A pedagogic grammar is a description of how to use the grammar of a language to communicate, for people wanting to learn the target language. It can be compared with a reference grammar, which just describes the grammar of the language. Pedagogic grammars contain assumptions about how learners learn, follow certain linguistic theories in their descriptions, and are written for a specific target audience.
How English Works and Grammar in Use are pedagogic grammar books, as they help learners use the grammar of English for communication.
In the classroom
Learners can be asked to compare different explanations of a language point from different grammars. This allows learners to think about grammar and its role in communication.