Reflexões sobre a construção e evolução de conceitos geométricos nas séries intermediárias do ensino fundamental

This thesis represents a didactic research linked to the Post-graduation Programme in Education of the Universidade Federal do Rio Grande do Norte which aimed to approach the construction of the geometrical concepts of Volume of the Rectangular Parallelepiped, Area and Perimeter of the Rectangle adding a study of the Area of the Circle. The research was developed along with students from the 6th level of the Elementary School, in a public school in Natal/RN. The pedagogical intervention was made up of three moments: application of a diagnostic evaluation, instrument that enabled the creation of the teaching module by showing the level of the geometry knowledge of the students; introduction of a Teaching Module by Activities aiming to propose a reflexive didactic routing directed to the conceptual construction because we believed that such an approach would favor the consolidation of the learning process by becoming significant to the apprentice, and the accomplishment of a Final Evaluation through which we established a comparison of the results obtained before and after the teaching intervention. The data gathered were analyzed qualitatively by means of a study of understanding categories of mathematical concepts, in addition to using descriptive statistics under the quantitative aspect. Based on the theory of Richard Skemp, about categorization of mathematical knowledge, in the levels of Relational and Instrumental Understanding were achieved in contextual situations and varied proportions, thus enabling a contribution in the learning of the geometrical concepts studied along with the students who took part in the research. We believe that this work may contribute with reflections about the learning processes, a concern which remained during all the stages of the research, and also that the technical competence along with the knowledge about the constructivist theory will condition the implementation of a new dynamics to the teaching and learning processes. We hope that the present research work may add some contribution to the teaching practice in the context of the teaching of Mathematics for the intermediate levels of the Elementary School

A teoria de Dienes no ensino de transformação de medidas de comprimento, área e volume no curso de pedagogia

The study was aimed to test a teaching module on the Zoltan Paul Dienes theory, focusing on the content: The transformation of measurements: length, areas and volumes. The study based on constructivist theory consisted in a methodological intervention with students of the 7th period of the Course of Pedagogy, in Central Campus, Federal University of Rio Grande do Norte (UFRN). A preliminary study with 40 students called diagnostic evaluation found that students did not understand the concept of measurements transformation and its processing steps. The latter was performed only with the help of the table of measurements transformation with no understanding of the content. He applied a pretest, a set of activities and a post-test. The latter was used as a tool for evaluation of the student learning process. The answers of these ones were evaluated according to the concept of reflective abstraction of Jean Piaget, one of the authors who influenced the Dienes theory

Avaliar na alfabetização: uma reflexão sobre as dificuldades docentes

Our work leads up to the context of evaluation during alphabetization process as a moment of an educational action cycle that requires planning, teaching and learning of reading and writing. It aimed to research the difficulties lived by teachers of a public elementary school during the specific task of evaluating children in the alphabetization process. This qualitative research took place as a case study at Emília Ramos Municipal School, in Natal, capital city of Rio Grande do Norte State, Brazil. Semi-structured interview and questionnaire were used as fact-gathering proceedings. Two pedagogical advisers and seven teachers formed the group of research subjects. All of them worked with elementary school first cycle classes, in that school, in the year of 2003. The analysis shows that teachers difficulties concern to theoretic questions of conceptual and methodological orders, although these questions indicate an important knowledge of teachers about alphabetization and evaluation. Our reflection about these problems articulates two points: alphabetization and evaluation. Concerning alphabetization, we took reference on Psychogenetic studies of Ferreiro and Teberosky (1985) which emphasizes fundamental points for a coherent evaluation practice: a) objective knowledge is not a beginning data; it is a construction process, which the learner does not conquest step by step on a linear way; b) objective knowledge acquisition happens through a global re-construction, and some of them may seem mistakes if we consider conventional writing but these mistakes are constructive and necessary. We also took reference on Interactionist-constructivist theory. Here, Vygotsky (1984) proposes that writing must be specially understood as language, symbolical activity, cultural practice. So, acquisition of writing process, as language learning, must be understood as a development of abilities relative to symbolical and communicative activity of sense production. On this way, Hoffmann (1994) advises that is necessary to overtake current evaluation practices, limited by their terminality character, only pointing right or wrong questions. According to a new paradigm, valuation appears as one of the mediations by which teachers must indicate re-ordination of pupil s knowledge, and re-organize their own practices too. The comprehensions of these questions plays decisive part in order to overtake our difficulties in evaluating. Besides, it points a way to build a coherent valuate practice, with an emancipating character and able to create new teaching-and-learning situations, leading to a better alphabetization Pedagogy