Assuming that the after school program takes place on school grounds, the answer is yes, the school does have a duty to supervise its students. The second part of the question, i.e., the specific nature of the school's duty to supervise under New York law, is where it gets trickier, however.

If the after school activity is a "voluntary participation in an intramural or extracurricular school sport," then the school need only act as a reasonably prudent person under the circumstances; conversely, if the activity is a graded class, then the school will be held to the higher standard of care of a reasonably prudent parent.

For additional information on this topic, please see "The Duty of a New York School to Supervise Its After School Programs" and "Why This NY School Negligence Decision is Really No Big Deal."