A geometria analítica em livros didáticos de autores brasileiros para o ensino superior: circulação no contexto da UFJF nas décadas de 1960 e 1970

Abstract

This Professional Master's research in Mathematics Education investigated the teaching of AG in higher education based on an analysis of Analytic Geometry textbooks published in the 1960s and 1970s and circulated in the context of UFJF. In the context of the history of mathematical education, we relied on the following theoretical and methodological approaches: Cultural History, discussed by Burke (2008) and Chartier (1990); the concepts of professional knowledge (to and for teaching), which are the fruit of research developed by the Research Team in the History of Educational Sciences (ERHISE) at the University of Geneva and are being appropriated by GHEMAT-Brasil; The History of School Subjects (HDE) discussed by Chervel (1990); Choppin (2002; 2004), which contributes to the understanding and treatment of the textbook as a research source; Valente (2007) with an approach to writing in the history of mathematics education; School culture as a historical object put into debate by Julia (2001) reinforces the understanding of research sources and the context of the time when these documents are analyzed. In order to select the historical sources used, we carried out a survey of analytical geometry books for higher education and selected physical works from the UFJF library collections. We analyzed five books, looking at how GA teaching is systematized in each one, what the main contents are and which of them we can systematize as knowledge. Considering the observations made according to the analyses, we identified the following as indications of knowledge to and for teaching analytic geometry in higher education in works from the 1960s and 1970s: the use of the language of set theory, vector language in the plane and in space, algebraic treatment, use of trigonometry concepts and flat and spatial Euclidean geometry, didactic organization of the content by topics and with the use of graphical representations. Finally, this work encourages the existence of the textbook in the process of teaching and learning mathematics, and in particular analytic geometry.