Análisis ontosemiótico de un problema que promueve la puesta en funcionamiento del razonamiento conjetural

Abstract

This work is part of a research in Mathematics Didactics, whose general objective is the analysis of argumentative processes to elaborate and contrast conjectures in the mathematics class of the 4th year of high school. To carry out our objective we select a series of situations–problems that promote
the functioning of the conjectural reasoning in the students, and we perform an a priori analysis of them that will constitute a meaning of intended reference for the later analysis of the personal meanings of the students when facing this type of situations. One of these situations and their respective analyzes will be presented in this work. 
As a didactic theoretical framework to carry out these analyzes, we have taken tools from the Ontosemiotic Approach to Mathematical Knowledge and Instruction (OSA), as well as from research that addresses specific and transversal questions about conjectural reasoning.
The analyzes carried out reveal the ontosemiotic complexity of this mega process of production of conjectures, the dependence of this process on the diversity of objects and cognitive processes involved as well as the potential and effective semiotic conflicts, all of which provide tools for reflect on some
guidelines to improve the degree of epistemic, cognitive and instructional suitability of the situation posed and analyzed.