The inquiry held for the construction of this dissertation, which belongs to the line of research: History of Mathematics Education, brought to investigate the conceptualization and dissemination of the intuitive method, and its presence in the Manual Lessons Things, more specifically with regard to the teaching of arithmetic, Norman Allison Calkins, translation by Rui Barbosa de Oliveira, and Primary Arithmetica by Antonio Bandeira Trajano. Having a theoretical and methodological contribution of Cultural History, founded by Marc Bloch, André Chervel, Alain Choppin and Dominique Julia, among other authors / researchers. The data collected in this research. and therefore taken as historical sources, were collected in books, newspaper clippings, laws, ordinances, among other records substantiate this search. Analysis of the sources revealed "new" teaching practices, changes in meaning for teaching of number and the introduction of new content in school arithmetic, as had been found the presence of the school founded by the intuitive method in elementary arithmetic Trajano and Calkins. Observed the importance of these books, consequently their authors, for educational developments experienced during the 19th and begin 20th century. Scrutinizing the analytical reading of each arithmetic analyzed, connecting to the linked graphics to content, activities, and organizations of the exercises we unraveled the methodological contexts used by the authors.
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