Pensamento instrumental e pensamento relacional na educação matemática

• Autor(a) principal: Wielewski, Sergio Antonio
• Data de Publicação: 2008
• Tipo de documento: Tese
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações da PUC_SP
• Texto Completo: https://tede2.pucsp.br/handle/handle/11325
• topic: História da matemática; Representação matemática; Pensamento instrumental e relacional; Conceitos; Conhecimento -- Teoria; Matematica -- Estudo e ensino; Matematica -- Filosofia; Mathematic history; Mathematical thinking; Mathematical representation; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA

This doctoral thesis contains theoretical discussions as well as results of an empirical study. The general starting point has been the thesis that our mathematical thinking is largely ruled by certain dualities or complementarities of which that between the representational and instrumental aspects of concepts is best known. Ernst Cassirer, presents in his famous book Substanzbegriff und Funktionsbegriff (Substance and Function) of 1910 the general thesis that the historical development of science could be described as a transition from merely referential Aristotelian concepts to operative concepts or functions. The very same duality has been discussed widely in mathematics education starting from the work of Richard Skemp. Our first goal has consequently been to find connections between Cassirer and Skemp. The discussion of these connections and differences leads then in a second part of the thesis to a presentation of the results of an empirical case study with fourteen participants. These had been confronted with a number of problem situations and their problem solving activities have afterwards been analyzed in terms of the aforementioned complementarity between relational and operative thinking