The Sag Harbor School District identified the child as sixth-grader Cesar Albarracin Guncay.
Superintendent Jeff Nichols said in a letter to parents the accident occurred during the annual class trip to the Poconos.
"On behalf of the entire district, we extend our deepest condolences to Cesar's family and loved ones during this extraordinarily difficult time," Nichols said in the statement. "We ask our community to honor Cesar's memory and keep his family in our thoughts."
A large group was rafting Wednesday around 5 p.m. when the raft flipped over.
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The coroner's office said the 12-year-old had already been removed from the water before the deputy coroner's arrival. The child was pronounced dead at the scene.
Drone video showed a raft overturned and pinned against a fallen tree in the river. Police could also be seen near the Bowmanstown boat ramp off Bowman Road near the Rt. 895 bridge.
Nichols said school counselors will be available for students and staff.
"There are no words to adequately express the depth of this loss. Cesar was a cherished member of our school family, a child who mattered deeply to all who had the privilege of knowing him," Nichols said. "His absence will leave an irreplaceable space in our classrooms, our hallways and our lives."