A álgebra escolar nos elementos de álgebra de Cristiano Ottoni (segunda metade do século XIX)

Abstract

This text presents the results of a study conducted in the field of History of Mathematics Education, supported by the framework of cultural history as well as by studies that address specific knowledge for the teaching profession. These studies are approached with the aim of establishing surveys about the school algebra that is present in Ottoni's Elements of Algebra compendium. In addition, the Couto Ferraz reform, contemporary to the launch of Ottoni's compendiums, is discussed, together with the author's biography, with a view to presenting the historical and social context in which the work is inserted. Regarding the analysis carried out, mathematical contents and the didactic options of the books are discussed, such as, for example, the exercises, synthesis procedures such as the “general rule”, definitions, among others. The chapters considered are: “Operations with polynomials and first-degree problems”, “Elementary theory of the greatest common divisor”, “The impasse in solving problems with negative numbers”, “Impossible and indeterminate problems”, “Solving second-degree problems” and “Applications of algebra”. What supports the choices of these themes is that, in these spaces, detailed discussions were found, often different from those presented in contemporary books, making them capable of fostering the elaboration of conjectures in the context of the History of Mathematics Education regarding the following questions: What didactic alternatives does the work use to present the algebraic content? What characteristic of the subject School Algebra is present in the work compiled by Ottoni? Answering these questions refers to the objective of the research, which is to describe the organization of School Algebra in the book Elements of Algebra. In view of this survey, similar aspects and ruptures existing between the works compiled by Ottoni are addressed, in order to deal with the teaching of Algebra in the time frame between 1852 and 1893, the period that includes the first and last edition found for the development of the present analysis.