Caracterización del razonamiento algebraico elemental de estudiantes de primaria según niveles de algebrización

Abstract

This work shows the end results of a research project conducted in the frame of a Mathematics Education masters’ program. The research addresses the correspondence between the algebraization levels proposed by Godino, Ake, Gonzato and Wilhelmi, (2014), the tasks of algebraic nature in textbooks, and the performances exhibited by elementary schoolchildren when faced with such tasks. The research was conducted with students from "Montessori School," in the city of Medellin, Colombia. The text book used was "Envision Math" (Ed Pearson). Godino’s et.al proposal is recent and has not been contrasted neither with textbooks, nor with the performances of students in elementary school. The research considers four stages: the first stage refers to the classification of algebraic character tasks proposed in the textbooks analyzed, the second stage relates to the design of a test to be applied to children; the exercises included in the test were taken from the textbooks analyzed. Furthermore, the third stage concerns the application of the test and the fourth stage refers to the contrast between levels algebraization attributed to the tasks and the children’s performance. During the first stage it was found that the description of algebraic properties proposed by Godino-Ibid- did not include certain types of algebraic nature tasks included in the texts analyzed. The proposal for Godino et.al., was complemented by the taxonomy of algebraic performance of Burkhardt (2001). A report on the consistency between algebraization expanded levels, the tasks proposed in textbooks, and children's performance is given.