I used to have an umowa o działo when I worked (myself) as a freelance language teacher but I have heard that the law changed and now this isn't possible. Is it true?
In principle, this occurrence should not have happened. Teacher should be employed for an indefinite period.
BUT there is an exception to this rule.
W przypadku zaistnienia potrzeby wynikającej z organizacji nauczania lub zastępstwa nieobecnego nauczyciela, w tym w trakcie roku szkolnego, z osobą rozpoczynającą pracę w szkole, z nauczycielem kontraktowym lub z nauczycielami, o których mowa w ust. 5, stosunek pracy nawiązuje się na podstawie umowy o pracę na czas określony.
source: Karta Nauczyciela Art. 10, paragraph 7
It says that in case of a need resulting from organization of teaching or replacement of the absent teacher employment is established on the basis of a contract of employment for a definite period (such as Umowa o Dzieło).
This form of 'teaching organisation' is not precisely specified. But since your teacher works just for a few hours a week - maybe it fits the rule. Better ask an lawyer to be sure.
Poor teacher.. (and of course you, as an employer in Poland - you don't have a paradise here)
