The title of the book is Critique as Uncertainty. Thus Ole Skovsmose sees uncertainty as an important feature of any critical approach. He does not assume the existence of any blue prints for social and political improvements, nor that certain theoretical structures can provide solid foundations for a critical activities. For him critique is an open and uncertain activity. This also applies to critical mathematics education. Critique as Uncertainty includes papers Ole Skovsmose already has published as well as some newly written chapters. The book addresses issues about: landscapes of investigations, students' foregrounds, mathematics education and democracy, mathematics and power. Finally it expresses concerns of a critical mathematics education.

Dialogue and Learning in Mathematics Education is concerned with communication in mathematics class-rooms. In a series of empirical studies of project work, we follow students' inquiry cooperation as well as students' obstructions to inquiry cooperation. Both are considered important for a theory of learning mathematics.
Special attention is paid to the notions of dialogue' and critique'. A central idea is that dialogue' supports critical learning of mathematics'. The link between dialogue and critique is developed further by including the notions of intention' and reflection'. Thus a theory of learning mathematics is developed which is resonant with critical mathematics education.

The book provides an overview of state-of-the-art research from Brazil and Germany in the field of inclusive mathematics education. Originated from a research cooperation between two countries where inclusive education in mathematics has been a major challenge, this volume seeks to make recent research findings available to the international community of mathematics teachers and researchers. In the book, the authors cover a wide variety of special needs that learners of mathematics may have in inclusive settings. They present theoretical frameworks and methodological approaches for research and practice.

This book is a product of the BACOMET group, a group of educators-mainly educators of prospective teachers of mathematics-who first came together in 1980 to engage in study, discussion, and mutual reflection on issues in mathematics education. BACOMET is an acronym for BAsic Components of Mathematics Education for Teachers. The group was formed after a series of meetings in 1978-1979 between Geoffrey Howson, Michael Otte, and the late Bent Christiansen. In the ensuing years, BACOMET initiated several projects that resulted in published works. The present book is the main product of the BACOMET project entitled Meaning and Communication in Mathematics Education. This theme was chosen because of the growing recognition internationally that teachers of mathematics must deal with questions of meaning, sense making, and communication if their students are to be proficient learners and users of mathematics. The participants in this project were the following: Nicolas Balacheff (Grenoble, France) Maria Bartolini Bussi (Modena, Italy) Rolf Biehler (Bielefeld, Germany) Robert Davis (New Brunswick, NJ, USA) Willibald Dorfler (Klagenfurt, Austria) Tommy Dreyfus (Holon, Israel) Joel Hillel (Montreal, Canada) Geoffrey Howson (Southampton, England) Celia Hoyles-Director (London, England) Jeremy Kilpatrick-Director (Athens, GA, USA) Christine Keitel (Berlin, Germany) Colette Laborde (Grenoble, France) Michael Otte (Bielefeld, Germany) Kenneth Ruthven (Cambridge, England) Anna Sierpinska (Montreal, Canada) Ole Skovsmose-Director (Aalborg, Denmark) Conversations about directions the project might take began in May 1993 at a NATO Advanced Research Workshop of the previous BACOMET project in VIII PREFACE

More than ever, our time is characterised by rapid changes in the organisation and the production of knowledge. This movement is deeply rooted in the evolution of the scientific endeavour, as well as in the transformation of the political, economic and cultural organisation of society. In other words, the production of scientific knowledge is changing both with regard to the internal development of science and technology, and with regard to the function and role science and technology fulfill in society. This general social context in which universities and knowledge production are placed has been given different names: the informational society, the knowledge society, the learning society, the post-industrial society, the risk society, or even the post-modern society. A common feature of different characterisations of this historic time is the fact that it is a period in construction. Parts of the world, not only of the First World but also chunks of the Developing World, are involved in these transformations. There is a movement from former social, political and cultural forms of organisation which impact knowledge production into new forms. These forms drive us into forms of organisation that are unknown and that, for their very same complexity, do not show a clear ending stage. Somehow the utopias that guided the ideas of development and progress in the past are not present anymore, and therefore the transitions in the knowledge society generate a new uncertain world. We find ourselves and our universities to be in a transitional period in time. In this context, it is difficult to avoid considering seriously the challenges that such a complex and uncertain social configuration poses to scientific knowledge, to universities and especially to education in mathematics and science. It is clear that the transformation of knowledge outside universities has implied a change in the routes that research in mathematics, science and technology has taken in the last decades. It is also clear that in different parts of the world these changes have happened at different points in time. While universities in the "New World" (the American Continent, Africa, Asia and Oceania) have accommodated their operation to the challenges of the construction in the new world, in many European countries universities with a longer existence and tradition have moved more slowly into this time of transformation and have been responding at a less rapid pace to environmental challenges. The process of tuning universities, together with their forms of knowledge production and their provision of education in science and mathematics, with the demands of the informational society has been a complex process, as complex as the general transformation undergoing in society. Therefore an understanding of the current transitions in science and mathematics education has to consider different dimensions involved in such a change. Traditionally, educational studies in mathematics and science education have looked at changes in education from within the scientific disciplines and in the closed context of the classroom. Although educational change in the very end is implemented in everyday teaching and learning situations, other parallel dimensions influencing these situations cannot be forgotten. An understanding of the actual potentialities and limitations of educational transformations are highly dependent on the network of educational, cultural, administrative and ideological views and practices that permeate and constitute science and mathematics education in universities today. This book contributes to understanding some of the multiple aspects and dimensions of the transition of science and mathematics education in the current informational society. Such an understanding is necessary for finding possibilities to improve science and mathematics education in universities all around the world. Such a broad approach to the transitions happening in these fields has not been addressed yet by existing books in the market.

In Nineteen Eighty-Four George Orwell gives a description of different forms of suppression. We learn about the telescreens placed everywhere, through which it is possible for Big-Brother to watch the inhabitants of Oceania. However, it is not only important to control the activities of the inhabitants, it is important as well to control their thoughts, and the Thought Police are on guard. This is a very direct form of monitoring and control, but Orwell also outlines a more imperceptible and calculated line of thought control. In the Appendix to Nineteen Eighty-Four Orwell explains some struc tures of 'Newspeak', which is going to become the official language of Oceania. Newspeak is being developed by the Ministry of Truth, and this language has to substitute 'Oldspeak' (similar to standard English). Newspeak should fit with the official politics of Oceania ruled by the Ingsoc party: "The purpose of Newspeak was not only to provide a medium of expression for the world-view and mental habits proper to the devotees of Ingsoc, but to make all other modes of thought impos sible. It was intended that when Newspeak had been adopted once and for all and Oldspeak forgotten, a heretical thought - that is, a thought diverging from the principles of Ingsoc - should be literally unthink able, at least as far as thought is dependent on words."

The book Critical Mathematics Education provides Ole Skovsmose's recent contribution to the further development of critical mathematics education. It gives examples of learning environments, which invite students to engage in investigative processes. It discusses how mathematics can be used for identifying cases of social injustice, and it shows how mathematics itself can become investigated critically. Critical Mathematics Education addresses issues with respect to racism, oppression, erosion of democracy, sustainability, formatting power of mathematics, and banality of mathematical expertise. It explores relationships between mathematics, ethics, crises, and critique.

Connecting Humans to Equations: A Reinterpretation of the Philosophy of Mathematics presents some of the most important positions in the philosophy of mathematics, while adding new dimensions to this philosophy. Mathematics is an integral part of human and social life, meaning that a philosophy of mathematics must include several dimensions. This book describes these dimensions by the following four questions that structure the content of the book: Where is mathematics? How certain is mathematics? How social is mathematics? How good is mathematics? These four questions refer to the ontological, epistemological, social, and ethical dimension of a philosophy of mathematics. While the ontological and epistemological dimensions have been explored in all classic studies in the philosophy of mathematics, the exploration of the book is unique in its social and ethical dimensions. It argues that the foundation of mathematics is deeply connected to human and social actions and that mathematics includes not just descriptive but also performative features. This human-centered and accessible interpretation of mathematics is relevant for students in mathematics, mathematics education, and any technical discipline and for anybody working with mathematics.

This survey provides a brief and selective overview of research in the philosophy of mathematics education. It asks what makes up the philosophy of mathematics education, what it means, what questions it asks and answers, and what is its overall importance and use? It provides overviews of critical mathematics education, and the most relevant modern movements in the philosophy of mathematics. A case study is provided of an emerging research tradition in one country. This is the Hermeneutic strand of research in the philosophy of mathematics education in Brazil. This illustrates one orientation towards research inquiry in the philosophy of mathematics education. It is part of a broader practice of 'philosophical archaeology': the uncovering of hidden assumptions and buried ideologies within the concepts and methods of research and practice in mathematics education. An extensive bibliography is also included.

In Nineteen Eighty-Four George Orwell gives a description of different forms of suppression. We learn about the telescreens placed everywhere, through which it is possible for Big-Brother to watch the inhabitants of Oceania. However, it is not only important to control the activities of the inhabitants, it is important as well to control their thoughts, and the Thought Police are on guard. This is a very direct form of monitoring and control, but Orwell also outlines a more imperceptible and calculated line of thought control. In the Appendix to Nineteen Eighty-Four Orwell explains some struc tures of 'Newspeak', which is going to become the official language of Oceania. Newspeak is being developed by the Ministry of Truth, and this language has to substitute 'Oldspeak' (similar to standard English). Newspeak should fit with the official politics of Oceania ruled by the Ingsoc party: "The purpose of Newspeak was not only to provide a medium of expression for the world-view and mental habits proper to the devotees of Ingsoc, but to make all other modes of thought impos sible. It was intended that when Newspeak had been adopted once and for all and Oldspeak forgotten, a heretical thought - that is, a thought diverging from the principles of Ingsoc - should be literally unthink able, at least as far as thought is dependent on words."

This book is a product of the BACOMET group, a group of educators-mainly educators of prospective teachers of mathematics-who first came together in 1980 to engage in study, discussion, and mutual reflection on issues in mathematics education. BACOMET is an acronym for BAsic Components of Mathematics Education for Teachers. The group was formed after a series of meetings in 1978-1979 between Geoffrey Howson, Michael Otte, and the late Bent Christiansen. In the ensuing years, BACOMET initiated several projects that resulted in published works. The present book is the main product of the BACOMET project entitled Meaning and Communication in Mathematics Education. This theme was chosen because of the growing recognition internationally that teachers of mathematics must deal with questions of meaning, sense making, and communication if their students are to be proficient learners and users of mathematics. The participants in this project were the following: Nicolas Balacheff (Grenoble, France) Maria Bartolini Bussi (Modena, Italy) Rolf Biehler (Bielefeld, Germany) Robert Davis (New Brunswick, NJ, USA) Willibald Dorfler (Klagenfurt, Austria) Tommy Dreyfus (Holon, Israel) Joel Hillel (Montreal, Canada) Geoffrey Howson (Southampton, England) Celia Hoyles-Director (London, England) Jeremy Kilpatrick-Director (Athens, GA, USA) Christine Keitel (Berlin, Germany) Colette Laborde (Grenoble, France) Michael Otte (Bielefeld, Germany) Kenneth Ruthven (Cambridge, England) Anna Sierpinska (Montreal, Canada) Ole Skovsmose-Director (Aalborg, Denmark) Conversations about directions the project might take began in May 1993 at a NATO Advanced Research Workshop of the previous BACOMET project in VIII PREFACE

More than ever, our time is characterised by rapid changes in the organisation and the production of knowledge. This movement is deeply rooted in the evolution of the scientific endeavour, as well as in the transformation of the political, economic and cultural organisation of society. In other words, the production of scientific knowledge is changing both with regard to the internal development of science and technology, and with regard to the function and role science and technology fulfill in society. This general social context in which universities and knowledge production are placed has been given different names: the informational society, the knowledge society, the learning society, the post-industrial society, the risk society, or even the post-modern society. A common feature of different characterisations of this historic time is the fact that it is a period in construction. Parts of the world, not only of the First World but also chunks of the Developing World, are involved in these transformations. There is a movement from former social, political and cultural forms of organisation which impact knowledge production into new forms. These forms drive us into forms of organisation that are unknown and that, for their very same complexity, do not show a clear ending stage. Somehow the utopias that guided the ideas of development and progress in the past are not present anymore, and therefore the transitions in the knowledge society generate a new uncertain world. We find ourselves and our universities to be in a transitional period in time. In this context, it is difficult to avoid considering seriously the challenges that such a complex and uncertain social configuration poses to scientific knowledge, to universities and especially to education in mathematics and science. It is clear that the transformation of knowledge outside universities has implied a change in the routes that research in mathematics, science and technology has taken in the last decades. It is also clear that in different parts of the world these changes have happened at different points in time. While universities in the "New World" (the American Continent, Africa, Asia and Oceania) have accommodated their operation to the challenges of the construction in the new world, in many European countries universities with a longer existence and tradition have moved more slowly into this time of transformation and have been responding at a less rapid pace to environmental challenges. The process of tuning universities, together with their forms of knowledge production and their provision of education in science and mathematics, with the demands of the informational society has been a complex process, as complex as the general transformation undergoing in society. Therefore an understanding of the current transitions in science and mathematics education has to consider different dimensions involved in such a change. Traditionally, educational studies in mathematics and science education have looked at changes in education from within the scientific disciplines and in the closed context of the classroom. Although educational change in the very end is implemented in everyday teaching and learning situations, other parallel dimensions influencing these situations cannot be forgotten. An understanding of the actual potentialities and limitations of educational transformations are highly dependent on the network of educational, cultural, administrative and ideological views and practices that permeate and constitute science and mathematics education in universities today. This book contributes to understanding some of the multiple aspects and dimensions of the transition of science and mathematics education in the current informational society. Such an understanding is necessary for finding possibilities to improve science and mathematics education in universities all around the world. Such a broad approach to the transitions happening in these fields has not been addressed yet by existing books in the market.

Dialogue and Learning in Mathematics Education is concerned with communication in mathematics class-rooms. In a series of empirical studies of project work, we follow students' inquiry cooperation as well as students' obstructions to inquiry cooperation. Both are considered important for a theory of learning mathematics.
Special attention is paid to the notions of dialogue' and critique'. A central idea is that dialogue' supports critical learning of mathematics'. The link between dialogue and critique is developed further by including the notions of intention' and reflection'. Thus a theory of learning mathematics is developed which is resonant with critical mathematics education.

The title of the book is Critique as Uncertainty. Thus Ole Skovsmose sees uncertainty as an important feature of any critical approach. He does not assume the existence of any blue prints for social and political improvements, nor that certain theoretical structures can provide solid foundations for a critical activities. For him critique is an open and uncertain activity. This also applies to critical mathematics education. Critique as Uncertainty includes papers Ole Skovsmose already has published as well as some newly written chapters. The book addresses issues about: landscapes of investigations, students' foregrounds, mathematics education and democracy, mathematics and power. Finally it expresses concerns of a critical mathematics education.