Some have suggested adding an or into the sentences. May the student complete his or her homework. This clogs our language, and while I'm treading carefully here not to piss anyone off, my standing battle is for clarity and simplicity. And if his or her writing reflects his or her intent to soothe his or her desire to create a gender neutral setting where his or her peers all feel equal, then so be it, but it's sludgy and I'm already lost. Furthermore, if we get picky, why is the he pronoun first? We should have to flip it around each time to make it fair: If his or her writing reflects her or his intent to soothe his or her desire . . . . Swapping pronouns requires greater effort on the reader's part and highlights the author's political intent. The reader stops reading what the author says and instead reads the author's social statement.
That's two down, what else is left? We could use the unisex pronoun derived from Nordic or Anglo-Saxon roots: thon. It sounds epic, but does thon really want thons writing to sound like a mix of Shakespeare and Norse-speak? Doubtful. And if this is the first time thon has heard of this word, then let that be another indication of its popularity in thons language.
They might work, but if we're being strict with grammar, it's plural, and if a single author writers their book, does that mean this author wrote a book for the proletariate, or this author has multiple personalities? Style books often complain about they, as he has also been used for centuries as a gender-neutral pronoun and contains no sexist undertones, which, they argue, were added in recent decades. Many of these books tell the reader to suck it up and use he (and she) and not fuss about modern interpretations of those words.
We could use s/he, but I hate it, because it reads like the author isn't certain what he wants (hark, a sexist pronoun!), and wants to force the readers to decide how they want to interpret it. But I'm an indecisive reader, and I read this as s-sh-he; that's not a word. Don't use it.
My best advice is, as I did in the previous paragraph, to pick one pronoun and stick with it, but to use the plural forms where possible. Notice that I made author singular—I wanted the example situation to contain one author whose actions directly influenced readers, which I made plural so as to avoid using the he pronoun again. Thus, where possible, switch to plural to avoid sexist writing (though keep in mind that he as a gender-neutral pronoun existed for hundreds of years, and only recently did people make a fuss about it). Sometimes the plural form won't fit, but often it will. Instead of reader use readers, and student use students. Use they or we instead of he or she. You won't lose quality to your writing, and it will remain clear and concise. But otherwise pick one pronoun, use it, and don't make a scene about it. Writers hate scenes.