Exploring real numbers as the union between algebraic and transcendent numbers: an approach for basic education

Abstract

Building mathematical concepts based on intuitive problems and the student's prior knowledge is a way of exercising student autonomy in the teaching-learning process, which is a widely discussed topic in the context of Basic Education. In particular, in Mathematics Teaching, the Problem Solving methodology aims to develop this autonomy. In this article, we discuss the importance and possibility of working with high school students on concepts commonly used in higher education, more specifically, the initial concepts of Transcendent Number Theory. To this end, we propose a didactic sequence that aims to address the definitions of Algebraic Number and Transcendent Number based on knowledge about Numerical Sets, already acquired in Elementary School. Addressing more abstract concepts of mathematics in basic education using the Problem Solving methodology contributes to awakening curiosity and interest in the area, in addition to contributing to the development of logical and deductive reasoning.