Richard Stanley Peters appreciates the centrality of concepts for everyday life, however, he fails to recognize their pedagogical dimension. He distinguishes concepts employed at the first-order (our ordinary language-use) from second-order conceptual clarification (conducted exclusively by academically trained philosophers). This distinction serves to elevate the discipline of philosophy at the expense of our ordinary language-use. I revisit this distinction and argue that our first-order use of concepts encompasses second-order concern. Individuals learn and teach concepts as they use them. Conceptual understanding (...) is an obligation that all individuals, and not just academically trained philosophers, must fulfil. I conclude that the role of philosophy in education is to provide a conversational context for the pedagogical dimension of concepts. I draw upon the philosophies of Cora Diamond, Stephen Mulhall, Iris Murdoch and Rush Rhees. (shrink)