Update: The APA Style Blog weighs in on the singular “they.”
Why can’t I use “they” as a singular pronoun? I tried to use “he or she” instead, but it’s cluttering up my writing! Are there any other options?
The short answer for students is as follows: avoid the singular “they” in formal writing unless you’re a language-change renegade, you’re working in a progressive discipline, or you know your professor is OK with it. Use plurals instead.
This is a hot topic, so we created a Slideshare to answer the question.