Matemática, adjetivo: a demonstração pela ótica da cultura

ResumoO presente texto visa explicitar alguns valores presentes na matemática escolar, especificamente no procedimento dedutivo, e, portanto, na demonstração. Nosso olhar para a matemática e sua organização lógico dedutiva ocorrerá de um ponto de vista cultural, respaldado por abordagens provenientes do campo da etnomatemática que discutem que toda prática é imbricada de valores. Mostraremos que, nas orientações curriculares e em guias do Programa Nacional de Livros Didáticos atuais, a demonstração permanece sendo valorizada na matemática escolar. Para explicitar os valores serão consideradas demonstrações contidas em “Os Elementos” de Euclides de forma a mostrar como a matemática, mais especificamente a geometria, incorporou a lógica aristotélica assim como a valorização do conhecimento dedutivo sob o indutivo. Sendo a matemática vista como uma ciência dedutiva, argumentamos que nela ainda se coloca a superioridade desta em relação a outros conhecimentos. Os processos dedutivos realizados na matemática escolar serão problematizados para além da noção de rigor, trazendo valores associados a eles.Palavras-chave: valores; dedução; silogismo; lógica; Os Elementos de Euclides.Mathematics, adjective: The demonstration by the perspective of cultureAbstractThe present text aims to clarify some values in school mathematics, specifically in the deductive procedure, and therefore in demonstration. Our approach to mathematics and its deductive logical organization will focus on a cultural perspective, based on ethnomathematics which discuss that every practice is closely tied to values. We will show, both in the current curricular guidelines as in National Textbook Program, that demonstration is valuable in school mathematics. To clarify these values, we will take into account demonstrations contained in Euclid’s Elements, in order to show how mathematics, specifically geometry, incorporated Aristotelian logic as well as the appreciation of deductive knowledge under the inductive. Since math is conceived as a deductive science, we argue that it still gives it a higher position in relation to other forms of knowledge. Deductive procedures held in school mathematics will be discussed beyond the notion of accuracy, bringing some related values. Keywords: values; deduction; syllogism; logic; Euclid’s Elements.

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The Theories of Interconstitutionality and Transconstitutionalism. Preliminary Insights from a Jus-cultural Perspective (With a view to Transnational Social Justice)

Unio - EU Law Journal ◽

10.21814/unio.1.5 ◽

2015 ◽

Vol 1 ◽

pp. 55-76 ◽

Cited By ~ 3

Author(s):

Luís A. Malheiro Meneses do Vale

Keyword(s):

Social Justice ◽

Semantic Networks ◽

Social Differentiation ◽

Cultural Perspective ◽

Spanish Speaking ◽

Present Text

In the following pages, some light will hopefully be shed into the recent proposals of interconstitutionality and transconstitutionalism – deemed highly influential among Portuguese and Spanish-speaking countries – considering them against the backdrop defined by the more general disquisitions recently devoted to interculturality and transculturality in their quality of practical responses to the globalization and social differentiation phenomena. Acknowledging the fact that, even inside the juridical linguistic game and within the juristic community of interpreters, the new narratives interwoven through the above mentioned concepts are becoming more and more intricate – v.g., including epistemic and normative, as well as subjective and objective perspectives, giving birth to new elaborate semantic networks and covering an ever growing territory – it is important to admonish, at the outset, that, in this stance, we cannot but provide a preliminary and provisory map of the vast continent thereby comprised. As a consequence, the present text will limit itself to the signalling of some landmarks and the rough drawing of the basic lineaments for further (and certainly wiser and more competent) cartographic and exploratory endeavours.

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Methods of Teaching or Discovery? Analysis and Synthesis from Zabarella to Spinoza

History of Universities Volume XXXIII/2 ◽

10.1093/oso/9780192893833.003.0005 ◽

2020 ◽

pp. 85-112

Author(s):

Helen Hattab

Keyword(s):

Seventeenth Century ◽

Geometrical Method ◽

Aristotelian Logic ◽

Analysis And Synthesis ◽

Euclid’S Elements

This contribution looks directly at the so-called novatores and their own appropriation and reworking of the traditional methodological and pedagogic approaches. It shows how academic approaches and established tradition worked not only as a polemical target but also as a crucial resource that nourished the growth of alternatives to academic and Aristotelian approaches. This point is developed by discussing in detail the problem of method in Spinoza, and by connecting it with its scholastic background. By the mid-seventeenth century proponents of controversial philosophies appropriated more familiar didactic genres to convey their radical doctrines. For instance, the first book of Thomas Hobbes’s De Corpore follows the familiar order of standard Scholastic Aristotelian logic textbooks, and Baruch Spinoza’s Ethics emulates Euclid’s Elements, by presenting astounding conclusions about nature and extension more geometrico. There is a long-standing debate regarding whether Spinoza’s geometrical method is a method of discovery or merely a method of presentation. This contribution examines Spinoza’s reflections on method in the Treatise on the Emendation of the Intellect in the context of contemporaneous conceptions of analysis and synthesis found in the works of Zabarella, Burgersdijk, Descartes, and Hobbes to identify the most plausible readings of his method in the Ethics.

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An Analysis of the Use of Graphs in People’s Daily Life

Revista Colombiana de Educación ◽

10.17227/rce.num83-10608 ◽

2021 ◽

Vol 1 (83) ◽

Author(s):

José David Zaldívar-Rojas ◽

Francisco Cordero-Osorio

Keyword(s):

Empirical Evidence ◽

Mathematical Knowledge ◽

Daily Life ◽

School Mathematics ◽

School Environments ◽

Social Functions ◽

Reference Framework ◽

People’S Daily ◽

People's Daily ◽

Forms Of Knowledge

This paper addresses the issue of the lack of connection between people’s knowledge and school mathematics. It is stated that this issue generates a phenomenon of opacity in People’s Daily Life and the uses of mathematical knowledge; this means that other social functions of the mathematical knowledge apart from school environments are not considered. To highlight this phenomenon, empirical evidence is built from the analysis of cultural forms of knowledge concerning the uses of graphs in a movement situation; this evidence is overshadowed by school mathematics because they are immerse in non-conventional argumentations. A reference framework of the uses of graphs that resignifies trajectory and curve is then conformed; in this framework the search for permanence and invariants when things vary conforms a proper argumentation of people’s mathematical knowledge that is, however, obscured in school mathematics.

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