This school building may be difficult to identify which district it served. It is a guess that the photo was taken sometime around the turn to the twentieth century.
Most of the schoolhouses in Green County at that time were made of wood and typically had three or four tall windows on each side. Of course, they had to have a chimney since they used wood burning stoves to heat the building. If there is something about this photo that will substantiate what school district this school was in, let Matt Figi know at 608-325-6503 or mfigi48@tds.net.