Abstract
The role of the teacher in orchestrating a mathematical discussion is undeniably essential. This role becomes even more determinant in a discussion happening online and synchronously. In this paper, using instrumental orchestration and the Model of Aware and Effective Attitudes and Behaviors, we analyze the features of an online synchronous mathematical discussion taking place in an 11th-grade class in Italy, focusing particularly on the teacher’s attitudes and behaviors in orchestrating it. The discussion occurred under distance learning conditions and addressed a notoriously challenging topic: the study of parametric
functions with a focus on the meaning of variables and parameters in an early calculus task designed to foster conceptual rather than procedural knowledge. The analysis illustrates the roles assumed by the teacher within the specific learning environment considered, and how these roles serve to highlight and give value to conceptual aspects relevant to the teaching of parametric functions. Although this study is difficult to replicate, it demonstrates that meaningful online synchronous discussions are possible. The effective roles assumed by the teacher are decisive in orchestrating such a mathematical discussion and in guiding students toward the creation of new conscious knowledge.