I checked my daughter's textbook and found sentences of the same structure. I still think they sound odd to me. I'd think if the same subject is involved in the two clauses linked by "while", at least the second time the subject should be omitted to make it smoother. E.g.
I was eating popcorn while watching my favorite movie.
I was eating popcorn while I was watching my favorite movie.
So, any ideas anyone?