Formalização em Epistemologia Genética e Digrafos

One of the principal themes of genetic epistemology is the study of the psycho-genetic and historical-critical constitution of knowledge and its necessary structures. A main topic in this area is the relationship between abstract logical-mathematical structures and the epistemological-psychological structures of the epistemic subject. In genetic epistemology, formalizing and axiomatizing epistemological-psychological structures constitute one of the principal methods for showing the correlation between the two types of structures: the formalization of the epistemological-psychological structureresults in an axiomatic formal system which also expresses the abstractlogical-mathematical structure. In this context, it is interesting to note that some epistemological-psychological structures have been resistant to formalization and axiomatization, as in the case of the structure of concrete operational period groupings. Cases like these lead us to ask if there are general methods of formalizing that are consistent with the results and the general basis of genetic epistemology and genetic psychology, especially with regard to the claim that formalizing is a process, not a state, and that such general methods must therefore conform with the possibility of the continuous constitution of epistemological-psychological structures. In this paper we present some reflections, based on the general concepts of genetic epistemology and psychology and on the logical-mathematical structures of digraphs, on proposing a general method of formalization consistent with the results and the general basis of these two areas, including the possibility of the continuous constitution of epistemological-psychological structures.

A geometria euclidiana na licenciatura em matemática do ponto de vista de professores formadores

Pós-graduação em Educação Matemática - IGCE