El aprendizaje de la matemática a largo plazo: un análisis a la experiencia en el aula

Abstract

Using grounded theory methods in the framework of a qualitative research, the productions of seven Colombian high school students are analyzed when solving three mathematical problems that seek to promote long-term mathematical learning. Nine actions categorized in four levels are identified, according to the functions assigned by the participants during the solution of the problems, and the way in which they are articulated in a general repeated reasoning scheme constituted by four fundamental aspects: i) the general category and problem-instances, ii) the Basic Unit of Actions-BUA, iii) the Unit of Adjustment Actions - UAA, and iv) the organized and reorganized mental schemes. The idea of a recursive view of problem solving, as established by Kieren and Pirie (1990), is concluded and reinforced, and the same view is adopted for repeated reasoning when solving mathematical problems.