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I asked the following question Writings about mathematics education by famous mathematicians, which was closed after a few minutes.

I would like to understand whether the community agrees it should be closed. My impression from other threads on meta was that lists of resources were encouraged. In any case I certainly feel that the views of world-famous mathematicians on teaching mathematics are on topic.

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  • $\begingroup$ Note that all the answers so far were by me. It's a topic I'm interested in and I wanted to share what I'd found so far, and to set an example for the answers. I care not about reputation points and such. $\endgroup$ – Marius Kempe Mar 26 '14 at 17:45
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    $\begingroup$ Jon Ericson provided his reasons in his comment, and I agree with him. This question had a combination of factors leading to its closure: big list questions are frowned upon throughout the stack exchange network (though some have snuck through), 'easy' questions are frowned upon (though some have snuck through), and questions with the word 'discuss' in them are frowned upon (and very few of those sneak through). This question had all three negative factors. $\endgroup$ – Brian Rushton Mar 26 '14 at 17:53
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    $\begingroup$ Thanks for bringing this up on meta. I can go into more depth on my reasoning here, if you like. But ultimately the site will be moderated by regular users so I'd prefer to get other people's feedback. $\endgroup$ – Jon Ericson Mar 26 '14 at 19:15
  • $\begingroup$ @JonEricson I've posted my thoughts below, and I've also asked a couple of questions that I'd like to hear your thoughts on. $\endgroup$ – Jim Belk Mar 26 '14 at 22:04
  • $\begingroup$ I've cast a reopen vote; others can vote to reopen or leave it closed as they wish. $\endgroup$ – Brian Rushton Mar 27 '14 at 11:46
  • $\begingroup$ Would you be happy with the rephrase suggested by Benjamin Dickman? $\endgroup$ – quid Mar 27 '14 at 16:45
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A main issue I see here is one of (perceived) consistency or fairness. Moderation on an SE site can never be an exact science, but it should not show too much variance either.

Personally, and those that know me from MO might confirm this, I am not that big a fan of big lists. However, they are popular, and good and interesting "lists" likely should have their place on this site (and they have shown on other sites to be in certain ways valuable). Indeed, there are already several such list on this site.

To me this one seems at least if not more focused and specialized than some other lists we already have. It is not very clear why this one should be closed while others stay open.


Added: Of course the standard's of a site can and should evolve over time, either smoothly and organically or when some (new) concensus or absent this at least modus vivendi is found on some issue. I thus certainly do not want to say: since we had one list we need to allow all lists. Only, it seems to me that here the change was a bit quick and/or not announced (or at least perceived as such).


Added 2: Upon request, some list-like questions.

These ask for certain books/written accounts, I would say pretty much like the one we discuss (and when pressed I would rather say less than more specific).

What are some great books for exploring mathematics? (not kids' books and not textbooks)

What are some great books for inspiring children to explore mathematics?

Books/(auto)biographies/references on how mathematicians study/studied (as students)?

This one asks for various presentations (note, it was controversial, but not mainly since it was a list).

Showcase of Powerpoint / Keynote / Beamer Presentations

Requests for poblems, examples, and so on, rather list like (somewhat different, but quite possibly would be CWed tagged big-list elsewhere).

Good, simple examples of induction?

Impressive examples where a "proof by picture" goes wrong

Mathematical problems for preschoolers

Finally, let me add there was a meta question

Books and materials recommendations

that allows certain requests for books and related resources. (Disclaimer: I gave the positive answer, but there was not much though a little opposition either).


Afterthought: It is in my opinion unreasonable to discourage such list questions too much early on. People like to ask about and share favorite things. And, this is not because they are used to CW and lists from math.SE or MO; to wit, Sue VanHattum is new to the SE thing and asked two lists. Also, having such questions around can also encourage new users to participate, really new ones not from the network, being a low entrance point. Maybe some SE veterans will raise an eyebrow seeing some lists, but I doubt this will ultimately affect if they join or not.

And as long as the site is somewhat small it is not really a problem to have such things; it starts to be a problem if the lists create too much "noise" and/or grow that large that they get unusable. If/when the site grows we can and will have to get stricter. But being overly strict at the start is not a good idea. Obviously, some standards need to be preserved, but too much

Opinion? No! List? No! Discussion? No!

will alienate too many people not yet used to it.

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    $\begingroup$ I'n not entirely sure which other lists you're referring to. Could you perhaps add links to them? $\endgroup$ – Jim Belk Mar 26 '14 at 23:13
  • $\begingroup$ I added an incomplete list of lists (and some additional remarks). $\endgroup$ – quid Mar 27 '14 at 0:18
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Edit (4/13/14): I will leave my original post below, but here are my current thoughts (which are also left in the form of a comment at the corresponding question):

If this is re-phrased so that posts must involve two components [namely, (1) writings about math ed by mathematicians, and (2) an indication of what the math ed literature says about such viewpoint(s)] then I would certainly vote to re-open. Note that this would render the existing answers inappropriate in their current form (so that they should be either deleted or have the salient point(s) summarized along with comments from math education).


Earlier response: I think the question is good and not at all too broad.

You want instances in which exceptional mathematicians (approximated by: "roughly anybody with a result or object named after them") wrote specifically about Mathematics Education.

Of course, the question should be made Community Wiki, but I don't see a reason for putting it on hold.

I might have phrased the question differently (I'll include an example below) but the fundamental question seems appropriate (and significantly less broad than many of the other queries posted thus far).


Re-phrase:

Professional mathematicians - given that they spend a lot of time thinking about mathematics, and, in many cases, teaching mathematics - often have strong opinions about Mathematics Education.

What are examples of well-known mathematicians (e.g., ones who have a result or object named after them) writing specifically about (issues in) Mathematics Education?

Ideally, responses would be limited to one source per answer, and would contain meaningful (and representative) excerpts, so that even those who do not read the entire article/book can glean something about the author's viewpoint.

Lastly, if there is evidence for or against the ideas espoused by these mathematicians that come from research in Mathematics Education, then pointers to these results would be welcomed as well.

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I must admit that I don't like the question, not because it is a "big-list" question, but because of the danger of the impression that it gives. That is that just because someone is a big-shot research mathematician then their opinions on education should be more highly regarded than anyone else's. Benjamin's rephrasal in his answer is slightly better due to the final paragraph, but nonetheless I'd still be unhappy with it.

The problem is that as we are practitioners in maths education rather than researchers, a lot of what we write here will be based on experience and anecdotal evidence. That's unavoidable, but to be a useful source I think we need to exert positive pressure away from this and towards research-based findings (take a look at some of Neil Strickland's answers to see what I'd like to see more of). So a question like this that sets out to ask for pure speculative opinion with no opportunity for judgement on that opinion is not a good fit. To see what I mean, I think that Arnol'd's opinion has been pretty comprehensively debunked so should I down-vote it to indicate that I think it is a load of hokum? But then the answer is a genuine answer to the question so why should the poster get down-voted for it?

In short, if it isn't clear what a vote on an answer should mean then it isn't a good fit for the SE network.

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  • $\begingroup$ That seems definitely like a reasonable objection. (Personally I am not keen on the question either.) However, one could turn this around and say that this collection might generate some comments that actually point out what you say more concretely. So that in the long run it would be positive for the devellopement of the community. $\endgroup$ – quid Mar 27 '14 at 9:20
  • $\begingroup$ To further elaborate on the above comment: I can follow the general objection. But the particular one on voting on answers being difficult seems like a red herring or a bit formalistic. So, had OP said they are looking for "good" writings (with some elboration on what good is supposed to mean) it would work. But ultimately it would not change much. Atually it might be worse. Why not collect original sources in a neutral way? $\endgroup$ – quid Mar 27 '14 at 11:08
  • $\begingroup$ One could vote on effort that went into an answer: if there is a lot of material for some person collected and presented nicely it's a better answer than just some link to an interview that touches upon the subject in passing. And if something that is not really math education but something else is mentioned it gets a downvote. $\endgroup$ – quid Mar 27 '14 at 11:08
  • $\begingroup$ I think there's a good question lurking in there; feel free to re-phrase my re-phrasing to make it a better fit! $\endgroup$ – Benjamin Dickman Mar 27 '14 at 15:11
  • $\begingroup$ How can you possibly think statements like The theorem of classification of surfaces is a top-class mathematical achievement and "The subtle poison of mathematical education" (in F. Klein's words) for a physicist consists precisely in that the absolutised model separates from the reality and is no longer compared with it have been "comprehensively debunked"? $\endgroup$ – Marius Kempe Mar 30 '14 at 17:56
  • $\begingroup$ @MariusKempe I had in mind specifically the story about the child saying that 2+3 was 3+2 and Arnol'd using this as evidence that education (in France) had become too Bourbaki'ed. $\endgroup$ – Andrew Stacey Mar 31 '14 at 8:10
  • $\begingroup$ @quid Actually, no. That's the whole point. If I see answers on a question and want to know which to follow up, my primary information is the votes of others. Unlike, say, TeX-SX, I can't simply cut-and-paste the code and see if it works. So here the votes on an answer actually mean something. If it isn't clear from the question how I should interpret those votes then the votes really should be there, and if they shouldn't be there then the question isn't a good fit for the SE system. $\endgroup$ – Andrew Stacey Mar 31 '14 at 8:13
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    $\begingroup$ But which answer to follow up will depend on what you (a reader) want to do with the answer. Perhaps you want writings in line with current thinking in the education community, but perhaps OP wants all, and perhasp somebody else is mainly interested in those debunked (for some reason). So, why not compile a collection of sources that is useable by everybody for whatever purpose they please and is validated via votes, as what it claims to be, that is a collection of writing on math education of well-known mathematicians, just that not more and not less. $\endgroup$ – quid Mar 31 '14 at 10:36
  • $\begingroup$ @quid In which case, what is the value that is added by using the Stack Exchange system? This would work far better on some sort of maintained wiki or database. I used to be one of the "Let's use MO for everything" brigade but after a while I realised that that was a Bad Idea and became one of MO's hardest hard liners (before leaving altogether). I think that if there is a place for such a collection (something I'm not convinced of) then SE is not a good one. $\endgroup$ – Andrew Stacey Mar 31 '14 at 10:41
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I originally suggested that the question should be community wiki, and flagged it for moderator attention. After Jon Ericson closed it, I left the following comment:

As Jon Ericson points out, this question is indeed quite broad. I like the motivation behind this question because I'd love to talk about, say, Thurston's "Mathematical Education". But perhaps the right way to fit this into the Stack Exchange format is to ask some more specific pedagogical questions related to what Thurston or Arnold says.

I wasn't anticipating that the question would be closed, since I'm more used to how things work on Math Stack Exchange and Math Overflow. However, it seems to be consistent with the attitudes that Jon expressed about a potential "big-list" tag in this thread, as well as this blog post about the future of community wiki. In particular, both Jon and the blog post mention:

Questions rarely, if ever, need community wiki.

Although the idea of community wiki questions is entrenched at Math Stack Exchange and Math Overflow, the Stack Exchange team would prefer for new sites to mostly avoid having such questions.

My attitudes about this are as follows:

  1. Obviously we should respect the wishes of the Stack Exchange team. After all, it's ultimately their site, and we're simply guests. If they would prefer for us to not have any "big-list" or community-wiki-type questions, then we won't.

  2. Moreover, this policy is based on the experiences of some of the other Stack Exchange sites, where community wiki questions were ultimately seen as harmful (see here, for example). This is valuable experience that we shouldn't discount, even if it may not be obvious to us why community wiki questions might be a problem.

  3. Just because a question is interesting to members of the community, that doesn't mean it's a good fit for a Stack Exchange site. I like that Stack Exchange sites (including Math Stack Exchange and Math Overflow) are so focused on specific questions and answers. It's a model for a website that works well, but it's also a model that must be constantly enforced.

  4. I was personally a little disappointed that the question was closed---I found the question very interesting, and I was looking forward to seeing the links that would be posted---but I support closing the question if it's necessary in view of points 1 - 3.

Now, as Jon points out, this site will eventually be moderated by members of the community, and those moderators will need some guidelines for how to handle "community wiki" type posts. So my questions (for Jon or other moderators) are,

Would you advise that we simply disallow community wiki questions during the beta phase?

If the answer is "yes", I think that's fine, for the reasons I've outlined above. In this case, our eventual community moderators should presumably close any questions that don't meet the criterion for a "normal" question.

If the answer is "no", I would also ask:

What are some examples (if any) of community wiki questions that should be allowed?

Alternatively, what features do you think should be present in a "good" community wiki question? You've already mentioned a few in your comments, but it would be helpful to have a more thorough discussion.

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    $\begingroup$ My opinion on the policy on list from a self-deleted answer (as it seemed premature there) from the big-list thread: "We should allow big-list questions exactly if and as long as they are actually creating a useful, useable, and on-topic resource. Best, they should be actively maintained by OP or somebody else. (Checking for duplicates, chategorizing answer, and so on.)" This is compatible with, and rather stricter than, practice on other SE sites and I doubt much stricter policy will be enforcable without major complaints. $\endgroup$ – quid Mar 26 '14 at 22:36
  • $\begingroup$ re 'consistency' the closure is no doubt consistent with some general principles yet not with what mainly happened on this site so far. Yet I did notice that Jon Ericson voiced concerns on related question and answer. The intent of my answer (if this should have been understood like this) was not to suggest some personal inconsistency, yet to articulate what I think could be an issue with this closure. In case this question is the one where policy should change, this is in principle also alright, but I think it should be communicated clearly. And, my opinion on the policy is above. $\endgroup$ – quid Mar 26 '14 at 22:50
  • $\begingroup$ @quid On the consistency issue, it's possible that other list-type questions simply weren't noticed by the moderators. In my mind, the question is what principles we should use going forward. My sense is that the community here would be perfectly happy to allow any and all list-type questions, but that doesn't seem compatible with current Stack Exchange policies. Moreover, list-type questions have apparently gotten out of hand in some communities, and it's important to make sure that doesn't happen here. $\endgroup$ – Jim Belk Mar 27 '14 at 0:20
  • $\begingroup$ Noticed or not, this is ultimately irrelevant. As I said it is about the perception. But actually, no, it is not possible it was not noticed, because on at least one of them there is a (critical, to be sure) comment by Jon Ericson (which I mentioned earlier). But, it was not closed. But as said this is not my point. I know it is perfectly compatible and consistent with all kinds of policy to close such question, but first it was not executed like this up to now on this site, and second I would consider it as a mistake to adopt such policy dogmatically. But(cont.) $\endgroup$ – quid Mar 27 '14 at 0:31
  • $\begingroup$ @quid Re: Consistency. Actually, now that I think about it, it may be my fault that this issue came up for this particular question. I flagged the question for moderator attention, with a request that it be made community wiki, which I haven't done for any other question. Presumably the moderators are more comfortable taking action on a question when it has already been flagged by a member of the community. $\endgroup$ – Jim Belk Mar 27 '14 at 0:42
  • $\begingroup$ no this community would not be perfectly happy to allow any and all list-type question. As I said I, personally, am willing to allow them only if and as long as they create a useful, usable, and ontopic resource. Of course, we need to be careful things do not get out of hand. But we also should not be too worried. $\endgroup$ – quid Mar 27 '14 at 0:43
  • $\begingroup$ @quid In any case, I'd really like some more guidance from the moderators on this issue. If they already have rules in mind that they'd like us to adhere to, then that's that. If they just have attitudes as opposed to rules, i.e. if they just want to make sure that list-type questions are very rare, then we need to have a serious discussion as a community about how to implement that. It would also help to know more about what other recent Stack Exchange sites have done with this issue. $\endgroup$ – Jim Belk Mar 27 '14 at 0:50
  • $\begingroup$ Yes, presumably, it was closed because it got noticed while "fresh." Still there is no reason it needs to stay close. Actually, Jon Ericson said he closes it 'for now.' And on meta explictly solicited input from the community. I thus really do not think there is that strict non-negotiable SE policy. I rather took it as some advice to think about such aspects. Also I absolutely do not consider it as some kind of big problem he closed it. Only, I think it would be unfortunate if it stayed closed without some general discussion on the matter of lists. $\endgroup$ – quid Mar 27 '14 at 0:50
  • $\begingroup$ Ah. Did not see your last comment. I think we agree basically. $\endgroup$ – quid Mar 27 '14 at 0:51
  • $\begingroup$ I wouldn't say that no questions should be community wiki. But I do think that if you are in the habit of asking for questions to be marked CW you take a moment to consider why. I find the feature a particularly blunt hammer; a careful edit to the question can often avoid the need and create a better artifact. But, of course, I'm not going to be moderating this site after the pro tems are picked. It will be up to the community to weigh the costs and benefits of having these sorts of questions and having them be CW. Feel free to ignore me then. ;-) $\endgroup$ – Jon Ericson Mar 27 '14 at 4:48
  • $\begingroup$ @JonEricson Ok, thanks. That makes things clearer. Also, aside from The Future of Community Wiki blog post and the linked How to kill off 'community wiki' entries post on AskDifferent Meta, do you have any suggested reading on community wiki questions? $\endgroup$ – Jim Belk Mar 27 '14 at 12:57
  • $\begingroup$ I feel that framing this along the lines of community wiki already adds some addtional layer of complication. It is true that for various reason various communities and the software turn questions that (tend to) generate many answers into CW. And, while there are good reasons for this, there is also no inevitability to this. I thus think it is better just to discuss if we want a certain type of question and if so how we would want to handle them. (We can then decide whether CW or not feels better for this. But the CW-ing is a technicallity, IMO.) $\endgroup$ – quid Mar 27 '14 at 16:53

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