Números complexos: uma proposta de mudança metodológica para uma aprendizagem significativa no ensino médio

This work presents a proposal of a methodological change to the teaching and learning of the complex numbers in the Secondary education. It is based on the inquiries and difficulties of students detected in the classrooms about the teaching of complex numbers and a questioning of the context of the mathematics teaching - that is the reason of the inquiry of this dissertation. In the searching for an efficient learning and placing the work as a research, it is presented a historical reflection of the evolution of the concept of complex numbers pointing out their more relevant focuses, such as: symbolic, numeric, geometrical and algebraic ones. Then, it shows the description of the ways of the research based on the methodology of the didactic engineering. This one is developed from the utilization of its four stages, where in the preliminary analysis stage, two data surveys are presented: the first one is concerning with the way of presenting the contents of the complex numbers in math textbooks, and the second one is concerning to the interview carried out with High school teachers who work with complex numbers in the practice of their professions. At first, in the analysis stage, it is presented the prepared and organized material to be used in the following stage. In the experimentation one, it is presented the carrying out process that was made with the second year High school students in the Centro Federal de Educação tecnológica do Rio Grande do Norte CEFET-RN. At the end, it presents, in the subsequent and validation stages, the revelation of the obtained results from the observations made in classrooms in the carrying out of the didactic sequence, the students talking and the data collection

Dificuldades na construção de gráficos de funções

This study describes about graduation s students difficulties of to draw functions graph. Specifically, we intend to observe their abilities evolution, as well as their difficulties during Calculus I subject in engineering course. For that, we show them publications about the elaboration of graphs and its difficulties in obstacle terms and some researches witch contain this subject and that it was done during postgraduate studies in mathematical education. It shows by research methodology aspects related to French didatic s mathematic and some theories of cognitive psychology considering the high value between theoretical-methodological relation that was evidenced in both theoretical conceptions about ways to understand and teach mathematic. This methodology is based on didactic engineering purpose, that consist in preliminaries analysis, conception and didactic sequence analysis prior, trials by application followed analysis up and conclusion. We had also used pedagogicals actions and analysis of results achieved, to classify types of errors made by the 2005 s students during second semester, from conceptions related to the episthemologic and didactics obstacles

As provas metafísicas da existência de deus em René Descartes

Le but de cet article est de présenter les éléments de preuve de l existence de Dieu présentée dans les Méditationes Métaphysiques de René Descartes, en soulignant son importance et son rôle dans le projet philosophique cartésien. La recherche visait á comprendre comment Descartes, étant um homme de science, la recherche de Dieu dans le pilier et d assurer leur philosophie. Par consé quence que Descartes propose de remplacer lui promettant de construire une nouvelle science fondée sur des bases sûres. Ainsi, le texte suit um ordre qu une partie de doute méthodologique comme um élément essentiel pour surmonter une connaissance née de l incertitude et généralisée et d opinions comme étant de droite, pour finalement atteindre la vérité dans les sciencies, Grace à la découverte Du premier cours, le cogito, moi pensant, alors existantes. Trouvé cette certitude, le sujet qui a en elle l idée d um être infini qui contient toutes perfections et, comme Il fera la démonstration de la preuve a posteriori et a priori. Et donc cet être ne peut pas être considéré comme inexistant projet assurant Descartes