If a piece of information goes over someone's head, [they] do not understand it.
My teacher explained to me that it is informal usage for an indefinite pronoun, the formal usage should be "his or her".
If the first sentence is informal, I wonder if this is a formal one:
If a piece of information goes over someone's head, [he or she] does not understand it.
Both are in practice. When you describe an epicene pronoun, you can call them either 's/he' or 'they'. Some also call this as a 'singular they'.
It states:
Singular they is the use of they, or its inflected or derivative forms, such as them, their, or themselves, to refer to a single person or an antecedent that is grammatically singular. It typically occurs with an antecedent of indeterminate gender.
So to answer, both of those sentences are okay.
