They and their as gender neutral pronouns

In the sentence, Any student who forgets his homework will be punished with exemplary severity , the his is singular to reflect the singular nature of student.
The problem with this is that my classroom has women in it. So let's try:

Any student who forgets her homework will be punished with exemplary severity.

Now it sounds like I am letting the men off more lightly.


What can I do?

Well I could do this:

Any student who forgets his or her  homework will be punished with exemplary severity.

That works, but his or her is a bit wordy. 

Happily, it is now acceptable to use their, nominally the plural third person possessive pronoun, to serve as a gender-neutral term:

Any student who forgets their homework will be punished with exemplary severity.

The same gender-neutral  use may be made of they.

If a student has forgotten their homework, they had better have a good excuse ready.

You can always get around the problem by pluralizing the whole thing:

Any students who forget their homework will be punished with exemplary severity.