In this usage, the article is correct. The sense is 'an appearance of puzzlement which seemed strange'.
Compare 'He accepted the compliments with a becoming modesty.'
'She displayed her work with a shy pride'.
The answers so far ignore the way that "as" can be followed by a post or role without an article: as president, as secretary, as mediator, as champion, as referee, as recipient.
Teacher is usually seen as a profession, rather than a post or a role, so as a teacher is more likely. But it could be a specific role: consider as head teacher, or as ...