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.
An Invitation to Critical Mathematics Education deals with a range of crucial topics. Among these are students’ foreground, landscapes of investigation, and mathematics in action. The book is intended for a broad audience: educators, students, teachers, policy makers, anybody interested in the further development of mathematics education. The book discusses concerns and preoccupation. This way it provides an invitation into 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.
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. Ole Skovsmose has published what I might call his magnum opus, a 280-page synthesis and extension of his work simply called Critical Mathematics Education. In it he brings together his deep philosophical understanding and theorisation of mathematics itself, mathematics in society from a critical perspective, and mathematics in the teaching, learning and formation of students. For the mathematics education community, especially those concerned with social justice, philosophy, critical pedagogy and the nature of mathematics this is likely to be the publishing event of the year. In this book he offers something lacking in the literature, a philosophy of applied mathematics, as well as much more. Paul Ernest, Emeritus Professor, University of Exeter, UK
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.
Virtual worlds and other virtual environments offer an adaptable context for applied and situated learning experiences. In this book, educators, instructional designers, librarians, administrators and scholars reflect on how to leverage constructivist, authentic, collaborative and complex interactive educational experiences through the use of these multisensory environments.
Have you ever felt stuck with methods, tools and skills that do not match the increasing complexity you are part of? Would you like to work in new ways that strengthen thinking, communication and collaboration? Visual Collaboration introduces a new and innovative way of working and collaborating that will help you successfully manage complexity for yourself, your team, and your entire organization. The method of this book unlocks any teams ability to collaborate in complex projects and processes. By using a systematic and proven approach to drawing and visualizing. Visual Collaboration is a unique visual business book that will enable you to develop visual languages to fit any scenario, create engaging and powerful questions to assist your visual process design and turn a white canvas into a visual template that can improve any meeting, project, or process. The core of the book - a practical and easy-to-follow method - THE FIVE BUILDING BLOCKS will most likely become your preferred way of working. The method is supported by plentiful examples, 4-color drawing, chapter summaries, and clearly defined learning objectives. Enjoyable and powerful, this book will help you: Use visualization as a tool to explore opportunities and challenges Translate complex concepts into easy-to-understand actions Engage employees and team members with effective strategic processes Incorporate drawing into your strategic organizational toolbox to strengthen communication and collaboration Develop and apply powerful visual literacy skills The authors, internationally-recognized experts in strategy communication and visual facilitation, have helped incorporate visual collaboration into more than 500 organizations such as LEGO, IKEA, the Red Cross, the United Nations, and many others. This book is the must-have resource for you to follow their example.
Contemporary society is marked and defined by the ways in which mobile goods, bodies, vehicles, objects, and data are organized, moved and staged. Against the background of the ‘mobilities turn’ this book articulates a new and emerging research field, namely that of ‘mobilities design’. The book revolves around the following research question: How are design decisions and interventions staging mobilities? It builds upon the ‘Staging Mobilities’ model (Jensen 2013) in an exploratory inquiry into the problems and potentials of the design of mobilities. The exchange value between mobilities and design research is twofold. To mobilities research this means getting closer to the ‘material’, and to engage in the creative, exploratory and experimental approaches of the design world which offer new potential for innovative research. Design research, on the other hand, might enter into a fruitful relationship with mobilities research, offering a relational and mobile design thinking and a valuable basis for design reflections around the ubiquitous structures, spaces and systems of mobilities.
A leading Danish historian presents a detailed account of the epic naval conflict between Denmark and a British fleet led by Vice Admiral Nelson. Fearing an alliance between Denmark and France, Britain sent a fleet of more than fifty ships to form a blockade off Great Yarmouth to prevent collaboration and ensure its naval superiority. But a series of diplomatic failures sent Vice Admiral Horatio Nelson into battle at Copenhagen. Written by the leading Danish authority on the period, this splendid work brings to life Nelson’s historic victory immortalized by his so famously turning a blind eye to his superior’s order to halt operations. As well as describing the brilliance of the British tactics, the work fascinatingly reveals the desperate action and great bravery displayed by the Danish defenders who suffered appallingly in the fighting.
Foregrounds contributes to the development of theories of learning, in particular to theories of learning mathematics. It is relevant to students, student teachers, and researchers in the field of education as well as in mathematics education. Foregrounds contains six parts. Part I provides a summary of the notion of foreground as it has developed since the author introduced the idea in Towards a Philosophy of Critical Mathematics Education. In Part II, the reader meets some students who tell us about their neighbourhood, about drug dealing, violence, and about playing football. They tell us about their teachers, about mathematics, and about what they would like their teachers to do. They tell us about their hopes, expectations, and frustrations. Part III presents the notions of intentionality and life-world as developed by Brentano and Husserl. However, in Part IV the author provides a radical reinterpretation of these two notions. He describes “real-life intentionalities” and “real-life worlds” as profoundly structured by a range of social factors. Part V is composed as a meeting between, on the one hand, the students and their experiences as presented in Part II, and on the other hand these notions of “real-life intentionalities” and “real-life worlds”. Through this meeting the author develops further the notion of foreground. The concluding part (Part VI) brings more examples as illustrations. Ole Skovsmose has a special interest in critical mathematics education. He has investigated the landscape of investigation, students’ experience of meaning, project work, mathematics education and democracy, mathematics in action, and mathematics and power. He has published more than 20 books in Danish, English and Portuguese as well as a huge number of articles. Sense has published the following books by Ole Skovsmose: Travelling through Education, In Doubt, An Invitation to Critical Mathematics Education, and Opening the Cage: Critique and Politics of Mathematics Education, which is edited together with Brian Greer.
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.
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.
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.
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