Elementos do saber profissional do professor que ensina matemática: uma aritmética para ensinar nos manuais pedagógicos (1880 - 1920)

Some reviews covering the education of teachers who act on the initial years of basic education in Brazil have indicated the difficulty in describing the professional knowledge of teaching, and this extends to the professional knowledge of the mathematics teacher. From a socio-historical perspective, and using pedagogical textbooks as documental sources, this research was guided by the following question: which elements from the professional knowledge of the teacher who acts in the initial years of education can be described as an “arithmetic for teaching”, in the pedagogical textbooks (1880–1920)? Searching for this description, this research’s theoretical-methodological framework is composed of authors who placed objectified knowledge in a central position in the study of the professional education of teachers (articulating knowledges to teach and knowledges for teaching) and of those who consider that the interpretation of knowledge, based on information, happens in stages (scientization of knowledge). From this framework, two subgroups of pedagogical textbooks were analyzed: Arithmetic textbooks and Pedagogy textbooks. In the first subgroup the research aimed to describe a “multiplication for teaching”; and the second, a “calculation for teaching”. The analysis of the Arithmetic textbooks offered methodological criteria for the analysis of the knowledges for teaching in textbooks. The presentation, the explanation, the graduation, the articulation, the generalization, and the evaluation were each able to delineate a multiplication for teaching: traditional multiplication for teaching; traditional-intuitive multiplication for teaching; intuitive multiplication for teaching; and intuitive-bespoke multiplication for teaching. The analysis of the Pedagogy textbooks indicated objectification directives for an oral calculation for teaching which should precede the written calculation, at times in the defense of an intuitive calculation, and at other times of an inductive, or an intuitive-abstract, calculation for ...