Grammar

Grammar is the field of linguistics that describes the way any given natural language is used. It includes morphology and syntax, often complemented by phonetics, phonology, and semantics.

Each language has its own distinct grammar. "English grammar" is a description of the way the English language is used. A reference book describing the grammar of a language and presented in a "rules" format is called a "reference grammar" or simply "a grammar".

A fully explicit grammar exhaustively describing the grammatical constructions of a language is called a descriptive grammar. This can be contrasted with a prescriptive grammar, which tries to enforce some hypothetical governing rules about how a language should be used.

Teaching grammar
It is probably inevitable that English language coursebooks created for the instruction of non-native speakers will be well into the prescriptive side of the descriptive/prescriptive spectrum. Teachers should be aware that the grammatical explanations presented in such books are explicitly simplified for consumption by non-native students and may not always represent the whole truth.

Those who would like a more profound understanding might wish to read The English Verb by Michael Lewis - a book specifically written with such native language teachers in mind.

Nevertheless teachers who have to work from a coursebook should be careful about criticizing it to their students as this may cause them to start to lose faith in all the material in the book, a consequence which would impede their learning.

Teacher's tip
For teachers looking to giving their students extra grammar work, How English Works (Oxford ISBN 0-19-431456-1), by Michael Swan and Catherine Walter is excellent for self study.

For teachers themselves, Swan speaks highly of The Cambridge Grammar of English, by Carter and McCarthy; The Comprehensive Grammar of the English Language (Longman, 1985) by Quirk, Greenbaum, Leech and Svartvik; and The Cambridge Grammar of the English Language (CUP, 2003), by Huddleston, Pullum et al.