Operational Invariants and Instrumentalization of Artefact Study and Research Path for High School: A Case Study

Resumo

Background: one of the challenges of a teacher’s activity is to use, assimilate and adapt the available resources with which the functional teaching of a mathematical knowledge will be created. Objective: we are interested in the instrumentalization process from which a mathematics teacher uses and assimilates a new artefact: a study and research path (SRP) on the operation of parabolic antennas. Design: This is a case study. Setting and participants: an experienced teacher and a group of students of a French high school (aged 15-16). Data collection and analysis: SRP formulations, registers and transcripts of two interviews carried out with the teacher before and after the implementation of the SRP, and video recordings of the development of eight class sessions. Results:   based on the instrumental approach and Vernaug’s definition of operational invariant (OI), we identify and classify into four types the OIs that guide the teachers’ mathematical and didactic activity, whose goal is to get the SRP device to work in a mathematics course: linked to the study aids, the mathematical knowledge (explained in the official programme), the time (controlled by the teacher), and the teacher. Conclusions: The OIs are not the absolute ‘the situation’, ‘the institution’, the accreditation’, ‘the qualification’, etc. They are combined so that the teacher uses the OIs associated with a classical way of teaching. The instrumentalization process produces an instrument that moves away from the initial SRP artefact.