Research findings, comparative studies, and the establishment of educational standards have led to a shift in perspective regarding school-based mathematics learning. In the future, learners are expected not only to accumulate knowledge and skills but also to acquire competencies. Competency orientation, alongside managing diversity, represents one of the major challenges that many educators and teacher trainees feel inadequately prepared for. How can process-oriented competencies be effectively promoted? How can learners be encouraged to argue and communicate mathematically? What role does modeling play in the classroom, and what implications does this have for specific teaching situations? This volume illustrates, through numerous tested practical examples from secondary education, what characterizes competency-oriented mathematics instruction.