The term pedagogic linguistics is used in AWE to label the work that we do in trying to teach students about how to use English better. (In our case, it is specifically targeted on those who want to write academic English better for the purposes of Higher Education in the UK. Pedagogic is derived from pedagogy, which is the 'craft, art or science' of teaching. Linguistics here refers not to the science known as linguistics, but to the adjective linguistic, meaning 'to do with language' - in our limited ambition, 'to do with the English language'.
The whole of this guide is dedicated to the idea of showing learners how to meet the requirements upon them, and guiding to become more confident users of the language for their purposes in taking qualifications designed to fit them for professional lives.