Development of elementary algebraic reasoning through numerical and geometric patterns and sequences

Abstract

This article reports the results of a work carried out with 38 students from a Colombian public educational institution, in which the development of their elementary algebraic reasoning was analyzed, using numerical or geometric patterns and sequences. The work was carried out in three phases: diagnostic, interventional and contrast, in addition, during the development of each test, interviews were carried out based on the tasks that the students solved. The results show that the initial solutions addressed a heuristic: identifying a recursive rule, which they used to find a missing term, the one they expressed in numerical, natural or iconic language, using extensive objects and arithmetic processes. The implementation of the proposal allowed the students a progressive increase in heuristic power in problem solving, giving varied and rich solutions to the activities that were presented to them, and some managed to generalize patterns using natural or symbolic-literal language. It can be concluded that the mathematical activity of most of the students is located between levels zero to two of algebrization, standing out, levels one and proto-algebraic of level two, solving problems of missing values, without modifying the expressions algebraic produced.