Husserl's two notions of completeness: husserl and hilbert on completeness and imaginary elements in mathematics

In this paper I discuss Husserl's solution of the problem of imaginary elements in mathematics as presented in the drafts for two lectures he gave in Göttingen in 1901 and other related texts of the same period, a problem that had occupied Husserl since the beginning of 1890, when he was planning a never published sequel to Philosophie der Arithmetik (1891). In order to solve the problem of imaginary entities Husserl introduced, independently of Hilbert, two notions of completeness (definiteness in Husserl's terminology) for a formal axiomatic system. I present and discuss these notions here, establishing also parallels between Husserl's and Hilbert's notions of completeness. © 2000 Kluwer Academic Publishers.

O jogo de escopa adaptado para o uso em sala de aula

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A interdisciplinaridade no ensino da matemática pela perspectiva da pedagogia histórico-crítica: superando a pedagogia de projetos

Pós-graduação em Docência para a Educação Básica - FC

Contribuições da pedagogia histórico-crítica para o ensino da geometria no ciclo de alfabetização

Pós-graduação em Docência para a Educação Básica - FC

Futuros Matemáticos e suas concepções sobre o conhecimento matemático e seu ensino

Taking referential theoretical conceptions of mathematical knowledge present in some of the main mathematics philosophical currents and considering that the teacher´s practice is influenced by his conception of mathematical knowledge, this research aims to understand the conceptions of mathematical knowledge and its teaching and learning teaching of future mathematicians. It follows a qualitative approach (case study) in which the data were collected by semi-structured interviews and document analysis. This investigation has pointed out that Mathematics together with Mathematics Teaching (or part of this: on the didactic and pedagogical knowledge of how to teach) could be important to formation of the future mathematician, who will probably teach in a college or university.

A resolução de problemas no contexto do estágio curricular supervisionado: dificuldades e limites de licenciandos em matemática

The aim was to investigate the difficulties and limits of four future mathematics teachers to conduct classes in regencies approach of problem solving. Based on participation in a course this approach, undergraduates elaborated three didactic sequences, which were taught by the activity of conducting classroom discipline Supervised Curricular Training. After this work, participated in an individual interview to report what had developed in classroom. The results showed difficulties in the following aspects: in the elaboration of didactic sequences; in providing an environment for discussion of resolution strategies students. Furthermore, the data analysis showed limits related: the lack of space at the school teacher to allow implementation of lessons developed; lack of basic mathematical knowledge of the students.

Concepções de alunos do ensino médio sobre o tema água: subsídios para o planejamento de atividades investigativas interdisciplinares

Meaningful learning occurs when new knowledge to be aggregated are grounded in other students already possess. In preparing didactic sequences for teaching concepts, one should take into account these concepts and knowledge to produce more effective and lasting learning, and build new concepts that will become subsumes for subsequent learning. This research was developed in a subproject linked to institutional Scholarship Program Initiation to Teaching (PIBID) of a Universidade Estadual Paulista. The proposal is based on the articulation of the Public School and the University, strengthening the initial training of undergraduates, and continued teacher network, improving the quality of education. The proposed work is based on interdisciplinary research and teaching by investigation. Undergraduates in Biology, Physics, Mathematics and Chemistry jointly propose interdisciplinary teaching activities and investigative applied to high school students of Public School partner. To survey the views of these students on the theme Water, they were asked to draw up an essay entitled "The importance of water", with the aim of organizing information for planning a teaching strategy that articulates the disciplines of training of undergraduates. In this paper we present a qualitative analysis of these essays, performed based on content analysis. The analysis allowed to identify existing concepts in students' cognitive structure and classify them into adequate and inadequate compared to scientifically accepted concepts. Several misconceptions were raised indicating the need to produce didactic sequences that in addition to working the concepts presented in the curriculum of disciplines take into consideration the possibility of more meaningful learning. This research produced the elucidation of existing concepts, indicating where deficiencies were larger. One major contribution was the realization that concepts that may be considered by teachers as simple and already acquired by the students often come so misguided in their explanations. From the results obtained, integrated activities have been planned and implemented, and more relevant to the needs of students aiming to recover and enrich the knowledge they possessed, encouraging the use of scientific concepts and their application to daily living situations.

Algumas potencialidades didáticas do setor trigonal na interface entre história e ensino de matemática

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

The interactive whiteboard in primary school: a case study of a brazilian district school

Interactive whiteboards (IWB) consist of a set of technological equipment organized in order to fulfill a specific task, enabling the development of didactic activities. Because they are associated to computers’ potentiality, interactive whiteboards can provide bigger interactivity between: teacher and students, students and content, and among students. This work’s main objective is to present some of the results yielded from a research related to the way students perceive interactive whiteboards in the classroom. In order to analyze the IWB usage dynamics, some educational applications in the field of mathematics were applied in the 3rd grade of elementary school. Aside from observation, video recordings were made and students were interviewed about the interactive whiteboard, in order to understand how these students observe and engage with the technological tool. IWB do not transform classroom’s reality by themselves, however, their physical presence and usage amount to external reinforcement can change student’s behavior positively.

Resolução de problemas com aplicações em funções

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A língua portuguesa no 5º ano do ensino fundamental: repertórios de ensino no contexto da Prova Brasil/ SAEB

Pós-graduação em Psicologia do Desenvolvimento e Aprendizagem - FC

Guerra e o desenvolvimento científico: uma superaula interdisciplinar e investigativa construída em torno de um experimento central

This research presents the description of the assembly, development and execution of an experiment and of an interdisciplinary and student research activity built by some undergraduates from Biological Sciences, Physics, Mathematics and Chemistry PIBID subprojects of the Faculty of Science, FC - UNESP, Bauru/SP Campus. These subprojects are part of a single interdisciplinary group, which has as its main activity the Superclass, which consists of an intervention of the PIBID members during the class schedule, with an interdisciplinary and student research didactic sequence, applied by four groups of ten members, in two local State Schools. The experiment treated in this assignment was a miniature cannon (minicannon), and it was used in a Superclass that had the War and Science Development as its theme, wherein the knowledge of all areas were built from the analysis of the multiple variables involved on the cannon shots. These variables were surveyed with the students through the experiment research, during the Superclass, being focused on three of them: the shot and the explosives; the trajectory; and the target. The experiment was extremely successful, because it could instigate the students, who were interested, questioning and debaters for several times during the class. The minicannon made possible the interdisciplinary and the student research work among the four areas of science involved. Despite it has been a laborious experiment in its construction, it has proven to be innovative, and its use has transformed the students‟ ingenuous curiosity into epistemological curiosity, a key factor in the construction of scientific knowledge, wherein the dialogue established in the Superclass explored this new curiosity

O papel das tecnologias digitais em disciplinas de álgebra linear a distância: possibilidades, limites e desafios

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Formação de professores de matemática da educação superior e as tecnologias digitais: aspectos do conhecimento revelados no contexto de uma comunidade de prática online

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Programação no ensino de matemática utilizando Processing 2: Um estudo das relações formalizadas por alunos do ensino fundamental com baixo rendimento em matemática

Pós-graduação em Educação para a Ciência - FC