Five dollars a week.

That’s what Fort Greene resident Nia Hoyte pays so that her three-year-old son, Kaiden Neith, can learn to read. These days, although he’s not old enough to understand all of the words, Kaiden’s a bit of a bookworm.

“Every day he comes home he’s like, ‘Mommy, read, read, read,’” Ms. Hoyte said last Tuesday morning after dropping her son off at Duffield Children’s Center on Fleet Place, a 15-minute walk from their apartment. “We read on the bus, we read on the train.”

Duffield, which is run by the Brooklyn Bureau of Community Service (BBCS), is a publicly funded day care center serving a number of children from nearby public housing developments and lower income families. Duffield also is one of two centers in Fort Greene that might have to close if a proposal to shutter 15 care centers in gentrifying areas citywide goes through.

To the city, the leases for some of the centers — the list of which also includes Farragut Day Care Center on Gold Street — are draining money from a tight budget. Located in neighborhoods where real estate values are rising, the spaces themselves are no longer affordable.

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