The purpose of this didactic project is to analyze a current research question, namely how student teachers’ knowledge of Abelian groups contributes to their understanding of an essential aspect of teaching algebraic concepts by extending numbers and arithmetic operations. The theoretical approaches employed are Subject Matter Knowledge, and the choice of algebraic content with focus on students’ learning of algebra. The analysis includes a broad perspective of modern algebra that leads to logical, conceptual consequences, and, for the student teachers, a course of education adapted to provide sustainable development of students’ mathematical knowledge. For example, special attention should be given to the Abelian groups as a framework for teaching and learning algebra.

The outcome of this didactic analysis is a follow-up of an earlier research project titled Student teachers’ knowledge of and perceptions of mathematics. This analytical result has been implemented and tested at the teacher training programs for courses in mathematics and mathematics didactics at the K-3 and 4-6 programs at Södertörn University in Sweden.