Análisis de los errores en tareas geométricas de argumentación visual por estudiantes con talento matemático

Zusammenfassung

In this work, we analyze the mistakes made by a group of twenty-five students, aged between 13 and 16 years, when involved in the resolution of geometrical tasks while participating in a project for stimulation of the mathematical talent, during three curricular enrichment sessions focused on reasoning techniques. Specific visual argumentation mistakes are identified (namely making false analogies between plane and space, not discussing all the possible cases, and reasoning from concrete limited examples), as well as those derived from the incorrect use of reasoning elements, contents, and mathematical procedures. From the study of correlations, it is apparent that most of the mistakes are independent, both amongst each other and with respect to the scores obtained in three visual and intellectual capability tests. The ANOVA results from repeated measurements show that the frequency of appearance of specific visual argumentation mistakes decreases throughout the three sessions.