Unidade entre o lógico e histórico no movimento conceitual do sistema de numeração proposta por Davýdov e colaboradores para o ensino das operações da adição e subtração

• Ano de defesa: 2015
• Autor(a) principal: Silveira, Gisele Mezzari
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Palavras-chave em Português: Educação Matemática; Teoria Histórico-Cultural; Proposição davydoviana; Sistema de numeração; Operações de adição e subtração
• Link de acesso: https://repositorio.animaeducacao.com.br/handle/ANIMA/3519

This investigation was performed in the Mathematics Education context, focusing on the way of teaching organization based on the Historic-Cultural Theory assumptions. From this Theory, Davýdov and co-workers elaborated propose for Mathematics Teaching with the aim to promote the theoretical thoughts development on students. In this investigation, the object of study consists in the unity between the logical and the historical on the conceptual movement of the proposition by Davýdov for the operation of the numbering system, specifically on addition and subtraction. The research presents theoretical nature an its foundation on the dialectical materialism as method. Among its categories, the logical, historical, universal, particular and singular were privileged. The hypothesis is the conceptual movement adopted in the teaching proposition by Davýdov for operate the numbering system contemplates the unity between the logical and the historical. This hypothesis is inserted in the following research problem scope: What is the unity expression between the logical and historical on the conceptual movement proposed by Davýdov and co-workers for teaching operate the numbering system? The assumption is the unity between the logical and the historical is expressed on the connection between the universal, the particular and the singular. The aim is centered on the dialectic investigation presents among the universal, the particular and the singular on the conceptual movement, expressed on the teaching proposition by Davýdov and co-workers for operate the numbering system. The textbooks and teacher guiding of the proposition by Davýdov for the Elementary School second grade constituted the data source. The investigation process was carried out in three stages. Firstly there was the appropriation of each tasks; then, the analysis of the different ways of development; and finally, the revelation of the interconnection among them. For the research exposure process, we considered the procedure from the abstract to the concrete. In it, we considered the development process of the numbering system from the sensory to the rational one, through the stages object, graphic, literal and numeral on different number bases. We revealed the essential relation of the numbering system, which consists on the formation of its orders, addition and subtraction operation genesis. We conclude the essence of addition and subtraction operations, in the proposition by Davýdov, is constituted by grouping and regrouping of orders, determined by the value of the number base, what enriches the logical of the numbering system, because cover its development. We also conclude that the unity between the logical and historical of operates the numbering system is expressed on the connection among the universal (whole-part relation in which occurs the grouping and the regrouping of orders), the particular (base number adopted) and the singular (result of the operation).