Why There Was A Vandewater Club At PS 114

Because that was its name!
Along with its proximity to the now gone Vandewater Street, it was probably named after this early mayor.

Jacobus Benjamin Van de Water was born in 1643 to parents Benjamin Jacobus Van de Water, and Eisjbet de Maersman. Jacobus’ Dutch parents from Rotterdam immigrated to America in 1651. They settled in New Amsterdam, now known as New York City. Jacobus soon followed, immigrating in 1658. Once settled Jacobus married Engeltje Jeuriansz and had seven children (Lysbeth, 1667; Benjamin, 1669; Cornelius, 1673; Jacobus, 1676; Johanna, 1678; Jeuriaen, 1684; Neeltje, 1687). Jacobus established his family’s name in New Amsterdam in 1674 when he was elected as one New York City’s first mayors. Jacobus also served as the Clerk of the King's Court from March 28, 1700 until June 11, 1702. Jacobus died on November 16, 1710.

PS 114, 1927

I wonder what that Vandewater Club was all about?

Fourth Ward, Before The Smith Projects: 1921

Clicking to enlarge will make the bath house/gym visible on Cherry and Oliver Street.
Also visible in the middle is PS 114, which would later become Metropolitan Vocational High School. There's also a moving picture studio on 76 Catherine Street, a Salvation Army at 94 Cherry Street and a Horton's Ice Cream place on 28 Oak Street.