Comprensión del conjunto solución de inecuaciones lineales en dos variables para proponer una descomposición genética

The objective of this research is to analyze the understanding of a group of students in order to proposea Genetic Decomposition (GD) on the solution set of a linear inequality in two variables (SSLITV). We employ the APOE Theory(Action, Process, Object, and Scheme) as a theoretical and method-ological framework. Three undergraduate mathematics students participated, selected based on their good academic performance. For data collection, we conducted three virtual sessions that were recorded using Google Meet; during these sessions, participants solved and discussed nine tasks. The findings revealed that students graphically represent the SSLITVby constructing three types of processes: utilizing points, rays, or generalizing properties from ℝto ℝ2. Furthermore, we found that they conceptualize the SSLITVas an area or region where some points satisfy the inequality. Lastly, we recommend further research to expand upon the proposed GD.