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In my process of studying math, I am often amased by how much different understandings of the same concept can really deepen one's comprehension. And I am also shocked by how much a wrong or incomplete understanding can slow down one's progress or even leads him/her to the wrong path. I am sure both cases have happened to everyone. But for the 2 months I've been on this site, I have hardly seen such problems. There's proof/solution-verification but no understanding-verification.

What I am picturing is: a poster asks a question, in which he/she states his/her understanding of a specific topic. If it is wrong, then other people can correct it; if it is incomplete, then other people can complete it or even enrich it with their own understanding.

I don't think this type of question violates any code of this site:

(1) Showing efforts: the poster must have been thinking to ask such questions

(2) Specific: it can be about the understanding of a very specific topic

(3) Answerable: it cannot be more "unanswerable" than proof/solution-verification type of questions

So why is it so rare? Is it not encouraged here or have people simply never thought of it?

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    $\begingroup$ Do you have any examples showing what "understanding-verification" means? The term "understanding" seems vague. Also, "incomplete" understanding may lead to poorly phrased questions. $\endgroup$
    – user9464
    Jul 8, 2019 at 17:09
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    $\begingroup$ I like this understanding-verification type of question a lot, and I'd like to see more of them. $\endgroup$
    – littleO
    Jul 8, 2019 at 20:53
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    $\begingroup$ @littleO Yes, me too. Do you think there's something we can do to encourage this? $\endgroup$
    – trisct
    Jul 9, 2019 at 1:43
  • $\begingroup$ I have personally posted a few such questions about difference sets. $\endgroup$
    – The Count
    Jul 10, 2019 at 12:40

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Is it not encouraged here?

It is not discouraged, as far as I know. As long as it reasonably follows the advice on quality, it should be OK.

have people simply never thought of it?

Obviously not so, since you did, and if you search "is my understanding" in the search bar you'll discover quite a few questions like that.

So why is it so rare?

I don't think it is, except when compared to the proportion of non-understanding questions. I think there are probably a great deal of questions which ask this question implicitly as they struggle with a concrete problem. And there are quite a few that ask it explicitly.

I think the reason they are relatively rare is probably this: a preponderance of users are at the stage where they are more concerned with specific problems and not high-level views of concepts. This is just a matter of their level of mathematical maturity. As far as I know, this is completely normal from a developmental standpoint: becoming curious about conceptual correctness usually happens later in math education.

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    $\begingroup$ +1 I have asked a few questions which include "is my understanding correct?" and have received reasonably good answers. $\endgroup$
    – Paramanand Singh Mod
    Jul 9, 2019 at 1:32
  • $\begingroup$ Your answer makes perfect sense to me. Maybe I haven't seen many because I haven't been here for that long. Nonetheless, do you think maybe we can somehow encourage this, like maybe adding a tag? $\endgroup$
    – trisct
    Jul 9, 2019 at 1:41
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    $\begingroup$ @trisct People who follow the philosophy of tagging management better may correct me, but I think it is not a good idea for a tag. It could arguably be applied to a great percentage of questions. It does not really help organize questions by subject matter. I don’t think tags should really be used to encourage posting behavior. I also don’t see why it needs to be particularly encouraged: it just happens naturally. $\endgroup$
    – rschwieb
    Jul 9, 2019 at 2:38
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    $\begingroup$ @trisct the closest thing we have may be [intuition], but I think that’s rather a legacy thing. $\endgroup$
    – rschwieb
    Jul 9, 2019 at 2:44

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