Dynamics of change of mathematics education in Brazil and a scenario of current research

Mathematics education in Brazil, if we consider what one may call the scientific phase, is about 30 years old. The papers for this special issue focus mainly on this period. During these years, many trends have emerged in mathematics education to address the complex problems facing Brazilian society. However, most Brazilian mathematics educators feel that the separation of research into trends is a theoretical idealization that does not respond to the dynamics of the problems we face. We raise the conjecture that the complexity of Brazilian society, where pockets of wealth coexist with the most shocking poverty, has contributed to the adoption and generation of different strands in mathematics education, crossing the boundaries between trends. At a more micro level, we also raise the conjecture that Brazilian trends in research are interwoven because of the way that Brazilian mathematics educators have experienced the process of globalization over these 30 years. This tapestry of trends is a predominant characteristic of mathematics education in Brazil. © FIZ Karlsruhe 2009.

Structuralism and the Applicability of Mathematics

In this paper I argue for the view that structuralism offers the best perspective for an acceptable account of the applicability of mathematics in the empirical sciences. Structuralism, as I understand it, is the view that mathematics is not the science of a particular type of objects, but of structural properties of arbitrary domains of entities, regardless of whether they are actually existing, merely presupposed or only intentionally intended.

Pedagogical practices carried out during an in-service teachers education project: approaching history and philosophy of science to physics teaching

We report here part of a research project developed by the Science Education Research Group, titled: "Teachers’ Pedagogical Practices and formative processes in Science and Mathematics Education" which main goal is the development of coordinated research that can generate a set of subsidies for a reflection on the processes of teacher training in Sciences and Mathematics Education. One of the objectives was to develop continuing education activities with Physics teachers, using the History and Philosophy of Science as conductors of the discussions and focus of teaching experiences carried out by them in the classroom. From data collected through a survey among local Science, Physics, Chemistry, Biology and Mathematics teachers in Bauru, a São Paulo State city, we developed a continuing education proposal titled “The History and Philosophy of Science in the Physics teachers’ pedagogical practice”, lasting 40 hours of lessons. We followed the performance of five teachers who participated in activities during the 2008 first semester and were teaching Physics at High School level. They designed proposals for short courses, taking into consideration aspects of History and Philosophy of Science and students’ alternative conceptions. Short courses were applied in real classrooms situations and accompanied by reflection meetings. This is a qualitative research, and treatment of data collected was based on content analysis, according to Bardin [1].

The Development of Science Education Research in Brazil and Contributions from the History and Philosophy of Science

Over the last 50 years a new research area, science education research, has arisen and undergone singular development worldwide. In the specific case of Brazil, research in science education first appeared systematically 40 years ago, as a consequence of an overall renovation in the field of science education. This evolution was also related to the political events taking place in the country. We will use the theoretical work of Rene Kaes on the development of groups and institutions as a basis for our discussion of the most important aspects that have helped the area of science education research develop into an institution and kept it operating as such. The growth of this area of research can be divided into three phases: The first was related to its beginning and early configurations; the second consisted of a process of consolidation of this institution; and the third consists of more recent developments, characterised by a multiplicity of research lines and corresponding challenges to be faced. In particular, we will analyse the special contributions to this study gleaned from the field known as the history and philosophy of science.

The Rechtslehre doctrine and Kant's philosophy of history

The text is divided in two phases. In the first phase, consisting of three parts, the main concepts of Kant's Doctrine of Right are considered in a comprehensive approach related to: the issue of the relations between natural right and positive right, problem closely connected to that of the relations between natural state and civil state, private right and public right; to the doctrine of property and its connection with political right. on treating the right in its several types, we intend to appoint the practical reasoning as a background of the Doctrine. In the second phase, concerning its last section, the consideration on the presence of the practical reasoning into the right is placed before some specificities of Kant's phylosophy of history, with the intent of establishing the possible relation between Rechtslehre and that philosophy.

Humanization of health care: a reflexive theoretical essay based on the philosophy of Emmanuel Lévinas

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

The USAID and the teaching of mathematics in Rio Grande do Norte

In the 1960s occurred great changes in the general education and, specially in the mathematical teaching, throughout Brazil. Besides the Law Diretrizes e Bases for Education (law 4024/1961), such changes also was occurred by opposite educational movements. In one side, those ones that valorized the popular education and culture and, for the other side, the international agreements between universities and government organs, like SUDENE and MEC, with United States Agency for International Development (USAID). These agreements purposed the cultural alignment. In this article we will expose some of these agreements and their interference in two courses for teachers' education. These teachers taught mathematics for the elementary school, in Rio Grande do Norte.

Trends in Brazilian academic production in the History of Mathematics Education: directions from EBRAPEM

The number of papers on History of Mathematics Education presented at EBRAPEM (Brazilian Meeting of Graduate Students in Mathematics Education) has increased significantly between 2003 and 2008. This article presents a study with the aim of identifying themes, periods in focus, and sources and theoretical and methodological references used by the authors of the papers on History of Mathematics Education published in the proceedings of VII, VIII, IX, X, XI and XII EBRAPEM. The study indicates that the approach of ongoing research in History of Mathematics Education in Brazil has been similar to the approach of research in History of Education in general. However, the institutional separation between these two areas of investigation is noted as a factor rendering communication between both groups of researchers difficult.

Experiencing Manipulative Material for the Teaching and Learning of Mathematics

This paper presents some outcomes from research based on classroom experiences. The main themes are the use of mirrors, kaleidoscopes, dynamic geometry software, and manipulative material considering their possibilities for the teaching and learning of Euclidean and non-Euclidean geometries.

Windows into Elementary Mathematics:Alternate public images of mathematics and mathematicians

Research on students’ (and teachers’) images of mathematics and mathematicians reveals a number of stereotypical images, most of which are negative. In this paper we present an overview of some these images and stereotypes and consider the questions: (1) how might the image of mathematics and mathematicians be a problem in mathematics education, and (2) what can be done to remedy the situation? Also, we consider an outreach project called Windows into Elementary Mathematics. In this project mathematicians are interviewed about their perspectives on elementary mathematics topics and their interviews are videotaped and are posted online, along with supporting images and interactive content. In this context we consider the questions: (3) what is the Windows project about, and (4) how might it offer an alternate (and perhaps better) image of mathematics and mathematicians? Lastly, we share an example where activities from the project were used in a math-for-teachers course.

O intuitivo e o lógico no conhecimento matemático: análise de uma proposta pedagógica em relação a abordagens filosóficas atuais e ao contexto educacional da matemática

In this paper, we consider Meneghetti & Bicudo's proposal (2003) regarding the constitution of mathematical knowledge and analyze it with respect to the following two focuses: in relation to conceptions of mathematical knowledge following the fundamentalist crisis in mathematics; and in the educational context of mathematics. The investigation of the first focus is done analyzing new claims in mathematical philosophy. The investigation of the second focus is done firstly via a theoretical reflection followed by an examination of the implementation of the proposal in the process of development of didactic materials for teaching and learning Mathematics. Finally, we present the main results of the application of one of those materials.

Platão e Aristóteles na filosofia da matemática

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)