Axisymmetric?! Practices, Social and Socio-Mathematical Norms of Justifying Axial Symmetry of Plane Figures in Primary School

Social negotiation processes are an essential part of teaching. Through them, shared knowledge, as well as expectations, about what is expected from a solution or justification and what characterizes them as acceptable and complete, are constituted. This paper deals with the subject matter of axis symmetry and analyzes which social, socio-mathematical norms and practices are established in the verification and justification of axis symmetry for plane figures in classroom discussions. The data set comes from design experiments of a design research study with third grade students in the teaching-learning laboratory at University of Paderborn. The experiments are based on a learning environment focusing on the classification of square axisymmetric and non-axisymmetric figures. In form of local theories, it is shown that a need for justification of a classification as a social norm only arises by demanding a justification by the teacher. Referring to a verification procedure and contrasting are significant practices in the argumentation process while proving the axial symmetry of a figure. These are related to the socio-mathematical norms, doing an empirical proof or explaining a concept-defining characteristic. Moreover, expectations about the completeness of a justification could be made visible. The extent to which practices are established seems to depend mainly on the extent to which the need for justification is indicated.