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.

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.

Collectives of humans-with-media in mathematics education: Notebooks, blackboards, calculators, computers and ... notebooks throughout 100 years of ICMI

The main aim of this study was to present evidence of the ways in which different media have conditioned and dramatically reorganized education, in general, and mathematics education, in particular. After an introduction of the theme, we discuss the epistemological perspective that provides the foundation for our analysis: the notion of humans-with-media. Then, we briefly illustrate how the medium is related to the scientific production of mathematical knowledge. We take a detour into the world of art to examine how devices and instruments have historically been associated with the production of mathematical knowledge. Then, we review studies on the history of education to show how traditional media were introduced into schools and have influenced education. In particular, we examine how devices such as blackboards and notebooks, which were novelties a 100 years ago, came to be accepted in schools and the mathematical activities that were promoted with their use. Finally, we discuss how information technology has changed education and how the Internet may have an impact on mathematics education comparable to that of the notebook over a century ago. © FIZ Karlsruhe 2009.

Ensino de Ciências e os sistemas de avaliação em larga escala na educação básica: processos formativos e aprendizagens profissionais da docência

Pós-graduação em Educação para a Ciência - FC

Online distance mathematics education in Brazil: research, practice and policy

In this article, we address online distance mathematics education research and practice in Brazil, which are relative newcomers to the educational scene. We present the national context of education in Brazil, highlighting the organization of the educational system, and also a summary of national legislation on distance education and an overview of digital inclusion in the country. We outline the potential and relevance of distance education for the Brazilian educational system and show how it could intervene in the system. With respect to research and practice in online mathematics education, we present support for research, examples of studies and highlight different aspects being addressed, including its essential components. In addition, we discuss the synergy between distance education and teacher education, and mathematics distance education and modeling, as well as other initiatives in the national scenario.

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.

Physical education in schools, sport activity and total physical activity in adolescents

Less than half of adolescents reach the recommended 300 minutes per week of physical activity (PA). Physical education classes and sports participation provide opportunities for adolescents to accumulate more time for PA practice; however, little is known about the influence of these variables on the level of total physical activity of adolescents. The aim of this study was to investigate the association between the practice of physical education (PE) in schools and sports activities (SA) with the practice of total PA of adolescents. The study was cross-sectional and involved 467 adolescents of high school (15.8 ± 0.9 years-old) from the city of Rio Claro, in the State of São Paulo. Participants completed the Physical Activity Questionnaire to Older Children (PAQ-C) and questions related to the practice of PE and SA in schools. We performed a logistic regression with p<0.05 using SPSS. Girls had lower prevalence of PA than boys, 9.4% and 26.8%, respectively. Boys who did not participate of PE classes (OR=0.25, 95% CI=0.09-0.66) and SA in schools (OR=0.34, 95% CI=0.12-0.95) were less likely to be active in PA than boys who practiced these activities. The participation in PE classes or engagement in some SA were positively associated with the practice of total PA in boys.

THE MAPPING IN THE CONTINUING EDUCATION OF TEACHERS: AN EXPERIENCE THROUGH DISTANCE LEARNING

In this work, we show the experience of continuing teacher education in Cartography in the period from 03/11/2009 to 03/11/2010, it was held by the Center for Continuing Education in Mathematics Education, Science and Environment (CECEMCA) - UNESP - Rio Claro, in DL (Distance Learning). This experience was through the extension course set in TelEduc platform. The course was titled Introduction to Cartography and aimed primarily: Present concepts of systematic and thematic mapping and its potential application in teaching practices, increase knowledge in the areas of Geography, Cartography and Environment; Offer alternatives for implementing content mapping in the classroom.

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.

Higher education in evening courses in Brazil: history, growth and public policies at the beginning of the XXI Century

There are three distinct and complementary objectives in this article in order to clarify the higher education outline in Brazil, specifically evening courses (classes are held on weekdays, generally from 7:00 pm to 10:30 pm) and thesecurrent sector policies. The first objective is to present a short historical overview on the establishment of evening courses in Brazil, including those in the higher education level, occurred on the middle of last century. The second objective is to demonstrate the growth of evening higher education in Brazil, considering that in 1998, of the 2.1 million college enrollments, 55.3% were enrolled in evening courses; in 2010, twelve years later, of the 5.4 million students enrolled, there were 63.5% enrolled in evening courses. This expansion is due to the growing need of many students who must work while attending college, to defray costs of the study as well as personal and family costs. The reality of the working student is hostile considering external factors, such as transport problems, public security and lack of legislation for flexible working hours. The third objective is to discuss current public policies to expand eveningopenings in public institutions which represent nowadays only 16.1% of the 3.4 million enrollments for evening classes, including federal (6.8%), state (7.0%) and municipal (2.3%) institutions. In the third objective it is included the discussion of programs for scholarships and tuition loans. The methodology applied was to rescue historical information on the establishment and the expansion of evening courses in Brazil, analyzing the current general Brazilian policies and the specific ones from the State of São Paulo. The research results pointed to the importance of federal programs for scholarships and tuition loans for students from private institutions such as the 1,382,484 scholarships since 2004 (PROUNI Program) and the 847,000 tuition loans since 1999 (FIES Program). Important steps have been made by the Brazilian government. Considering that there are 3,987,424 enrollments in private institutions, the effectiveness of the programs for scholarships and tuition loans is still insufficient to meet the universal benefits for the student’s needs. Evening courses became the real instrument of social inclusion for many Brazilian youths and must be expanded quantitatively and qualitatively, with aggressive public policies, including also, scholarships and tuition loans.

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.