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

Opiniões sobre estágio curricular e prática de ensino na licenciatura em química: o caso do CEFET-PB

The Brazilian legal documents are directing the reformulation of the courses that prepare students to be teachers. Through out the country many institutions look for to fit themselves in such documents. On the other hand, other IES (Superior Education Institutions), when they are setting up such courses they looked for to be adequate to the new public politics. Based on the National Curricular Norms to form teachers for Basic Education, in tertiary level, in 2004 it was created at the CEFET-PB,the Chemistry Course (Licenciatura) to prepare people to be teachers, whose organization. This work presents the results of a research of phenomenological nature that aimed to comprehend the teachers opinions, in the range of discussions about the current politics of formation, particularly related to the CNE/CP 1 and CNE/CP 2/2002 resolutions. This work based on the curricular proposal for the Chemistry Course (Licenciatura), presents the relationship between the probationary period and the teaching practice at the CEFET-PB, in order to contribute for a reflection about these categories to clarify the teachers of the course. It started from the consideration of all changes operated in contemporary society implies changes on teacher's pedagogical practices. It was used tow instruments for the data collection: a questionnaire with open and closed questions and recordable interviews. Nine teachers form the CEFET-PB took apart and four licensed teachers. It was based in a theoretic frame as a support for discussions about the different models of teachers formation. We concluded that the representations of teachers about probationary period the practice on the activity for the teachers formation was strongly anchored in characteristic elements of the formative tendency of a institution that historically acted on a technician formation, and the results pointed to strong signs of attitudes based on a model of the technical rationality

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

O espaço formativo na escola: um estudo com professoras dos 4º e 5º anos do ensino fundamental.

Es extensa, de parte de los docentes, la discusión sobre la articulación de actividades y estrategias de enseñanza que vengan a proporcionar una participación más activa del alumnado. Sin embargo tal tarea constituye un desafío para muchos profesores ya que, muchas veces, la formación inicial no siempre los prepara para esta perspectiva. Nosotros entendemos que es necesario desarrollar en los maestros una autonomía crítica, tomando la escuela como espacio formativo. El objetivo de este trabajo fue él de incentivar un espacio de discusión y reflexión para profesores en ejercicio de los 4° y 5° años de la Enseñanza Fundamental I. Ese espacio que era orientado para que ellos estudiasen y articulasen, entre otras cosas, el conocimiento disciplinar de Ciencias y la organización y sistematización de actividades de enseñanza que lleven a una participación más activa de los estudiantes. La investigación se realizó en una escuela privada de Natal/RN, que atiende a estudiantes desde la educación infantil hasta la enseñanza secundaria. Se desarrolló en cuatro fases: la 1ª, de familiarización, cuyo objeto de estudio se dio a través de la observación del salón de clase y del análisis de la planificación anual: la 2ª, de identificación de las dificultades de los maestros, teniendo como instrumentos encuestas con preguntas abiertas y elaboración de textos. La 3ª, en la perspectiva de proporcionar una intervención, se usó como instrumentos de investigación, el diario de clase y otras actividades como talleres, cursos y la elaboración de material didáctico. En la 4ª fase, para reconocer los posibles cambios en la práctica docente, ocurrieron nuevas observaciones en el salón de clase, el análisis de las planificaciones. Los datos obtenidos fueron organizados en tablas y clasificados. Los resultados señalan cambios en la práctica de esos profesionales, la introducción de la disciplina de Ciencias en el espacio formativo y el material didáctico elaborado ha sido un subsidio importante para ayudarlos en las clases

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

Uma abordagem histórica para o ensino do princípio da inércia

Placed in the field of Didactic of Science, this paper proposes an approach to the introduction of the History of Science in science education, at high school level. It was designed and implemented a series of activities regarding the history of the Principle of Inertia. The aim of this approach was to give more meaning to scientific education, while opening new avenues for a better understanding of the processes of construction of scientific knowledge. The preparation of the activities involved a study of the historical development of the concept of motion, from the Aristotelian physics through physical movement concepts at medieval period, from Galileo, Gassendi, Descartes, until the first law of Newton. The strategy of teaching was applied to three classes of high school (night period) of a state public school at the city of Natal (RN). The results indicated the difficulty of overcoming alternative conceptions about movement by students. Nevertheless, we consider that the implementation of this strategy of teaching both represented gains for the learning of students, and contributed to the resizing of pedagogical practices of the teacher-researcher

Opiniões de professores do ensino médio: refletindo sobre os projetos escolares e a interdisciplinaridade

Official documents indicate to a curriculum organization that promotes the dialogue in different areas of knowledge. Among the proposals strategies are the "School Projects". This research appears from the staff need evidenced in the development of practice of the researcher in recent years as Pedagogical Advisor in high school. The comments made in the daily work on the kinds of projects and how they were developed in the school, generated concerns. They aroused the interest in further the discussion, aiming to reflect with teachers about the implementation of a pedagogic action on the use of educational projects in the classroom, as a didactic strategy which promotes the learning of students. In this sense, it seeks to develop studies and discussions by the application of questionnaires and the holding of a workshop with teachers in the area of Science of Nature and Mathematics in private high school institutions from Natal, searching opinions of them as the preparation and development of school projects. As general purpose, it aims to contribute with elements to the reflection of the teachers on the use of this strategy of education. For both, we propose: the knowledge of ideas/opinions of teachers on planning, development and evaluation of projects, both disciplinary and interdisciplinary, identifying the main difficulties of these teachers about the work with projects at school; reviewing projects developed at school after the press conference in a meeting with teachers, incorporating the identified aspects as weak points. In the course of the methodology research, questionnaires were used with open and closed questions for the lifting of preliminary ideas for teachers in order to subsidize the planning of a developed meeting later in the school itself on the subject in question. 10 teachers took part of the first step and 17 in the second one (pressconference). In the third stage, an individual interview was carried out and analysis of projects already developed. It is observed that, as the main difficulty for the development of projects in school, pointed to the time factor in the planning team, followed by excessive working hours for teachers that, generally, also work in other schools. Some teachers say they do not develop projects for not having knowledge of how to develop school projects, neither disciplinary, nor interdisciplinary

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

Uma proposta para o ensino de eletromagnetismo no nível médio

This paper aims at building a proposal for teaching of electromagnetism in the secondary level in the state public school in Natal, RN, encompassing at the most possible comprehensive manner the fundamental aspects of electromagnetism. The methodology employed here is prioritize physical concepts rather than instruments (such as the mathematics), which should have the connotation of just tools, or of aids in the context of physics teaching in the referred teaching level. The proposal is to give teachers a consultation resource, from differentiated lesson plans, which have as main focus activities based primarily in texts and active participation of students in the teaching- learning process and the implementation of the PCN+ proposals (BRAZIL, 2000), which suggest alternative ways to make the practice in the classroom more exciting, targeting a significant teaching-learning process for both the teacher and the student. This material was applied during the 3rd and 4th term (i.e., bimester) throughout the school year of 2007, in the State School Teacher Varela Barca in two classes (3V1 and 3V2) of 3rd grade of secondary level. As evaluation of the implementation of this proposal one can cite that students were more secure when to apply the concepts, when conducting the experiments, and less anxious when formal evaluation of the evidence, showing greater motivation when presented to electromagnetism contextualized in their everyday situations. The product of this educational work includes, besides the dissertation, the lesson plans, itineraries and experimental assessment of the instruments used (Annex E to I)

As Ciências Espaciais, o saber e o fazer docente no ensino fundamental

This study aims to include topics related to Space Science in elementary education from an experiment that aims to rescue the science teachers in public schools of São Tomé, RN, a taste for experimentation and exploration of advanced technologies. During this research with teachers found that they knew enough about the subject, but this knowledge was restricted to the events disclosed by the media. Regarding scientific knowledge, that same surface, they had many conceptual difficulties which hindered the approach of these topics in their classes. To overcome this difficulty, a workshop was held where teachers had the opportunity to discuss the historical aspect of Space Science, some physical concepts related to it, and the conduct of experiments with PET bottle rockets that recover from the curiosity typical of how the science. The results were outlined in the form of Planning Didactic built by teachers and using themes related to space science, from there, discussing content already provided in the composition of the schools curriculum. Therefore, this work allowed the teachers a minimum training required for them to not only reproduce, but readjusted and build, from this, their own paths in the classroom at the fundamental level

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.