Well, if we're now allowed to use they as singular then the ACT is wrong. In my past year of schooling we've gone over a large bit of grammar, including much concerning the ACT and SAT. I've been told that if you're going to use singular in a sentence, such as Bingley's example, it should be written as "Each student should check his or her work carefully and correct their own mistakes." I think it sounds a little awkward myself, but yes, we're supposed to use "his or her" rather than "their." Now, we can use just "his" or just "her", but it's considered politically correct to alternate. Of course, we can also use "one" as in "One should be careful about what one is saying."