The hyperreal numbers and the understanding of the concept of the derivative of a function in the course of calculus.

摘要

A new system of numbers exists, ampler than the Real Numbers, which the process of teaching-education of the students of Calculus in the United States has facilitated. This new approach does not use the theory of limits in the education of Calculus, but the idea of infinitesimals. This system is the System of Hyperreal Numbers.;This investigation is a phenomenological study on the cognitive and meta-cognitive process when the System of Hyperreal Numbers for the understanding of the concept of the derivative of a function in the course of Calculus is included. The intentions of this study were to investigate what cognitive and meta-cognitive process shows the student when he or she was exposed to the approach of the Hyperreal Numbers' System; how it influenced this new conception in the solution of problems that require Calculus; and which curricular implications pronounced when east system to the education of the course of Calculus is included.;The design of the investigation was qualitative and strategies of the method of the "Study of Case" were used. These strategies were the reflective interview, observations while the students solved problems which student thought aloud. The participants were four voluntary students of the University of Puerto Rico, Rio Piedras Campus, who took the course of Non Standard Calculus.;When compiling and analyzing the information we found that the understanding of the derivative of a function occurred through meta-cognitive and cognitive process that allowed having an additional tool to the theory of limits to solve the problems of the derivative of a function, between the students interviewed. The use of the Non Standard approach constitutes one better curricular tool for the teaching of Calculus because it foments and incites the use of cognitive and meta-cognitive processes. A greater use of meta-cognitive skills implies greater understanding. Best education is that than it goes directed to the cognition and meta-cognition of the students.;Also, one was that the way in that these students think when they solve problems in other courses that involve limits is through the idea of infinitesimals and not in limits.