The Nebraska State Historical Society checked into it and came up with this information: This school was not created in a photographer’s studio but, as Mr. Simon suspected, it’s not an ordinary classroom either. Actually, this is a photograph of a small school for white children that was held in the home of a white doctor—Dr. E. J. DeBell—on the Rosebud Indian Reservation in Nebraska. Two of Dr. DeBell’s children were students at the school (though they’re not identified in the photo).
The room pictured may have been used for other purposes (entertaining, etc.). Hence the place's makeshift appearance. The subjects, of course, had to be posed, due to the long exposures required to shoot interiors back then. So the “action” looks stiff. However, this was truly a shot of school in session.
This picture is part of an extensive collection from an amateur photographer named Lily Bruner Monroe (maiden name: DeBell), who was the doctor’s daughter. The teacher is identified as Ella J. Bruner.