Isekai Teni shite Kyoushi ni Natta ga, Majo to Osorerareteiru Ken: Aoi-sensei no Gakuen Funtou Nisshi

Stripped of her life for reasons unknown, Aoi Konominato wakes up as a child in an unfamiliar world, still haunted by regret and goals left unfulfilled. After twelve years of learning under the tutelage of an elven sage named Owain, she's mastered the art of sorcery and is sent by her wise—if eccentric—mentor to the renowned Fiddich Academy to serve as an instructor and further her studies. Bitter memories of her past life as a fledgling teacher still nip at her heels, yet despite her initial reluctance, Aoi knows that this is her chance to do things better. Determination won't be enough, though. Between misbehaving students of noble birth and elitist instructors, Aoi may have bitten off more than she can chew...or she might just be the missing ingredient the academy needs to become a paragon of educational equality and discipline. Class is in session, and the fearsome witch of Fiddich Academy has come prepared to teach them all a lesson they won't soon forget. (Source: J-Novel Club)