CONSTRUÇÃO DOS NÚMEROS RACIONAIS NA LICENCIATURA: UM ESTUDO DESENVOLVIDO À LUZ DOS TRÊS MUNDOS DA MATEMÁTICA - Flôres, Marcia Viaro (2020)
The teaching experience in an initial formation course allowed difficulties to be perceived regarding the approach of some mathematical subjects, as in the case of rational numbers. It is known that this subject is treated early in Basic Education, but it is questioned what place it occupies within degree courses in education and what approach is given when it is taught to future teachers of mathematics. Through the pursuit of research that worked with aspects related to teaching and learning of rational numbers, it was possible to broaden the comprehension of the problem that permeates this subject on the degree courses in education and, by becoming aware of this, this research is presented. This study aimed to know how the principles from the theory of the Three Worlds of Mathematics – Embodied World, Symbolic World and Formal World, advocated by David Tall, can sustain a purpose of formation of future Mathematics’ teachers about concepts related to rational numbers and perceive which results the proposition produces about the learning of these concepts. The subjects and context chosen for the application of the study were eight students regularly enrolled in the discipline of Fundamentals of Analysis of the Degree in Mathematics of an Federal Institute, in the second semester of 2018. This research had a qualitative character, being organized based on a teaching sequence based on the theory of the Three Worlds of Mathematics, by mathematician and mathematical educator David Tall. This theory enables to analyze the development of mathematical thinking from its most elementary to the most advanced form, developing a theoretical framework that allows us to indicate how humans learn to think mathematically. Besides the assistance on the construction of tasks, this theoretical framework also was used in data analysis, which was collected through the production and interviews of students and the researcher’s logbook. With the results obtained by applying the teaching proposal, it can be seen that students were able to understand the axiomatic construction of rational numbers, and most of them had their productions with characteristics of the Symbolic World, with some evidence of the Formal World. Still, it was possible to work the relations of the formal construction performed with aspects of rational numbers seen in Basic Education. From the research, it was found that both the axiomatic construction and the relations produced were of fundamental importance in the initial formation of students.