Conway's most controversial responsibility as Education Minister was managing the government's legislation for full funding to Ontario's Roman Catholic separate schools. Conway's grandfather, Thomas Murray, had championed a similar initiative in the 1930s, and was disappointed when Mitchell Hepburn backed away from a previous commitment in the face of Protestant opposition. Conway had supported the announcement of full funding by Bill Davis's Progressive Conservative government prior to the 1985 election, and was responsible for significantly increasing the actual revenues to the Catholic system after a mathematical error in the Davis government's funding formula came to light. He also guaranteed hiring rights for non-Catholics within the system, and exempted non-Catholic children from compulsory religious education in separate high schools.