Algebraization levels reached by first grade secondary school students in solving a structural rational number task

Abstract

The objective of the report is to analyze the features of the algebraization levels of first grade secondary school students in the resolution of tasks involving operations and properties of rational numbers, an activity considered as a structural task in the framework of Elementary Algebraic Reasoning. The activity demands the elaboration of conjectures and their validation, which in turn demand generalization processes using variables. For the design and analysis of the mathematical activity developed, elements of EOS and qualitative research are used. It is concluded that the traits identified in the students' work correspond predominantly to algebraic reasoning level 1, since the students made arguments in their procedures generalizing and finding a pattern (extensive-intensive duality), in addition there is no presence of properties.