The purpose of the present article is a reflection on the concept of cultural sensitivity as the major element of the (inter)cultural competence presented in The Common European Framework of Reference for Languages: Learning, teaching, assessment (Council of Europe, 2001), juxtaposed with the leading paradigm of interculturality in glottodidactics. Whereas this dominant ap-proach often focuses mainly on the question of differences and similarities be-tween cultures, our model allows us to take a look ‘from the inside’ by trying to adopt an attitude of reflectiveness towards cultural standards, among oth-ers. After analysing some of the theories concerning developing intercultural sensitivity, such as the sociological model of Bennett or the educational sys-tem of Byram, we proceed to justify why we would promote the cultural ap-proach in glottodidactics. We seek to explain how we can specify cultural sen-sitivity, what elements which encourage this attitude and what would block it. In the last part of the article, we concentrate on the specificity of media dis-course in the context of cultural sensitivity and on ways of using authentic mass media materials in the teaching-learning process, providing some exam-ples taken from a pilot study conducted by the author for her Master’s thesis.