Subject Matter Knowledge in Mathematics Teacher Training: study of the complementarity of synthetic and analytical geometries

Abstract

The objective of this article is to analyze the knowledge of the discipline put into practice when studying the complementarity and continuity of the synthetic and analytical geometries of the plane in teacher training. The research is qualitative, with a descriptive-interpretive scope for a case study. A content analysis is carried out on an intentionally designed proposal, which involves working on both approaches and their respective implementation in the Plane Geometries subject of the Mathematics Teaching course at the National University of Rosario. From a theoretical perspective, the model of mathematical knowledge for teaching is adopted and the analysis categories correspond to the domains proposed in this framework and corresponding to the knowledge of the subject, in articulation with modalities related to the synthetic and analytical geometries developed in previous studies. Among the main findings is the influence of how the statements are presented when proposing a work assignment, as well as the contribution that discussions between teachers and students make to the complementarity of approaches when comparing and confronting them. This analysis in disciplinary subjects is detected as a fertile situation that could contribute to the configuration of mathematical knowledge for the teaching of future teachers.

Synthetic and Analytical Geometries; Teacher training; Mathematical Knowledge for Teaching; Knowledge of the discipline