To+ ing how to use it properly?

This to+ ing drives me mad. Is this sentence correct or not? Why? If not how I should rewrite it?

This method derives from the traditional.approach to teaching Classical languages such as Latin and Greek.

Thanking you in advance!

The sentence:

This method derives from the traditional approach to teaching Classical languages such as Latin and Greek.

is correct, because what follows "to" (which is a gerund) is equivalent to a noun. Notice you can also say:

This method derives from the traditional approach to the teaching of Classical languages such as Latin and Greek.

Other expressions where the gerund will follow "to" are look forward to, be used to, be accustomed to, be devoted to, be committed to, advantage to, drawback to, witness to, prey to, home to, key to, heir to, toast to, changes to, addiction to, different to, lead to, pay attention to, say yes/no to, similar to, stick to.

A rule of thumb is: if you can replace the non-finite with the word "something" (or "somebody"), then a gerund will be used.