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Edited by Ángel Gutiérrez and Paulo Boero

"This volume is a compilation of the research produced by the International Group for the Psychology of Mathematics Education (PME) since its creation, 30 years ago. It has been written to become an essential reference for Mathematics Education research in the coming years.
The chapters offer summaries and synthesis of the research produced by the PME Group, presented to let the readers grasp the evolution of paradigms, questions, methodologies and most relevant research results during the last 30 years. They also include extensive lists of references. Beyond this, the chapters raise the main current research questions and suggest directions for future research.
The handbook is divided into five sections devoted to the main research domains of interest to the PME Group. The first three sections summarize cognitively oriented research on learning and teaching specific content areas, transversal areas, and based on technology rich environments. The fourth section is devoted to the research on social, affective, cultural and cognitive aspects of Mathematics Education. Finally, the fifth section includes two chapters summarizing the PME research on teacher training and professional life of mathematics teachers.
The volume is the result of the effort of 30 authors and 26 reviewers. Most of them are recognized leading PME researchers with great expertise on the topic of their chapter. This handbook shall be of interest to both experienced researchers and doctoral students needing detailed synthesis of the advances and future directions of research in Mathematics Education, and also to mathematics teacher trainers who need to have a comprehensive reference as background for their courses on Mathematics Education.

Making Connections

Comparing Mathematics Classrooms Around the World

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Edited by David Clarke, Jonas Emanuelsson, Eva Jablonka and Ida Ah Chee Mok

In this book, comparisons are made between the practices of classrooms in a variety of different school systems around the world. The abiding challenge for classroom research is the realization of structure in diversity. The structure in this case takes the form of patterns of participation: regularities in the social practices of mathematics classrooms. The expansion of our field of view to include international rather than just local classrooms increases the diversity and heightens the challenge of the search for structure, while increasing the significance of any structures, once found. In particular, this book reports on the use of ‘lesson events’ as an entry point for the analysis of lesson structure. International research offers opportunities to study settings and characteristics untenable in the researcher’s local situation. Importantly, international comparative studies can reveal possibilities for practice that would go unrecognized within the established norms of educational practice of one country or one culture. Our capacity to conceive of alternatives to our current practice is constrained by deep-rooted assumptions, reflecting cultural and societal values that we lack the perspective to question. The comparisons made possible by international research facilitate our identification and interrogation of these assumptions. Such interrogation opens up possibilities for innovation that might not otherwise be identified, expanding the repertoire of mathematics teachers internationally, and providing the basis for theory development.

Mathematics Classrooms in Twelve Countries

The Insider's Perspective

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Edited by David Clarke, Christine Keitel and Yoshinori Shimizu

This book reports the accounts of researchers investigating the eighth grade mathematics classrooms of teachers in Australia, China, the Czech Republic, Germany, Israel, Japan, Korea, The Philippines, Singapore, South Africa, Sweden and the USA. This combination of countries gives good representation to different European and Asian educational traditions, affluent and less affluent school systems, and mono-cultural and multi-cultural societies. Researchers within each local group focused their analyses on those aspects of practice and meaning most closely aligned with the concerns of the local school system and the theoretical orientation of the researchers. Within any particular educational system, the possibilities for experimentation and innovation are limited by more than just methodological and ethical considerations: they are limited by our capacity to conceive possible alternatives. They are also limited by our assumptions regarding acceptable practice. These assumptions are the result of a long local history of educational practice, in which every development was a response to emergent local need and reflective of changing local values. Well-entrenched practices sublimate this history of development. The Learner’s Perspective Study is guided by a belief that we need to learn from each other. The resulting chapters offer deeply situated insights into the practices of mathematics classrooms in twelve countries: an insider’s perspective.

Edited by Jürgen Maasz and Wolfgang Schlöglmann

Mathematics education research has blossomed into many different areas which we can see in the programmes of the ICME conferences as well as in the various survey articles in the Handbooks. However, all of these lines of research are trying to grapple with a common problem, the complexity of the process of learning mathematics. Although our knowledge of the process is more extensive and deeper despite the fragmented nature of research in this area, there is still a need to overcome this fragmentation and to see learning as one process with different aspects. To overcome this fragmentation, this book identifies six themes: (1) mathematics, culture and society, (2) the structure of mathematics and its influence on the learning process, (3) mathematics learning as a cognitive process, (4) mathematics learning as a social process, (5) affective conditions of the mathematics learning process, (6) new technologies and mathematics learning. This book is addressed to all researchers in mathematic education. It gives an orientation and overview by addressing some carefully chosen questions on what is going on and what are the main results and questions what are important books or papers if further information is needed.

Redesigning Pedagogy

Reflections on Theory and Praxis

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Edited by Wendy D. Bokhorst-Heng, Margery D. Osborne and Kerry Lee

This book brings together selected papers from a conference focusing on Redesigning Pedagogy, organized by the Centre for Research in Pedagogy and Practice, National Institute of Education, Singapore. The papers are organised around seven key themes: Literacy Education, Relations of Power, Reflection, Meaning Making, Evaluation, and Mathematics and Science. There are two distinctive features in this title. First is its international focus. In addition to providing readers with an introduction to pedagogy in Singapore, it contains discussions on the environments in Australia, Canada, Hong Kong, South Africa, and the United States. A second focus is a strong commitment to transnational research. Although influenced by the theoretical perspectives of Bourdieu, Luke, and others, the authors are primarily focused on classroom practices.
This title will be of interest to students, researchers, and practitioners who are interested in broad thematic and comparative issues. With a number of chapters on Literacy Education, Mathematics, and Science, it will also be of appeal to those more interested in content specific areas.

Travelling Through Education

Uncertainty, Mathematics, Responsibility

Ole Skovsmose

This is a personal notebook from a conceptual travel. But, in a different sense, it also represents a report on travelling. The main part of the manuscript was written in Brazil, Denmark and England, whilst notes have also been inspired by visits to other countries. So, the book not only represents conceptual travel, it also reflects seasons of real travelling. In Part 1, the book comments on the critical position of mathematics education, and also indicates some concerns of critical mathematics education. Part 2 comments on mathematics in action, and considers the discussion of mathematics as an applied discipline in the contexts of technology, management, engineering, economics, etc. In Part 3, the book comments on mathematics and science in general. These comments are then generalised into a discussion of ‘reason’ and of the ‘apparatus of reason’. Finally, Part 4 returns to the discussion of mathematics education, and comments on notions that could become ‘sensitive’ to the critical position of mathematics education. Ole Skovsmose is also travelling between different academic fields. He touches upon mathematics and mathematics education, the philosophy of mathematics, technology and science, as well as sociological issues, glancing over issues such as globalisation, ghettoising, learning society, and risk society.
Travelling with the author, the reader will become aware of connections between many of these different issues.