Difficulties in arguing the use of semiotic registers in quadratic variation problems/Dificultades para argumentar el uso de registros semióticos en problemas de variación cuadrática

Abstract

It is presented a qualitative case study with an experimental approach in which we sought to understand the lack of participation in class of a group of 14 9th grade students in a public institution in the department of Chocó. We inquired about the operational issues they develop when solving a quadratic variation problem by presenting several semiotic registers of the task and focusing on the arguments they offer to justify their reasoning. We found a marked preference for the tabular register, although it is not the optimal one to solve the task, and a difficulty to offer arguments based on evidence that give more strength to their reasoning. Class participation should be promoted through open tasks, starting to develop argumentative processes in lower grades and minimizing teaching focused on memorization and application of algorithms to develop mathematical thinking.