Proposições de Davydov para o ensino de matemática no primeiro ano escolar : inter-relações dos sistemas de significações numéricas

Abstract

Resumo: Na presente tese, de natureza teorica, investigamos os possiveis nexos e relacoes entre os sistemas de significacoes nas proposicoes davydovianas, para introducao do conceito de numero. Davydov expressa que suas proposicoes de ensino superam ou minimizam o divorcio existente entre as significacoes aritmeticas e a algebricas. Nesse contexto, definimos a tese de que suas proposicoes nao so minimizam tal divorcio como nao permitem o distanciamento, alem de incluir as significacoes geometricas. Os fundamentos teoricos e metodologicos da investigacao derivam da Teoria Historico-Cultural, com enfase nas questoes filosoficas, psicologicas e matematicas. A referencia da analise e o manual das proposicoes davydovianas para o professor. Durante a investigacao, revelamos a base geneticamente inicial da interconexao entre as significacoes aritmeticas, algebricas e geometricas, modelamos sua forma universal e procedemos a sintese. No decorrer da tese ficou demonstrado que, nas proposicoes davydovianas, as multiplas relacoes entre significacoes algebricas, aritmeticas e geometricas do conceito de numero sao interconectadas no seguinte movimento: geral . particular . universal. particular . singular.

Abstract: In this theoretical thesis, it was investigated the possible links and relationships between systems of signification in Davydov’s propositions to introduce the concept of number. Davydov claims that his propositions of teaching enable to overcome the gaps between arithmetic and algebra. In this context, the present thesis shows that Davydov’s preposition not only minimizes such gaps but also includes the geometric meanings. The theoretical and methodological backgrounds are based on the historical-cultural theory, with emphasis philosophical, psychological and mathematical issues. The data analyses are from the Davydov’s prepositions for the teacher. During the investigation, it was revealed the genetic initial basis of the interconnection between the arithmetic, algebra and geometry meanings, and its universal form is presented followed by the synthesis. Throughout this thesis it was shown that, in Davydov’s propositions, the several relations between algebraic, geometric and arithmetic meanings of the concept of numbers are interconnected in the following motion: general . particular . universal . particular . singular.