For the purpose of improving the quality of education people suggest to emphasize intrinsic values of education instead of regarding education merely as a means to extrinsic values. In spite of the general agreement on putting emphasis on intrinsic values in education, we are not sure of what “intrinsic values” are. R.S. Peters influentially argues that theoretical inquires such as science, history, mathematics and philosophy, have intrinsic values because they can be justified transcendentally. So he claims that theoretical inquiries have to be taught primarily in school. Because of Peters' influential argument, we tend to identify intrinsic values with theoretical inquiries. But is it plausible interpretation of “intrinsic values” in education? In this study I try to show, first, how complicated the phrase “intrinsic values” is. I argue that the identification of “intrinsic values” with theoretioal inquiries is an oversimplification. I also examine Peters' transcendental argument and point out its problems. Next, I suggest to change the focus of discussion from asking what kind of things have intrinsic values so as to be school subject-matters, to asking how we can teach subject-matters in the way to reflect their internal values. In oreder to recognize values internal to a subject-matter, we should understand the subject-matter as an activity which has internal values. To explain this I introduce MacIntyre's concept of “a practice”. After introducing Maclntyre's concept of “values internal to a practice,” I further develop the idea of “values internal to a subject-matter,” and explore its educational implications.