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Perspectives on Mathematical Practices by Bart van Kerkhove,jean paul van bendegem Pdf
In the eyes of the editors, this book will be considered a success if it can convince its readers of the following: that it is warranted to dream of a realistic and full-fledged theory of mathematical practices, in the plural. If such a theory is possible, it would mean that a number of presently existing fierce oppositions between philosophers, sociologists, educators, and other parties involved, are in fact illusory.
New Perspectives on Mathematical Practices by Bart Van Kerkhove Pdf
This volume focuses on the importance of historical enquiry for the appreciation of philosophical problems concerning mathematics. It contains a well-balanced mixture of contributions by internationally established experts, such as Jeremy Gray and Jens Hoyrup; upcoming scholars, such as Erich Reck and Dirk Schlimm; and young, promising researchers at the beginning of their careers. The book is situated within a relatively new and broadly naturalistic tradition in the philosophy of mathematics. In this alternative philosophical current, which has been dramatically growing in importance in the last few decades, unlike in the traditional schools, proper attention is paid to scientific practices as informing for philosophical accounts.
New Perspectives on Mathematical Practices by Bart van Kerkhove Pdf
This volume focuses on the importance of historical enquiry for the appreciation of philosophical problems concerning mathematics. It contains a well-balanced mixture of contributions by internationally established experts, such as Jeremy Gray and Jens Hoyrup; upcoming scholars, such as Erich Reck and Dirk Schlimm; and young, promising researchers at the beginning of their careers. The book is situated within a relatively new and broadly naturalistic tradition in the philosophy of mathematics. In this alternative philosophical current, which has been dramatically growing in importance in the last few decades, unlike in the traditional schools, proper attention is paid to scientific practices as informing for philosophical accounts.
Quantitative Measures of Mathematical Knowledge by Jonathan Bostic,Erin Krupa,Jeffrey Shih Pdf
The aim of this book is to explore measures of mathematics knowledge, spanning K-16 grade levels. By focusing solely on mathematics content, such as knowledge of mathematical practices, knowledge of ratio and proportions, and knowledge of abstract algebra, this volume offers detailed discussions of specific instruments and tools meant for measuring student learning. Written for assessment scholars and students both in mathematics education and across educational contexts, this book presents innovative research and perspectives on quantitative measures, including their associated purpose statements and validity arguments.
Explanation and Proof in Mathematics by Gila Hanna,Hans Niels Jahnke,Helmut Pulte Pdf
In the four decades since Imre Lakatos declared mathematics a "quasi-empirical science," increasing attention has been paid to the process of proof and argumentation in the field -- a development paralleled by the rise of computer technology and the mounting interest in the logical underpinnings of mathematics. Explanantion and Proof in Mathematics assembles perspectives from mathematics education and from the philosophy and history of mathematics to strengthen mutual awareness and share recent findings and advances in their interrelated fields. With examples ranging from the geometrists of the 17th century and ancient Chinese algorithms to cognitive psychology and current educational practice, contributors explore the role of refutation in generating proofs, the varied links between experiment and deduction, the use of diagrammatic thinking in addition to pure logic, and the uses of proof in mathematics education (including a critique of "authoritative" versus "authoritarian" teaching styles). A sampling of the coverage: The conjoint origins of proof and theoretical physics in ancient Greece. Proof as bearers of mathematical knowledge. Bridging knowing and proving in mathematical reasoning. The role of mathematics in long-term cognitive development of reasoning. Proof as experiment in the work of Wittgenstein. Relationships between mathematical proof, problem-solving, and explanation. Explanation and Proof in Mathematics is certain to attract a wide range of readers, including mathematicians, mathematics education professionals, researchers, students, and philosophers and historians of mathematics.
Multiple Perspectives on Mathematics Teaching and Learning by Jo Boaler Pdf
Multiple Perspectives on Mathematics Teaching and Learning offers a collection of chapters that take a new look at mathematics education. Leading authors, such as Deborah Ball, Paul Cobb, Jim Greeno, Stephen Lerman, and Michael Apple, draw from a range of perspectives in their analyses of mathematics teaching and learning. They address such practical problems as: the design of teaching and research that acknowledges the social nature of learning, maximizing the impact of teacher education programs, increasing the learning opportunities of students working in groups, and ameliorating the impact of male domination in mixed classrooms. These practical insights are combined with important advances in theory. Several of the authors address the nature of learning and teaching, including the ways in which theories and practices of mathematics education recognize learning as simultaneously social and individual. The issues addressed include teaching practices, equity, language, assessment, group work and the broader political context of mathematics reform. The contributors variously employ sociological, anthropological, psychological, sociocultural, political, and mathematical perspectives to produce powerful analyses of mathematics teaching and learning.
The Philosophy of Mathematical Practice by Paolo Mancosu Pdf
Contemporary philosophy of mathematics offers us an embarrassment of riches. Among the major areas of work one could list developments of the classical foundational programs, analytic approaches to epistemology and ontology of mathematics, and developments at the intersection of history and philosophy of mathematics. But anyone familiar with contemporary philosophy of mathematics will be aware of the need for new approaches that pay closer attention to mathematical practice. This book is the first attempt to give a coherent and unified presentation of this new wave of work in philosophy of mathematics. The new approach is innovative at least in two ways. First, it holds that there are important novel characteristics of contemporary mathematics that are just as worthy of philosophical attention as the distinction between constructive and non-constructive mathematics at the time of the foundational debates. Secondly, it holds that many topics which escape purely formal logical treatment - such as visualization, explanation, and understanding - can nonetheless be subjected to philosophical analysis. The Philosophy of Mathematical Practice comprises an introduction by the editor and eight chapters written by some of the leading scholars in the field. Each chapter consists of short introduction to the general topic of the chapter followed by a longer research article in the area. The eight topics selected represent a broad spectrum of contemporary philosophical reflection on different aspects of mathematical practice: diagrammatic reasoning and representation systems; visualization; mathematical explanation; purity of methods; mathematical concepts; the philosophical relevance of category theory; philosophical aspects of computer science in mathematics; the philosophical impact of recent developments in mathematical physics.
Mathematics Education and Philosophy by Paul Ernest Pdf
Currently there is a great deal of interest in philosophical issues in the teaching and learning of both mathematics and science education. In this book Ernest has collected together papers from the foremost researchers and practitioners in the philosophy of mathematics education and related areas, together with a selection of papers from the International Congress of Mathematics Education held in Quebec in 1992. Throughout, the outstanding feature of the collection is its multidisciplinary approach to the field of study. This book is the second in Paul Ernest's "Studies in Mathematics Education" series.
Global Perspectives and Practices for Reform-Based Mathematics Teaching by Kartal, Ozgul,Popovic, Gorjana,Morrissey, Susie Pdf
Reform-based mathematics has become a popular topic in the education field as this teaching emphasizes classroom discourse and instructional goals related to student engagement and an understanding of mathematical reasoning, concepts, and procedures using instructional practices that build on students’ informal knowledge of mathematics. It also connects mathematics with other disciplines and the real world and provides opportunities for students to contribute and invent their own methods during problem-solving. Further study on the best practices, benefits, and challenges of implementing this teaching into education is required. Global Perspectives and Practices for Reform-Based Mathematics Teaching explores international perspectives on diverse reform-based practices in teaching and learning mathematics, describes challenges and issues for teachers and teacher educators, promotes reflection and academic discussion at various levels and in various educational systems, and raises questions for the field of mathematics education. Covering a range of topics such as teacher preparation programs and integrated learning spaces, this reference work is ideal for academicians, practitioners, researchers, instructors, educators, and students.
A Journey in Mathematics Education Research by Erna Yackel,Koeno Gravemeijer,Anna Sfard Pdf
Our objective is to publish a book that lays out the theoretical constructs and research methodologies within mathematics education that have been developed by Paul Cobb and explains the process of their development. We propose to do so by including papers in which Cobb introduced new theoretical perspectives and methodologies into the literature, each preceded by a substantive accompanying introductory paper that explains the motivation/rationale for developing the new perspectives and/or methodologies and the processes through which they were developed, and Cobb’s own retrospective comments. In this way the book provides the reader with heretofore unpublished material that lays out in considerable detail the issues and problems that Cobb has confronted in his work, that, from his viewpoint, required theoretical and methodological shifts/advances and provides insight into how he has achieved the shifts/advances. The result will be a volume that, in addition to explaining Cobb’s contributions to the field of mathematics education, also provides the reader with insight into what is involved in developing an aggressive and evolving research program. When Cobb confronts problems and issues in his work that cannot be addressed using his existing theories and frameworks, he looks to other fields for theoretical inspiration. A critical feature of Cobb’s work is that in doing so, he consciously appropriates and adapts ideas from these other fields to the purpose of supporting processes of learning and teaching mathematics; He does not simply accept the goals or motives of those fields. As a result, Cobb reconceptualizes and reframes issues and concepts so that they result in new ways of investigating, exploring, and explaining phenomena that he encounters in the practical dimensions of his work, which include working in classrooms, with teachers, and with school systems. The effect is that the field of mathematics education is altered. Other researchers have found his "new ways of looking" useful to them. And they, in turn, adapt these ideas for their own use. The complexity of many of the ideas that Cobb has introduced into the field of mathematics education can lead to a multiplicity of interpretations by practitioners and by other researchers, based on their own experiential backgrounds. Therefore, by detailing the development of Cobb’s work, including the tensions involved in coming to grips with and reconciling apparently contrasting perspectives, the book will shed additional light on the processes of reconceptualization and thus help the reader to understand the reasons, mechanisms, and outcomes of researchers’ constant pursuit of new insights.
Philosophical Perspectives on Mathematical Practice by Bart Van Kerkhove,Jonas De Vuyst,Jean Paul Van Bendegem Pdf
It has been observed many times before that, as yet, there are no encompassing, integrated theories of mathematical practice available.To witness, as we currently do, a variety of schools in this field elaborating their philosophical frameworks, and trying to sort out their differences in the course of doing so, is also to be constantly reminded of the fact that a lot of epistemic aspects, extremely relevant to this task, remain dramatically underexamined. This volume wants to contribute to the stock of studies filling this perceived lacuna. It contains papers by established, upcoming, as well as beginning scholars, covering general, metaphilosophical themes such as naturalism, semiotics, pragmaticism, or empiricism, next to more specific topics including the unity of mathematical theories, thruth-flow in mathematics, diagrammatic reasoning, erroneous argumentation, or numerical analysis.
Numeracy as Social Practice by Keiko Yasukawa,Alan Rogers,Kara Jackson,Brian V. Street Pdf
Learning takes place both inside and outside of the classroom, embedded in local practices, traditions and interactions. But whereas the importance of social practice is increasingly recognised in literacy education, Numeracy as Social Practice: Global and Local Perspectives is the first book to fully explore these principles in the context of numeracy. The book brings together a wide range of accounts and studies from around the world to build a picture of the challenges and benefits of seeing numeracy as social practice ̶ that is, as mathematical activities embedded in the social, cultural, historical and political contexts in which these activities take place. Drawing on workplace, community and classroom contexts, Numeracy as Social Practice shows how everyday numeracy practices can be used in formal and non-formal maths teaching and how, in turn, classroom teaching can help to validate and strengthen local numeracy practices. At a time when an increasingly transnational approach is taken to education policy making, this book will appeal to development practitioners and researchers, and adult education, mathematics and numeracy teachers, researchers and policy makers around the world.
Innovation and Technology Enhancing Mathematics Education by Eleonora Faggiano,Francesca Ferrara,Antonella Montone Pdf
This book addresses key issues of Technology and Innovation(s) in Mathematics Education, drawing on heterogeneous ways of positioning about innovation in mathematical practice with technology. The book offers ideas and meanings of innovation as they emerge from the entanglement of the various researchers with the mathematical practice, the teacher training program, the student learning and engagement, or the research method that they are telling stories about. The multiple theoretical or empirical perspectives capture a rich landscape, in which the presence of digital technology entails the emergence of new practices, techniques, environments and devices, or new ways of making sense of technology in research, teaching and learning.
The Argument of Mathematics by Andrew Aberdein,Ian J Dove Pdf
Written by experts in the field, this volume presents a comprehensive investigation into the relationship between argumentation theory and the philosophy of mathematical practice. Argumentation theory studies reasoning and argument, and especially those aspects not addressed, or not addressed well, by formal deduction. The philosophy of mathematical practice diverges from mainstream philosophy of mathematics in the emphasis it places on what the majority of working mathematicians actually do, rather than on mathematical foundations. The book begins by first challenging the assumption that there is no role for informal logic in mathematics. Next, it details the usefulness of argumentation theory in the understanding of mathematical practice, offering an impressively diverse set of examples, covering the history of mathematics, mathematics education and, perhaps surprisingly, formal proof verification. From there, the book demonstrates that mathematics also offers a valuable testbed for argumentation theory. Coverage concludes by defending attention to mathematical argumentation as the basis for new perspectives on the philosophy of mathematics.
