MALBA TAHAN: A LOOK AT DEFINITIONS IN MATHEMATICS

Abstract

This work emerges from observations related to the mathematical definitions contained in textbooks that, in general, are presented in a direct and technical way, without the concern of discussing other possibilities of presentation, such as those contained in the book The Problem of Definitions in Mathematics (1965), by Malba Tahan.  Observing the possibility of presenting other ways of defining mathematical objects, the following question arises: What types of definitions are presented in the book The Problem of Definitions in Mathematics, by Malba Tahan and how do they appear in mathematics textbooks of the current high school?  In order to obtain elements and arguments to support the answer to the question listed, it was established as a general objective to present definitions contained in high school mathematics textbooks that are in line with the definitions identified in the book The Problem of Definitions in Mathematics.  The research can be characterized as exploratory, since it seeks to stratify different scenarios and perspectives, allowing familiarization and the development of diverse perceptions about the situation under study. Finally, as for the procedures, bibliographic, since it was based on a bibliographic review, both in physical and electronic media.  From the analysis of textbooks, a set of definitions contained in high school textbooks was listed, according to the classification established by Malba Tahan. Therefore, the research evidenced the predominance of mathematical definitions presented in a technical and direct way in high school textbooks. The classification proposed by Malba Tahan in The Problem of Definitions in Mathematics proved to be a relevant tool to broaden the understanding and reflection on how definitions can be better worked. The study highlights the need to consider approaches that favor the contextualization and construction of meaning by students, contributing to more enriching pedagogical practices in the teaching of Mathematics.  Finally, we recommend the full reading of Malba Tahan's book, which includes other topics, including the study of point, line, angles, polygonal lines.