Ideias algébricas explicitadas por estudantes da EJA em espaços não formais: o caso do cursinho de Ribeirão Preto

Abstract

This research aims to investigate the EJA students ideas when they experience problem situations that involve the algebraic language in the nonformal education context. To do this we investigated the evolution of Algebra philosophically and historically, as well as its introduction in basic education. This study was fundamental to understand the gaps and also the resources the subjects of the research have when problem situations that require the use of the algebraic language are presented. The research is qualitative and is characterized as a case study. It took place in a non-formal learning place: a popular cursinho in Ribeirão Preto that serves young and adult workers from low income families that had finished elementary and high school in public schools. The problem that guided the study was: what are the algebraic ideas shown by EJA students when they experience problem situations in a nonformal space? . The data was collected between March and June 2010 by the researcher who acts as volunteer in this educational space. Because of this, the methodology of the research is based on research-action considering that the author of this text, together with her colleagues, creates the problem situations on the algebraic language based on the reflections in class and the necessities and difficulties the students have during class, compared to the contents dealt with in the different areas of knowledge. The results of this research show that although the youngsters and adults from the popular class who finish high school in public schools have some difficulties in understanding and manipulating the algebraic language, they are willing to look for alternatives and to share the algebraic ideas they have with the other members of the group to solve the situations that are presented to them. The importance these students give to the group reflections that happen during the resolutions of the problem situations is also observed, since it is from these reflections that happen in the classroom that these youngsters start to make sense of the algebraic concepts that haven t been noticed by them, even though they have studied for years at formal schools. 10 At the same time those reflections help the teachers of cursinho to prepare the lessons and to produce problem situations. In other words, when the students show the ideas they have about the algebraic language during the classes and when they participate on their planning, they can show the sense they give to the algebraic language and they can be considered co-authors of the situations planned by the teachers. Therefore teachers and students of EJA are protagonists of the mathematics lessons that take place in this non-formal space. Regarding the results, during the research we elaborated two educational products : 1) the four problem situations that involve the algebraic language created based on the EJA students needs and 2) the theoretical synthesis from the analysis elaborated based on the development of the four problem situations as an essay. The educational products reflect the movement of the classroom, as well as its methodology called dialogical. The educational products presented here do not intend to indicate some type of methodology that must be followed by those who teach algebra in nonformal spaces specially for EJA. It intends to invite teachers who give algebra lessons in non-formal and formal schools to think about an education that often excludes the student. And at the same time to create problem situations connected to the algebraic concepts that regard the context it is inserted. The problem situations presented are different from those presented in the majority of the didactic books since they have the interdisciplinarity as a starting point that is the base of the work proposal at the cursinho.