There are diverse attitudes in Islam about the roles of men and women, but in worship the roles are clearly defined. When worship takes place in a mosque there are different expectations of men and women.
Muslim women may attend the mosque but traditionally pray separately from men, either in a separate room or in a balcony so that men may not see them. Prayer is too important for people to be distracted so men and women have to pray Salat prayer in separate places.
Women are not obliged to attend the mosque, so many pray at home with their children. All that is needed is a clean place to pray so that they can show proper respect for Allah. The mother's role is important in teaching children prayers and readings from the Qur'an.
In a mosque, prayer is led by an imam, and traditionally imams have always been male.
This diversity in worship may be demonstrated in how men and women worship at home.
In daily prayers in a mosque, men are more likely to attend for Salat prayer, so women will perform Salat prayer at home, and lead children in prayer with them. In this sense women have a great deal of authority in prayer at home.