The growing use of technology for mathematics in higher education opens new pedagogical and technological challenges for teachers. The objective of this study was to analyze the teaching approaches and technology-related pedagogical competencies of 29 mathematics teachers (15 females and 14 males) from nine European countries. After conducting semi-structured interviews, the Approaches to Teaching Inventory (ATI-16) and the Technological Pedagogical Content Knowledge (TPACK) framework survey were applied. The results show large individual variations in teaching approaches, technological competencies, and institutional support. One-third of teachers apply a more student-centered approach, one-third a more teacher-centered approach, and one-third a mixed approach. Educating and supporting teachers in embracing educational technologies thus needs to be tailored strongly to individual needs and the available institutional support resources and infrastructure.