Noções de cálculo do ensino médio: uma visão através do livro didático

Abstract

This work aims to suggest and analyze some topics from high school textbooks that can convey a notion of calculus to students. To achieve this, a thorough analysis was necessary during the textbook selection process, always paying close attention to the recommendations made in the notices, textbook guides, catalogs, and reviews made available by the National High School Education Program (PNLEM). The analysis was conducted on three textbooks widely used in high school. Topics already familiar to students were covered, such as Functions, Geometric Series, and Natural Base Logarithms. This strategy emphasized the basics of calculus, which focuses more on limits, infinity, and infinitesimal values than on algebra. Also suggested, always with the support of the National High School Education Program (PNLEM), were some exercises that, if worked correctly, can perfectly convey notions of calculus to students, even without using specific calculus resources. In fact, these are exercises proposed from high school content itself, where at most, new notation would be introduced to the student. Finally, it was concluded that it is perfectly possible to convey a calculus concept to high school students, even without the dreaded complexity that is commonly encountered. Textbooks, however, played a fundamental role in this work, supporting pre-established ideas and making it clear that they cannot be the only learning option for students, nor even the sole reference for teachers. However, they can certainly serve as a great complement to both, as long as they are used appropriately.