When convection takes place in the mantle why does cool rock materiel sink and warm rock material rise?

This happens with all liquids which have varied heat through out it, in fact even in the air. This happens because when objects get hotter, they vibrate more, and thus take up more space. This means that the same mass takes up more space, meaning that the substance becomes less dense. Therefore, the hotter rock rises above the cooler rock because it vibrates more, so takes up less space, so is less dense.

From there, denser substances fall to the bottom because the heavier objects can push the lighter substances out of the way, which in this case, is upwards.