Obstáculos superados pelos matemáticos no passado e vivenciados pelos alunos na atualidade : a polêmica multiplicação de números inteiros

In Mathematics literature some records highlight the difficulties encountered in the teaching-learning process of integers. In the past, and for a long time, many mathematicians have experienced and overcome such difficulties, which become epistemological obstacles imposed on the students and teachers nowadays. The present work comprises the results of a research conducted in the city of Natal, Brazil, in the first half of 2010, at a state school and at a federal university. It involved a total of 45 students: 20 middle high, 9 high school and 16 university students. The central aim of this study was to identify, on the one hand, which approach used for the justification of the multiplication between integers is better understood by the students and, on the other hand, the elements present in the justifications which contribute to surmount the epistemological obstacles in the processes of teaching and learning of integers. To that end, we tried to detect to which extent the epistemological obstacles faced by the students in the learning of integers get closer to the difficulties experienced by mathematicians throughout human history. Given the nature of our object of study, we have based the theoretical foundation of our research on works related to the daily life of Mathematics teaching, as well as on theorists who analyze the process of knowledge building. We conceived two research tools with the purpose of apprehending the following information about our subjects: school life; the diagnosis on the knowledge of integers and their operations, particularly the multiplication of two negative integers; the understanding of four different justifications, as elaborated by mathematicians, for the rule of signs in multiplication. Regarding the types of approach used to explain the rule of signs arithmetic, geometric, algebraic and axiomatic , we have identified in the fieldwork that, when multiplying two negative numbers, the students could better understand the arithmetic approach. Our findings indicate that the approach of the rule of signs which is considered by the majority of students to be the easiest one can be used to help understand the notion of unification of the number line, an obstacle widely known nowadays in the process of teaching-learning

O fazer docente: representações sociais de alunos de curso de pedagogia da UFRN

Cuando consideramos los procesos de formación del profesorado pensamos en los nuevos conocimientos que podrían ser aprendidos por los estudiantes involucrados, centrándose en el debate de cuales contenidos y conocimientos deben estar presentes en la formación que se desea para estos profesionales. El propósito de esta investigación es analizar el tema desde un ángulo diferente, invertido, desde la perspectiva de los estudiantes de pedagogía en la formación inicial, mirando cómo utilizan los conocimientos adquiridos durante la licenciatura, en un proceso de construcción y reconstrucción de los conocimientos que empiezan a permear a sus prácticas pedagógicas. Dado este marco, nuestro propósito ha sido estudiar los elementos de construcción de la identidad de los futuros licenciados en Pedagogía por la UFRN, intentando caracterizar las representaciones sociales expresadas por estos estudiantes acerca del trabajo del maestro, a través de la identificación de los elementos definidores de las dichas representaciones (conocimiento del contenido de estas) y la comprensión de la forma dinámica de organización de tales elementos. Tomamos como referencia la teoría de las representaciones sociales (MOSCOVICI, 1978), que proporciona una idea de cómo los futuros docentes construyen sus representaciones acerca de los objetos de conocimiento que rodean la formación docente. Participaron del estudio 120 estudiantes de la graduación en Pedagogía, cuándo nos acercamos a los contenidos simbólicos traídos por ellos utilizando el Procedimiento de Múltiples Clasificaciones (PMC) como el enfoque metodológico. El material incautado por tal procedimiento se sometió a análisis multidimensional (Smallest Space Analysis (SSA) y Multidimensional Scalogram Analysis (MAS)) y de contenido, con la intención de un entendimiento más amplio de las dimensiones simbólicas. Los resultados de la investigación mostraron las siguientes dimensiones: la afectiva, con el nombramiento de las características necesarias a construcción simbólica del maestro; la formativa, que resalta los elementos necesarios para una enseñanza profesional; el aspecto ético y profesional, que aborda los elementos necesarios para el desempeño docente, en la perspectiva de transformación social mediante la educación; y la dimensión conflictiva, poniendo de relieve las dificultades del trabajo docente. Por lo tanto, estos aspectos muestran que la representación de ser maestro, construida por los estudiantes en la formación, parece constar de diferentes matices, articuladas y complementares, que dan sentido a la profesión, lo que justificará la práctica diaria de los futuros profesionales

O currículo escolar: uma análise na perspectiva da inclusão de alunos com deficiência intelectual

A mid the many transformations and advances that the contemporary society is going through, the right to education is a topic that does not end and becomes increasingly present, given the urgency of including students with disabilities in education. Given this new reality, schools are challenged to receive them with quality, and implement actions that promote favorable conditions for their development at school. Accordingly, it is fundamental the organizational restructuring of education to meet the specific needs of students. Thus, it is imperative that educational institutions defining the type of person who intend to form and the society proposing to build. These are aspects that precede any question, since the knowledge covered in the curriculum will contribute directly to the creation of human beings are involved there. Based on this theme, this assignment reports aspects of a survey of a local public school, located in Natal/RN, which deals with the analysis of the curriculum and its implementation in teaching practice in the classroom, before the inclusion of students with disabilities intellectual. Thus, to undertake a study of case with five professionals at school, involving documentary analysis and observation of the curriculum of the pedagogical practice of teachers in the classroom, as well as conducting an interview with all stakeholders. To this end, the data analyzed shows that, although the right of citizens with disabilities is guaranteed by constitutional law, the school, locus of this study, have not realized the extent of conquest. Does not recognize the fact of being in school and learn together with others is also a right of persons with disabilities. Thus, while your resume is to present a progressive vision, believed to be open, concerned with the selection and organization of content, with flexibility in defining the goals, with the search for diversification of the procedures adopted, as well as the planning activities teaching and learning based on the level of student learning, this is not effective in teaching practice, either through ignorance of the guidelines defined either by lack of knowledge about the proposal and an inclusive curriculum can provide answers to all educational students, including those with intellectual disability

Concepões e práticas pedagógicas de professoras da educação infantil na inclusão de alunos com deficiência

This research focuses on inclusive in childhood education. Its purpose was to investigate and analyze the conceptions and expectations of teachers of childhood education, childhood education center form Natal/RN, on the inclusion students with disabilities, school and pedagogical practices developed and implications for students learning. Theoric base of the cultural historic perspective, the search took by qualitative analysis of numbers form the case study method. It was used methodological procedures: documentary analysis, participant observation, field journal and semi structures interview.Three teachers participated in the survey of that school had student with disabilities in their classrooms. These teachers were called: Rapunzel, Snow white e Pretty. The teacher s nouns involved the refered kind of education. The data obtained from the observation indicated the regular school of childhood education provides educational practices that promote the participation and participation and development of students with disabilities, live situation that may create barriers to learning and to the development of these children. The analysing data of interview from Bardin content analysis (1994) was based in Cunha s studies (2001) Brun (2006, 2008), Mantoam (2006, 2008), Palacios, Paniagua (2007), among others. The dada showed that correlation and divergence of perceptions and expectations about the issues surrounding inclusion in childhood education. The results shaved that teaching strategies, affective ties, sensitivity and own routine of childhood education are factors that can promote inclusive proposal, but also needs a greater fulfillment individual differences of each child in order to their potentiality. The study also shaved that the negative of pedagogic support to teacher, the ignorance of them as guidelines and strategies that include the student s diversity, the importance having positive conceptions about the learning and development of student with severe learning disabilities and the need for a pedagogic training and of a collective work at school which everybody collaborates : parents, direction, coordination getting inclusive school. Believe that this study pointed relevant issues to be focus new research, since the theme is still lacking in study, therefore emphasize, the importance of conducting research that continuous this job

A prática pedagógica de professores de alunos com transtorno de déficit de atenção/hiperativadade

This study is inserted at the Line of Strategical Research of Thinking and Knowledge production which scientific projects about the relation of thinking and knowledge production are realized. The accomplishment of this dissertation involved an empiric research at a school of the municipal district of Natal RN. Our purpose was to investigate the practice of the staff working with students who present Disabilities and Attention Deficit Hyperactivity (DADH) at regular classes due to the organization of thinking in pedagogical strategies. The object of this study is presented at the center of the questions which involves the conscious analysis of the problems and needs that emerge at the school. Considering the specialty of the theme, we choose a methodology whose focus is the dialogue and the sharing of meanings with the partners of this research through the observation of the activities developed at class/school and interviews/conversations with six teachers of first and second cycles of primary education. According with the study, some theoretician presumptions of Mr. Freire (2001), Mr. Nóvoa (1995), Mr. Bohm (2005) and son on. The results reveled at the research indicate the fragility of a continuous formation directed to the development of critical-reflexive thinking of the teachers.The teachers revel conceptions due to formation, pedagogical practices and the relation with the parents and coordinators, through their performances and speeches, allowing us to identify some pedagogical strategies used. We identified some negative response about the process of learning-developing of these pedagogical strategies such as the one we call unconcern . The strategy of sitting the student at the front row chairs can have positive and negative responses depending on the way the teacher act and follow the student. Other strategies identified as positive response bringers at the learning-developing process and that should be reinforced by the staff are the playful and the group assignments . At this perspective, the school needs to develop a collective project between the pedagogical team and teachers to overcome the needs of all students, and as a consequence, of the staff and improve the positive strategies, minimizing the negative ones and allowing the organizations of new strategies that promotes the improvement of learning-teaching process of the students with DADH

Um estudo de aplicação das teorias da expectativa e da ancoragem na motivação para o desempemho de alunos do ensino médio

This thesis presents a study on Tversky & Kahneman s (1974) Anchoring theory, and Vroom s (1964) Expectance theory in the context of education and students motivation. It is surveyed 424 students of a secondary and agricultural technical school in Brazil Northeast (EAJ). The survey form try to capture the Vroom s Expectance Theory constructs of Valence, Instrumentality, Expectation and Motivational Force, and also the Tversky and Kahneman Anchoring effect in terms of grade expected. The main findings suggest that the minimum grade required by the school is much strong in driving the students motivation and performance than the Expectancy Theory. It was found that the different grades required drive the students to pursue different grade in the same way

A tabela periódica: um recurso para a inclusão de alunos deficientes visuais nas aulas de química

Nowadays there are many reasons that aim to include people with special necessities, like those with visual deficiency, in the world of work, education, and in the society as a whole. However it is observed that when we talk about schooling inclusion, especially in High School, there is a huge gap between the theory and the practice. The lack of didactic resources, the inadequate installations, unprepared teachers, the families´ lack of information, are some of the factors that hinder the process of inclusion. Furthermore, the educators also have to deal with the roughness of the disciplinary contents and, refering to the study of Chemistry, with the use of signals related to this subject´s language. So, the objective of our research is to reflect about the apprehension of this language by the visually handicapped people, and try to contribute with their process of inclusion in the school life. On this perspective we work with the Periodic Table, which constitutes one of the indispensable tools necessary to the Chemistry learning. In order to acomplish it, the way followed by us happened in three passages. Initially, by means of a semistructured interview, we tried to get acquainted with the blind students opinion, who were participating in the research about the Periodic Table used by them throughout High School, as well as the dificulties felt when using it. After getting the answers, the Table was reelaborated to fill those students´necessities. Here, two new Tables were designed, one in Braille which shape is more compacted, and another made with high printed dots, built with sand and glue. On the third moment, the new designed Tables were tested by the students and, by means of a semi-structured interview, we tried to identify if this new resource would solve the problems concerned to the old Table. The students showed that the compacted Tables would facilitate the touch reading of the chemical elements simbols, making it clear and fast. We hope that, with the elaboration of this learning tools we can contribute with one of the elements to favor the effective participation of blind students in Chemistry classes, when studying the Periodic Table

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 desistência de alunos na licenciatura em física no Instituto Federal de Educação, Ciência e Tecnologia do Rio Grande do Norte (IFRN): causas e sugestões para o combate

This dissertation proposes studying the issue of withdrawal undergraduate in physics at the Instituto Federal de Educação, Ciência e Tecnologia do Rio Grande do Norte (IFRN) and collaborate with suggestions for dealing with this problem. The first chapter begins with an overview of two significant problems in the Brazilian educational system: the high dropout rates in degrees in physics and the lack of teachers with specific training in this science. Then, we discuss the relevance of this research to the area of physics teaching, as well as justify its completion as part of a professional master's degree. After, we present a proper definition for the term withdrawal, which is based on the existing problem in the IFRN. And, in the same chapter, we explicitly the focus, the objectives and the methodological aspects of this work. The results obtained in our investigation are presented in next four chapters. In the second chapter of this dissertation, we present: a brief history of the creation of IFRN degree in physics, the functioning of this course and the foundation of classrooms 2004.2 and 2006.1. We also show a kind of map of the withdrawal of the groups investigated (the dropout rate was 84.4% in both groups) and an analysis of the relationship between the curricula of each of them and the number of dropouts. In the third chapter, we display a descriptive statistics of the students which dropout and found that the largest dropout occurred with students who are women, married, parents of one kid; workers, joined with a minimum age of 23 years and completed high school at least 6 years. Then in the fourth chapter, we reveal and discuss the students' reports on the causes of their dropout. From the data presented, we can say that the answer to the question "What was the main reason for your dropout?" Is mainly in personal injury claims: another option for upper-level course and lack of time to devote to the course. In the fifth chapter, we show the results related to teacher s opinions about the phenomenon in question. We detected three main causes for the abandonment, according to teachers: the lack of dedication, the lack of interest and lack of integration in the course. In the sixth and final chapter, we discuss the results and present our conclusion and the proposed report - the product of this dissertation, presented as Annex. This report contains mainly suggestions for curricular and institutional actions that can contribute to reducing the dropout degree in Physics in the IFRN. The main actions suggested are: implementation of the curriculum in disciplines, implementation of programs or actions to combat this poor content of basic training, implementation of specific programs or actions for the student worker, and dissemination of IFRN degree in physics in schools through seminars or workshops

Uma proposta metodológica do ensino da química para alunos da Zona Rural :O estudo do leite

La enseñanza desarrolló, así como los métodos y las técnicas de enseñar. Aquí el he/she piensa un método instrucción, en que el estudiante está más de un oyente simple: además la parte íntegra, él se llama para intervenir continuamente, mientras tocando una parte ancho, interactivo e involucrando, del contextualização del tema para ser trabajado -inclusivo, asocie día a día al his/her y contextual al programa de la disciplina de Química, hasta la manera como ese tema debe explorarse. La leche, el tema pone en correlación al origen del grupo de los estudiantes seleccionados, fue explorado, dentro de una visión sistémica, bajo el punto de vista de la composición de las propiedades de la industrialización y de la comercialización. Buscando prever los caminos de la construcción y organización del conocimiento de los estudiantes, se usó el modelo de administración mental de Antoine de La Garranderie y la teoría de aprender de Ausubel. El conocimiento de los estudiantes se supervisó antes, durante y al final de las actividades desarrolladas, práctica que permitió verificar la evolución y el nivel de asimilación conceptual de éstos con respecto al tema en el estudio. El análisis de los resultados obtenidos, después de la aplicación de una encuesta que contempla veinte asuntos, todo pertinentes al tema, demostró un nivel del uso sobre el promedio, lo que merecido la pena el método de enseñanza propuesta

Refletindo dificuldades de aprendizagem de alunos do ensino médio no estudo do equilíbrio químico

This research intends to identify the main conceptual mistakes committed by High School students when studying Chemical Equilibrium and also how the didactic books can influence in their formation. For the data - collecting we applied 150 questionnaires with 11 open questions e 4 restricted ones. Students from three different private schools in Natal-RN were used in this survey. The questionary about the book analysis tried to understand how the subject has been boarded, making it easier or not for the knowledge building. The books were chosen by being usually the most used ones at the chemistry classes in the schools in town. On the didactic book analysis we evaluated 12 items that tried to identify the clarity with which the books would bring up the subjects, the contextualization of the exercises, the analogies used, the amount and the quality of exercises, the connections between the subjects, and the retaken of important concepts. The questionary given to the students tried to get their knowledge about the concepts related to Chemical Equilibrium. The main mistakes found were: the definition of the state of equilibrium in a chemical reaction, the constant, the double headed arrow, confusions between mass and concentration, the representation of a microscopic reaction in equilibrium, partial pressure and total pressure, and the function of the catalyser. The results demonstrated a lot of insecurity or lack of knowledge about the subject when it was realized that there was a big number of blank questions and a considerable percentage of questions with conceptual errors. We concluded that those errors could be eased or even avoided if the didactic books and the teachers boarded the contents in a more conceptual form with the application of a largest number of good quality exercices, watching the building of definitions by the students, avoiding this way the formation of wrong concepts

A interpretação dos sintagmas nominais com adjetivos atributivos por alunos de inglês instrumental

This present work has as objective to analyze the interpretation of the syntactic and semantic meaning performed by third graders in the nominal groups (NGs) with attributive adjectives in the English language in a text of the final exam in the ESP (English for Specific Purposes) discipline. The corpus is made up of 30 exams of two classes from a third grade institution of the biomedical area, corresponding to the basic and advanced levels of the second term in 2006. The text has 24 NGs of different lexical content, a total of 27 NGs in the whole text summing up to 810 analyzed occurrences. The analysis is carried out at the morphologic, syntactic and semantic levels using as theoretical background the traditional and functional grammars (QUIRK et al, 1985; CELSE-MURCIA et al, 1998; TUCKER, 1998), in their semantic aspects, the Semantics (FRAWLEY, 1992) and the Cognitive Linguistics (TAYLOR, 2002). We concluded that the main difficulties were due to the lack of vocabulary and to the use of mother tongue strategies instead of using the top-down strategies for reading a text in English to compensate this gap. We also observed that even when the vocabulary was known, there were difficulties in establishing the semantic and syntactic relations between modifier and noun head. We suggested improvements for the teaching of reading English texts at the third grade grounded in the obtained results such as a more comprehensive study of the several different morphologic and syntactic structures of the NGs with premodifiers and their semantic consequences, an approach of the morphologic, syntactic and semantic aspects of the NGs and the use of both top-down and bottom-up strategies when reading a NG in the English language

Mecanismos de coesão referencial na produção escrita de alunos concluintes do ensino fundamental

This work aims to identify, describe and analyze the main mechanisms of reference present in the texts produced by students that are finishing their fundamental school. With this in mind, we observe 46 Portuguese classes. The class was in its 9th Fundamental level, in a public school of the Cruzeta, RN. In this period, we collected our corpus that is composed by the papers that students produced. This research has an ethnographic approach and it has as theoretical support some studies about some mechanisms of reference, specifically, the lexical repetition and anaphor. In general, we are based on the studies about cohesive mechanisms from authors as Adam (2008); Beaugrande and Dressler (1981, 1997); Koch (1999, 2004, 2005, 2008), Marcuschi (1983, 1992, 2005, 2006); Bessa Neto (1991) and Neves (2006). In the corpus, we could identify some lexical repetitions (literal, with estrutural variation), as well as, anaphors, mainly pronominal ones. Then, we can notice that most students have showed difficulties in the use of those mechanisms of reference as a strategy of textual progression

Mecanismos de coesão referencial na produção escrita de alunos concluintes do ensino fundamental

This work aims to identify, describe and analyze the main mechanisms of reference present in the texts produced by students that are finishing their fundamental school. With this in mind, we observe 46 Portuguese classes. The class was in its 9th Fundamental level, in a public school of the Cruzeta, RN. In this period, we collected our corpus that is composed by the papers that students produced. This research has an ethnographic approach and it has as theoretical support some studies about some mechanisms of reference, specifically, the lexical repetition and anaphor. In general, we are based on the studies about cohesive mechanisms from authors as Adam (2008); Beaugrande and Dressler (1981, 1997); Koch (1999, 2004, 2005, 2008), Marcuschi (1983, 1992, 2005, 2006); Bessa Neto (1991) and Neves (2006). In the corpus, we could identify some lexical repetitions (literal, with estrutural variation), as well as, anaphors, mainly pronominal ones. Then, we can notice that most students have showed difficulties in the use of those mechanisms of reference as a strategy of textual progression

Autoria e escrita: uma reflexão acerca do autorar em memórias de leituras de alunos de 9º ano do ensino fundamental

This paper presents results concerning studies conducted during the master's research in the area of Applied Linguistics of the Graduate Program in Language Studies - PPgEL, linked to the Federal University of Rio Grande do Norte. We approached this study the question of authorship, which has gained ground increasingly important in academic research, because the act of authoring, in view of the amount of circulating discourses socially, becomes increasingly questionable. We understand authorship as related to a positioning of the subject than to take responsibility, in the Bakhtinian sense, by its text, it makes their views, ideologies, beliefs and values, from ownership and restructuring of the speech of others. This research is methodologically inserted in a qualitative, interpretive in nature and has a corpus analysis of the ten productions written memoir genre of readings produced by students in 9th grade in elementary school. Research aimed to analyze the students' written productions held in the school environment, to identify these texts marks or evidence of authorship and investigate how the restructuring of ownership and voices of others in the process of authoring. We adopt a concept of language from bakhitinianas concepts and understand the text in a vision Geraldiana. The analyzes in this study showed that in most texts there is the strong presence of voices of others, either implicitly and/or explicit. That is, students, to build their sayings, if embraced the voices of others in various formats, in particular styles, namely, by what Bakhtin names as linear style and pictorial style. Some proved his statement highlighting their positions through direct quotes from authors of books, family, teachers, showing us that their voices are filled with voices of others with whom they approve, deny, analyze, think and reflect. We therefore conclude that students were constituted as subjects of their texts, authors, since they leave marked the voices of others so presentified and restructured voices of others who do not actually sounded like voices of others, but as present voices from a discursive restructuring producer