It is well known that pre-service teachers might experience a double discontinuity between school and university. They often see little or no connections of university mathematics to their future profession. We offer a theoretical contribution on how this second discontinuity can be addressed in teaching abstract algebra by considering design principles for developing non-local knowledge for teaching. Based on previous research, a logical structure for the principle of “Sequencing the learning arrangements by building-up, (re-)learning, stepping-down”, and the principle of “Relating local and non-local representations” by contrasting and comparing are elaborated. Exemplary realizations for the contents of solving equations and arithmetic properties are presented.