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Pedagogical grammar refers to the grammatical content taught to a student learning a language other than his or her first language or the methods used in teaching that content. The goal of this type of grammar is primarily to increase fluency and accuracy of speech, rather than to impart theoretical knowledge. Someone studying in an applied linguistics field such as Teaching English to Speakers of other Languages (TESOL) is likely to be required to take a course in pedagogical grammar.
Courses in pedagogical grammar often teach students about grammatical concepts that are intuitive to a native speaker, but may be difficult for a non-native speaker. A native English speaker needs little instruction in order to invert words in a sentence to form a question; that is, "You do know me" becomes "Do you know me?" Someone learning English as a second or foreign language, however, might need an explanation of how to make this inversion. This is especially true if his or her first language forms questions in a completely different way. While explicit teaching on this area of grammar would be tedious and unnecessary for first-language speakers, it may be important in pedagogical grammar.
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.
A pedagogical grammar book is intended to help a language learner gain grammatical understanding. It may be organized in such a way that the learner works his or her way through it like a math textbook, with examples and practice exercises. This contrasts reference books on grammar, which contain detailed prescriptions of a particular language designed for someone who has a good working understanding of linguistic principles, rather than for someone trying to learn a new language.