We explain certain learning difficulties in computer science education as resulting from a clash between the students' culture as computer users and the professional computing culture. We propose the concept of fertile zones of cultural encounter as a way of overcoming these learning difficulties. This pedagogical approach aims to bridge the gap between cultures by designing interventions that are appreciated by members of both cultures, yet also guide the student to engage in the practices of the professional culture. The learning difficulties are demonstrated by a detailed analysis of episodes taken from an advanced high school computer science course in concurrency. We show that fertile zones of cultural encounter can be successful in significantly improving learning of this subject.