This text is the result of reflections and considerations coming from the results of the dissertation of the author of that proposal. That work sought to answer the question: how is algebra in primary education characterised to solve arithmetic problems in the teaching books of Otelo de Souza Reis and Tito Cardoso de Oliveira? Looking at those two teaching books in the 1910s, taking into account the professional knowledge, described by Borer, from a historical perspective, drawn up in the course of a history of knowledge, we consider the teaching environment in mathematics to be an area in which his own exercise produces practices and representations. To that end, the aim of that work is to illustrate the possibility of incorporating new knowledge into the training of primary teachers, so that the latter may be part of a modern society at that time. The practices and representations there, formulated and appropriate in school culture, are considered under the knowledge that can be formalised and systematised. It is therefore considered that, as regards the problems of arithmetic and its resolutions, in the two sources used, algebra is regarded as a professional knowledge specific to teaching. They illustrate an algebrae to teach how to solve arithmetic problems, in a society which in their time is the springboard of new knowledge in teaching teaching, to teach mathematics.