Os sentidos da autonomia docente no desenvolvimento curricular

Ese estudio se firma en el camino de la formación y del desarrollo profesional de profesores de Matemáticas, objetivando comprender, a partir del discurso de profesores de dicha asignatura, el sentido atribuido a la autonomía profesional y cómo ese sentido es reflejado en la producción y desarrollo curricular de la asignatura de Matemáticas. Para tal, utilizamos la entrevista comprensiva, metodología basada en el supuesto fundamental de la palabra en la construcción del objeto de estudio. A partir del discurso de cinco profesores que imparten la asignatura de Matemáticas en el Centro Federal de Educación Tecnológica de Rio Grande do Norte, percibimos que la autonomía está unida a una posición de soberanía en aula, lo que se traduce en un trabajo volcado al individualismo. Constatamos que las reuniones pedagógicas, espacios por excelencia para discusiones y reflexiones acerca de la enseñanza de Matemáticas y consecuente desarrollo profesional, no contribuyen para la mejora de la enseñaza de dicha disciplina. Percibimos, también, que el libro didáctico es utilizado para estandarizar el trabajo de los profesores y que la selectividad todavía es punto de referencia en lo que concierne al currículum de Matemáticas en la institución, lo que impide la realización de un desarrollo curricular de la asignatura de Matemáticas en que sean considerados conjuntamente todos sus componentes

Práticas etnomatemáticas no Liceu do Paracuri :a propósito dos ornamentos geométricos da cerâmica

The present study analyzes the ethnomatematics practices presents in the creation of the geometric ornaments of the icoaraciense ceramic, originated and still practiced in the neighborhood of Paracuri, District of Icoaraci, belonging to Belém, capital of the State of Pará/Brasil. The object of our study was centered at the workshops supplied by the artisans master of the School of Arts and Occupations, Master Raimundo Cardoso. Referred school provides to its students, formation at fundamental level as well professional formation, through vocational workshops that help to maintain alive the practice of the icoaraciense ceramic. Our interest of researching that cultural and vocational practice appeared when we got in touch with that School, during the development of activities of a discipline of the degree course of mathematics. In order to reach our objective, we accomplished, initially, a research about the icoaraciense ceramic historic, since the first works with the clay until to the main characteristics of that ceramic. Soon afterwards, we discussed on ethnomatematics, culture, knowledge, cognition and mathematical education. At the end, we analyzed the creation of the geometric ornaments of the icoaraciense ceramic, considering the proportion concepts, symmetry and some geometry notions, that are used by the artisans when they are ornamenting the pieces of that ceramic. We verified that, in spite of the artisans, usually, do not demonstrate to possess a bit of domain on the mathematical concepts that they are working with, for instance, the ones of translaction symmetry, rotation and reflection, they demonstrate full safety in the use of those concepts, as well as the capacity to recognize them, even if in a singular specific and very peculiar way, what opens the possibility of a partnership among mathematics teachers and master-artisans of the archeological ceramic and icoaraciense workshops

A dinâmica do pensamento geométrico :aprendendo a enxergar meias verdades e a construir novos significados

This work is a case study to investigate the dynamics of the historians thought as they produce a knowledge about the history of the area measurement systems as forms of historical expressions and representations. We refer to some of the ideas of David Bohm (1989, 1992, 1994, 1996) to support our theoretical understanding about the operation of thought. We chose a period that is recognized by the theorists as the origin of the geometrical thought -embracing the knowledge developed by the Egyptians, Babylonians, Chinese, Hindus, Greeks and Romans- and is referred to as containing a cycle in the development of this knowledge, described as beginning, apogee and decline. We assume this history, as told by the theorists, as a version that we organize and tell with the help of three sets of categories. The first refers to the elements that take part in the measurement practices; the second refers to the historians understanding about the development of the scientific knowledge. This exercise allowed us to extract the theorists main beliefs, that we criticized in the light of the knowledge about Cubação (Dal Pian, 1990). We stress the importance of the methodological approach adopted in this study to the teaching of Geometry and its history

Um estudo sobre a aprendizagem de números irracionais no ensino médio

The present study describes theoretical practical relationships between development and application of activities in Mathematics education. It s proposed a methodological approach to Mathematics in the first grade of Ensino Médio, supported by an experiment involving Irrational Numbers education by using constructive activities, applied obeying an educational sequence. Constructivism is used as an important theoretical reference in teaching learning process of Mathematics. The methodological intervention was done with two classes of students of the first grade of Ensino Médio, in two public schools, a state one and a federal one, located on the city of Natal, Rio Grande do Norte. The development, application and testing of the activities used on this experiment led us to think more profoundly about the value of constructivism ideas and understand that the use of activities that obey an educational sequence favors the learning. It s also discussed the research results, commented on a way to contribute to the advances of the proposal and it s more constant use. The participation and testing of the students were analyzed and judged using Skemp s Instrumental Understanding and Relational Understanding concepts. The results of the research were considered good, so we believe this methodological intervention can be used more frequently in the classes of Ensino Médio and also be applied to teachers in courses of initial education and continuous formation

Descrição anátomo-topográfica do coração da paca (Agouti paca)

Background: The domestic animals heart is a conical hollow viscera, surrounded by pericardium, laterally compressed, accompanying the thorax shape. Atriums constituted the heart basis and their auricles partially bound the initial portion of the aorta and pulmonary trunk. In mammals, heart is kept suspended in the thoracic cavity and the pericardic sac is fixed dorsally by great veins and arteries roots, and ventrally fixed to the sternum, although its fixation to the diaphragm varies among species. This paper aimed to describe morphological aspects of the heart of the paca, the second biggest Brazilian rodent.Materials, Methods & Results: There were used 12 hearts of adult pacas for this study, obtained from the UNESP, Jaboticabal, SP, which died due fights or anesthesia during bandages or radiograph exams. The thoracic aorta was filled with colored latex and the animal was set in a 10% formaldehyde solution for at least 72 hours. The thoracic cavity was dissected and hearts individualized and measured with a paquimeter, lateromedially, craniocaudally and dorsoventrally. The paca heart is placed between the first and fifth intercostal space (ICS), in a craniocaudal oblique position; its basis is craniodorsally positioned, on the middle third between the first and second ICS and its apex is located near the sternodiaphragmatic joint, on the fifth ICS, tilted to the left antimere. The heart is surrounded by pericardium, which from ventrocaudally is originated the sternopericardic ligament, that continues as phrenopericardic ligament. At the heart basis, the rising of the pulmonary trunk was observed and the conus arteriosus formed a typical projection. The aorta also rised from the heart basis and its arch, which was caudally curved, crossed dorsally the pulmonary trunk; the right cranial and caudal cava veins drained to the right atrium. There is a left cranial cava vein, which surrounded the left atrium and joined the right caudal cava vein on the right atrium. The azygos vein joins the right cranial cava vein and four pulmonary veins drained to the left atrium. At palpation, a hard structure on the rising of the aorta was observed, similarly to a cartilaginous tissue, which would be part of the cardiac skeleton. The left and right coronary arteries were observed in all hearts.Discussion: The paca heart is anatomica and topographically similar to those of domestic mammals, differing from them for being placed one intercostal space more cranial and due to the presence of two cranial cava veins, the left and the right ones, besides the presence of the caudal cava vein. This vascular description is similar to that of small rodents, as rats and mice. In paca heart, the sinus venous, the terminal crest, the oval fossa, the atrioventricular valvae, the papillary muscles and tendinous cords, besides smooth atriums and auricles covered by pectinate muscles, were observed. The sternopericardic ligament, which is dorsally elongated as phrenopericardic ligament, is similar to the one present in humans, pigs, castors, and different from the one observed in carnivorous, that presents the phrenopericardic ligament and from the one of horses and ruminants, which present the sternopericardic ligament.

De solutione problematum diophanteorum per números integros : o primeiro trabalho de Euler sobre equações diofantinas

The present dissertation analyses Leonhard Euler´s early mathematical work as Diophantine Equations, De solutione problematum diophanteorum per números íntegros (On the solution of Diophantine problems in integers). It was published in 1738, although it had been presented to the St Petersburg Academy of Science five years earlier. Euler solves the problem of making the general second degree expression a perfect square, i.e., he seeks the whole number solutions to the equation ax2+bx+c = y2. For this purpose, he shows how to generate new solutions from those already obtained. Accordingly, he makes a succession of substitutions equating terms and eliminating variables until the problem reduces to finding the solution of the Pell Equation. Euler erroneously assigns this type of equation to Pell. He also makes a number of restrictions to the equation ax2+bx+c = y and works on several subthemes, from incomplete equations to polygonal numbers

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

As geometrias urbana e isoperimétrica: uma alternativa de uso em sala de aula

The main goal of the present study is to propose a methodological approach to the teaching of Geometry and, in particular, to the construction of the concepts of circle (circumference) and ellipse by 7th and 8th grade students. In order to aid the students in the construction of these concepts, we developed a module based on mathematical modeling, and both Urban Geometry (Taxicab Geometry) and Isoperimetric Geometry. Our analysis was based on Jean Piaget's Equilibrium Theory. Emphasizing the use of intuition based on accumulated past experiences, the students were encouraged to come up with a hypothesis, try it out, discuss it with their peers, and derive conclusions. Although the graphs of circles and ellipses assume different shapes in Urban and Isoperimetric Geometry than they do in the standard Euclidian Geometry, their definitions are identical regardless of the metric used. Thus, by comparing the graphs produced in the different metrics, the students were able to consolidate their understanding of these concepts. The intervention took place in a series of small group activities. At the end of the study, the 53 seventh grade and the 55 eighth grade students had a better understanding of the concepts of circle and ellipse

Incorporação de lodo de esgoto na massa cerâmica para fabricação de tijolos maciços: uma alternativa para a disposição final de resíduo

The disposal of sewage sludge is a growing problem face up to management of sanitary sevices. Otherwise, because its making process characteristic, the Ceramic Industry can tolerate the presence of this wastes as raw material. This study has as object to confirm the use of the sewage sluge in the Ceramic Industry like a sustentable alternative for its disposal. Futhermore, this study quests to evaluate the maximum proportion for incorporation of sludge wich result in technically and enviromentally suitable bricks. For found this proportion, the research consisted of (1) making of bricks in full scale, adde up 0%, 5%,10%, 15%, 20%, 25%,30%, 35% e 40% sludge, with size 220x105x45 mm, hand-molded by rammer and baked by industrial kiln; and (2) tecnical and enviromental evaluation of this bricks, according to Brazilian norms. The raw material uses were two distinct clays come from Goianinha/RN and sewage comes from a septic system tank and pumped into tank vehicle, of Natal/RN. The technical evaluation allowed to conclude the addiotion of the sludge brings about signifcant lost of mass and the water absorption grew up according to increase of sludge: every sludge-amended clay bricks absorved more water than control group. Thus, the compressive strength was signicantly decreased because the increase of sludge: bricks with 5% sludge added lost 45% of strength achieved at control group; the bricks made with 10 and 20% lost almost 70% of bigger strength. With up to 25% sludge added to the bricks, the streght decreased over 90%. Concerning heavy metal leaching, the two maximum proportion wich have tecnical approval, it means bricks sludge added with 15 and 20%, can say there is no risk of enviromental contamination using those bricks. This way, in this work context, it can to conclude the maximum proportion atends the technical and enviromental criterion is 20%

Caracterização dos resíduos esgotados de sistemas de tratamento individual de esgotos de Natal

In Natal still dominates the use of individual disposal systems for domestic sewage, once only 29% of the city has a sewarage system. Wastes that are accumulated in these individual treatment systems should be exhausted periodically, service provided by collector entrepreneurs. Some of these companies causing major damage to the environment. In Natal, only two companies have their own septage (RESTI) treatment system, which were designed with parameters from domestic sewage generating strain and inefficient systems. Therefore, the characterization becomes essential as a source of parameters for their design. Thus, this work presents the physical-chemical and microbiological characterization of waste pumped from individual sewage treatment systems. Samples collections were made weekly from 5 different trucks at the reception point on the treatment plant on the point of the preliminary treatment. From each truck it was taken 5 samples during the discharge in order to make a composite sample. Afterwards, samples were carried out to laboratory and analyses for determination of temperature, pH, conductivity, BOD, COD, nitrogen (ammonia e organic), alkalinity, oils, phosphorus, solids, faecal coliforms and helminth egg. The results were treated as a single database, and ranked according to its generating source (multi and single house, lodging, health, services and / or food), area of origin (metropolitan, south and north) and type of system (cesspits, septic tank and / or sink). Through these data it was possible to verify that the type of system adopted by most in Natal and the metropolitan region is cesspit, besides to confirm the difference between the septage of areas with a population have different social and economical characteristics. It was found that the septage have higher concentrations than domestic sewage, except for thermotolerant coliforms that showed concentrations of 1,38E+07. Among the parameters studied, is the median values identified for COD (3,549 mg / L), BOD (973mg / L) and total solids (3.557mg / L). The volatile fraction constitutes about 70% of the total solids of the septage. For helminths has been a median of 7 eggs/L. In general, the characteristics of the waste followed the variability found in the literature reviewed for all variables, showing high amplitudes

Caracterização do conteúdo de fossas e tanques sépticos na cidade de Natal

Only 32% of the population of Natal is attended by sewage, while the remaining population use pits and septic tanks. The characterization of the contents of septic tanks and pits contributes to the performance of such system and may guide the decision on treatment of these contents. The main of this research is to characterize the contents of interior residential pits and septic tanks in the greater Natal, with the following specific goals: to develop and manufacture a sampler capable of collecting a representative sample of the entire column (the surface scum, the clarified liquid and sludge bottom); to compare the contents of the tanks with the pits; to compare the contents of the septage from vacuum trucks; to relate the composition content with socioeconomic characteristics of households; to compare the content in both chambers of the septic tanks in series; to assess the situation of the content before and six months after the cleanness; and ultimately propose a pilot scale plant for treatment of septage. Once the sampler was developed, samples were collected within 14 septic tanks and 10 pits in many districts of Natal. Medians of the 24 systems were obtained: temperature, pH, conductivity, oil and grease, total solids, total suspended solids and sediments of 28.0 °C, 6.95; 882 mS/cm, 75.2 mg/L; 10,169 mg/L, 6,509 mg/L and 175 mL/L respectively; 111.0 mgN/L for ammonia, 130.5 mgN/ L for organic nitrogen, 0.2 mgN/L for nitrite, 0.4 mg/L for nitrate; 8935 mgO2/L for COD, 29.2 mgP/L for total phosphorus, thermotolerant coliforms from 9.95 E +06 CFU/100mL helminth eggs and 9.2 eggs/L with a maximum concentration of 688 eggs/L and minimum of 0 eggs/L. Medians of organic nitrogen and TKN were significantly different between groups of tanks and pits. The systems with cleanness gap from 11 and 20 years presented the higher concentrations for most variables. The effluent from the toilets and bathrooms participate more effectively in contributing fractions of solids, alkalinity, nitrogen, COD, total phosphorus, thermotolerant coliforms and helminth eggs. The systems used by socioeconomics class with income from R$ 3,700.00 to R$ 7,600.00, presented higher concentrations for COD, nitrogen, solids and helminth eggs. The first of the two chambers had always presented higher concentrations over the second compartment. The analysis of variance for most variables, showed that the values of septic tanks, pits and septage from vacuum trucks belong to the same group. In the samples taken after cleanness, the median of pH and temperature increased, while alkalinity, COD, organic nitrogen, total phosphorus, ammonia and helminth eggs decreased. The oils and greases and thermotolerant coliforms had slightly varied due to the continuous release of sewage into the systems that maintained their steady state concentrations.

Dificuldades no processo ensino aprendizagem de trigonometria por meio de atividades

This study analyses the difficulties that teachers of high school face in the process of the teaching of trigonometry through activities in a construtivist focus. It contains a review of some publications and dissertations related with the study of trigonometry elaborated in the last years by several authors. It resorts to the study of teaching engineering as an instrument used in the research. It also presents a set of activities which will serve as sample to other teachers of mathematics; and points ways for the overcome of the difficulties found

Uma análise dos questionamentos dos alunos nas aulas de números complexos

This work presents a contribution for the studies reffering to the use of the History of Mathematics focusing on the improvement of the Teaching and Learning Process. It considers that the History of Matematics, as a way of giving meaning to the discipline and improve the quality of the Teaching and Learning Process. This research focuses on the questions of the students, classified in three categories of whys: the chronological, the logical and the pedagogical ones. Therefore, it is investigated the teaching of the Complex Numbers, from the questions of the students of the Centro Federal de Educação Tecnológica do Rio Grande do Norte (Educational Institution of Professional and Technology Education from Rio Grande do Norte). The work has the following goals: To classify and to analyse the questions of the students about the Complex Numbers in the classes of second grade of the High School, and to collate with the pointed categories used by Jones; To disccus what are the possible guidings that teachers of Mathematics can give to these questions; To present the resources needed to give support to the teacher in all things involving the History of Mathematics. Finally, to present a bibliographic research, trying to reveal supporting material to the teacher, with contents that articulate the Teaching of Mathematics with the History of Mathematics. It was found that the questionings of the pupils reffers more to the pedagogical whys, and the didatic books little contemplate other aspects of the history and little say about the sprouting and the evolution of methods of calculations used by us as well

A matemática sob a ótica do Tarô: Uma experiência com a educação de jovens e adultos

La recherche de la formation des citoyens critiques et participatifs, dans le travail pédagogique avec les jeunes et les adultes, a besoin d un entraînement pédagogique qui va au delà de l attitude traditionnelle d'apprendre avec des méthodes mécaniques et arbitraires qui, en insistant excessivement sur l image du professeur, donnent priorité à l'enseignement, au détriment de l apprentissage. Dans ce sens, la présente étude, cherchant la possibilité de réalisation d'un travail alternatif pour l'enseignement des Mathématiques, dans une perspective transdisciplinaire, dans le sens de développer l apprentissage significatif des étudiants jeunes et adultes du Projet Croire, présente les résultats d'une recherche-intervention qui a utilisé les lettres du tarot comme ressource didactique en salle de classe. On prétend, avec cela, montrer cet instrument comme facilité d apprentissage de contenus des Mathématiques comme systèmes de numération, nombres entiers et géométrie, en amenant les Mathématiques dans une perspective historique et culturelle et donnant un traitement global à l'acte complexe d'apprendre. Dans ce travail, le jeune étudiant et l étudiant adulte est pris comme individu concret, prenant en considération les aspects cognitifs et les aspects d attitude de son apprentissage, ce qui est favorisé par la nature des lettres du tarot et par la compréhension adoptée, des mathématiques comme système symbolique

Aplicações das atividades estruturadas de Skemp para a construção do conhecimento matemático

The present study constitutes a discussion about the application of Structured Activities to the construction of the mathematical knowledge, proposed by Richard Skemp. The discussion is based on the research that the author carried out in a public school of the state education chain buy using procedures of the research-action. It investigates the possibility of adoption of the proposal of Skemp in a new reality. It utilizes explanations from several theorists to understand the necessity and, at the same time, to enhance the efficiency of the referred activities in first grades of elementary school when students have their first mathematics teachings. It emphasizes the important rule of the teacher, as mediator to the mental constructions of the child. It presents considerations about the results achieved by the research, noticing the possibility of adoption of the studied proposal even though it is necessary an adjustment of the procedures to appropriate didactic-pedagogic requirements to the educational reality in which this project was done