The prescriptive or traditional approach takes the view that grammar is a set of rules and, in order to learn a language, you must master these rules. There is a right and a wrong way to use language, independent of what people actually do. A prescriptive approach, for instance, would teach that "whom" is the correct word for an object, eg "With whom were you dancing last night?" because the underlying rules of language dictate that a prepostion (like "with") must be followed by an object.
The descriptive approach is more popular nowadays. This aims to see how language is actually used, and explain this to students. With this approach, you would teach your students that "Who were you dancing with last night?" is a better question because this is how everybody actually talks, which is more important than the underlying principles of language. Winston Churchill summed up the debate perfectly in his famous memo "This is the sort of English up with which I will not put."
The descriptive approach is more popular nowadays. This aims to see how language is actually used, and explain this to students. With this approach, you would teach your students that "Who were you dancing with last night?" is a better question because this is how everybody actually talks, which is more important than the underlying principles of language. Winston Churchill summed up the debate perfectly in his famous memo "This is the sort of English up with which I will not put."