Boy with Songkok and Stick, Bedok South
The evolution of the songkok can be traced back to 1830 in the form of the Ottoman fez. From there, it spread to South Asia and eventually to Indonesia, Malaysia and Brunei.
The songkok is most commonly used by the Malay men and boys in Singapore. Notice the songkok the satay man is wearing in the mural.
More on songkok on Wikipedia.