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Semiotics in Mathematics Education

Epistemology, History, Classroom, and Culture


Edited by Luis Radford, Gert Schubring and Falk Seeger

Current interest in semiotics is undoubtedly related to our increasing awareness that our manners of thinking and acting in our world are deeply indebted to a variety of signs and sign systems (language included) that surround us.
Since mathematics is something that we accomplish through written, oral, bodily and other signs, semiotics appears well suited to furthering our understanding of the mathematical processes of thinking, symbolizing and communicating. Resorting to different semiotic perspectives (e. g., Peirce’s, Vygotsky’s, Saussure’s), the authors of this book deal with questions about the teaching and learning of mathematics as well as the history and epistemology of the discipline. Mathematics discourse and thinking and the technologically-mediated self of mathematical cultural practices are examined through key concepts such as metaphor, intentionality, gestures, interaction, sign-use, and meaning.
The cover picture comes from Jacob Leupold’s (1727) Theatrum Arithmetico-Geometrico. It conveys the cultural, historical, and embodied aspects of mathematical thinking variously emphasized by the contributors of this book.

Edited by Gerald Kulm

This book presents a coherent collection of research studies on teacher knowledge and its relation to instruction and learning in middle-grades mathematics. The authors provide comprehensive literature reviews on specific components of mathematics knowledge for teaching that have been found to be important for effective instruction. Based on the analysis of video data collected over a six-year project, the chapters present new and accessible research on the learning of fractions, early concepts of algebra, and basic statistics and probability.

The three sections of the book contain chapters that address research on the development of mathematics knowledge for teaching at the undergraduate level, instructional practices of middle-grades teachers, and the implications of teacher knowledge of mathematics for student learning. The chapters are written by members of a research team led by the Editor that has been working for the past six years to develop practical and useful theories and findings on variables that affect teaching and learning of middle grades mathematics.

Mathematics knowledge for teaching is a topic of great current interest. This book is a valuable resource for mathematics education researchers, graduate students, and teacher educators. In addition, professional developers and school district supervisor and curriculum leaders will find the concrete examples of effective teaching strategies useful for teacher workshops.

Edited by Erkki Pehkonen, Maija Ahtee and Jari Lavonen

The Finnish students’success in the first PISA 2000 evaluation was a surprise to most of the Finns, and even people working in teacher education and educational administration had difficulties to believe that this situation would continue. Finland’s second success in the next PISA 2003 comparison has been very pleasing for teachers and teacher educators, and for education policymakers. The good results on the second time waked us to think seriously on possible reasons for the success. Several international journalists and expert delegations from different countries have asked these reasons while visiting in Finland. Since we had no commonly acceptable explanation to students’success, we decided at the University of Helsinki to put together a book “How Finns Learn Mathematics and Science?”, in order to give a commonly acceptable explanation to our students’success in the international PISA evaluations. The book tries to explain the Finnish teacher education and school system as well as Finnish children’s learning environment at the level of the comprehensive school, and thus give explanations for the Finnish PISA success. The book is a joint enterprise of Finnish teacher educators. The explanations for success given by altogether 40 authors can be classified into three groups: Teacher and teacher education, school and curriculum, and other factors, like the use of ICT and a developmental project LUMA. The main result is that there is not one clear explanation, although research-based teacher education seems to have some influence. But the true explanation may be a combination of several factors.

How should I know?

Preservice Teachers' Images of Knowing (by Heart ) in Mathematics and Science


Kathleen T. Nolan

Elementary preservice teachers’school experiences of mathematics and science have shaped their images of knowing, including what counts as knowledge and what it means to know (in) mathematics and science. In this book, preservice teachers’ voices challenge the hegemony of official everyday narratives relating to these images.
The book is written as a parody of a physical science textbook on the topic of light, presenting a kaleidoscope of elementary preservice teachers’ narratives of knowing (in) mathematics and science. These narratives are tied together by the metaphorical thread of the properties of light, but also held apart by the tensions and contradictions with/in such a critical epistemological exploration. Through a postmodern lens, the only grand narrative that could be imag(in)ed for this text is one in which the personal lived experience narratives of the participants mingle and interweave to create a sort of kaleidoscope of narratives. With each turn of a kaleidoscope, light’s reflection engenders new patterns and emergent designs. The narratives of this research text highlight patterns of exclusion, gendered messages, binary oppositions, and the particle nature and shadowy texture of knowing (in) mathematics and science. The presentation format of the book emphasizes the reflexive and polyphonic nature of the research design, illustrated through layers of spoken text with/in performative text with/in metaphorical text.
The metaphor of a kaleidoscope is an empowering possibility for a critical narrative written to both engage and provoke the reader into imag(in)ing a critical journey toward possibilities for a different “knowing by heart” in mathematics and science and for appreciating lived experience narratives with/in teacher education.

Mathematisation and Demathematisation

Social, Philosophical and Educational Ramifications

Edited by Uwe Gellert and Eva Jablonka

In this volume scholars from diverse strands of research have contributed their perspectives on a process of mathematisation, which renders social, economical or political relationships increasingly formal. At the same time, mathematical skills lose their importance as they become replaced by diverse technological tools; a process of demathematisation takes place. The computerization of financial transactions, calculation of taxes and fees, comparison of prices as well as orientation by means of GPS, visualisation of complex data and electronic voting systems—all these mathematical technologies increasingly penetrate the lifestyle of consumers. What are the perils and promises of this development? Who is in charge, who is affected, who is excluded?
A common concern of all the authors of this volume is an attempt to draw attention to issues related to the formatting power of mathematics and to its role as implicit knowledge, which results in a process of demathematisation. This process, having once received considerable attention, is now threatened to be eclipsed by the proliferation of a discussion of school mathematics, which shows a tendency of cutting off its own philosophical and political roots. Taken together, the contributions reveal a rather complex picture: They draw attention to the importance of clarifying epistemological, societal and ideological issues as a prerequisite for a discussion of curriculum.

Margaret Walshaw

Education has a long tradition of opening itself up to new ideas and new ideas are what Working with Foucault in Education is all about. The book introduces readers to the scholarly work of Michel Foucault at a level that it neither too demanding not too superficial. It demonstrates to students, educators, scholars and policy makers, alike, how those ideas might be useful in understanding people and processes in education. This new line of investigation creates an awareness of the merits and weaknesses of contemporary theoretical frameworks and the impact these have on the production of educational knowledge.
Working with Foucault in Education engages readers in selected aspects of education. Its ten chapters take a thematic approach and include vignettes that explore issues relating to curriculum development, learning to teach, classroom learning and teaching, as well as research in contemporary society. These explorations allow readers to develop a new attitude towards education. The reason this is possible is that Foucault provides a language and the tools to deconstruct as well as shift thinking about familiar concepts. They also provide the means for readers to participate in educational criticism and to play a role in educational change.


Link between Traditions and Modernity

Ubiratan D'Ambrosio

In this book, Ubiratan D’Ambrosio presents his most recent thoughts on ethnomathematics—a sub-field of mathematics history and mathematics education for which he is widely recognized to be one of the founding fathers. In a clear, concise format, he outlines the aim of the Program Ethnomathematics, which is to understand mathematical knowing/doing throughout history, within the context of different groups, communities, peoples and nations, focusing on the cycle of mathematical knowledge: its generation, its intellectual and social organization, and its diffusion. While not rejecting the importance of modern academic mathematics, it is viewed as but one among many existing ethnomathematics. Offering concrete examples and ideas for mathematics teachers and researchers, D’Ambrosio makes an eloquent appeal for an entirely new approach to conceptualizing mathematics knowledge and education that embraces diversity and addresses the urgent need to provide youth with the necessary tools to become ethical, creative, critical individuals prepared to participate in the emerging planetary society.

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.

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.

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.