Análisis de razonamientos abductivos por docentes en formación: Un estudio exploratorio

The training of pre-service mathematics teachers must include formative tasks to revise and develop an adequate knowledge of reasoning and proving processes. This text presents results from the implementation of a teaching experiment with pre-service teachers on the conjecture and proof of the inscribed angle theorem. Specifically, MTSK (Mathematics Teacher’s Specialized Knowledge) model and the REP (Role of Examples in Proving) framework are used to analyse behaviours when validating or refuting a possible justification of the theorem, based on a false relationship, that is proposed as an abductive reasoning. It is characterized the work of four pairs, all of whom were able to identify, with the provided script of questions, counterexamples to the relationship, but only one pair showed an understanding of their role in refuting the relationship.