Um estudo sobre a aprendizagem de alguns conceitos algébricos e geométricos

The objective of the present work was develop a study about the writing and the algebraic manipulation of symbolical expressions for perimeter and area of some convex polygons, approaching the properties of the operations and equality, extending to the obtaining of the formulas of length and area of the circle, this one starting on the formula of the perimeter and area of the regular hexagon. To do so, a module with teaching activities was elaborated based on constructive teaching. The study consisted of a methodological intervention, done by the researcher, and had as subjects students of the 8th grade of the State School Desembargador Floriano Cavalcanti, located on the city of Natal, Rio Grande do Norte. The methodological intervention was done in three stages: applying of a initial diagnostic evaluation, developing of the teaching module, and applying of the final evaluation based on the Mathematics teaching using Constructivist references. The data collected in the evaluations was presented as descriptive statistics. The results of the final diagnostic evaluation were analyzed in the qualitative point of view, using the criteria established by Richard Skemp s second theory about the comprehension of mathematical concepts. The general results about the data from the evaluations and the applying of the teaching module showed a qualitative difference in the learning of the students who participated of the intervention

Comparação entre metodologias de extração de HPAs em água utilizando um planejamento fatorial com quantificação no CG/EM

PAHs (Polycyclic Aromatic Hydrocarbons) are a group of organic substances which receive considerable attention because of the carcinogenic and mutagenic properties of some of them. It is therefore important to determine the PAHs in different environmental matrices. Several studies have shown the use of gas chromatography coupled to mass spectrometry as a technique for quantification of PAHs by presenting excellent detection limits. This study aimed to develop an analytical methodology for the determination of 16 PAHs listed by the USEPA, test two methods for extraction of PAHs in water from a 23 factorial design, quantify them through the analytical technique coupled to gas chromatography mass spectrometry (GC/MS) using the method developed, and finally apply the results in chemometrics. The sample was synthesized and subjected to tests of the 23 factorial design, which has the factors: the type of extraction technique (ultrasound and digester), the ratio solvent / sample (1:1 and 1:3) and the type of solvent (dichloromethane / hexane and acetone / dichloromethane). The responses of eight combinations of the factorial design were obtained from the quantification by external calibration in GC/MS. The quantification method was developed from an optimized adaptation of the USEPA Method 8270. We used the full scan mode as a way of acquiring the mass spectra of 16 PAHs. The time in which the samples were subjected to ultrasound was fixed at 10 min and held an investigation to establish the conditions of power and time in the digester. We had the best response in the investigation of the digester power of 100 watts and the time of six minutes. The factorial design of liquid-liquid extraction showed that the most representative factors were: the use of the digester as extraction technique, the ratio solvent / sample 1:1 and the use of a 1:1 mixture of dichloromethane / hexane as a solvent more suitable. These results showed that the 1:1 mixture of dichloromethane / hexane is an excellent mixture to recover the extraction of PAHs an aqueous sample using the microwave digester. The optimization of the method of separation, identification and quantification of PAHs in the GC/MS was valid for 16 PAHs present in each chromatogram of the samples

A relação de Euler para poliedros

In this paper we analyze the Euler Relation generally using as a means to visualize the fundamental idea presented manipulation of concrete materials, so that there is greater ease of understanding of the content, expanding learning for secondary students and even fundamental. The study is an introduction to the topic and leads the reader to understand that the notorious Euler Relation if inadequately presented, is not sufficient to establish the existence of a polyhedron. For analyzing some examples, the text inserts the idea of doubt, showing cases where it is not fit enough numbers to validate the Euler Relation. The research also highlights a theorem certainly unfamiliar to many students and teachers to research the polyhedra, presenting some very simple inequalities relating the amounts of edges, vertices and faces of any convex polyhedron, which clearly specifies the conditions and sufficient necessary for us to see, without the need of viewing the existence of the solid screen. And so we can see various polyhedra and facilitate understanding of what we are exposed, we will use Geogebra, dynamic application that combines mathematical concepts of algebra and geometry and can be found through the link http://www.geogebra.org

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