Could they have been part of the property since the school opened in 1923 as the Brookside School? My spouse attended Sheffield Middle School in the 1970s and remembers the scrapers were there then.
I hope that the boot scrapers get a good home before the school building is eventually demolished; either in a display at the new school or at the Sheffield Village Historical Society.
Bob Vila's website has a little bit of information about boot scrapers. It notes that they date back to the days when horse-drawn wagons were a standard (and often messy) mode of transportation, and slowly disappeared as cars replaced horses, and dirt roads began to get paved.
I guess it makes sense that the school had these scrapers. As the photo below shows, Colorado Avenue was still a dirt road in front of the school back in the 1920s.