In this studied it is presented the results of a research with 23 Mathematics teachers
who attended postgraduation in Mathematics Didactics, about how to conceive the
algebra and how to introduce the theme of Equations from the First Degree. The
objective was to verify which characteristics of the dominant epistemological model
on teaching algebra are revealed in the conceptions of the teachers investigated. The
key point of the research was: In which measures the establishment of a didactic
system with characteristics of a Course of Study and Research interferes in the
spontaneous epistemology of Mathematics teachers about teaching the equations of
the first degree? The research was realized in 06 sessions in which it wasused a
questionnaire with the subjects; recorded the socialization of his ideas about their
conceptions of algebra and its teaching. To accomplish the sessions it was adopted
as the methodological procedure Course of Study and Research. The results show,
as the spontaneous epistemology teacher, the predominant view of algebra in the
sense of operation with letters and numbers and generalizing patterns, which
characterizes it as generalized arithmetic. In this sense, algebra is seen as an
extension and generalization of arithmetic practices. In respect to the question of the
research, it was found that the process of study permitted to the subjects
consciousness of taking into account the epistemological aspects of teaching
algebra, however, it was not seen significant changes in their spontaneous
epistemology, after comparing their discourses at the beginning of the research by
presenting their research at the end of praxeology.
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