Final answer:
The school nurse should apply direct pressure, elevate the injured arm, and immobilize it until factor replacement therapy can be initiated.
Step-by-step explanation:
The school nurse should take supportive measures for the boy with hemophilia who fell on his arm during recess. These measures should focus on controlling bleeding and providing comfort to the student until factor replacement therapy can be initiated. Firstly, the nurse should apply direct pressure to the injury site using a sterile cloth or bandage to help control bleeding. Secondly, the nurse should elevate the injured arm to minimize blood flow to the area and help reduce swelling. Lastly, the nurse should immobilize the arm by using a splint or wrap to prevent further injury and to promote healing.