Cognitive construction of the solution set of a system of linear inequalities in two variables

Abstract

The objective of this research is to identify the mental structures and mechanisms used by a group of students to understand the solution set of a system of linear inequalities in two variables (CSSIL). 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, we developed a preliminary genetic decomposition (PGD) and based on it we designed three tasks. For data collection, we applied these tasks to a group of 19 students (between 18 and 22 years old). Later, we selected the three participants who provided the most detailed answers to conduct a semi-structured interview. [Results] The results showed that the participants constructed the CSSIL Object by coordinating the Solution Set Process of the Linear Inequality in Two Variables (CSIL) with the Set Intersection Process. We observed that the participants associated the CSSIL with a polygon and did not consider it to be an empty, convex or bounded set. [Conclusions] We conclude that those participants who constructed the action structure or a CSIL process showed the same type of structure in relation to CSSIL. We suggest new research 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 CSSIL learning.