The concept-based learning proposed in the Historical-Cultural Theory and Activity Theory,
which seeks to explain the role of school education in the formation of scientific concepts,
especially mathematical concepts and their importance for the student's intellectual
development, was the basis for the elaboration of this study that was punctuated in the article
of Talizina denominated of the Formation of the mathematical concepts, that approaches on
how one can work the mathematical concepts and dimensions of the mathematical objects to
aid in the theoretical foundation of the teaching action in the teaching of mathematics, for
through the formation of concepts. It was from this preliminary conception that it served as
the basis for the elaboration of this reflective study of an introductory character, whose main
objective was to find notes based on the Historical-Cultural Theory. This reflexive process
about the teaching organization took place within the subproject of the Institutional Program
of the Initiation to Teaching Grant (PIBID) of the Mathematics Degree Course of the Federal
University of Tocantins - UFT, at the Marechal Rondon State School in the city of Araguaina,
in the North of Tocantins, during the period from 2014 to 2017, with Elementary School
students in the afternoon shift, however, although the analyzes presented here are derived
from activities developed under the subproject. These have only served as a starting point
since, along the way, the need to translate the article from Spanish into Portuguese has arisen
because of the difficulties of understanding the original written text by the scholars. So this
study gained the nuance of a translation. On the part of the students in this period were
observed several difficulties in the learning and understanding of mathematical contents, in
this aspect entered the need of a study about what we could use of the works of Taliniza. As a
result of the readings it was possible to perceive the importance of the teaching of the
concepts whose contributions of this theory were shown to contribute to the teaching of
mathematical concepts, since such concepts need to be understood from the characteristics of
the studied mathematical objects. The study of the article by Talizina contributed to the
teaching practice based on the conceptions of the Soviet school.
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