Understanding the Solution Set of Linear Inequalities in Two Variables to Propose a Genetic Decomposition
DOI:
https://doi.org/10.35763/aiem27.6017Keywords:
Comprehension, Inequalities, APOS, Genetic decomposition, Bachelor's degreeAbstract
The objective of this research is to analyze the understanding of a group of students in order to propose a 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 methodological 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 SSLITV by constructing three types of processes: utilizing points, rays, or generalizing properties from to . Furthermore, we found that they conceptualize the SSLITV as an area or region where some points satisfy the inequality. Lastly, we recommend further research to expand upon the proposed GD.
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Copyright (c) 2025 Adrian Muñoz Orozco, Gustavo Martinez-Sierra, Marcela Ferrari-Escolá
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