How to drag with a worn-out mouse? Searching for social justice through collaboration

We consider what a concern for social justice in terms of social inclusion might mean for teacher education, both practising and prospective, with particular reference to the use of information and communication technology (ICT) in mathematics education taking place at a borderland school. Our discussion proceeds through the following steps: (1) We explore what a borderland position might denote to address what social inclusion might mean. (2) We consider the significance of mathematics education and the use of ICT for processes of social inclusion. (3) We briefly refer to the Interlink Network, as many of our observations emerge as reflections on this project. (4) We present different issues that will be of particular importance with respect to teacher education if we want to establish a mathematics education for social inclusion. These issues concern moving away from the comfort zone, establishing networks, identifying new approaches, moving beyond prototypical research, and getting in contact. This brings us to (5) final considerations, where we return to the notion of social justice. © Springer Science+Business Media B.V. 2009.

Educaçãdo matemática na realidade do ciberespaço - Que aspectos ontológicos e científicos se apresentam?

The question that leads this article is What is this virtual space in the on-line mathematics education process? We focus on the question of the real and virtual as issues taken as components of cyberspace. We investigate these notions in the history of philosophy, looking to Granger to find their meaning, to enable us to understand them and fit them into the sphere of Mathematics Education. This theoretical-philosophical article, then, claims that the virtuality of cyberspace is supported by the computer screen, built by the unification of the sciences (mathematics), technology and its applications. Software and the actions taken by Internet users update the capability of these programs in a variety of characteristics and possibilities such as space-time flow interconnections as well as during the mathematics education process.

Analisando imagens: Um ensaio sobre a criação de fontes narrativas para compreender os Grupos Escolares

This paper is an essay on how photos can be analysed and used to create narratives which may serve as resources for historical studies about school practices. As an exercise, we deal with six old photographs taken in Grupos Escolares, a Brazilian educational institution founded in the last decade of the 19th Century and extinguished in the 1970's. According to some authors, these schools represented the beginning of the public educational system in Brazil.

Uma caracterização do Centro de Educação Matemática - CEM (1984-1997) como uma Comunidade de prática de formação continuada de professores de matemática

This paper presents some results of a study on the Centre for Mathematics Education (Centro de Educação Matemática, CEM), a group of mathematics educators from the city of São Paulo-SP (Brazil), active mainly during the years 1984 to 1997. To establish a position on the process of identity constitution of CEM, we bring forth the method of Oral History and theories of identity. In this essay, an exercise in constituting the identity of CEM from the characterisation of this community's publications within its practice, we assume that the processes of identity constitution do not refer to what CEM is or was, but rather to a set of possibilities for apprehending it on the basis of strategies and initiatives set in given historical conditions and times. We make explicit three aspects that are present as their practice is converted into a source of coherence (mutual commitment, joint enterprise and shared repertoire), which allow one to reveal actions and production in the history of mathematics teacher education in the metropolitan region of São Paulo.

Um novo jogo para o estudo do raciocínio combinatório e do cálculo de probabilidade

We present an educational proposal for the study of combinatorial reasoning and calculation of probabilities based on a game and problem solving methodology, aiming to support the teaching of mathematical content. A review of the literature related to the teaching and learning of the concepts of combinatorial reasoning and probability is presented. The game is original, using a board game similar to Tic-tac-toe, and the movements of its parts have some similarities, in particular those made with the rook and pawn pieces of the game of chess. We formulate various activities (problems) involving the game which, in the process of solving them, using the problem solving methodology and with the appropriate intervention of the teacher, encourage students to develop strategies for counting, an indispensable tool in the initial study of Combinatorial Analysis and Calculation of Probabilities.

O conceito de saber escolar clássico em Dermeval Saviani: Implicações para a Educação Matemática

The aim of this paper is initially to consider some issues related to the relationship between humanization and alienation in the process of historical social development of human gender. These considerations are fundamental for understanding the concept of classical in Dermeval Saviani and the consequences for research about the historical development of Mathematics currently found in school curriculums. The intention is to value the appropriation of school mathematics as a humanizing element that becomes accessible through the activity of teaching.

Educação estatística no contexto da educação crítica

This article deals with the development of three competencies defined and studied in the context of Statistics Education (literacy, thinking and statistical reasoning). These competencies based on interpretation and understanding of critical information from real data are associated with an education geared toward the formation of critical citizenship and are in agreement with the principles that guide Critical Education. In this context, we consider Mathematical Modeling as a concrete possibility for integration between Critical Education and Education Statistics. We show that work with modeling projects in the classroom takes place in a context in which teaching is guided by the fundamentals of Critical Education. We present a project entitled Teaching Statistics and the financial market which illustrates the congruence between the objectives of Education Statistics and Critical Education.

Uma proposta didático-pedagógica para o estudo da concepção clássica de probabilidade

We present in this paper a pedagogical-didactic proposal for the teaching of Laplace Probability. The starting point for building the concept of probability is a game situation associated with the methodology of problem-solving. The theoretical reference for the concept of game is constructivist teaching of mathematics. Mathematical knowledge is constructed based on problems that generate new concepts and / or new content. The proposed game is original. Our proposal can be used both in the last cycle of basic education but also in high school, and may inform the practice of teachers who teach basic concepts of probability.

A Pesquisa sobre o ensino de probabilidade e estatística no Brasil: Um exercício de metacompreensão

This article presents an exercise in meta-comprehension of what has been researched on teaching probability and statistics in Brazil. This research was based on the work on this subject presented in the third International Symposium for Research in Mathematics Education (III SIPEM). Articles were selected from the proceedings of the event analyzed hermeneuticly according to the procedures of phenomenology. We observed no evidence of clustering of research on this topic in terms of region or institutions, and we also emphasize that research on the teaching of Probability and Statistics needs to advance toward a theoretical discussion that transcends the subjects being studied and makes broader and deeper links between theory and practice. Findings also indicate that this sub-area of research in mathematics education is in the process of constituting itself.

Pesquisando Práticas e Táticas em Educação Matemática

The present article, which is one study among others, seeks to understand practices and tactics of day-to-day school, spanning and being spanned by three studies in Mathematics education. The diversity of scenes, people and strategies used by actors in everyday school, considered from the theoretical perspectives of Foucault and Deleuze, shed light on the ways Mathematic alphabetization takes place and evidence regarding what is present in the black box of school culture, in a constant problematization about what a school can do. Maps are presented that establish cartographies, revealing smooth and striated territories, on a path created by the research done in those schools, where life is always invented.

Calculadoras, Computadores e Internet em Educação Matemática: dezoito anos de pesquisa

In this paper, we present GPIMEM, a group that has been developing research in Mathematics Education related to computers and other media since 1993 to understand how mathematical knowledge can be produced with these technological resources, in face-to-face as well as online distance education. Members of the group dialogue with different fields of knowledge such as philosophy, history, psychology, anthropology, sociology, arts and technology, among others, to inform their research. The research addresses various topics relevant to Mathematics Education, including methodological and epistemological aspects of teaching and learning, of mathematical modeling and teacher education, always within a qualitative research perspective. We begin with the historical presentation of the group, revealing its dynamics and organization of work, followed by reflections on qualitative research methodology and description of research conducted over the past five years. Finally, we present a synthesis of the theories developed by the group and expectations for the future.

Pesquisa em Resolução de Problemas: caminhos, avanços e novas perspectivas

We discuss the knowledge that has been constructed regarding Problem Solving in Math Education as a result of research developed by GTERP - Work and Study Group in Problem Solving, UNESP-Rio Claro/SP. The research is guided by the following general questions: How do students construct mathematical knowledge and how do teachers implement the methodology of Math Teaching-Learning-Evaluation through Problem Solving? Historical aspects of Problem Solving are very important in the configuration of the current trends for Problem Solving. One of them is the Methodology of Math Teaching-Learning- Evaluation through Problem Solving, based on clear foundations and an approach of renewal. In addition to that methodology, two aspects have been developed by the group: The conception of Math as a science of pattern and order and Discrete Mathematics. The knowledge constructed and the scientific production of GTERP prove its relevant contribution to intensifying dialogues between research and educational practice, students and teachers, and to increasing the possibilities of that practice particularly in Math work.

A Educação Matemática Focalizando Questões Sociais Maiores

Excessive specialization and the fascinating advances of technology and the sciences, particularly of mathematics, cause a false dichotomy between the sciences and technology and the arts and humanities. The survival of civilization is threatened. Clearly, the fragility of the current social organization allows for the exclusion of the larger part of the population from the benefits of progress. We need to revert this scenario, moving into a civilization without inequity, without uncontrolled consumerism and with respect for social and environmental conditions. In this paper, we discuss these issues and we illustrate with some examples how this can be achieved. We discuss the development of mathematics in Brazil, environmental crimes and its prevention through mathematical education, and a proposal for alternative educational models, using as an example the Waldorf Educational System.