interesting, but not on-topic for the site. – Mark Fantini yesterday

  2. It looks like a fruitful question to me. – Sue VanHattum♦ yesterday

  3. [Not deleted] Generically speaking, when students ask about generalization in nontraditional places it leads to new thinking for me. It's very rare. – James S. Cook yesterday

  4. Since this is a site about Mathematics Education: Is the idea to recall student questions that led to new insights/research directions in mathematics or in math education? I think that an answer of either one (and at any level) makes the question too broad, but my (gentle) suggestion is that we wait a bit before voting to close. – Benjamin Dickman yesterday

  5. Seconding @BenjaminDickman's comment. A big list of "insightful questions from students in any context" could grow too large to be helpful to future readers. But I can see a thread like, say, "Insighftul questions from college calculus classes", or "The best/most surprising questions that primary school students have asked", as a wonderful addition to this site. – brendansullivan07 yesterday

  6. I see. I'll leave the vote for now since if I retract I can't vote again, but hopefully this will become a good question. If the community is in for it, I'll retract the vote soon enough. – Mark Fantini yesterday

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It sounds like there's agreement that we should keep this question. I am concerned that the comments on it are distracting. Do we normally take those comments away once we've established that we'll keep the question?

Also, is there a need to edit it? I do not personally see a need. If we do want to edit it, I would prefer to keep more of the original wording than Mark Fantini suggests, as my answer focuses on the deeper understanding, and not on the new research.

I think my answer shows why I would not want this question separated into different subjects (elementary, algebra, calculus, etc). The use of the answers is in how they link our teaching to our thinking, at whatever level.

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  • $\begingroup$ Please let me know how you do that, @Benjamin. $\endgroup$ – Sue VanHattum Oct 19 '14 at 23:41
  • $\begingroup$ You need two things: (1) The link itself. You can find this for any question or answer by clicking share just after it; you can find it for a comment by clicking the time stamp just after it. (2) To insert a hyperlink when posting or editing, the easiest way is to select the text that you want to serve as the link (above, I used my answer) and then click the image of a chain link (it should be just to the right of the B I for emphasizing and italicizing text, respectively). Then you can paste the URL to which you wish to link and click Ok. (Let me know if this is unclear...) $\endgroup$ – Benjamin Dickman Oct 20 '14 at 0:04
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    $\begingroup$ Duh, now I see the share thing. Yeah, I know the second part. I do lots of links in my posts. I just didn't know how to get the url for my answer. Thank you much. $\endgroup$ – Sue VanHattum Oct 20 '14 at 3:54
  • $\begingroup$ I went ahead and edited the question slightly and deleted the comments (this is something that is done on some sites a lot and on some others less; how we do it here is for the community to decide). I removed the "most" as it feels not necessary and is a sort of "trigger word" for "opinion based" critique. Also, I narrowed the scope to mathematical understanding and mathematics research (as opposed to math education) as I believe this was OP's intent and it is what the first two answers are about. $\endgroup$ – quid Oct 20 '14 at 6:12
  • $\begingroup$ I mentioned a possible rewrite, by no means the only one. Another possibility is "Can you share examples of how a student question helped you examine your own beliefs about mathematics and deepen them?" This seems closer to what people have been answering. $\endgroup$ – Mark Fantini Oct 20 '14 at 8:15
  • $\begingroup$ I made one more edit, as the title with which the question ended up after my edit was very general. I tried to include both understanding and research. My aim was to take in some of @MarkFantini's suggestion while keeping the context given and the orginal style. I feeel to preserve the story about the professor has some value as motivation for the question. $\endgroup$ – quid Oct 20 '14 at 10:37

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