The word "pedagogic" means of or relating to "pedagogy". Pedagogy is the art or profession of teaching. Pedagogic grammar is that which focuses on the correct or proper use of grammar in the target language. It would focus on rules of grammar and the correct application of those rules. Some would call this type of grammar "prescriptive" because it focuses on the way people should speak and write. Another way of looking at grammar is the "descriptive" approach, which catalogues how people speak and write, without judging whether their usage is correct or incorrect.