Fases del razonamiento inductivo que presentan profesores de matemáticas al resolver un problema de generalización

Abstract

Se reportan seis fases del razonamiento inductivo que presentaron 19 profesores de matemáticas de secundaria al resolver un problema de generalización de un patrón cuadrático. Los datos se recolectaron mediante sus respuestas escritas y entrevistas. El análisis se realizó con base en el modelo de Cañadas y Castro (2007). Se encontró que, para generalizar de manera correcta, no basta con reconocer las regularidades en varios casos particulares, sino que se precisa de asociar esas regularidades con estructuras matemáticas que describan el patrón de manera general, y se detectaron dificultades en algunas fases que impidieron a los profesores llegar a generalizar.

This investigation reports six inductive reasoning stages presented by nineteen middle school mathematics teachers when solving a generalization problem of a quadratic pattern. The data was collected through their written responses and interviews. The analysis was performed based on the model of Cañadas and Castro (2007). It was found that the correct generalization not only needed the recognition of regularities in some particular cases, but an accurate association between those regularities and the mathematical structures that describe the pattern in a general way. Furthermore, several difficulties that prevented the teachers from achieving a generalization were detected.