In the last two decades, educators have been following the terminology of Computational Thinking first posed by Wing. Different viewpoints and commentaries have been adopted, and accordingly course syllabi and learning materials were developed, particularly for K-12. The field has become a mandatory part of the curriculum in various countries, even for preschool age. The paper presents an academic course for pre-service teachers with the main aim to facilitate and instruct students in the process of building their understanding and interpretation of Computational Thinking, in the context of teaching their own discipline. The course pedagogical approach emphasizes the adoption of Computational Thinking while identifying significant, non-trivial, computational processes in different disciplines. The course model was implemented with three pre-service teacher populations studying for their teaching certificate in: (1) sciences for high school; (2) humanities and social sciences for high school; and (3) various disciplines for elementary school. The course allows future teachers to experience for themselves learning activities that are recommended for implementation with their future students. The course pedagogical approach and rationale are presented, followed by detailed course structure and learning assignments. The teaching, learning, and assessment approach yielded impressive achievements, although not without obstacles and difficulties. The details of the course presentation enable its implementation with different populations of pre-service and in-service teachers, and can also be implemented in schools.