Material para o ensino do cálculo diferencial e integral: referências de Tall, Gueudet e Trouche - Almeida, Marcio Vieira de (2017)
This thesis presents a material for the teaching of Differential and Integral Calculus, composed by seven activities, which were based on theoretical references of Mathematical Education. The concepts of function, continuity, differentiability, solution of a differential equation, integral and limit of sequences were approached in these activities. The intention was to defend that one of the ways to establish the narrowing of the relation of theory and practice in this area of investigation is done through the elaboration of materials for teaching with this goal. The concepts of generic organizer, cognitive root, and Three Worlds of Mathematics by Tall and collaborators and the idea of resource of Documental Genesis of Gueudet and Trouche were used. The use of the computer and the construction of tools on GeoGebra were productive procedures to obtain a material with the planned qualities. The research, which had as a result the material for teaching, followed the methodological orientation of a type of fundamental research, in which the goal is the filling of gaps in knowledge related to the solution of problems through practice. An explanatory, theoretical posture was adopted, the construction of considerations with rigor and logical coherence to validate the obtained results. In the scope of theoretic-methodological references seven activities were elaborated for the teaching of Calculus organized in three components which, compose a resource (mathematics, material and didactics) in the conception of Documental Genesis, incorporating cognitivist ideas of Tall and his associates. Using the components (mathematics, material and didactics) allows that the material may configure itself as an element of the set of resources, according to the Documental Genesis, which a teacher of Calculus can use for the development of a class. As a result it is possible to demonstrate that the way of elaboration proposed for a material for teaching, in which theories of Mathematical Education are elaborated and adequate software is used, may be a powerful way to favor the integration of theory and practice, pursued and necessary for Mathematic Education, besides contributing with learning