Sistemas numéricos: uma proposta utilizando UEPS e história da matemática

Abstract

With the advancement of technology, electronic devices such as cell phones, computers, notebooks, among others, are developed using numerical systems such as binary and hexadecimal, which do not have their deserved attention in the teaching of mathematics in the scope of Basic Education. The same is true with the study of the development of numerical systems, which, by appearing little in mathematics classes, may allow the idea, even if not explicit, that the mathematics we use today, has always been that way, and always will be. However, since primitive times man has used actions that today we characterize as Mathematics, as when counting in a two-way manner to control a flock of sheep (one stone for each sheep), for example. Over time, each civilization, according to its needs, created its own number systems. In this context, the objective of this work is to present aspects of different numerical systems and to discuss two activities, our proposal, to approach the theme through the pedagogical approach of History of Mathematics. It is about putting students to discuss number systems through the proposals created, analyzing evidence, creating systems and interpreting cases from the past, without considering the historical evolution of some of the most important number systems in the world, since their creation, needs of the time, adaptations and trajectory. The emergence of numerical systems linked to numbers, leads us to the intention of presenting the importance of teaching numerical systems in the final years of elementary school and high school, since we have witnessed, due to the decrease in mathematics classes over the years. years, less and less concern in teaching these themes. The two proposed activities discussed in the work are structured based on the precepts of the Potentially Significant Teaching Units (UEPS) and the historical approach as a source of motivation and methodology that facilitates teaching and learning. The History of Mathematics is used as a means of arousing student interest, analyzing the evolution and development of systems, aiming to achieve the objective of UEPS, meaningful learning. The first proposal seeks to work with the construction of numerical systems with the objective of leading students to reflect that all systems have been “built” and that the symbols we use are representative of the idea of number, and may represent different ideas if used in base systems many different. The second proposal aims at working with the historian that exists in each student, with the objective of instigating students to infer, from the investigation of a historical table and based on the alphabet and numbers of a Sumerian numerical system, possible interpretations of historical records.