Problemas e modelos que contribuíram com o desenvolvimento do cálculo diferencial e integral: dos gregos à Newton

This article refers to a research which tries to historically (re)construct the conceptual development of the Integral and Differential calculus, taking into account its constructing model feature, since the Greeks to Newton. These models were created by the problems that have been proposed by the history and were being modified by the time the new problems were put and the mathematics known advanced. In this perspective, I also show how a number of nature philosophers and mathematicians got involved by this process. Starting with the speculations over scientific and philosophical natures done by the ancient Greeks, it culminates with Newton s work in the 17th century. Moreover, I present and analyze the problems proposed (open questions), models generated (questions answered) as well as the religious, political, economic and social conditions involved. This work is divided into 6 chapters plus the final considerations. Chapter 1 shows how the research came about, given my motivation and experience. I outline the ways I have gone trough to refine the main question and present the subject of and the objectives of the research, ending the chapter showing the theoretical bases by which the research was carried out, naming such bases as Investigation Theoretical Fields (ITF). Chapter 2 presents each one of the theoretical bases, which was introduced in the chapter 1 s end. In this discuss, I try to connect the ITF to the research. The Chapter 3 discusses the methodological choices done considering the theoretical fields considered. So, the Chapters 4, 5 and 6 present the main corpus of the research, i.e., they reconstruct the calculus history under a perspective of model building (questions answered) from the problems given (open questions), analyzing since the ancient Greeks contribution (Chapter 4), pos- Greek, especially, the Romans contribution, Hindus, Arabian, and the contribution on the Medium Age (Chapter 5). I relate the European reborn and the contribution of the philosophers and scientists until culminate with the Newton s work (Chapter 6). In the final considerations, it finally gives an account on my impressions about the development of the research as well as the results reached here. By the end, I plan out a propose of curse of Differential and Integral Calculus, having by basis the last three chapters of the article

Utilizando processos geométricos da história da matemática para o ensino de equações do 2º grau

The present work had as principal objective to analyze the, 9th grade students understanding about the solutions of an equation of the 2° degree, using geometric processes of the History of the Mathematics. To do so, the research had as base the elaboration and application of a group of teaching activities, based on Jean Piaget's construtivism. The research consisted of a methodological intervention, that has as subjects the students of a group of 9th grade of the State School José Martins de Vasconcelos, located in the municipal district of Mossoró, Rio Grande do Norte. The intervention was divided in three stages: application of an initial evaluation; development of activities‟ module with emphasis in constructive teaching; and the application of the final evaluation. The data presented in the initial evaluation revealed a low level of the students' understanding with relationship to the calculation of areas of rectangles, resolution of equations of the 1st and 2nd degrees, and they were to subsidize the elaboration of the teaching module. The data collected in the initial evaluation were commented and presented under descriptive statistics form. The results of the final evaluation were analyzed under the qualitative point of view, based on Richard Skemp's theory on the understanding of mathematical concepts. The general results showed a qualitative increase with relationship to the students' understanding on the mathematical concepts approached in the intervention. Such results indicate that a methodology using the previous student‟s knowledge and the development of teaching activities, learning in the construtivist theory, make possible an understanding on the part of the students concerning the thematic proposal

Matemática Védica no ensino das quatro operações

This paper describes a study on the possibilities of teaching Vedic Mathematics for teaching the four operations. For this various literature sources were consulted considering three main aspects. The first of a historical-cultural, in order to gather information about the Mathematics originated from Vedic civilization, which highlight (Plofker, 2009), (Joseph, 1996), (Bishop, 1999), (Katz, 1998), (Almeida , 2009). This sought to emphasize relationships of the development of this culture with the math involved in the book Vedic Mathematics written by Tirthaji and published in 1965. In this respect the work brings notes on the history of mathematics on the development of mathematics in ancient India. The second aspect was related to teaching mathematics through research activities in the classroom, in this sense, I sought a bibliography to assist in the construction of a proposed activity to teach the four operations, based on the sutras of Vedic Mathematics, but within an investigative approach, assisting in the development of mental calculation strongly stimulated by the Vedic Mathematics Sutras. The authors were adopted (Mendes, 2006, 2009a, 2009b), Bridge (2003). The third aspect considered to search for books on teaching Vedic Mathematics, written by other authors, based on the book by Tirthaji. This revealed Vedic Mathematics textbooks adopted in schools and free courses in the UK, USA and India, all based on the book Vedic Mathematics of Tirthaji. From the bibliographical studies were prepared didactic guidelines and suggested activities for the teacher, to assist in teaching the four operations. The educational product, consisting of Chapters 4 and 5, is the body of the dissertation and consists of didactic guidelines and suggestions for activities that aim to contribute to the teachers who teach initial years of elementary school

Avaliação de usabilidade em materiais interativos de ensino a distância da UFRN-SEDIS

This study aims to assess the usability of Interactive Materials developed for the courses offered by UFRN SEDIS the modality of distance education (DE), using the techniques of focus group cooperative evaluation and assessment of satisfaction. The Interactive Materials are intended to serve as an avenue where the course content reaches the student in an educational, stimulating and self-instructive enough for the student to engage and find no difficulty in using it so. After the survey data in this context were selected four Interactive Materials ("Introduction to Applied Calculus", "Science, Technology and Society", "studies the Semi-Arid" and "Cultural Geography") that adopt the framework established by UFRN for SEDIS be evaluated for their usability. Initially, a preliminary test was conducted from cooperative assessment with a student interacting with the four learning objects in order to reveal and map the major failures of usability, supporting deeper questions later. The recordings of this preliminary test were analyzed by a focus group composed of two graphic designers and two multimedia designers, and developers responsible for these objects, which helped to analyze the gap between "what was designed" and "as was used "structuring and supplementing the roadmap for cooperative evaluation and assessment of subsequent satisfaction. The cooperative evaluation was applied individually to ten students of undergraduate UFRN that tested each of the four materials. At the end, every student completed a questionnaire assessing satisfaction form adapted Wanted (Questionnaire for User Interaction Satisfaction). The analysis of the data collected in this study revealed positive, negative and notes to be considered to guide the future development of Interactive Materials, in the context of UFRN SEDIS, feedback to the process of design and evaluation with user participation

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.