tea.mathoverflow.net - Discussion Feed (Should "The Standard Course On Number Systems Be Abandoned?" be closed?)

Scott Morrison comments on "Should "The Standard Course On Number Systems Be Abandoned?" be closed?" (7111)

Scott Morrison — Fri, 16 Jul 2010 07:34:11 -0700

@Noah, the way to change the "category" of a thread is to edit the first post in the thread. I've done it

Yemon Choi comments on "Should "The Standard Course On Number Systems Be Abandoned?" be closed?" (7100)

Yemon Choi — Thu, 15 Jul 2010 23:50:55 -0700

Alex_O: The "interesting question" you've found is sufficiently different that it should be asked separately - and I think we've established it isn't what the original questioner was asking, so it wouldn't be stepping on his toes to ask it as a separate question.

And John Stillwell's answer, while containing good points, doesn't really address the core of the question, which concerns going from Peano to R, rather than from Q to R. The latter seems reasonable and common; the former seems a much more daunting thing to insert into a curriculum

alex_o comments on "Should "The Standard Course On Number Systems Be Abandoned?" be closed?" (7099)

alex_o — Thu, 15 Jul 2010 23:45:13 -0700

Noah Snyder wrote: "...if you agree that it's a very poorly phrased question. Why not vote down and request that the question be changed to a good question? Why do you want to *encourage* the asking of questions like this one? "

Because I think there is an interesting question in there, if you look past the writing, and the incorrect premise that many universities have an entire course dedicated to the construction of the real number system. It is "do you think there's some reasonable compromise way of presenting this material to students as part of the standard curricula?"

Because I found this interesting, I voted it up, even despite various defects in the original formulation of the question. Perhaps I give upvotes too freely. But I don't see how anyone can deny that there is, after all, an interesting question lurking in there, which deserves to be edited rather than closed. For example, John Stillwell gives an answer arguing that students can't really understand real analysis until they understand the construction of real numbers. If true, this would imply that the standard undergraduate math curriculum needs to be completely restructured. Surely this is exactly the sort of discussion of math education that belongs on mathoverflow?

VP comments on "Should "The Standard Course On Number Systems Be Abandoned?" be closed?" (7098)

VP — Thu, 15 Jul 2010 23:16:43 -0700

Since my name was mentioned, you may be interested to know that I see no merit in this question (after having gone through the comments, it doesn't even seem salvageable). In response to Noah: yes, this would be a clear case of quick closing of a bad question (at least, if no one edits it again into something totally different).

NB I am thrilled by comparison to Emerton, albeit not by the way it was construed.

Yemon Choi comments on "Should "The Standard Course On Number Systems Be Abandoned?" be closed?" (7097)

Yemon Choi — Thu, 15 Jul 2010 23:00:44 -0700

Andres: I won't do any more editing for a while, but I would again hope that we are playing the ball and not the man. By the way, the original poster was asking specifically about a course which starts with Peano, gets N, then gets Z, then gets Q, then gets R. So while it may not be set theory per se ,that seemed the closest fit - but I see you are better placed to judge than I am.

Qiaochu Yuan comments on "Should "The Standard Course On Number Systems Be Abandoned?" be closed?" (7096)

Qiaochu Yuan — Thu, 15 Jul 2010 22:55:03 -0700

@Yemon: Agreed. I've abstained from voting to close for precisely that reason.

Andres Caicedo comments on "Should "The Standard Course On Number Systems Be Abandoned?" be closed?" (7095)

Andres Caicedo — Thu, 15 Jul 2010 22:48:01 -0700

Yemon: Please do not add tags to this question, let it die quickly. Also, please do not add a "set theory" tag; this is nothing of the sort.

Pete L. Clark comments on "Should "The Standard Course On Number Systems Be Abandoned?" be closed?" (7094)

Pete L. Clark — Thu, 15 Jul 2010 22:33:32 -0700

@Yemon: Really, a Thundercats reference? You're putting a lot of stock in the universality of Gen X American pop culture. (You're probably right.)

Yemon Choi comments on "Should "The Standard Course On Number Systems Be Abandoned?" be closed?" (7093)

Yemon Choi — Thu, 15 Jul 2010 22:29:43 -0700

Noah: I have more of a problem with revenant questions, which drop off the front page and keep coming back, than with a question like this which I predict might get a few more responses in the next 8-12 hours and then sink.

The fact also remains that you're giving the impression we don't want to give people who might find something in this question time to see it -- and here I have in mind actual professors, people who have to deal with curriculum oddities and what to teach and which arguments to have with syllabus committees. Given that perception of cliquey-ness seems to be a problem MO is going to increasingly face, and given that we get enough grief about closing even more obvious things than this one, I think this is an instance where we actually lose more than we gain if we "pile on".

That said, I am not raising an objection or counter to your vote to close. Just suggesting that we don't need, just yet, to use the Sword of Omens to summon 3k+ users to stamp out this menace.

Noah Snyder comments on "Should "The Standard Course On Number Systems Be Abandoned?" be closed?" (7092)

Noah Snyder — Thu, 15 Jul 2010 22:17:57 -0700

Don't add tags we don't want it to stay on the front page.

Anyway having read the comment exchange with Andy I've had enough and voted to close.

Yemon Choi comments on "Should "The Standard Course On Number Systems Be Abandoned?" be closed?" (7091)

Yemon Choi — Thu, 15 Jul 2010 22:00:39 -0700

I am by now (apart from being amused in a grim kind of way) not strongly opposed to closing. I might add a set-theory tag to see if we get some worthwhile answers from some of the "high-rep" MOers who dig that kinda thang.

Andy Putman comments on "Should "The Standard Course On Number Systems Be Abandoned?" be closed?" (7090)

Andy Putman — Thu, 15 Jul 2010 21:53:04 -0700

OK, now that Andrew L has convinced me that he really intended to ask about having an entire course devoted to the real number system, the question seems overly parochial and a bit silly. I strongly support voting to close.

Yemon Choi comments on "Should "The Standard Course On Number Systems Be Abandoned?" be closed?" (7089)

Yemon Choi — Thu, 15 Jul 2010 21:21:36 -0700

Noah: although this is off-topic, I feel http://mathoverflow.net/questions/32035/are-nets-and-filters-useful-in-geometry-and-topology was a question founded on dodgy premises and a slightly callow/presumptuous perspective - but it appears to have been popular, despite being of less interest to me than the question I've currently edited Andrew L's into.

Noah Snyder comments on "Should "The Standard Course On Number Systems Be Abandoned?" be closed?" (7088)

Noah Snyder — Thu, 15 Jul 2010 21:19:18 -0700

(Yeah, sorry about the "Feature Requests" thing, that's the default setting and I didn't notice that the subject heading was there. And once I started the thread there didn't seem to be a way to change it.)

Noah Snyder comments on "Should "The Standard Course On Number Systems Be Abandoned?" be closed?" (7087)

Noah Snyder — Thu, 15 Jul 2010 21:18:01 -0700

Alex, thanks for showing up.

That seems a very low bar for voting up, if you agree that it's a very poorly phrased question. Why not vote down and request that the question be changed to a good question? Why do you want to *encourage* the asking of questions like this one?

Yemon Choi comments on "Should "The Standard Course On Number Systems Be Abandoned?" be closed?" (7086)

Yemon Choi — Thu, 15 Jul 2010 21:16:18 -0700

By the way, although it doesn't really matter, this whole thread appears to be in the "Feature Requests" section rather than the "Is This Question Appropriate?" section...

Andy Putman comments on "Should "The Standard Course On Number Systems Be Abandoned?" be closed?" (7085)

Andy Putman — Thu, 15 Jul 2010 21:15:48 -0700

My feeling is that in its current form, I'd not oppose voting to close. I do think there is a reasonable question hiding in there, namely the one I wrote above. If it were that, then I probably wouldn't vote it up or answer it or anything, but I would probably support its existence.

Yemon Choi comments on "Should "The Standard Course On Number Systems Be Abandoned?" be closed?" (7084)

Yemon Choi — Thu, 15 Jul 2010 21:14:57 -0700

Glad to see my inexpert editing skills aren't too rusty, then ... ;-)

alex_o comments on "Should "The Standard Course On Number Systems Be Abandoned?" be closed?" (7083)

alex_o — Thu, 15 Jul 2010 21:13:47 -0700

I really don't see a case for closing. After edits by Andy Putman and Yemon Choi, the current version of the question has none of the defects of the original. At this point, it reads like a garden variety pedagogy question to me.

alex_o comments on "Should "The Standard Course On Number Systems Be Abandoned?" be closed?" (7082)

alex_o — Thu, 15 Jul 2010 21:10:13 -0700

I am one of the people who voted this up.

Why: because there is a valid educational question in the post which I would like
to see answered, namely, where in the standard math curriculum should the construction of the real numbers go, if at all?

Yes, I also was annoyed by the high ratio of polemics to question, and yes, I also don't know what a "number systems course" is.

Yemon Choi comments on "Should "The Standard Course On Number Systems Be Abandoned?" be closed?" (7081)

Yemon Choi — Thu, 15 Jul 2010 21:04:38 -0700

Noah: how do we know this question isn't going to be popular in terms of up-votes, like other popular questions I don't like? Timezones, schedules, and all that.

Yemon Choi comments on "Should "The Standard Course On Number Systems Be Abandoned?" be closed?" (7080)

Yemon Choi — Thu, 15 Jul 2010 21:03:42 -0700

Noah: in the hope that people realize why we are closing these things as bad questions: see the comments on other threads of VP, and at a more temperate level Emerton.

Noah Snyder comments on "Should "The Standard Course On Number Systems Be Abandoned?" be closed?" (7079)

Noah Snyder — Thu, 15 Jul 2010 21:00:31 -0700

Also I'd like to hear from anyone whether this is a case where there's any good reason not to just close quickly. This doesn't actually strike me as a controversial case. The question is quite bad, the user is fond of asking bad questions, and it's not a very popular question in terms of upvotes. My intuition is that this one should actually be non-controversial and a quick close. But I wanted to give people a chance to disagree since closing debates is such a source of agita.

Yemon Choi comments on "Should "The Standard Course On Number Systems Be Abandoned?" be closed?" (7078)

Yemon Choi — Thu, 15 Jul 2010 20:59:33 -0700

Just done another edit, trying to preserve the good parts of the original rather than write a new question over it.

Andy Putman comments on "Should "The Standard Course On Number Systems Be Abandoned?" be closed?" (7077)

Andy Putman — Thu, 15 Jul 2010 20:44:35 -0700

@Scott : Good point! I just edited it as above.

Scott Morrison comments on "Should "The Standard Course On Number Systems Be Abandoned?" be closed?" (7076)

Scott Morrison — Thu, 15 Jul 2010 20:37:53 -0700

@Yemon, I'd intended "I would vote to close" to mean "I'm not going to vote to close, but would if I could cast a nonbinding vote." Unfortunately it appears from the comments that the asker doesn't agree there's any problem with the question, so I doubt there'll be any editing.

It is community wiki, so if any has the energy they are welcome to completely revamp the question, of course!

Yemon Choi comments on "Should "The Standard Course On Number Systems Be Abandoned?" be closed?" (7075)

Yemon Choi — Thu, 15 Jul 2010 20:34:18 -0700

Scott: I just think that if we wait on this a bit, it will come across better, given the recent discussions on meta about the Arbitrariness of the Illuminati.

Certainly there are other questions which have been popping back to the front page, whose worth I'm not convinced by, and where some of the answers have seemed naive/callow.

Scott Morrison comments on "Should "The Standard Course On Number Systems Be Abandoned?" be closed?" (7074)

Scott Morrison — Thu, 15 Jul 2010 20:28:21 -0700

I would vote to close: it's not a question that admits a definitive answer --- "What do you think?" is not a good start. As Yemon points out, a good question could be made out of this one, but we're not there yet!

Yemon Choi comments on "Should "The Standard Course On Number Systems Be Abandoned?" be closed?" (7073)

Yemon Choi — Thu, 15 Jul 2010 20:27:24 -0700

Noah: I would suggest that, now we have the meta thread up and signposted, we wait a bit before voting to close, in order to give some of those who are keener on maths-education questions/topics a chance to contribute if they wish.

Andy Putman comments on "Should "The Standard Course On Number Systems Be Abandoned?" be closed?" (7072)

Andy Putman — Thu, 15 Jul 2010 20:27:01 -0700

Maybe he's talking about spending a week or so constructing the real numbers in the midst of a broader real analysis course?

As a piece of advice to the questioner, I've noticed that many of his questions and answers include a lot of personal anecdotes and opinions. I suspect that people would react better to them if he made them a bit less personal and stuck more closely to the math (or math ed). It would also help to be a bit more concise and to-the-point.

For instance, here is how I'd phrase the question at hand (this is an interpretation of it, so I might be misinterpreting it).

"It is common in intro real analysis courses to spend a lot of time constructing the real numbers from the natural numbers (by constructing the integers, then the rationals, and finally the reals, the latter via a device like Dedekind cuts). Though this is historically important, many people seem to find it tedious. Do you think that this is a good use of classroom time, or do you think it is better to write down the axioms for the real numbers, assert that they exist, and get on with things?"

Yemon Choi comments on "Should "The Standard Course On Number Systems Be Abandoned?" be closed?" (7071)

Yemon Choi — Thu, 15 Jul 2010 20:26:02 -0700

As I commented, I think there might be a worthwhile question under it, but I don't really agree with the premises of the question (such as the ubiquity or tedium of this course). I was hoping that other people from USian institutions could shed some light on this. In particular, I wanted to know if

I notice that in spite of all this, a course in the number systems continues to be taught in most programs

despite the fact most mathematicians deplore the task and most students leave the course wondering what the hell they wasted thier time for.

have actually been observed by others.

Noah Snyder comments on "Should "The Standard Course On Number Systems Be Abandoned?" be closed?" (7070)

Noah Snyder — Thu, 15 Jul 2010 20:15:56 -0700

I think it's a bad questions: it's not specific, it's very argumentative, and it doesn't make any sense (what on earth is the standard course on number systems??). So I'm starting a meta thread if people want to talk me out of voting to close.

ED: http://mathoverflow.net/questions/32104/should-the-standard-course-on-number-systems-be-abandoned