Interpretação e comunicação em ambientes de aprendizagem gerados pelo processo de modelagem matemática

Esta pesquisa teve por objetivo observar, compreender e descrever a produção de sentidos mediante as interações dos alunos entre si, e destes com o professor ao desenvolverem projetos de modelagem matemática. A investigação foi realizada em uma turma de 5ª série de uma Escola de Ensino Fundamental e Médio da Rede Federal de Ensino na cidade de Belém do Pará. A observação participante foi à técnica predominantemente utilizada para a coleta de dados, que foram registrados através do diário de campo, de vídeos-gravações das aulas e áudios capitados nos grupos de alunos, quando desenvolviam as atividades propostas, constituindo assim a metodologia adotada. Desse modo, a pesquisa, de cunho qualitativo, se caracterizou como pesquisa-participante. O referencial teórico que subsidiou a pesquisa foi composto, predominantemente pela filosofia da matemática de Ludwig Wittgenstein, que entende o jogo de linguagem como uma forma de vida, ressaltando que a aplicação de regras e seus sentidos fazem parte desse jogo; o conceito de resíduo de Gilles-Gaston Granger, que se refere aos significados que estão além do texto matemático formal, ou seja, os aspectos que escaparam da malhas da rede lingüística; o conceito da educação matemática crítica, que se refere aos aspectos políticos da educação matemática e que traz para o debate, questões ligadas ao tema poder, que refletem nas interações entre os sujeitos no ato cognoscitivo, estabelecendo padrões de comunicação; além dos autores que tratam da modelagem matemática no ensino. As análises apontam para possibilidades de produção de ambientes de aprendizagem apropriados para transitar um padrão de comunicação que desempenhe sua função primordial em situação de ensinoaprendizagem: a comunicação através da linguagem ou dos jogos de linguagem.

Platão e a matemática: uma questão de método

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Ethical Care of the Self and the Teacher in the Pedagogical Relationship: Reflections Based on the Latest Foucault

Our conception of education is that it is the responsible action whereby man becomes human, trains and faces the challenges that life and the world present, as man enters a larger, shared cultural tradition and thus joins the world. However such sharing implies that we must not just rely on tradition, but remain open to new ideas. It is essential for schooling to preserve a field where the art of living intersects with the world for which future generations are being prepared. It is in this field of intersection that this essay seeks to discuss Michel Foucault's thought, care of the self and the role played by others in the acquisition of ethical attitudes pertaining to one's conduct in life. Through reconstructing Foucault's ideas, we elaborate on the hypothesis that, before morally shaping students, teaching them values, or aiding in their skill acquisition in the sense prevailing in schooling today, it is important to understand the notion of care of the self (and how the notion implies interaction with others for effective care of the self). Care of the self is vital for thoroughly understanding the relationships between ethics and education in school. We particularly examine how Foucault's ideas and his analysis of the teacher's role in shaping the student's life conduct can help educators rethink pedagogical action in an ethical sense and find within it a certain openness to the formation of attitudes in educators and students

Positive Solution for a Class of Degenerate Quasilinear Elliptic Equations in R-N

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Heating value of eucalypt wood grown on SRC for energy production

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Before dividing we have to add: inter-viewing the foregrounds of indigenous students

Students' cultural diversity is an important factor to consider in a mathematics education concerned with equity. We argue that the significance of mathematics education is not only given by the understanding of mathematical concepts but also by students' foreground, that is, the students' perception of their future possibilities in life as made apparent to the individual by his/her social-political context. For students in a cultural borderline position, different reasons and intentions for engaging in mathematics learning may be related to the construction of meaning in mathematics. Through inter-viewing Brazilian Indian students' foreground, we illuminate the different types of significance given to mathematics education in their particular situation.

A etnomatematica e suas contribuições para o conteúdo da matemática escolar

In this research we set out to understand the Ethnomathematics Program such as it is said by some authors of Mathematics Education. To this end we conducted an exploratory study. The objective of to study this program is to analyze its contribution to understanding of the content of mathematics in the school environment. The authors studied are Ubiratan D'Ambrosio, considered the precursor of the Ethnomathematics Program and researchers as Paulus Gerdes, Maria do Carmo Santos Domite, Eduardo Sebastiani Ferreira and Gelsa Knijnik, that develop research in Ethnomathematics and may contribute to the comprehension of what in the study we intend to do. Although recourse to authors of Education and Education Philosophy as Maria Aparecida Viggiani Bicudo and Joel Martins to intend the idea of curriculum and its importance in the school environment. The study carried showed that the Ethnomathematics Program goes beyond of to explicit the mathematical knowledge produced by cultural groups, transcending the description of procedures that reveal the construction of knowledge hitch to school subjects. That is, the program seeks the valuing the human being, concerning itself with the construction of a worthy citizen and able to relate with their natural environment, social and intellectual

Fourier series for quaternions and the square of the error theorem

In this paper we introduce a type of Hypercomplex Fourier Series based on Quaternions, and discuss on a Hypercomplex version of the Square of the Error Theorem. Since their discovery by Hamilton (Sinegre [1]), quaternions have provided beautifully insights either on the structure of different areas of Mathematics or in the connections of Mathematics with other fields. For instance: I) Pauli spin matrices used in Physics can be easily explained through quaternions analysis (Lan [2]); II) Fundamental theorem of Algebra (Eilenberg [3]), which asserts that the polynomial analysis in quaternions maps into itself the four dimensional sphere of all real quaternions, with the point infinity added, and the degree of this map is n. Motivated on earlier works by two of us on Power Series (Pendeza et al. [4]), and in a recent paper on Liouville’s Theorem (Borges and Mar˜o [5]), we obtain an Hypercomplex version of the Fourier Series, which hopefully can be used for the treatment of hypergeometric partial differential equations such as the dumped harmonic oscillation.

Philosophical problem of relations according to Peirce: alliances towards an ontology of relations regarding two aspects of Synechism

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A educação matemática e o cuidado de si: possibilidades foucaultianas

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A classificação das disciplinas matemáticas e a Mathesis Universalis nos séculos XVI e XVII: um estudo do pensamento de Adriaan van Roomen

Pós-graduação em Educação Matemática - IGCE

As concepções de função de Frege e Russell: um estudo de caso em filosofia e história da matemática

Pós-graduação em Educação Matemática - IGCE