This is the adverb cousin of pedagogical. You use it when you want to say “in a way that has to do with teaching” or “if we think about how people learn”. “Pedagogically speaking, this book is too hard” means “if we think about teaching, this book is too hard for these students”. It is formal, like the adjective. You will hear it from teachers talking to other teachers, or in talks about education. In everyday talk, people usually just say “for teaching” or “for learners”. It does not mean “in a strict way” or “like a know-it-all”; that would be closer to pedantically, a different family.