Ionic Compound vs Covalent Compound

I found students quite confused over these basic concepts, even though I have shown them computer simulation, diagrams, etc.

Ionic Compound consists of ions.

• Positively charged ions and negatively charged ions are attracted by strong electrostatic force/ionic bond.

Covalent Compound consists of molecules.

• Molecules are attracted by weak intermolecular force/van der Waals force.

Therefore, ionic compound

• has high melting and boiling point
• can conduct electricity in molten state or aqueus solution.  WHY?

Covalent compound

• has low melting and boiling point
• cannot conduct electricity in all state. WHY?