As a sugar syrup is cooked, water boils away, the sugar concentration increases, and the temperature rises. That means that when you drop a bit of it into cold water to cool it down, it will form a soft ball.
Continue boiling, uncovered, not stirring the mixture but shaking the saucepan occasionally to distribute the heat as the mixture turns amber in about 9 minutes, then darker amber as it registers 305 degrees on the thermometer (hard-crack stage ), about 3 minutes longer.