Timeline for The role of the mean value theorem (MVT) in first-year calculus
Current License: CC BY-SA 3.0
51 events
| when toggle format | what | by | license | comment | |
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| Dec 10, 2017 at 23:18 | review | Close votes | |||
| Dec 11, 2017 at 8:22 | |||||
| Dec 10, 2017 at 22:23 | history | edited | Martin Sleziak | CC BY-SA 3.0 |
removed (tag-removed) tag
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| Feb 27, 2012 at 15:00 | answer | added | Lee Mosher | timeline score: 4 | |
| Nov 23, 2010 at 17:24 | history | edited | Michael Hardy | CC BY-SA 2.5 |
The meaning of this question has been essentially altered.; deleted 1 characters in body
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| Nov 23, 2010 at 12:57 | answer | added | Mike Hall | timeline score: 0 | |
| Nov 23, 2010 at 6:13 | answer | added | Eric Wofsey | timeline score: 5 | |
| Nov 23, 2010 at 4:19 | answer | added | Niyazi | timeline score: -1 | |
| Nov 23, 2010 at 2:12 | comment | added | Michael Hardy | The "scope" seems to be that it's a forum for discussion among mathematicians qua mathematicians, and not for discussion between mathematicians and others. That being the case, topics like this seem perfectly appropriate. Attempts to codify the scope have seemed not altogether consistent with actual practice. | |
| Nov 23, 2010 at 2:09 | comment | added | Michael Hardy | ....and people post on that subject frequently. | |
| Nov 23, 2010 at 1:47 | comment | added | Greg Marks | My reading of the F.A.Q. "What kind of questions can I ask here?" is that MO is not an appropriate forum for questions about undergraduate teaching. Yet there is a "mathematics-education" tag. So I think it might be helpful to clarify the scope and purposes of this site. | |
| Nov 22, 2010 at 20:24 | answer | added | roy smith | timeline score: 7 | |
| Jul 15, 2010 at 16:32 | history | edited | Michael Hardy |
edited tags
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| Jul 15, 2010 at 2:56 | history | edited | Michael Hardy |
tag
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| Jul 13, 2010 at 11:03 | answer | added | Pete L. Clark | timeline score: 21 | |
| Jul 12, 2010 at 15:58 | comment | added | Kim Morrison | Please continue this discussion, if necessary, at meta: tea.mathoverflow.net/discussion/502/mathematics-education-on-mo I'll use my last soapbox opportunity to say: many of us participating in the thread above should have moved this to meta already! As soon as a comment thread has become contentious, I'd encourage you to take the higher ground and say "let's move this to meta". | |
| Jul 12, 2010 at 10:00 | history | edited | O.R. | CC BY-SA 2.5 |
making precise questions, making it look less like a rant
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| Jul 12, 2010 at 8:04 | comment | added | Franz Lemmermeyer | For what it's worth: I also think that question like this one are more interesting than some I have seen in the recent past which have gotten loads of upvotes. | |
| Jul 12, 2010 at 8:01 | history | reopened |
Pete L. Clark Emerton Yemon Choi Andy Putman Franz Lemmermeyer |
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| Jul 12, 2010 at 5:30 | comment | added | Theo Johnson-Freyd | If you do rewrite, I recommend also some more instruction for the answerers to narrow down the possible answers. MO is not very well suited for long discussions and discussion-board issues. (With that in mind, sometime soon this comment section should migrate to a meta.MO page. I'll let someone else do that, so that they can have the last word here.) | |
| Jul 12, 2010 at 4:56 | comment | added | S. Carnahan♦ | I've made the question community wiki, so those of you who think it can be turned into a reasonable question are welcome to "remove the soapbox" by editing. | |
| Jul 12, 2010 at 4:53 | history | made wiki | Post Made Community Wiki by S. Carnahan♦ | ||
| Jul 12, 2010 at 4:49 | comment | added | Theo Johnson-Freyd | Then again, "Oh, I see. Most of the people closing it are under 30. I was pretty weird then too. Doesn't really explain why Robin Chapman joined them, though." makes me much less eager to vote to reopen. | |
| Jul 12, 2010 at 4:48 | comment | added | Theo Johnson-Freyd | I maintain that the original question was a little ranty. My stronger objection was that it wasn't actually a question, but rather OP had, or seemed by the writing, anyway, to have, a strong, preformed opinion on the matter, and was using MO as a soapbox disguised as a rhetorical question. In my mind, that's what "closed as subjective and argumentative" means. I don't vote to close for "subjective", but "argumentative" I don't like. That said, I will vote to reopen if the question is sufficiently rewritten as to make a reasonable, honest question, also incorporating Scott's suggestions. | |
| Jul 12, 2010 at 3:17 | comment | added | Yemon Choi | Also, at the risk of banging the same drum, why does this merit closure while "hey? tell me some cool math puzzles I can mention to people at dinner, 'cause that's what we do, right?" doesn't? | |
| Jul 12, 2010 at 3:16 | comment | added | Michael Hardy | .......so this suggests a question: to what extent is mathematics education considered a proper topic for MO? | |
| Jul 12, 2010 at 3:16 | comment | added | Michael Hardy | @Scott: Then why is mathematics education included among the topics among which postings appear to be welcomed? How can you possibly discuss education, the most disagreed-about of all topics (even more so than religion, perhaps) without getting stuff like this? Can anyone discuss how education should be conducted without this kind of thing? My impression from some of the topics was that MO is for questions that professional mathematicians would be interested in, but should not include questions that for professionals are routine and straighforward. | |
| Jul 12, 2010 at 3:15 | comment | added | Yemon Choi | The reason I don't think this question is so subjective and argumentative that it warrants closure, is that it invites answers from people who have experience of teaching, or trying to teach, such things, some of whom may have survived many calculus texts thrust into their hands as The Way The Students Should Be Taught; and it's these answers I want to read. | |
| Jul 12, 2010 at 3:11 | comment | added | Yemon Choi | Michael: subjective and argumentative is not bad per se, but I don't think it's a good use of MO (I don't think it should be a forum or an "online place to hang out"). On the other hand, your question strikes me as eminently worthwhile -- I'll soon be teaching caculus and analysis courses, and the kind of issue you raise is the sort I want ultimately to think about more. Voting to reopen. | |
| Jul 12, 2010 at 3:08 | comment | added | Kim Morrison | @Michael, remember MO is intended primarily for precise, technical questions, which (ideally) admit a definite answer. As such, yes, "subjective and argumentative" is absolutely considered in some sense bad, for MO. | |
| Jul 12, 2010 at 3:07 | comment | added | Michael Hardy | Oh, I see. Most of the people closing it are under 30. I was pretty weird then too. Doesn't really explain why Robin Chapman joined them, though. | |
| Jul 12, 2010 at 3:03 | comment | added | Emerton | I have voted to reopen this question (the second such vote), since I agree with Pete and others that this is an interesting question, and I am learning from the answers and comments. As an aside to Andrew L: you paint with a very broad brush. (I am a researcher, one of many on the site in addition to the five who voted to close.) | |
| Jul 12, 2010 at 2:59 | comment | added | Michael Hardy | I'm surprised to find that "subjective and argumentative" is regarded as in some sense bad. | |
| Jul 12, 2010 at 2:56 | comment | added | Michael Hardy | I agree with the Pete L. Clark's comment about "this (particular) freshman calculus class". I think I had in mind the kind taught to the sort of typical non-math-major students who take calculus in state universities in the USA. I.e. not particularly mathematically inclined students, who, if they are interested in the course, are interested in it primarily as a means of seeing if they can answer a challenge to learn something difficult. | |
| Jul 12, 2010 at 2:16 | comment | added | The Mathemagician | Should have known Harry Gindi would be involved in this............ | |
| Jul 12, 2010 at 2:15 | comment | added | The Mathemagician | SIGH. Another terrific educational question closed for no good reason other then it annoyed the researchers. | |
| Jul 12, 2010 at 0:44 | history | closed |
Robin Chapman Gerald Edgar Charles Siegel Harry Gindi Andrea Ferretti |
not constructive | |
| Jul 11, 2010 at 23:18 | comment | added | john mangual | Besides RC's remark, I don't see anything polemical about this question. He has questions about MVT and he is entitled to ask them on this site. There have been lots of successful math pedagogy questions in the past on MO such as: mathoverflow.net/questions/2755/… and mathoverflow.net/questions/21552/… and mathoverflow.net/questions/1291/… | |
| Jul 11, 2010 at 23:14 | comment | added | Pete L. Clark | Here is an important comment: I don't think either "Yes, we should cover MVT" or "No, we should not cover MVT" is the correct answer. One should begin with a declaration of goals: what are students supposed to get out of this (particular) freshman calculus class? I think it is clear that there are multiple reasonable goal sets and that MVT is an important part of some but not of others. | |
| Jul 11, 2010 at 23:10 | comment | added | Pete L. Clark | @Franklin: you're right; there are computational applications of MVT. I'd forgotten about that, since I've long since stopped covering them in my freshman calculus classes. Students have a lot trouble with e.g. MVT applications involving inequalities. | |
| Jul 11, 2010 at 23:05 | answer | added | Jeff Strom | timeline score: 30 | |
| Jul 11, 2010 at 21:59 | comment | added | O.R. | A note: Heine-Borel is also equivalente to MVT and to the continuity axiom of the reals (the existent of supp, or the nested interval thing). FTC is not, there is the analogous in other spaces $\sum_{k=a}^{b}(C_{k+1}-C_k)=C_b-C_a$. (Just to show once more how central MVT is) | |
| Jul 11, 2010 at 21:59 | comment | added | O.R. | If it is so important (and I agree it is) then it should have many applications. What I see in MVT is a failure of the professors in showing how useful it is in getting results. In one comment I read the claim that MVT only gives theoretical results. I don't think this is true. It can be perfectly well be used to get computational result, bounds of errors (estimations), inequalities (and this are the examples that come to my mind). | |
| Jul 11, 2010 at 21:02 | comment | added | The Mathemagician | I second Pete's objection to the closing.Many students struggle with this in elementary calculus and only students who go on to more advanced real analysis courses not only fully understand the MVT,but understand why it's so critical to differential calculus on the real line. Which is bad since with the exceptions of the Hiene-Borel theorum and the fundamental theorum of calculus,the MVT and it's related results are probably the most important theorums in classical analysis on the real line. | |
| Jul 11, 2010 at 18:34 | answer | added | vonjd | timeline score: 3 | |
| Jul 11, 2010 at 18:32 | comment | added | Theo Johnson-Freyd | I think a question in this direction would be great. As currently written, the question feels a little too argumentative for my tastes. I'm not going to vote to close, but I encourage OP to edit out some of the rant. | |
| Jul 11, 2010 at 18:18 | answer | added | Matt | timeline score: 4 | |
| Jul 11, 2010 at 17:55 | comment | added | Pete L. Clark | I disagree with RC: this is not about polemics but about math education. The role of MVT in freshman calculus has been discussed in several papers -- if anyone asks, I will supply references. I think it is an important question because (i) MVT (or something like it) is necessary to be able to give theoretical explanations of most of the basic facts of caclculus (and conversely, it seems to be of only theoretical use) and (ii) it is a standard topic in freshman calculus and one with which many students have trouble, so we should discuss what it is doing there and whether/why we need it. | |
| Jul 11, 2010 at 17:47 | answer | added | O.R. | timeline score: 3 | |
| Jul 11, 2010 at 17:17 | answer | added | Deane Yang | timeline score: 13 | |
| Jul 11, 2010 at 17:09 | comment | added | Robin Chapman | This seems to be just a dubious polemic about a topic remote from research mathematics. Voting to close. | |
| Jul 11, 2010 at 17:05 | history | asked | Michael Hardy | CC BY-SA 2.5 |