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    Álgebra para resolver problemas: as propostas de Otelo de Souza Reis e Tito Cardoso de Oliveira, década de 1910
    (Universidade Federal de São Paulo (UNIFESP), 2019-09-26) Rocha, Ivone Lemos Da [UNIFESP]; Bertini, Luciane De Fatima [UNIFESP]; Universidade Federal de São Paulo (UNIFESP)
    This text is the result of a research within the History of Mathematical Education. In the theme of arithmetic problems and algebra in the primary course, we sought to answer the question: how are the proposals of Otelo de Souza Reis and Tito Cardoso de Oliveira for the use of algebra in solving arithmetic problems? The analyzes performed here characterize the professional knowledge of the teacher (BORER, 2017) who teaches mathematics, working on the concept of articulations between knowledge to teach and the knowledge to teach (HOFSTETTER; SCHNEUWLY, 2017). These, in this appropriate work (CHARTIER, 1998), illustrate a mathematics proper to school culture (JULIA, 2000), a mathematics to teach and a mathematics to teach (BERTINI; MORAIS; VALENTE, 2017). Analyzed from a historical perspective (LE GOFF, 1990; BURKE, 2016), they assume aspects that illustrate how arithmetic problems are employed, constitute their own historiography. In these textbooks, a mathematics is perceived that matters to the teacher who teaches mathematics to know to teach how to solve problems: algebra, in its rudiments. It participates in the knowledge to teach how to solve them in the higher classes of primary, described by the Report of Committee of the Fifteen (1895) as riddles or conun-drums. To this end, these textbooks bring specific guidance for teaching, using a method that would be a tool for resolutions (VALENTE, 2016; 2017) for interest. This would be linked to themes of proportionality, everyday gifts with double, triple, halves and so on. In the algebraic method, it is proposed that the teacher who teaches mathematics lead his students in a march of reasoning that presents students the unknown quantity as an unknown x, previously agreed as a species, that would start a data transformation march; its operations would be identified by words such as giving, selling, buying, spending, more, less, withdrawing; put the problem into equation, its resolution should satisfy the transformation of the data; The final resolution would involve the arithmetic method with the fundamental operations. At their own pace, each author brings proposals of a method. There is an algebra with still very present arithmetic, a professional knowledge characterized as an algebra to teach how to solve arithmetic problems in the 1910s.