Modern architecture really kicked off just after 1900's. Partly a reaction to the ornate and over adorned Victorian and Edwardian buildings; partly due to due new building techniques and materials and partly a political and social revolution.
Some modernist architects were lucky enough to design large pubic buildings, some of them schools.
Here are some seriously cool schools. Sorry Hollingworth High School, you did not make the cut.
Hunstanton Secondary School by Alison and Peter Smithson
The Bauhaus Dessau by Walter Gropius
ADGB Trade Union School - Hannes Meyer
Haggerston School by Erno Goldfinger