According to David Crystal, British linguist, the appropriate way to say - at least in writing - is "they", "their", "them" as a sexless singular pronoun when not knowing whether it is a he or a she. Like in: Who has lost their meal? Many go round this issue by writing his/her, or somehow skipping it altogether. I also admit that "their" sounds awkward, but I have grown accustomed to it and I find it Ok now. I wish I could give you some references, I'll look up smth for you.
If that were on an assignment or in a letter, I would correct it: speak her mind or speak his mind. The sentence in question is about a known student; the teacher should know the student's gender, right?
Its is reserved for things, or humans that are viewed as things; e.g., from the Victorian Age, a child should know its place in society.