Search

The aim of this article is to provide some elements about the set of real numbers and a synthetic view on the motivation of its rigorous constructions in the 19th century. Since the seminal works of Cauchy and Weierstrass, such constructions became a requirement for the arithmetization of the mathematical analysis. We also analyze some didactic considerations regarding teaching the set of real numbers in high school and at the beginning of university. With this article, we hope to provide subsidies for the elaboration of epistemological models of reference (EMR) for studies and research on the contents of functions, limit and continuity, among others. [ABSTRACT FROM AUTHOR]

In this paper some theoretical tools are utilized that contributes the ontosemiotic approach of the mathematical cognition (Godino, 2002), in order to study how is put into play a network of objects and semiotic functions in the fragment of a textbook of the second course of High School --representative of the introduction to the defined integral-- in students of the Autonomous Comunity of Andalucia (Spain). The analysis has as purpose to characterize the ontosemiotic complexity of the text and the potential semiotic conflicts that can be produced in the students that use it. Previously, a synthesis of the theoretical framework is presented, that includes the theory of the institutional and personal meanings of the mathematical objects and the theory of the semiotic functions. [ABSTRACT FROM AUTHOR]

Copyright of Annals of Telecommunications is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)