64 resultados para Philosophy of Mathematics


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Pós-graduação em Educação Matemática - IGCE

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

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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

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Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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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.

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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

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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.

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

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

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Pós-graduação em Educação Matemática - IGCE