Cognitive Construction of the Solution Set of a System of Linear Inequalities in Two Variables - Muñoz-Orozco, Adrián; Martínez-Sierra , Gustavo (Uniciencia, 2025)
[Objective] The objective of this research is to identify the mental structures and mechanisms used by a group of Business Administration students to understand the solution set of a system of linear inequalities in two variables (SSSLI), as they establish Cartesian Connections. The theoretical foundations used are the APOS theory articulated with the concept of Cartesian Connection. [Methodology] This study is qualitative. For the design of the instrument, a preliminary genetic decomposition (PGD) was developed, and based on the PGD three tasks were designed. For data collection, these tasks were applied to a group of 19 students (between 18 and 22 years old). Later, the three participants who provided the most detailed answers were selected to conduct a semi-structured interview. [Results] The results showed that participants constructed the SSSLI Process by coordinating the solution set Process of the linear inequality in two variables (SSLI) with the set intersection Process. It was observed that participants associated the SSSLI with a polygon and did not consider it to be an empty, convex or bounded set. [Conclusions] It was concluded that those participants who constructed the action structure or a SSLI process showed the same type of structure in relation to SSSLI. New research is suggested that delves deeper into the mechanisms and mental structures described in this study, as well as into the design of teaching proposals that contribute to improving SSSLI learning.