Sistema de numeração posicional e a lógica da divisão de inteiros

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior

Uma justificava da validade do teorema fundamental da álgebra para o ensino médio

Among several theorems which are taught in basic education some of them can be proved in the classroom and others do not, because the degree of difficulty of its formal proof. A classic example is the Fundamental Theorem of Algebra which is not proved, it is necessary higher-level knowledge in mathematics. In this paper, we justify the validity of this theorem intuitively using the software Geogebra. And, based on [2] we will present a clear formal proof of this theorem that is addressed to school teachers and undergraduate students in mathematics

Dificuldades de aprendizagem do conteúdo de soluções: proposta de ensino contextualizada

The study of solutions is considered very important to chemist’s education because most of the chemical reactions occur in aqueous medium, being also required to understand other subject such as chemical changes, electrochemical and chemical balance. Nevertheless, it is noticed that many students indicate learning difficulties related to the content of solutions, how to pass among the macro-submicroscopic knowledge levels, and how to solve quantitative problems that demanding the establishment of a stoichiometric ratios. This thesis defended considers the use of contextualized teaching strategies about some subject associated to the study of solution, can foster student learning through reflection and understanding of their own difficulties, besides to provide motivation and active participation. The target group is formed by students of the undergraduate distance education with major in chemistry education of the Universidade Federal do Rio Grande do Norte (UFRN), and they were chosen because this education system is expanding and its learning difficulties publications number is reduced as well. Thus, the first methodological stage was to identify the student’s main learning difficulties associated to the study of solutions through literature sources. Next, using an adapted script of the Plano Nacional do Livro Didático para o Ensino Médio (PNLEM, Textbook National Plan for High School), the approach of the content of solutions printed in educational materials used by the target group was analyzed. Afterward, a teaching unit was planned in the last methodological stage and, finally, a new teaching unite was given with a sequence of contextualized activities such as video presentation, dialogued lecture, questionnaires application, exercises, and an experiment, where the target group’s main difficulties related to learning of solution were identified. The participants of the teaching unit activities had some learning difficulties in understand concepts of compound, ion, charge, entropy and solubility, as well as to identify the ion charge, interpret statements, decode tables, use the chemical language, perform mathematical calculations and use concentration units, similar results raised in the literature sources. In order to work on these difficulties, these students were encouraged to expose, question and test their ideas about the phenomenon under study, allowing learn from their mistakes and reflect on the organization strategy of scientific explanatory models they use. Therefore, activities and information about learning difficulties presented in this thesis need to be critical reflection object, because it can help both students in the process of acquiring knowledge about the content of solutions and professors in the planning of their lessons.

A compreensão de reação química como um sistema complexo a partir da discussão dos erros e dificuldades de aprendizagem de estudantes do ensino médio

The study of chemical reactions is among the most important contents to the understanding of Chemistry discipline in basic education. However, there are still few studies about chemical reactions as a complex system because, generally, this content is presented in textbooks, taught and even researched in a fragmented form. The thesis here presented aims to investigate, identify and characterize the mistakes and learning difficulties of the students about chemical reactions as a complex system, using for that purpose the analysis of the answers of 126 exams of candidates for the bachelor’s degree in Chemistry Teaching on the entrance exam for the Federal University of Rio Grande do Norte (UFRN). The mistakes and learning difficulties about the parameters ΔG°, Kp, Ea and of the calculation of the amount of substance in a chemical reaction have been identified, as well as the levels of development of the ability to interpret the chemical reaction as a system. The main theoretical source of this study is structured based on the mistakes and learning difficulties (NÚÑEZ, RAMALHO, 2012), of the chemical reactions as complex systems (NÚÑEZ, 1994; RESHETOVA, 1988; SANDERSON, 1968). As methodology, it was prioritized the analysis of the answers to the exams and the interview with the teachers. The results showed typical mistakes in the study of this subject, especially low levels and skill development. No student was able to integrate the different aspects in the systemic understanding of the chemical reaction. From the interviews with Chemistry teachers from High School, it was determined the reasons the teachers assign to those mistakes and learning difficulties. The interviews revealed that the teachers do not work in the perspective of integration of the contents which leads the students to present difficulties and make mistakes related to the content previously mentioned. The study presents a proposal for the organization of the contents of Chemistry discipline for High School as a possibility of a dialectic systemic integration of contents, understanding that this systematic vision, leads to important contributions to the development of the theoretical thinking of the students. We can mention as one of the conclusions of this study, the fact that the non-systemic organization of contents do not favor this kind of thinking in students.