A bucket hat is called in Hebrew "dumb hat", presumably because of its shape which resembles a dumbbell.

Nonetheless, the hat became the epitome of the Israeli sabra (a term that came into widespread use in the 1930s to refer to a Jewish person who had been born in the land of Israel).
It was manufactured in Israel in mid 1930s, becoming a favorite by settlers, strike force soldiers, and workers, thanks to covering both head and neck, having a lightweight design, and being able to be folded and placed in one's pocket. 

Those nostalgic hats were sewn by ATA.