A father brings his child to a Staten Island Pre-K program during the first day of school in 2019. New York City’s early childhood system is undergoing massive shifts, and many details about what next year’s pre-K program will look like remain up in the air. Michael Appleton/Mayoral Photography Office Families can now apply for New York city’s Pre-K for All and 3-K programs. But the backbone of the city’s heralded free preschool for 3- and 4-year-olds — independent providers who contract with the city — say they are facing an uncertain school year. That is the case for Violet Rouse, who has taken care of children in Brooklyn’s Bedford-Stuyvesant neighborhood for almost two decades. She spent last summer adding another classroom to her child care center, VernyKidz, in the hopes of expanding the 3-K program there.