Americans have grown increasingly likely to believe that women and men should have equal roles at work, in politics and at home. But a significant share still say that men’s and women’s roles should be different at home — even when they believe they should be equal at work.

A new study, based on national survey data from 1977 to 2016, helps explain why the path to equality seems in some ways to have stalled — despite the significant increases in women’s educational and professional opportunities during that period.

Two-thirds of Americans and three-quarters of millennials say they believe that men and women should be equal in both the public sphere of work and the private sphere of home. Only a small share of people, young or old, still say that men and women should be unequal in both spheres — 5 percent of millennials and 7 percent of those born from 1946 to 1980.

But the study revealed that roughly a quarter of people’s views about gender equality are more complicated, and differ regarding work and home. Most of them say that while women should have the same opportunities as men to work or participate in politics, they should do more homemaking and child-rearing, found the study, which is set to be published in the journal Gender and Society.