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.

Interface entre história da matemática e ensino: uma atividade desenvolvida com base num documento do século XVI

Este artigo propõe a construção de uma interface entre história e ensino de matemática a partir de um diálogo entre historiadores e educadores da matemática. Para tanto, consideramos aspectos epistemológicos e metodológicos ligados à história da matemática, pautada em tendências historiográficas atuais, juntamente com a metodologia baseada no movimento lógico-histórico. A interface contemplou o movimento do pensamento na formação dos conceitos e o contexto no qual tais conceitos foram desenvolvidos, de modo a conduzir à reflexão sobre o processo histórico da construção do conhecimento para a elaboração de atividade didática. Esta atividade teve por base um documento do século XVI dedicado à construção e uso de instrumentos matemáticos, e sua elaboração levou em consideração uma intencionalidade e um plano de ação que viabilizaram o seu desenvolvimento. A organização do ensino articulou as conexões internas e externas trazidas pela análise do documento e a forma do pensamento do desenvolvimento do conceito.

Mathematics teaching life histories in the study of teachers' perceptions of change

The aim of this paper is to discuss teachers' perceptions of change in their thought and/or practice over time and their perceptions of what kind of experiences or challenges might have influenced those changes. Two mathematics teaching life histories of Brazilian teachers are examined, considering a context of curriculum development in the state of São Paulo, Brazil. Reflection on teachers' thought and practice and interest in their own development, including interest in their own learning of mathematics, seemed to be the most important internal aspects influencing change and development. Close support seemed to be the most important external aspect. The retrospective analysis put a good face on personal change and development. (C) 2000 Elsevier B.V. Ltd. All rights reserved.

VOICES FROM THE SOUTH: DIALOGICAL RELATIONSHIPS AND COLLABORATION IN MATHEMATICS EDUCATION

This chapter presents a collaborative experience between two neighbouring countries from South America: Argentina and Brazil. Our purpose is to share a model of international collaboration that we consider to be an alternative to the classical movement of early mathematical and scientific knowledge between East and West and between North and South. We start our chapter with a general discussion about the phenomenon of globalization considering some local examples. We characterize our collaboration exploring the tensions and difficulties we faced along our own professional development at the local as well as the international level. We describe the development of our prior collaborative work that established the foundation for our international collaboration portraying the local mathematics education communities. We refer to some balances that were created among our relationships, the expansion of our collaborative network, and how this particular collaboration allows us to contribute to the regional field and inform the international one. We discuss the way that the search for balance and symmetry, or at least a complementary asymmetry in our collaborative relationships, has led us to generate a genuine and equitable collaboration.

Phenomenological perspective on mathematics education

This is a philosophical essay on a phenomenological way to understand and to work out Mathematics Education. Its philosophical grounding is the Husserlian work, focusing on its key word "going to the things themselves" in order to keep us away from the theoretical educational truth, took as the unique one. We assume the attitude of being on the life-world with the students and Mathematics as a field of research and practice that show and express themselves through lived experiences and through language. We assume to be in search of understanding of education, learning and Mathematics, as we take care, consciously, of what we are doing and saying in the same movement of saying and doing it.

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.