Higher education institutions are responsible for delivering university-level mathematical knowledge to prospective mathematics teachers in a manner relevant to their future professional practice for teaching a core competency of 4C skills. The ability to teach these skills in the mathematics classroom is demanded by educational reform in the 21st century. However, creating learning experiences that allow them to acquire 4C skills is becoming increasingly difficult. Thus, the study was interested in discovering challenges faced by teacher education institutions in equipping prospective mathematics teachers with 4C skills-based instruction by considering similar challenges experienced by school teachers in the classroom. The study used semi-structured interviews to gather data from 10 teacher educators seeking university perspectives and 10 in-service teachers for school perspectives. A constant comparative analysis of gathered data yielded five themes, discovering critical challenges experienced by participants in integrating 4C skills. The study highlights that prospective mathematics teachers did not receive proper training in teaching 4C skills because educators had limited knowledge, facilities and support. This study suggests universities employ a dynamic new learning system to equip incoming mathematics teacher graduates with the essential resources such as a School-University Partnership mediated Lesson Study (SUPER-LS) program as an approach to overcome the challenges. This novel TPD program supports the professional development of pre-service teachers at university and in-service teachers at school in two ways, including emphasising PD activities on mathematics transposition promoting student learning 4C skills and facilitating them through the collaborative learning communities of lesson study groups.