I saw a sign that said:
As your teacher I will not tolerate any student in this classroom doing anything that is not in their best interest or the best interest of the class.
I believe it should say:
As your teacher I will not tolerate any student in this classroom doing anything that is not in her best interest or the best interest of the class.
What is correct?
I would prefer:
As your teacher I will not tolerate any student in this classroom doing anything that is not in the student’s best interest or the best interest of the class.
I agree with you. “…anything that is not in his or her best interest…”
Strictly speaking it should be “in his best interest.” Yes, even if the class is all female.
But that construction is being phased out for obvious reasons. Using “their” is one of many options and it’s less clunky than “his or her” or making up a pronoun.
Best solution, though is recasting:
As your teacher, I will not tolerate any students in this classroom doing anything that is not in their best interest or the best interest of the class.
Neither is totally correct: both contain a dangling participle.
But the second one is closer to being correct: “student” is singular while “their” is plural. English does not contain a gender-neutral singular possessive pronoun (except for “its” which isn’t appropriate here), and the first version struggles against that limitation.
Some grammar descriptivists will tell you that either version is fine, but they is wrong.
I thought that switched some time in the early 90’s. Now, you use the female unless the class in all male.
Actually, on odd-numbered days of the month… 
Would you really prefer this?:
As your teacher I will not tolerate any student in this classroom’s doing anything …
That seems to me to be the only way to un-dangle the participle without changing word order.
Personally? I’d go with RealityChuck and just rephrase the damn thing.
Centuries of incorrect grammar!
14… Arth. & Merl. 2440 (Kölbing) Many a Sarazen lost their liffe.
1545 ABP. PARKER Let. to Bp. Gardiner 8 May, Thus was it agreed among us that every president should assemble their companies.
1563 WIN{ygh}ET Four Scoir Thre Quest. liv, A man or woman being lang absent fra thair party.
1643 TRAPP Comm. Gen. xxiv. 22 Each Countrey hath their fashions, and garnishes.
1749 FIELDING Tom Jones VII. xiv, Every one in the House were in their Beds.
1771 GOLDSM. Hist. Eng. III. 241 Every person…now recovered their liberty.
1845 SYD. SMITH Wks. (1850) 175 Every human being must do something with their existence.
1848 THACKERAY Van. Fair xli, A person can’t help their birth.
1858 BAGEHOT Lit. Studies (1879) II. 206 Nobody in their senses would describe Gray’s ‘Elegy’ as [etc.].
1898 G. B. SHAW Plays II. Candida 86 It’s enough to drive anyone out of their senses.
[From the OED]
How about simply, Behave yourself or else.
Presumably the message is addressed to more than one student:
Behave yourselves or else!
(But apart from that nitpick I like it)
As Terminus Est notes, the use of “them/their/s” with a singular antecedent, while against the “must agree in number” bugaboo of strict prescriptivism, is a time-honored construction for usages where members of an abstract or variable group of which you are unsure of the gender composition is being addressed or referenced.
Personally, I prefer ‘his or her’, or ‘his/her’ in writing, over singular ‘their’ – but that’s a matter of taste, and it can sometimes result in awkward constructions.
As Reality Chuck mentions, though, even better is to restructure the sentence so the “their” has a plural antecedent.
For me, it’s more like the possession arrow in a basketball game. If I can remember which gender’s pronoun I wrote last, I switch to the other. Him, her, he, she, his, her(s), and so on.
I think that could become very confusing. If you have “him” in one sentence, and “her” in the next without a new antecedent, I would be think at first there were two antecedents of different genders somewhere.
I have to admit, I enjoy this method. Oddly, the one place that I know uses it religiously is (or was) White Wolf.
I don’t have any difficulty with singular/plural their, any more than I have difficulty with singular/plural you, and any time I am speaking or writing informally, I will use it. Although I’d also like to tip my hat to Mr. Tobin, who once called us back as we were leaving English class, waving an object and saying “Sombody left his purse at his desk.” He enjoyed that just way too much.
I’ve seen this done in several textbooks in the 90s, and it drives me up a wall. I’m not sure which I hate more, gender-neutral pronouns changing from sentence to sentence or paragraph to paragraph, or the needlessly wordy “he/she” or “he or she” construction (or the ugly “(s)he.”)
In all but the most formal of writings, I will use the time-honored gender-neutral “they/them/their/etc” if recasting the sentence (as Reality Chuck suggested) is not desirable for whatever reason. In formal writing I will do my best to recast, or settle for the “gender neutral” masculine pronouns. Or, if I only occasionally need a pronoun, I might find myself using “he or she.”
Absolutely not true. Where did you ever hear this?
The best solution is to recast the sentence in all plural, students … their…
Saying student… their is fine for almost all purposes, except when your audience is primarily those I call the “ignorant pedants,” people who know everything about the English language except how it actually works. (**Randy Seltzer ** appears to be an example. Oops, hi, Randy. 
)
Saying student … her … for a generic example is always wrong because it calls attention to itself for no purpose, unless you really are trying to do one of those horrible exercises in alternating his and her, and I highly recommend never doing that because your readers will want to kill you before the end of the book.
It’s funny how someone can speak so strictly that they cease speaking correctly.
Seriously, that’s just not right. Though it’s true that your “strict” rule has been accepted for a long time by many language elites, it doesn’t hold up to more careful scrutiny of the language. That’s not the way we speak. “His” comes with the presumption that the person referred to is male. If our goal is to avoid such presumptions, then it’s best to avoid “his”.
The real answer to Two and a Half Inches of Fun is that the choice of “their best interest” is perfectly correct, and better than “her” which would come with the presumption that the students are female. Not only that, but the “singular they” form has been in use for centuries. It’s simply impossible for the usage to become more perfectly cromulent than it already is.
Recasting for the plural works just fine, too, but there’s nothing intrinsically “better” about it. It’s just a matter of taste.
A dangling participle is not necessarily incorrect.
You’re absolutely wrong. The “singular they” form has been used since Shakespeare’s time, was in fact used by Shakespeare, and it is the one of the most common choices, if not the most common choice. It “struggles” against nothing.
They’re not wrong about their methodology, although they can easily be wrong about individual observations. They’re human, after all. They’re not wrong on this topic, either.
And your last sentence was not grammatical. Even descriptive linguists would tell you that your sentence contained a grammatical error. That you actually thought you were making some kind of point with that just goes to show how little you understand the subject. Descriptivists (also known as “the people who are right”) study the way the language is actually spoken. They formulate their grammars not based on the absurd notion that everything a native speaker says is automatically correct. They simply sit and record, and when they have enough data, they attempt to describe the way that people actually speak. In other words, they shut up and listen when they’re trying to figure out the rules of language, instead of coming up with the rules first and then getting pissed when people diverge from their expectations.
Sometimes they misinterpret the data and come to wrong conclusions. But to approach the language in any other way is to engage in nothing less than Lingual Creationism, as if the Lord Almighty set down the proper rules for English with the publication of Strunk & White’s crappy little book, and every deviation from their holy tract makes the baby Jesus cry.
That’s not how it works.
It certainly is in some English dialects.