Demonstração de fórmulas matemáticas no ensino médio

The objective of this study is to analyze the validity of working with proofs in the classroom and to present a partial list of proofs of mathematical formulae of the Brazilian secondary/high school curriculum. The adaptation of the proofs into the knowledge and abilities of a secondary school student should also be considered. How the teaching of proofs is treated in official publications in Brazil and other countries is also described. Working with proofs provides a number of benefits to the students, including: the development of logical reasoning, argumentative capacity, analytical skills on a daily basis, as well as motivation and a better understanding of mathematics as a science. The convenience of including the teaching of proofs in Brazilian secondary school curriculum and the need of a balance between the abstraction of proofs and contextualization of the school programmes is discussed. The approach of the proof teaching in the classroom can become a motivating factor or, conversely, a discouraging one. The conclusion is that it would be very useful to create a reference list covering the mathematical expressions of school programmes with their respective proofs that can be understood by secondary school students.

Americanismo e fordismo nos boletins da comissão brasileiro-americana de educação industrial

This text thematizes the performance of the Brazilian-American Commission of Industrial Education (CBAI) since its installation at Rio de Janeiro, on 1947, and extinction in Curitiba, on 1963. The general goal consists in identifying if are there any relation between Gramsci’s Americanism and Fordism elements and the CBAI’s performance, by means of a speech analysis from de Newsletter of CBAI and other documental sources related to the organizations performance. The specifics objectives intend to contextualize the political and economic situation that Brazil was going through before and concomitant to CBAI’s performance, emphasizing some aspects of the Cold War feature that contributed to narrow the relations between United States and other countries of Latin America, especially Brazil. On the following, it intends to present the main aspects of Gramsci’s thought and the Americanism and fordism and Passive Revolution as key categories for a better understanding of the presence of an Americanization project on Brazilian’s professional education. As so, the object of this study are the Newsletters of CBAI. Finally, the speech’s analisys of the Newsletter was the methodology used to demonstrate CBAI as an Americanism diffuser. The documental research and sources served as groundwork, especially the Newsletters, were found at Departamento de Documentação Histórica of Universidade Tecnológica Federal do Paraná (DEDHIS) and at Biblioteca de Educação of Universidade de São Paulo (FEUSP). The theoretical foundation has as a workline for the conception of the categories the studies of Gramsci about the of work (and the Newsletters itself), and the speech’s analysis of main concepts from Bakhtin, Voloshinov’s and the Circle of studies about language philosophy. At last, this paperwork concludes that the attempt to disseminate an amerizanization project in Brazil obtneined significant results on the industrialization of the country according to the fordism’s racionalization standarts, nevertheless, this research considers that such a project corroborates the comprehension about the consolidation of a Passive Revolution’s project.