Inecuaciones: un análisis de las construcciones mentales de estudiantes universitarios

The main proposal of this work is to present a set of mental constructions or schemes that the student can develop in order to understand the concept of inequality. Based on this set of mental constructions I present my methodological proposal of teaching to improve the teaching-learning of this concept. I use the paradigm of pedagogical investigation and development created by RUMEC (Research in Undergraduate Mathematics Education Community) group which is composed of a cycle of three stages for research in mathematics education. One of the stages of this cycle is reduced to the theoretical analysis of the concept of inequality according to the theoretical reference of APOS (Action, Process, Object, Schema). This is based on Piaget’s ideas adapted by Ed Dubinsky for their use in the graduate level. In this stage I propose an initial mental scheme which will serve as reference for the elaboration and implementation of a first methodology of teaching in a Calculus class. I gather and analyze the data from this first implementation and redo the mental scheme, elaborate, and implement a second methodology of teaching. The results of the analyses of the new data gathered produced a final mental scheme for the conception of inequality. I also do the quantitative analysis of the improvement of the inequality study between a group of students who learned the contents according to the methodology presented in this work and a control group that did not have the teaching-learning proposal.