Teachers’ Facilitation of Students’ Mathematical Reasoning in a Dynamic Geometry Environment: An Analysis Through Three Lenses

Using three theoretical lenses, we investigate a teacher’s practice in a dynamic geometry teaching sequence aiming to support students’ development of mathematical reasoning. These lenses are the Danish KOM framework’s description of mathematics teacher competencies, the Theory of Instrumental Orchestration (TIO) and the theoretical construct of Justificational Mediations. The KOM framework supports ways to describe the practice of mathematics teachers, whereas the instrumental orchestration lens allows for a more fine-grained analysis of teachers’ practices in a technology rich environment. The construct of justificational mediations acts as a “bridge”, in our specific empirical case, between the mathematics teacher competencies that teachers rely upon and their identified orchestrations, which both lead to a certain choice of mediations in a dynamic geometry environment. The results from our analyses are discussed in terms of potentially networking KOM and TIO through the construct of justificational mediations for richer analyses of teachers’ facilitation of students’ learning in a dynamic geometry environment.