A leitura de fontes antigas como possibilidade didatica: um exemplo a partir do Almagesto de Ptolomeu

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior

Elaboração de atividades didáticas para o ensino de matemática a partir de livros antigos: o exemplo do leçons élémentaires de Lagrange

De nombreuses études sur l`utilisation pédagogique de l`histoire des mathématiques viennent a identifier les arguments qui sous-tiennent ces actions éducatives comme une façon d`aborder les mathématiques scolaires afin de mener les élèves à un apprentissage réflexif et significatif des mathématiques. Cherchant a vérifier, de manière pratique, comment ces relations entre histoire des mathématiques et l`enseignement des mathématiques peuvent se matérialiser sous la forme d`activités didactiques, nous avons effectué un sondage sur les oeuvres du mathématicien Joseph Louis Lagrange (1736-1813) et identifié le potentiel d`exploration éducatif, de l`oeuvre Leçons élémentaires sur les mathématiques données a l`École Normale en 1795, de cet mathématicien. L`objectif principal de notre étude était de faire des recherches sur le potentiel d`une oeuvre antique dédié à l`enseignement des mathématiques et de la considérer comme support conceptuel et didactique pour la création d`un modèle d`activités didactiques pour l`enseignement des mathématiques, dans la formation des enseignants de mathématiques et aussi en ce qui concerne l`apprentissage des mathématiques des élèves de l`école primaire. Nous avons fait une lecture, la traduction et l`ajout de notes et commentaires sur le travail et une recherche bibliographique sur la relation entre l`histoire des mathématiques et l`enseignement des mathématiques, de façon a comprendre les aspects conceptuels et didactiques pour l`élaboration d`um module activités didactiques pour l`enseignement des mathématiques basée sur certains chapitres du livre de Lagrange. À cette fin, l`oeuvre a été utilisé comme source primaire et a été étudié sous un fondement théorique appuyer sur les travaux des Institut de recherche sur l`enseignement des mathématiques IREM. Dans le module élaboré, les activités apportent les contenus dans une suite integrée à une logique de classe, à partir de la lecture directe des découpages du texte original, disposés entre les questions et les situations-problémes , historiquement mis en contexte avec la période et associés à des contenus spécifiques. Comme il s`agit d`une recherche basée sur l`exploitation de livres anciens, nous croyons que des modules d`activités basées sur des source primaires peuvent être utilisées comme un matériel pédagogique pour la formation des enseignants de mathématiques ainsi que pour les dernières années de l`école élémentaire, reformulées ou accrues d`autres questions telles l`intérêt de chaque enseignant qui l`utilise

Mecanismos de alojamento de magmas granitóides :exemplo do plúton de Japi(RN)

This dissertation describes the igneous suites of the Japi granitoid pluton, intrusive in the Paleoproterozoic gneiss-migmatite complex of the eastern domain of the Seridó Belt, northeastern Brazil. Field relations show that the pluton is affected by strong deformation associated to the Brasiliano orogeny (known as the D3 phase) , with a NW-trending extensionalleft-hand senestral shear zone (the Japi Shear Zone, JSZ) bordering the intrusive body to the west. Four plutonic suites are found in the main pluton and as satellyte intrusions, besides Iate pegmatite and pink leucogranites. An alkaline granitoid suite, dominated by syenogranites bearing sodic augite (and subordinate hornblende), define a main elliptical intrusion. In its northern part, this intrusion is made up by concentric sheets, contrasting with a smaller rounded stock to the south. These granites display a pervasive solid-state S>L fabric developed under high T conditions, characterized by plastic deformation of quartz and feldspar. It is especially, developed along the border of the pluton, with inward dips. A regular magmatic layering is present sometimes, parallel to the tectonic foliation. The syntectonic emplacement as regards to the Brasiliano (D3) event is indicated by the common occurrence of dykes and sheets along transtensional or extensional sites of the major structure. Field relations attest to the early emplacement of the alkaline granites as regards to the other suites. A basic-to-intermediate suite occurs as a western satellyte body and occupying the southern tail of the main alkaline pluton. It comprises a wide variety of compositional terms, including primitive gabbros and gabbro-norites, differentiated to monzonitic intermediate facies containing amphibole and biotite as their main mafic phases. These rocks display transitional high-K calc-alkaline to shoshonitic affinities. Porphyritic monzogranite suítes commonly occur as dykes and minor intrusives, isolated or associated with the basic-tointermediate rocks. In the latter case, magma mingling and mixing features attest that these are contemporaneous igneous suites. These granites show K-feldspar phenocrysts and a hornblende+biotite+titanite assemblage, displaying subalkaline/monzonitic geochemical affinities. Both suites exhibit SL magmatic fabrics overprinting or transitional to solid-state D3 deformation related to the JSI. Chemical data clearly show that they are related to different parental magmas. Finally, a microgranite suite occurs along a few topographic ridges paralell to the JSI. It comprises dominantly granodiorites with a mineralogy similar to the one of the porphyritic granitoids. However, discriminant diagrams show their distinct calc-alkaline affinity. The granodiorites display an essencially magmatic fabric, even though an incipient D3 solid-state structure may be developed along the JSI. Intrusion relationships with the previous suites, as well as regards to the D3 structures, point to their Iate emplacement. All these suites are intrusive in a Paleoproterozoic, high-grade gneiss-migmatite complex affected by two previous deformation phases (D1, D2). The fabrics associated with these earlier events are folded and overprinted by the younger D3 structures along the JSZ. The younger deformation is characterized by NE-dipping foliations and N/NE-plunging stretching lineations. In the JSZ northern termination the foliation acquires an ENE orientation, containing a stretching lineation plunging to the south. Symmetric kinematic cri teria developed at this site confirms the transpressional termination of the JSZ, as also shown by orthorrombic quartz c-axis patterns. E-W-trending d extra I shear zones developed in the central part of the JSZ are interpreted as antithetic structures associated to the transtensional deformation along the JSZ. This is consistent with its extensional-transcurrent kinematics and a flat-and-ramp geometry at depth, as shown by gravimetric data. The lateral displacement of the negative residual Bouguer anomalies, as regards to the main outcropping alkaline pluton, may be modelized by other deeper-seated granite bodies. Based on numerical modelling it was possible to infer two distinct intrusion styles for the alkaline pluton. The calculated model values are consistent with an emplacement by sheeting for the northern body, as already suggested by satellyte imagery and field mapping. On the other hand, the results point to a transition towards a diapir-related style associated to the smaller. southern stock. This difference in intrusion styles may relate to intensity variations and transtensional sites of the shear deformation along the JSZ. Trace element and Sr and Nd isotopes of the alkaline granites are compatible with their derivation trom a more basic crustal source, as compared to the presently outcropping highgrade gneisses, with participation (or alternatively dominated by) of an enriched lithospheric mantle component. Like other igneous suites in the Seridó Belt, the high LlL contents and fractionated REE patterns of the basic rocks also point to an enriched mantle as the source for this kind of magmatism. Geochemical and isotope data are compatible with a lower crustal origin for the porphyritic granites. On the basis of the strong control of the JSZ on the emplacement of lower crustal (porphyritic and alkaline granites) or lithospheric mantle (basic rocks, alkaline granites or a component of them) magmas, one may infer a deep root for this structure, bearing an important role in magma extraction, transport and emplacement in the Japi region, eastern domain of the Seridó Belt

Aplicação da modelagem estrutural computacional direta na análise da geometria de falhas: exemplo da falha de Baixa Grande (Bacia Potiguar - NE do Brasil)

The Baixa grande fault is located on the edge of the S-SW Potiguar Rift. It limits the south part of Umbuzeiro Graben and the Apodi Graben. Although a number of studies have associated the complex deformation styles in the hanging wall of the Baixa Grande Fault with geometry and displacement variations, none have applied the modern computational techniques such as geometrical and kinematic validations to address this problem. This work proposes a geometric analysis of the Baixa Fault using seismic interpretation. The interpretation was made on 3D seismic data of the Baixa Grande fault using the software OpendTect (dGB Earth Sciences). It was also used direct structural modeling, such as Analog Direct Modeling know as Folding Vectors and, 2D and 3D Direct Computational Modeling. The Folding Vectors Modeling presented great similarity with the conventional structural seismic interpretations of the Baixa Grande Fault, thus, the conventional interpretation was validated geometrically. The 2D direct computational modeling was made on some sections of the 3D data of the Baixa Grande Fault on software Move (Midland Valley Ltd) using the horizon modeling tool. The modeling confirms the influence of fault geometry on the hanging wall. The Baixa Grande Fault ramp-flat-ramp geometry generates synform on the concave segments of the fault and antiform in the convex segments. On the fault region that does not have segments angle change, the beds are dislocated without deformation, and on the listric faults occur rollover. On the direct 3D computational modeling, structural attributes were obtained as horizons on the hanging wall of the main fault, after the simulation of several levels of deformation along the fault. The occurrence of structures that indicates shortening in this modeling, also indicates that the antiforms on the Baixa Grande Fault were influenced by fault geometry

Correspondências científicas como uma relação didática entre história e ensino de matemática: o exemplo das cartas de Euler a uma princesa da Alemanha

Lettres àune Princesse d'Allemagne sur divers sujets de physique et de philosophie (Letters to a Princess of Germany on various topics of physics and philosophy) is the work taken as an object of study of this thesis. It is a literary success written in the eighteenth century by the Swiss mathematician and physicist Leonhard Paul Euler (1707-1783) in order to meet a request from the Prussian king, Frederick II, the Great (1712-1786) to accept to guide the intellectual education of his niece, the young princess Anhalt-Dessau (1745-1808). The method of teaching and learning through letters elected to the education of the German monarch resulted in a collection of 234 matches in which Euler theory is about music, Philosophy, Mechanics, Optics, Astronomy, Theology and Ethics among others. The research seeks to point out mathematical content contained in this reference work based on the exploitation and adaptation of original historical works as an articulator of development activities for teaching mathematics in basic education and in accordance with the National Curriculum Parameters of Mathematics (NCP) work. The general objective point out the limits and didactic potential of Lettres à une Princesse d'Allemagne sur divers sujets de physique et de philosophie as a source of support for teachers of basic education in developing activities for teaching mathematics. The discussions raised point to concrete possibilities of entanglement between the extracted mathematical content of the bulge of the work with current teaching methodologies from resizing the use of letters according to Freire's pedagogical perspective of the correspondence, and especially the use of new communication channels in the century XXI, both aimed at dialogue and approximation between those who write and those who read.

Vernaculares: a casa de fazenda seridoense do século XIX como exemplo de adaptação ao clima semiárido

The farm’s rural dwellings of creation from the Seridó Potiguar microregion, built in the nineteenth century, became a reference by its vernacular character, i.e. these buildings, besides having recognized relevance to the identity of the region, they are adapted to the conditions of the place in many aspects (economic, cultural, construction, physical, et.) and consist in protective spaces in relation to hostile characteristics of Seridó’s climate. Considering the above premise, the following question arises: What characteristics of the nineteenth century Seridó Potiguar’s cattle farms are crucial for them to be a protective space in relation to the semiarid climate? In order to answer the question, this research aim to identify which particularities of the Seridó’s farmhouses that contribute to adaptability in these buildings to semiarid climate, as protection environments; and contribute to the stock valuation of the architectural heritage concerned. Therefore, procedures were adopted divided into two stages. Were first identified the recurring characteristics in the studied buildings, through typological study performed from existing inventories (DINIZ, 2008; FEIJÓ, 2002; IPHAN, 2012). To define the type it worked up with the concept that merges Durand’s analytical typology that identifies the similarities and differences to classify buildings, having the character of historical survey and architectural documentation, with the definition proposed by Argan (1963) that the type is not defined a priory, but the deduction from a number of illustrative cases which have formal and functional similarity with each other. Then worked up in a sample of five different types with each other, defined by the possibility of access to the interior of the houses, proximity to other copies, good state of conservation and preservation. The contemplated farms were: Pitombeiras, Agenus e Garrotes in Acari’s town, and the municipality of Caicó, Palma and Penedo. The second stage consists of the architectural survey, photographic record, digital three-dimensional modeling (aiming to expand the existing documentation and registration) and thermal monitoring over approximately a representative day in five farmhouses, relating the thermal performance of the houses with their individual characteristics. The selected variables for analysis monitoring are based on the thermal comfort adaptive model (SPAGNOLO and DE DEAR, 2003 apud NEGREIROS, 2010). The characteristics of the houses were analyzed as meeting the passive thermal conditioning strategies recommended by NBR 15220 (ABNT, 2005), for the bioclimatic zone 7 where the municipalities of Caicó and Acari are located. The house’s analysis of the operating temperatures revealed that 90% of the times of day the environments are within the comfort range. The farmhouses, which had a higher degree of compliance with recommended bioclimatic strategies, had the best thermal performance. In environments (usually the kitchen and rooms with low ceiling heights, exposed to west radiation) which still had discomfort hours, the thermal comfort can be reached with air movement approximately 1,0 m/s.

Vernaculares: a casa de fazenda seridoense do século XIX como exemplo de adaptação ao clima semiárido

The farm’s rural dwellings of creation from the Seridó Potiguar microregion, built in the nineteenth century, became a reference by its vernacular character, i.e. these buildings, besides having recognized relevance to the identity of the region, they are adapted to the conditions of the place in many aspects (economic, cultural, construction, physical, et.) and consist in protective spaces in relation to hostile characteristics of Seridó’s climate. Considering the above premise, the following question arises: What characteristics of the nineteenth century Seridó Potiguar’s cattle farms are crucial for them to be a protective space in relation to the semiarid climate? In order to answer the question, this research aim to identify which particularities of the Seridó’s farmhouses that contribute to adaptability in these buildings to semiarid climate, as protection environments; and contribute to the stock valuation of the architectural heritage concerned. Therefore, procedures were adopted divided into two stages. Were first identified the recurring characteristics in the studied buildings, through typological study performed from existing inventories (DINIZ, 2008; FEIJÓ, 2002; IPHAN, 2012). To define the type it worked up with the concept that merges Durand’s analytical typology that identifies the similarities and differences to classify buildings, having the character of historical survey and architectural documentation, with the definition proposed by Argan (1963) that the type is not defined a priory, but the deduction from a number of illustrative cases which have formal and functional similarity with each other. Then worked up in a sample of five different types with each other, defined by the possibility of access to the interior of the houses, proximity to other copies, good state of conservation and preservation. The contemplated farms were: Pitombeiras, Agenus e Garrotes in Acari’s town, and the municipality of Caicó, Palma and Penedo. The second stage consists of the architectural survey, photographic record, digital three-dimensional modeling (aiming to expand the existing documentation and registration) and thermal monitoring over approximately a representative day in five farmhouses, relating the thermal performance of the houses with their individual characteristics. The selected variables for analysis monitoring are based on the thermal comfort adaptive model (SPAGNOLO and DE DEAR, 2003 apud NEGREIROS, 2010). The characteristics of the houses were analyzed as meeting the passive thermal conditioning strategies recommended by NBR 15220 (ABNT, 2005), for the bioclimatic zone 7 where the municipalities of Caicó and Acari are located. The house’s analysis of the operating temperatures revealed that 90% of the times of day the environments are within the comfort range. The farmhouses, which had a higher degree of compliance with recommended bioclimatic strategies, had the best thermal performance. In environments (usually the kitchen and rooms with low ceiling heights, exposed to west radiation) which still had discomfort hours, the thermal comfort can be reached with air movement approximately 1,0 m/s.