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

Investigação histórica nas aulas de matemática: avaliação de duas experiências

This study reflects on some procedural aspects about the development of mathematics learning from the experience with investigative activities concerning the resolution of second degree equation, which was tested a proposal for education, supported the use of texts in history of mathematics. The survey was conducted in two stages, taking the first-served basis for the second, which was carried out with a study group remainder of the first experiment. The intention was to investigate how the group participant, known as the study group, involved in the implementation of activities of research in mathematics, supported the use of the history of mathematics. Based on the results achieved during the study, it was possible to understand that the activities of research enable the development of students, range of learning mathematics and the development of skills and expertise for research as a vehicle for construction of their mathematical knowledge. This approach proposed research into the classroom is important, both for prospective teachers of mathematics and for students from elementary school, bringing a new phase for mathematical education that will come to schools

Investigação histórica na formação de professores de matemática: um estudo centrado no conceito de função

In this study we analyzed the development of a teaching experience, involving students with a bachelor s degree in mathematics from UFRN, based on the history of mathematics and mathematical investigations with the aim of contributing to the improvement of the teaching-learning of mathematics. The historical investigation tasks were planned and applied in the classroom, focusing on functional thought. The results obtained during the experience were described and evaluated based on authors who support the assumption of investigation and history as an alternative to the learning of mathematics. We emphasize that the material of analysis consisted of a work diary, audio recordings, questionnaires with testimony of the students involved, and, in addition, the assessment of the teacher of that subject. With regard to the mathematical content, the study was restricted to the concept of function, forms of representation and notation. It was evident that students showed great improvement with regard to the necessary formalization of the mathematical contents which were focused on, and to the active involvement of the students at different stages of the study. We can affirm that the completed study certainly represents significant contributions to an approach in the teaching-learning of functional thought

As Concepções da mobilidade e acessibilidade urbana aplicadas à implementação do ensino de física: uma interface pedagógica para sedimentação de conhecimentos

Abstract:It boards a study about the methodology applied in the classroom, with emphasis at the Physic teaching, but could be taken to the other matters of high school, mainly to that alumns with school delay and that needs a pedagogics resources to get the aproach of them to the subject showed trying to improve their learnship. The study was developed through the bibliographic research methodology, associated to the induce resource that allows to evaluate the methods of teaching praticed actually at High Schools, as the private as the public, to give to the teachers the resources that should change the dificulties of learning with prejudice the classmates performances. The results reacheds demonstrated that is perfectly possible to augment the physic teaching body, taking in consideration the expansion of the profit at the teaching­learnig procces, besides having allowed to shows that this methodology porpouse could be takes to others subjects of the High School to became this phase of school more suitable to the necessities of society. It concludes that the brazilian Education could receive a lot of augments, from the professional criativity on always that inside the classroom, really close of the problems showed by the classmates about learning collecting

A difícil aceitação dos números negativos: um estudo da teoria dos números de Peter Barlow (1776-1862)

The present study seeks to present a historico-epistemological analysis of the development of the mathematical concept of negative number. In order to do so, we analyzed the different forms and conditions of the construction of mathematical knowledge in different mathematical communities and, thus, identified the characteristics in the establishment of this concept. By understanding the historically constructed barriers, especially, the ones having ontologicas significant, that made the concept of negative number incompatible with that of natural number, thereby hindering the development of the concept of negative, we were able to sketch the reasons for the rejection of negative numbers by the English author Peter Barlow (1776 -1862) in his An Elementary Investigation of the Theory of Numbers, published in 1811. We also show the continuity of his difficulties with the treatment of negative numbers in the middle of the nineteenth century

O uso pedagógico de uma seqüência didática para a aquisição de algumas idéias relacionadas ao conceito de números complexos

The aim of the present work is to contribute to the teaching-learning process in Mathematics through an alternative which tries to motivate the student so that he/she will learn the basic concepts of Complex Numbers and realize that they are not pointless. Therefore, this work s general objective is to construct a didactic sequence which contains structured activities that intends to build up, in each student s thought, the concept of Complex Numbers. The didactic sequence is initially based on a review of the main historical aspects which begot the construction of those numbers. Based on these aspects, and the theories of Richard Skemp, was elaborated a sequence of structured activities linked with Maths history, having the solution of quadratic equations as a main starting point. This should make learning more accessible, because this concept permeates the students previous work and, thus, they should be more familiar with it. The methodological intervention began with the application of that sequence of activities with grade students in public schools who did not yet know the concept of Complex Numbers. It was performed in three phases: a draft study, a draft study II and the final study. Each phase was applied in a different institution, where the classes were randomly divided into groups and each group would discuss and write down the concepts they had developed about Complex Numbers. We also use of another instrument of analysis which consisted of a recorded interview of a semi-structured type, trying to find out the ways the students thought in order to construct their own concepts, i.e. the solutions of the previous activity. Their ideas about Complex Numbers were categorized according to their similarities and then analyzed. The results of the analysis show that the concepts constructed by the students were pertinent and that they complemented each other this supports the conclusion that the use of structured activities is an efficient alternative for the teaching of mathematics

Questões objetivas sobre funções das provas de matemática do vestibular da UFRN dos anos de (2001 a 2008): um diagnóstico sobre os erros que os candidatos cometem

La dificultad que los alumnos encuentran en el aprendizaje de matemática viene siendo objeto de investigación por estudiosos en educación matemática, tanto en Brasil como en el exterior. El objetivo de este estudio consiste em investigar las dificuldades en el aprendizado sobre funciones matemáticas y la influencia de las concepciones alternativas a partir de los errores que los candidatos acerca de las cuestiones sobre funciones en la prueba objetiva de matemática del acceso a la universidad de los años de 2001 a 2008. Teniendo como cuestiones de estudio para alcanzar el objetivo propuesto: identificar la relevancia del tema funciones que son contemplados en las pruebas de acceso a la Universidad; asi como cuáles han sido los tipos de funciones más privilegiados y menos privilegiados; analizar si la contextualización de la pregunta y la presencia de elementos no textuales han influenciado en el aumento de tal dificultad; analizar si la representación semiótica agrega mayor exigencia a la pregunta; analizar respecto a la exigencia matemática de la pregunta; analizar lo que se refiere al desempeño de los candidatos para verificar cuál pregunta tuvo mejor desempeño y cuál el peor e identificar los errores más frecuentemente cometidos por los candidatos en esas pruebas. Las reflexiones de los estudiosos como: Radatz (1980), Cury (1994), Socas (1997), Borasi (1997), Franchi e Rincón (2004), Pochulu (2004) presentan las dificultades en el aprendizaje matemático, que aparecen a partir de los errores cometidos por los alumnos, quando estos errores reciben la influencia de las concepciones alternativas. El estudio que se presenta en esta disertación configura un análisis de los errores que los candidatos han cometido en las preguntas objetivas sobre el tema funciones de las pruebas de acceso a la Universidad de los años de 2001 a 2008, a partir de los relatorios de la Comissão Permanente do Vestibular COMPERVE/UFRN. Con la intención de alcanzar los objetivos propuestos para este estudio, fueran sido construidas categorías de análisis. Los resultados encontrados han sido: El tema funciones es el más frecuente entre los demás con (28,1%); el tipo de función priorizada durante esos años ha sido la función logarítmica con (24%); la contextualización de las preguntas exige una mayor comprensión por parte del candidato de lo que las situaciones directas; la caracterización semiótica posee elementos que estructuran esas preguntas que el educando debe saber asociar al texto; la exigencia matemática posibilitó analizar que el procedimiento medio ha sido el más requisitado; el desempeño de los candidatos ha sido en la mayoría bajo (50%); y los principales errores que ellos han cometido han sido de realizar traducciones incorrectas de las expresiones que aparecen en las situaciones-problema; utilizar todos los datos que aparezcan en el problema sin tomar en cuenta si el cálculo realizado responde a la pregunta solicitada; no interpretar coherentemente las informaciones del gráfico; decodificar incorrectamente los valores representados por literales en una recta numérica. Los resultados señalizan la necesidad de una revisión didáctico-metodológicas de la enseñanza de funciones a raíz de las cuales las dificultades en el aprendizaje se han presentado

As quatro operações básicas: uma compreensão dos procedimentos algorítmicos

The current research had as main objective to analyze the possibility of knowledge elaboration/re-elaboration about ideas and algorithmic procedures related to basic operations by pupils of the 6th degree fundamental teaching in a significant learning process. This way the study had as basis a methodological intervention developed in a 6th degree class of a Fundamental Teaching Municipal School in the city of João Pessoa, PB. The research had as central steps the application of pre-tests (1 and 2); the execution of semi-structured interviews with the pupils involved in the theme deep studies; the elaboration and development of teaching activities, having as referential the significant learning and the application of a pre-test. The data collected in the pre-tests (1 and 2) showed a low level of the pupils comprehension about the contents related to the four operations. The answers to the post-test questions were analyzed mainly from the qualitative point of view based on the mathematic concepts comprehension theory proposed by Skemp (1980) having as complementary subsidy data collected through interviews. The analysis of the results obtained in the post-test showed that the major part of pupils reached a relational comprehension about the ideas and algorithmic procedures related to addition, subtraction, multiplication, and division. Such results showed us that the application of a teaching methodology that privileges the content comprehension, considering the pupils previous knowledge and the reflection about the action along the activities proposed, made possible the elaboration or re-elaboration of knowledge by pupils regarding to contents adopted as theme for our research

Física para geografia: desafios de uma proposta pedagógica interdisciplinar

This study has as its aim the elaboration, presentation and application of a proposal which makes possible an inter-disciplinary relationship between knowledge of physics and geography in the graduation course for forming geography teachers in the Dom Aureliano Matos Faculty of Philosophy in the city of Limoeiro do Norte in the State of Ceára. Initially, we observe in pertinent literature and opinions of specialists what capacities and abilities are suggested for a future teacher of geography. Following that, we select subject matter which broaches upon physic concepts and may be contextualized within topics present in the daily fare of a geography teacher, such as natural phenomena related principally to natural environment and climate, envolving astronomic features, using didactic materials and resources in easily understood language and without the excessive presence of mathematical formulas. An evaluation of the experience allows us to affirm that inter-disciplinary treatment, as an important alternative for curriculam organization, when applied in the classroom shows that there is better learning, a reduction in class evasion and a significant fall in failures when compared with traditional proposals for the teaching of physics in relation to geography. On the other hand, it is notable that to maintain and augment such measures it is a challenge to be met, with the purpose that students of other courses may perceive that physic concepts have much to do with their reality, and that understanding them is relevant for their professional and personal formation

Controvérsias sobre a natureza da luz: uma aplicação didática

Researches in the field of Science Teaching have shown, in recent decades, that students from high school level have difficulties in understanding basic concepts of science, in general, and physics, in particular. The specific literature indicates, as a priority for a scientific education of better quality, a more structured understanding about science. This work proposes the introduction of elements of History and Philosophy of Science in high school as an aid to learning the concepts of optics, in general, and of aspects concerning the nature of science, specifically. Making use of historical episodes regarding the controversy on the nature of light, especially during the seventeenth and eighteenth centuries, as well as clippings of the history of optics in relation to the development of models that explain the process of vision, we formulated a teaching unit and implemented it on two night high school classes of a public school in the city of Parnamirim (RN). The unit involved, primarily, the reading of three historical texts containing written questions followed by a collective debate ("moot"). The results indicated some difficulties in overcoming the misconceptions related to the process of vision and the nature of light. Nevertheless, we believe that the teaching unit has succeeded in relation to the learning of most students, both in relation to a better understanding of science as well as concepts of optics

Estudo histórico e pedagógico sobre ternos pitagóricos à luz de eugène bahier

At the present investigation had the purpose to achieve a descritive analysis pedagogy in the work of Recherche méthodique et propriétés des triangles rectangles en nombres entiers. According to the analysis achieved, we made and applyed the teaching module called Pitagories: one of tools to comprehension Pitagory Theorema, there were studying by public students in mathematic course in the UFRN , the new mathematic teachers in future. The analysis the was made with writen test the was showed that all students got the view comprehension in the teaching approach module, to apointed the difference in the learning qualytative with other reseach that was made with quastionaire and enterview. With this module that was made with the new future teacheres there was more attention the better comprehension with the Pitagory Theorema, that was good focus in the pitagory about the potential historical pedagogyc in the work studied.

A utilização de espaços de educação não formal por professores de biologia de Natal-RN

La práctica educativa en espacios no formales es un recurso didáctico catalizador de motivación e interese, tanto para alumnos como para los profesores. El crecimiento de los espacios no formales coincide con los cambios recientes en el mundo en los campos sociales, políticos, económicos y culturales. Como una de las consecuencias de esos cambios, tenemos el crecimiento de otras instancias difusoras de conocimientos rompiendo, así, la hegemonía de la escuela. De esa forma, en este trabajo busqué investigar la frecuencia y las formas de utilización de los espacios de educación no formal por profesores de biología, de la enseñanza media, de la Ciudad de Natal (RN). Procuré también, identificar cuales son los espacios de educación no-formal que son utilizados; describir los recursos y las acciones desarrolladas en eses espacios; identificar la existencia o no de interese y la importancia que atribuyen a los espacios para la enseñanza de biología, además de divulgar los espacios utilizados como recursos didácticos. Para alcanzar estos objetivos fueron hechas observaciones de los espacios, aplicados cuestionarios y realizadas entrevistas con los profesores que realizan actividades junto a tales instituciones. Para el análisis de los datos se utilizó tanto el abordaje cuantitativo como cualitativa. Nos basamos en referenciales teóricos de autores que buscan establecer las relaciones entre diferentes modalidades de educación para mejor comprender lo que es la educación no-formal y su trayectoria histórica. Constaté que los profesores utilizan los espacios de educación no-formales, aun la cantidad de visitas al año sea reducida, en virtud de varias dificultades por ellos apuntadas, tales como el transporte, la falta de recursos financieros y de apoyo para viabilizar la visita, entre otros. Verifiqué también que los profesores demostraron un alto interese por los espacios no-formales y apuntaron como principales justificativas para considerarlos importantes para la enseñanza de la biología la posibilidad de establecer conexiones entre la teoría y la practica, además de la complementariedad

A prática interdisciplinar como estratégia de aprendizagem na formação continuada: uma experiência com professores da área das ciências da natureza

The school is a privileged locus of pedagogical reflection and, therefore, can and must be the best place for the process of continuing graduation for teachers. This process can be very productive if executed with an interdisciplinary group, once interdisciplinarity enables sharing different disciplines and also different personal stories. This study aimed to build a continuing graduation opportunity with an interdisciplinary group of teachers to Natural Sciences area, in a private school in the city of Natal - RN. This opportunity was build using as a tool the elaboration of interdisciplinary class called dialog-lesson. The methodology was in accordance with the principles of the qualitative approach of search-action, and the methodological way consisted of three stages that sought to meet the specific objectives: the definition of multidisciplinarity and interdisciplinarity, which had teachers in the Natural Sciences area; present a proposal that emerged from group discussions, identifying some elements of the limits and possibilities of the activity developed by the group of teachers from the Natural Sciences area. The results showed a studies lack on the subject by teachers and induced the reading and studing the Education legal documents (LDB, PCNEM and OCNEM). The planning of lessons led to the need for meetings that established the process of continuing graduation in exercising at the school. The interdisciplinary practice enable many gains, for example, the cohesion of the teachers, the perception need to constantly update and use of teaching units for planning. But it was also possible to observe limits, such as the difficulty of working with large classes and the danger of the content become superficial. The experience has shown that continuing graduation at school is possible and can be beneficial the use of interdisciplinary groups for this purpose, because it allows the exchange of experiences and pratice reflection of teaching in the itself exercise of this teaching

A estratégia didática de resolução de problemas na formação de professores de química

In this work it is presented a research developed in the initial training of teachers of the chemistry graduation course at the Universidade Federal do Rio Grande do Norte (UFRN). The intervention was realized in two classes in the context of a discipline in the curricular structure with nineteen undergraduate students of chemistry. The study utilizes characteristics of the qualitative approach and uses observation, questionnaires, interviews and examination papers. The experiment involved a sequence of activities fundamented on the Problem Solving (PS) teaching strategy to approach chemical concepts. The proposal was planned and organized according to the theoretical presupposition of the work developed by the authors of the Science Education in PS, of teaching experience and from the initial hypotheses of the research. The goal was that the future teachers could experience the strategy and advance to the new meanings. The themes addressed in the activities were the difference between exercises and problems, exercises turning into problems, the steps of problem solving and some implications of the teaching strategy for the work of the teacher. The results showed evidence that through a process of collective reflection, and from the difficulties experienced in the strategy practice, the undergraduates are introduced to new perspectives of reflection and action of teaching practice, and understanding some benefits of innovative proposals for the teaching of chemistry. It also showed that, although this theme is approached, in some moments of the graduation, the future teachers don‟t know when or how to realize activities in this perspective. From the aspects that rose in research we highlighted the difficulties in the problem solving steps, the use of the strategy in school and the knowledge and skills of the teacher for planning activities in Problem Solving

Educação científica no contexto pós-ontológico: por uma concepção plural de conhecimento e educação

The development of this work arises from the research of sociological and philosophical characters contemplating also other approaches which aims to answer the followingquestions: what is the responsibility of science teaching for the image one has about science? ; which scientific education should be designed for nowadays? . After considering the assumptions brought along by rationalism and the criticisms to the illuminist model proposed by sociology and philosophy of science, as well by the biology of the knowing process, going through discussions concerning post-modernity issues, one is given to understand that the image of science has become the central point of discussion in the last hundred years, including what concerns the area of science teaching, and that practically none of those discussions really reached natural science classes indeed. We adopt the term postontological to characterize the recent proposals on philosophy and sociology, because we evaluate that this term allows a better identification of the scientific realism crisis, which supports the existence of an ontological domain which science, and only science, is able to understand. One notices that the general public is not aware of those discussions, mainly if they are science teachers and students. So we believe that discussing the logic in which science is structured, the new understandings concerning the scientific undertaking, especially those of an externalist character, and the relationship between science and society, all of this contributes to build up a science teaching which contemplates a reflective contribution, besides allowing the inclusion of the study of other epistemologies in the educational practice. We argue that a revisionist posture seems to be the most appropriate for the contemporary scientific education, contemplating, besides the teaching of the usual science contents, discussions on the issues involving that knowledge, as well as respecting epistemologies alternative to the modern Western scientific one, in order one can work on the perception of local knowledge generated from other epistemological bases. We describe here practical activities we did involving teachers (short-term courses) and high-school students in an inland school in the Rio Grande do Norte state, in Brazil, as a way to demonstrate the possibility of interventions which can take those conceptions, discussions and changes to the classroom