Pedagogical grammar occupies a middle ground between the areas of prescriptive and descriptive grammar. Simply put, prescriptive grammar sets forth rules about how language should be used correctly. It prescribes language the way a doctor prescribes medicine by saying what ought to be done. Descriptive grammar, on the other hand, describes how speakers actually use language without consideration for whether it conforms to "proper" rules.
Since the goal of pedagogical grammar is to help non-native speakers achieve fluency, some of both approaches is necessary. In order for a language learner to speak well, most of his or her utterances will need to conform to the grammatical rules set forth in prescriptive grammar. On the other hand, it helps to understand the way native speakers actually use language; through descriptive grammar. This is necessary for the learner to make sense of slang or other non-standard ways of speaking, such as ending sentences with prepositions.