Contribuições da Didática da Matemática para compreensão dos impactos do vazio didático na prática dos professores de Matemática que evoca as inter-relações entre os domínios numérico-algébrico e geométrico.

This paper presents some results of a poll developed during the PhD of the author who, in 2010 in France first defended the study of the interrelations between the numericalgebric and geometric domains (NAG) in teaching Mathematics. This research aims to analyze how teachers use and guide students on how to use the NAG and study how the use of such interrelations can facilitate the teaching-learning process of Mathematics. Based on the theory of educational anthropology developed by Yves Chevallard we began with the hypothesis that there is an educational emptiness about these interrelations as tool and object. We presented some of the teaching practices features about NAG in the context of the Observatory of the Numeric Practices initiated by Bronner & Farias (2007). From data collected in this survey, in which methodology was the clinical type, I approached and analyzed mathematical objects based on some data collected by a professor and his students in a class, when searching thanks to the NAG. The work included a historical and epistemological study, a study of curricula and textbooks and teachers' practices. Through this work, we tried to highlight the current conditions of teaching, and noticed a problem, which doesn't seem didactically identified or even underestimated by teachers as regards the role of interrelations between the different mathematical domains. This work reveals that, despite the empty course, interrelations are present in the practices of teachers, that they have a place and an important role in teaching Mathematics. This emptiness may constitute an obstacle for students in performing activities which involves both the numeric-algebric and geometric domains but, also, in the construction of a new knowledge. [ABSTRACT FROM AUTHOR]