Processos históricos para o cálculo da área do círculo: uma análise em livros didáticos

Abstract

The principal objective of this Course Completion Work is to analyze some didactic books present in the National Program of Didactic Book (PNLD 2017) destined for the final years of Elementary School, in order to verify the presence of historical processes on the calculation of the area of the circle. In their search we describe the proposals brought by the official documents of curricular orientation, on the calculation of the area of the circle. In relation to our objectives, there search is of the exploratory type, and characterized as a documentary research, because it sought to analyze the approaches present in the textbooks adopted by the teachers of the municipality of Jacaraú - PB, Rio Tinto - PB and Mamanguape - PB. To base our research we turn to authors Fossa (2001), Boyer (2004) and Eves (2010) who talk about the History of Mathematics, making a brief history about the use of the History of Mathematics in teaching. We also analyze the teaching proposals on the area of the circle contained in the National Curricular Parameters (PCNs) in the Curricular Frameworks of the Elementary School of the State of Paraíba (RCEF / PB) and in the National Curricular Common Base (BNCC); we also addressed the Guide to the National Textbook Program (PNLD 2017). Thus, this work brings a brief history of the area calculation of the circle, some explanations for the formula developed by the Egyptians, presents still a bit of the history of the number pi and shows possible ways of using the History of Mathematics in the classroom. It also brings out what we have analyzed in the main curricular guidance documents for mathematics teaching in order to verify the guidelines for the area teaching of the circle. We have seen that these documents refer to the use of the History of Mathematics as a resource which can stimulate mathematics classes and arouse the interest of the student, but do not provide specific guide line show this teaching should occur, as well as how to do this specific approach to the circle area. In the analyzed collections, which were Mathematics Understanding and Practice of Ênio Silveira (2015) and Willingness to Know Mathematics of Souza and Pataro (2015), we perceive that they approach the content in an analogous way, however one of the collections makes a small use of historical contexts and the other presents only an exercise with historical contexts, we observe in general that the approach of the History of Mathematics occurs in the textbooks analyzed.