BUILDING VIRTUAL TREES OF POSSIBILITIES: WHAT CAN STUDENTS LEARN BY DISCUSSING COMBINATORIAL RELATIONS?

Abstract

With the aim of analysing the influence of building trees of possibilities in solving combinatorial problems with the use of an educational software, this research was based on the Theory of Conceptual Fields by Vergnaud (1986), which argues that there are three fundamental dimensions of concepts: meanings, symbolic representations and invariants. The participants were 20 5th grade students in the Elementary School of two public schools in the city of Recife, divided into two groups. Students participated in a pre-test, in different forms of intervention and in post-tests (immediate and delayed). Group 1 (G1) constructed trees of possibilities making use of the “Diagramas de Árbol” software and Group 2 (G2) formed the assisted control group who worked with multiplicative but not combinatorial problems, through drawings. With just one intervention session, significant quantitative and qualitative improvements were achieved by students of early years of the experimental group. The use of the software enabled advances in understanding different combinatorial meanings, leading students to reflect on relationships and properties of different situations.
It is concluded that it is possible to work with different kinds of combinatorial situations since the Early Years and through efficient symbolic representations, such as the virtual tree of possibilities. Therefore, the research aims to contribute to the debate about the best possibilities of Combinatorics learning in the Early Years of Elementary School.

Keywords: Combinatorics; Trees of possibilities; “Diagramas de Árbol” Software; Early Years of Elementary School.

DOI: http://dx.doi.org/10.14244/19827199740