Mathematical education of young and adults: pedagogical implications of historical-cultural theory

Univ Estadual Paulista Julio de Mesquita Filho UN, Dept Didat, Programa Posgrad Educ, Fac Filosofia & Ciencias, Ave Hygino Muzzi Filho 737, Marilia, SP, Brazil


Introduction
The historical development of mathematical education as a theoretical field shows us, among other relevant formulations, that the attempts to explain the difficulties with the learning of Mathematics go through the ideas of inadequate working conditions in the school, inadequate teacher training (Ponte, 2003; (Danyluk, 1993;Oliveira & Moreira, 2010), and every aspect of the teaching of Mathematics (Danyluk, 1993, Oliveira & Moreira, 2010, problems of student assimilation, school devaluation, inadequate teaching programs, of this problem deserves consideration and plays a role for students' performance in mathematical learning. The difficulties of mathematical learning of young people and adults are due in general to the school culture whose methodological procedure is still marked by the association of models, that is, a didactic conduct in which, if the student observes well the teacher does, he must learn, prevailing the utilitarian view and the Platonic view of Mathematics as we can conclude based on Chacón (2003).  (Cury, 2007). It presupposes, on the contrary, a fundamental role of the collective instances where the professors carry out their professional activity, emphasizing the schools, the pedagogic movements and the associative structures. One of the major obstacles to the affirmation of a research culture in teachers is the old opposition between theory and practice. In this opposition, theory is something fanciful, unsuitable for the interpretation of reality, useless or even pernicious. Practice is the realm of normality and the inevitable, where all problems always find external justification (whether students, caregivers, explainers, lack of working conditions or Ministry policy). It is a bizarre conception of theory and practice. In fact, theory and practice are two sides of the same coin. They always coexist. Where there is a theory there is a practice and where there is a practice there is a theory. What is needed is whether the theory serves or does not serve and whether the practice is commendable or problematic. (Ponte, 2003, p. 18-19) ii .
The citation is long, but it is illuminating for our discussion as the The relationship between thought and word is a living process: thought is born through words. A word devoid of thought is a dead thing, and a thought not expressed by words remains a shadow. The relationship between them is not, however, something already formed and constant: it appears throughout development and also changes. ... The word was not the beginningaction already existed before it: the word is the end of development, the crowning of action. (Vygotsky, 1991, p. 131)  obtained. In this way, the present article discusses issues that daily apprehend in this process of action-reflection-action.
We also believe that mathematical knowledge can be taught, but that its appropriation must be based on the relations that the subject establishes between objects, facts and events.
Knowledge, therefore, imposes on the  In fact, it is ... access to objects necessarily passes through semiotic representation.
Moreover, this explains why the evolution of mathematical knowledge leads to the development and diversification of registers of representation. (Duval, 2003, p. 21)  A special aspect of the human species -which comes at a very early age -is the perception of real objects. This is something that does not find correlate in the animal species. By this term I understand that the world is not seen simply in color and form, but also as a mural with meaning and meaning. (Vygotsky, 1995, p. 37)  ... the original, starting and universal form of existence of the logical figure is the real, sensorial -practice activity of man. Verbal thinking can be understood scientifically as a derived form of practical activity. This thesis is, in our view, unacceptable for traditional formal logic and for the traditional psychology of thought. On the contrary, this thesis is completely legitimate for the dialectical materialist logic and for the psychology which is consciously and consequently based on its principles. It is clear that logic and psychology must start from a common understanding of the activity that tends to accomplish the goals of man and his main types. (Davidov, 1988, p. 20)  purpose. According to him, By activity, we designate the processes psychologically characterized by that to which the process as a whole is directed (its object), always coinciding with the objective that stimulates the subject to perform this activity, that is, the motive. (Leontiev, 1988, p. 68). viii There will only be activity, therefore, when the motive and the goal coincide. It is important, then, that mediator teachers consider the concept of activity and its implications for the teaching process, which brings us back to the problem of training.
The study activity then reports to a specific form of activity directed towards the assimilation of theoretical knowledge, with a view to the formation of theoretical thinking.
For Davidov (1988), psychic activity develops as the subject plans and selects the objects (instruments) and the way (strategy) to use them, according to the purpose of the moment. The ability of planning, in turn, depends on the development of needs, which are always social.
Every activity is triggered by a need.
Activity always seeks, as purpose, that which is not yet real, but that there is possibility of being real -this is the main characteristic of vital activity. Thus Davidov (1988, p. 33 Thus, Davidov (1982) considers that the objective of schooling should be the parsimonious pursuit of the development of theoretical thinking, beyond empirical thought. In its formulation, the study activity, through specific tasks, has as a goal to lead the student to the appropriation of more general laws that involve a mathematical concept, so that they are Researches such as those developed by Bruner (1997) Davidov (1988), content is the basis of teaching that promotes development.
In this way, subjects of the EJA need to establish the connection of the universal or the general with the particular or singular, that is, operate with the concept in the transition from general to specific. In the words of the author, By its content, the theoretical concept appears as a reflection of the processes of development, of the relation between the universal and the singular, the essence and the phenomena; by its form, appears as a procedure of ascension from the abstract to the concrete. (Davidov, 1988, p. 152)

Conclusion considerations
In recent theoretical formulations,