Cloche hats

Here's the Wiki:

The cloche hat is a fitted, bell-shaped hat that was popular during the 1920s. (Cloche is the French word for bell.) Caroline Reboux is the creator of the cloche hat.

Cloche hats were usually made of felt so that they conformed to the head. The hat was typically designed to be worn low on the forehead, with the wearer's eyes only slightly below the brim. By 1928-1929, it became fashionable to turn the brims on cloche hats upwards. This style remained prevalent throughout the early 1930s until the cloche hat became obsolete around 1933-1934.

Often, different styles of ribbons affixed to the hats indicated different messages about the wearer. Several popular messages included: An arrow-like ribbon which indicated a girl was single but had already given her heart to someone, a firm knot which signaled marriage or a flamboyant bow which indicated the wearer was single and interested in mingling...

Photo via My Ear-Trumpet Has Been Struck by Lightning.