Correctly means doing something the right way, without mistakes or errors. When you spell a word correctly, every letter is in its proper place. When you solve a math problem correctly, your answer matches what the problem asked for. When you follow directions correctly, you do exactly what was intended.

Notice that doing something correctly often requires careful attention: you need to understand what's being asked, know the right method or approach, and carry it out properly. A pianist who plays a piece correctly hits all the right notes at the right times. A scientist who conducts an experiment correctly follows each step of the procedure precisely.

Correctness means matching what's expected or required and following the proper standard or rule. If you're asked to draw a square and you draw a beautiful, perfect circle instead, you've drawn skillfully but haven't met the requirement. The circle might be excellent work, but it doesn't correctly answer what was asked for.