Element-specific classes are only taken by those who use that element, but the classes are only specialised into the four Greek classical elements (plus light, dark, and special variants of magic, but they don't count as elements, strictly speaking).
I would consider both Mindie and Tachi specialised air elementals (one specialising in weather and the other specialising in air-vibration - sound - manipulation) and Angel obviously a specialised earth elemental, so they could teach students who share the same general element their specialised techniques to give the students a well-rounded education on how versatile their element is.
So, in summary, I'm thinking Mindie teaches air manipulation (particularly weather manipulation, since that's a fairly common specialisation), proto-thaumism, and history, Tachi teaches advanced air manipulation (since sound manipulation would involve very delicate and precise control over the air), enchantment, and animism, and Angel teaches earth manipulation (particularly metal manipulation, since that's a fairly common specialisation), health, and first aid. Sound like what you had in mind for them?