This is the 12136th most frequent Polish word.
mającymi
"Having" or "possessing" (instrumental plural form).
Here, 'mające' is used as a present participle referring to people possessing experience.
Osoby mające doświadczenie w pracy z dziećmi są mile widziane.
People having experience in working with children are welcome.
In this sentence, 'mająca' describes the teacher as someone actively having duties at present.
Mająca dużo obowiązków nauczycielka ledwo miała czas na odpoczynek.
The teacher having many duties barely had time to rest.
Here, 'mające' identifies organizations whose goal is protection of the environment.