In recent years, some efforts have been made to consolidate out-of-field-teaching as research field in mathematics education. Taking teachers' professional knowledge as reference frame, out-of-field-teachers seem less qualified regarding CK and PCK in mathematics than teachers that were especially trained to teach their subject. In this paper, we approach the phenomenon of out-of-field-teaching by focusing on both teachers' beliefs and competencies while the latter is operationalized as skills in designing mathematical tasks for written exams. Data was collected throughout a qualification program particularly focusing on out-of-field-teachers' domain-specific professional knowledge. We discuss in detail design aspects of our ongoing research and give first insights into the changes of out-of-field-teachers' beliefs reflecting their professional development in the course of the qualification program.