Definition
Pedagogy is the art & science of teaching
Teaching is not just knowing your subject and saying it aloud. Pedagogy is the deliberate craft of helping others learn — the choices a teacher makes about how to present ideas, organise a class, ask questions and respond to learners. It is part evidence, part judgement, part art.
Pedagogy
The method and practice of teaching — how learning is designed, facilitated and sustained. From the Greek paidagogos, the slave who led a child to school. Today it means the whole craft of helping people learn.
Two teachers can cover the same chapter from the same textbook and produce completely different learning. The difference is pedagogy.