A question on the basic chemistry of a molecule dissolving in water...?

I'm a beginning biology and chemistry student in college. One of the first things we learn is the difference between a physical and chemical change. So, I know for sure that (for instance) salt dissolving in water is a physical rather than a chemical change. But now I'm learning about exactly how a salt molecule dissolves in water because the water molecule (H2O) contains a polar covalent bond while the salt molecule (NaCl) contains an ionic bond between sodium and chlorine. This is where I'm stumped. If the nature of the bonds causes the NaCl molecule to be broken up into Na and Cl when it's dissolved in the water, then how can it be said that this is a physical change and not a chemical change? Am I incorrect somewhere in my ysis of what goes on?