De solutione problematum diophanteorum per números integros : o primeiro trabalho de Euler sobre equações diofantinas

The present dissertation analyses Leonhard Euler´s early mathematical work as Diophantine Equations, De solutione problematum diophanteorum per números íntegros (On the solution of Diophantine problems in integers). It was published in 1738, although it had been presented to the St Petersburg Academy of Science five years earlier. Euler solves the problem of making the general second degree expression a perfect square, i.e., he seeks the whole number solutions to the equation ax2+bx+c = y2. For this purpose, he shows how to generate new solutions from those already obtained. Accordingly, he makes a succession of substitutions equating terms and eliminating variables until the problem reduces to finding the solution of the Pell Equation. Euler erroneously assigns this type of equation to Pell. He also makes a number of restrictions to the equation ax2+bx+c = y and works on several subthemes, from incomplete equations to polygonal numbers

Investigação histórica nas aulas de matemática: avaliação de duas experiências

This study reflects on some procedural aspects about the development of mathematics learning from the experience with investigative activities concerning the resolution of second degree equation, which was tested a proposal for education, supported the use of texts in history of mathematics. The survey was conducted in two stages, taking the first-served basis for the second, which was carried out with a study group remainder of the first experiment. The intention was to investigate how the group participant, known as the study group, involved in the implementation of activities of research in mathematics, supported the use of the history of mathematics. Based on the results achieved during the study, it was possible to understand that the activities of research enable the development of students, range of learning mathematics and the development of skills and expertise for research as a vehicle for construction of their mathematical knowledge. This approach proposed research into the classroom is important, both for prospective teachers of mathematics and for students from elementary school, bringing a new phase for mathematical education that will come to schools

Equações de segundo grau e mudança de variáveis

In this work are presented, as a review and in a historical context, the most used methods to solve quadratic equations. It is also shown the simplest type of change of variables, namely: x = Ay + B where A;B 2 R, and some changes of variables that were used to solve quadratic equations throughout history. Finally, a change of variable, which has been used by the author in the classroom as an alternative method, is presented and the result of this methodoly is illustrated by the responses of a test that was done by the students in classroom

Abordagens pedagógicas na formação de enfermeiros : compreensão de docentes de enfermagem

In the new world order is notorious changes in social, ethical, economical and political aspects in the society, which reach incisively higher education, requiring a number of modifications and a new vision in nursing education, in order to meet the demands of the Unique Health System. Thus, the Higher Education Institutes (HEI) and teachers are invited to face new challenges and reflect on their practices, using pedagogical approaches and innovative methodologies to meet the requirements of a globalized society. This study has as an objective to analyze the perspective of teachers in what concern the pedagogical approaches used in nursing education and to identify pedagogical approaches utilized by teachers in nursing education. This is a field research of exploratory kind, descriptive, of quantitative approach. The search was conducted at the Department of Nursing of the Federal University of Rio Grande do Norte UFRN, based in the city of Natal. The population consisted of forty-six teachers. From this population was selected a sample of twenty teachers. Data collection occurred from August to September 2011, through the utilization of the technique of interview and questionnaire. The obtained data were analyzed in two moments. In the first moment, was carried out the quantitative analysis that refers to the obtained data through the interview technique, methodological procedures were submitted to the content analysis proposed by Bardin. On the second moment, concerning the quantitative analysis of the questionnaires applied to the teachers and of the identification data, which were digitized and transferred to a spreadsheet electronic of Microsoft Excel XP, tabulated and organized into tables, containing their relative and absolute frequencies. It is worth mentioning that were respected the aspects of the CNS Resolution 196/96. With regard to the characteristics of research participants, 20% were male; with a degree of titration of 55% doctorates; regarding time of service there was a greater representation from 15 to 45 years, with 45%. The results showed that 90% of teachers who participated in the research have an appropriate understanding of non-critical pedagogical approaches, only 10% had an inadequate understanding. However, 70% of teachers, despite having an adequate understanding, reported difficulties when attempting to implement these pedagogies. Most teachers, with representability of 80% consider the non-critical pedagogies relevant in nursing education, as well as critical pedagogies, being represented by 95% of teachers. It was concluded that both critical and non-critical pedagogies are in teachers practice of undergraduate nursing education. It feels like a moment of transition, since the presence of new ways of teaching as a part of this educational context, with educational models that give value to scientific, ethical and personal aspects in the educational process. The research contains limitations, however highlights the contribution of new possibilities for action, reflection on the context of performance, maximizing the pedagogical skills necessary to conduct teaching process, in line with the new educational paradigm of higher education

Reflexões e contribuições para o ensino de gravitação clássica no nível médio

The subject of Classic Gravitation is part of the actual curriculum for High School in Brazil, and it is taught in the first year of that education level. This master thesis presents a research regarding the subject Classic Gravitation in High School. This research was based in two complementary guidelines of research and action. The first guideline was the analysis of 21 didactic books of physics which are the more frequently used in High School, in the city of Natal/RN. The second guideline, worked after being verified the most common deficiencies presents in the didactic books, was the elaboration, followed by a practical application, of a course suggesting how to approach that subject in the classroom. The Parâmetros Curriculares Nacionais para o Ensino Médio (National Curricular Parameters for High School PCNEM) defend that Classic Gravitation is very important in the student s formation and that its study helps the comprehension of many nature s phenomena. Because of this vision of that subject by the PCNEM, the 21 analyzed books were separated in two groups: the first one, containing 10 books, was edited before the spreading of PCNEM, and the second, with 11 books, after that spreading. Whatever the group to which the didactic books belonged, the great majority of them let that subject in a second plan; two of them even suggesting, in the teacher s orientations, that the subject Gravitation can be suppressed in case of insufficient time . These analyses points that the PCNEM had produced no changes in the conception of the authors that wrote books regarding that subject. To analyze the didactic books, we elaborated a script which was used as an analysis tool, in which we put in evidence the relative importance of the historic and philosophic contextualization of the subject, the quotidian experience of the students and the interdisciplinary approach, among other aspects. It became evident that the didactic books give very little emphasis to historic aspects of the knowledge construction, to the relations with the day-by-day questions and to the interdisciplinary character of the subject Gravitation. It calls attention the non concordance among the authors opinions regarding the necessary previous knowledge or prerequisites the students should fulfill in order to begin to study Gravitation. The course we elaborated was given to a group of teachers as well as to students. In those courses we treated theoretical and practical aspects and emphasized historical questions and the ones which are related to people s daily life. The course for teachers was realized as an extra-mural activity of the UFRN and was given by the author of this thesis at the Escola Estadual Francisco Ivo Cavalcanti (a state public school in Natal/RN). There were 23 teachers present, from several public schools and several fields of knowledge. The thesis supervisor and the master degree s colleagues of the author acted as collaborators , reporting the participants opinions and speeches. The course to the students, on the other hand, had the participation of 300 regular students who belonged to 6 different 1st year classes of the High School Escola Marista de Natal (RN), in which the author acts as a physics teacher. The student s course was realized as part of the regular curriculum activities, in which three classes stood under the responsibility of the author and other three classes in charge of another Marista s teacher, who participated as a collaborator . The teacher s course as well as the students one were given in two stages, with five hours each. The first stage was divided in two moments, the first one focused on the survey of the spontaneous conceptions about gravitation, in which we worked basically with experiments of free throwing and pendulum, and the second one focused in theoretical presentations and quarrels about universe s models. In the second stage of the course we improved the study of Kepler s laws and the Newton s Universal Gravitation law, and we used as motivating tools some practices involving the construction of the solar system in scale. As instruments for evaluating both courses we used questionnaires and reported the speeches with participants opinions, beyond usual written evaluations in the course for the students. The teachers who participated in the course showed very good wills in realizing interdisciplinary practices; nevertheless, according their own speeches, they frequently came across the difficulty of how to do . From the experience we had in both courses, we conclude that the approach we propose hear to the teaching of the subject Classic Gravitation , supported on the tripod theory, practice and historical and philosophical aspects, is viable and effective. One hopes that this research may contribute in the formation of a opinion, among the teachers, concerning how to approach the subject of Classic Gravitation, and may offer suggestions in order those who want to apply that approach may develop classroom practices aiming to improve the teaching of that subject, which has a singular importance in the formation of High School students

Variação entre os pronomes tu e você na função de sujeito na fala de Natal (RN): uma abordagem sociofuncionalista

In this dissertation, under the light of a sociofunctionalist approach (TAVARES, 2003; 2013; GORSKI; TAVARES, 2013), I analyze 378 data of pronouns tu and você extracted from 12 conversations belonging to Natal Conversational Data Base (CUNHA, 2010). I have the following objectives: (i) mapping linguistic and extralinguistic specialization trends of second person singular subject pronouns tu and você in the speech of Natal (RN); (ii) assessing the role of the principle of persistence (HOPPER, 1991) as a possible motivating factor of specialization trends of pronouns tu and você; (iii) identify in which of the six pronouns subsystems proposed by Scherre et al. (2009) is situated the speech community of Natal portrayed in this study. In order to achieve the proposed objectives, I submitted the data to multivariate statistical analysis, which have provided frequencies and relative weights.I obtained, as relevant factor groups, according to the statistical analysis, the nature of the relationship between the interlocutors (if the relationship is asymmetric, less intimate, and more formal, the use of você is favored; if the relationship is symmetrical, intimate and informal, the use of tu is favored); the degree of formality of the environment in which the conversation takes place (in more informal environments tu was favored; in more formal environments você were favored); and the type of discourse (reported / not reported) (tu was favored in not reported discourse and você was favored in reported discourse). Based on results regarding to these factors groups, I organized a panorama of specializations of pronouns tu and você, noting that tu seems specialized for more informal contexts of use than those for which você seems specialized. The motivation underlying these trends of specialization may be the principle of persistence, since along its historical development, você carries a trace of greater formality or, at least, less intimacy, when contrasted to tu. Finally, I concluded that, of the six pronoun subsystems proposed by Scherre et al. (2009), the speech community of Natal can be framed in the fifth, characterized by variable use of subject pronouns tu and você, with more frequent use of você than tu, and rare occurrence of agreement of tu with second-person singular verb.