I sometimes hear language teachers talking about cross-cultural communication as if it was something that the language teacher needed to learn in order to be a more effective teacher.
I do not believe this to be the case. It is the learner who must learn, not the teacher who must teach. The willingness and ability of the learner to cross into another culture is the single most important factor in language learning. The learner needs to be good at cross-cultural communication, not the teacher.
The more the learner listens and reads in another language the easier it becomes to cross into that culture, and , as long as the learner can choose content of interest, the more enjoyable it becomes. L’appetit vient en mangeant.” as they say in French.