I've always thought that using the word "his" as a gender-nonspecific pronoun has been acceptable; in recent years, however, I've been told off by people when I do this, saying it is now "politically" correct you use "her" for a gender-nonspecific pronoun. I've always have, since these occurrences, used "his/her" (or "his or her") instead, though I am now pondering which of these to use, for I am currently writing a paper, and have no idea which pronoun to use; the "his or her" seems a little clunky, and I would much rather prefer an alternative.
This is not a duplicate of this, because I am asking which is generally accepted; also I am unable to use the word "one," as my paper should be understood by little ones. I already know that the use of the singular "they" is frowned upon (by English professors, both mine and others'), and that using a plural noun doesn't work for a good deal of my sentences that encounter this problem.
Any clarification is appreciated!