Death Weapon Meister Academy

Death Weapon Meister Academy (or DWMA for short) in Soul Eater could be considered this, as they teach and train relatively normal children to become effective 'meisters' and 'weapons'. (The weapon children are naturally born with the ability to transform, but it's a trait common enough in the world to not be considered a 'super power'.) In the spinoff Soul Eater Not! it is stated that DWMA is recognized as a school that produces heroes of the world and its graduates are respected by the society.

Example of:
Hero Academy