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.

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.

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.

Establishing common elements among some science education references as a resource to design a Didactics of Physics program for teachers initial education

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

The Use of Vocabulary in an Eighth Grade Mathematics Classroom: Improving Usage of Mathematics Vocabulary in Oral and Written Communication

In this action research study of my mathematics classroom of eighth grade students, I investigated the use of mathematics vocabulary by focusing on improving the usage of this vocabulary in both oral and written communication. I discovered oral communication tended to show more improvements compared to written communication done by the same group of students. As a result of this research, I plan to continue to focus my teaching on the use of mathematics vocabulary in an effort to help my students gain a greater understanding of the daily use of that vocabulary.

CLIL materials in Secondary Education: focusing on the language of instruction in the subject area of Mathematics

[EN]Applying a CLIL methodological approach marks a shift in emphasis from language learning based on linguistic form and grammatical progression to a more ‘language acquisition’ one which takes account language functions. In this article we will study the elements of the “language of instruction” of the area of Maths in Secondary Education, by focusing on the analysis of the communicative functions, and the lexical and the cultural items present in the textbook in use. Our aim is to present the CLIL teacher with the linguistic and didactic implications that he or she should take into consideration when implementing the bilingual syllabuses with their students. In order to do that, we will present our conclusions emphasizing the need for coordination in different content areas, linguistic and communicative contents, between the foreign language teacher and the CLIL subject one.

A causal model of mathematics performance in early adolescence: the role of sex

Using path analysis, the present investigation was done to clarify possible causal linkages among general scholastic aptitude, academic achievement in mathematics, self-concept of ability, and performance on a mathematics examination. Subjects were 122 eighth-grade students who completed a mathematics examination as well as a measure of self-concept of ability. Aptitude and achievement measures were obtained from school records. Analysis showed sex differences in prediction of performance on the mathematics examination. For boys, this performance could be predicted from scholastic aptitude and previous achievement in mathematics. For girls, performance only could be predicted from previous achievement in mathematics. These results indicate that the direction, strength, and magnitude of relations among these variables differed for boys and girls, while mean levels of performance did not.