Pedagogic grammar is the grammar of a language rewritten for use in teaching and learning, not for theoretical linguistics or descriptive completeness. It differs from both reference grammar (exhaustive, for consultation) and theoretical grammar (formal models of competence) in that its first question is always: what does a learner need to know about this form to understand, notice, and use it at this point in their development?
A pedagogic grammar typically involves the following choices:
Michael Swan's Practical English Usage is the most widely used English pedagogic grammar in the world. Its entries are short, problem-oriented, heavy on examples, and written for teachers and advanced learners rather than linguists. Murphy's English Grammar in Use series applies a related pedagogy at a lower proficiency level, organising by double-page spreads with an explanation on the left and exercises on the right. Azar's grammar series does the same for American English. Halliday and Matthiessen's Introduction to Functional Grammar sits at the theoretical end of the pedagogic spectrum: a grammar for teachers of grammar.
Pedagogic grammar forces choices that reference grammar can evade. How much of the perfect aspect system does a B1 learner actually need? When does "a/an" before a specific noun signal emphasis rather than indefiniteness, and is that worth saying? Should modal verbs be taught by form (can, could, would) or by function (ability, possibility, politeness)? Good pedagogic grammars are distinguished by the intelligence of those choices, not by completeness.
Three standard objections recur:
Work by Michael McCarthy, Ronald Carter, Douglas Biber, and Susan Conrad has pushed pedagogic grammar toward corpus evidence. Cambridge Grammar of English, Longman Grammar of Spoken and Written English, and Biber et al.'s corpus-based work give teachers data on what English actually does, and in which register, which has changed the default answers to design questions that pedagogic grammarians previously decided by intuition.