Philosophy And The Mathematics Curriculum

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The Philosophy of Mathematics Education

Author : Paul Ernest
Publisher : Springer
ISBN 13 : 3319405691
Total Pages : 33 pages
Book Rating : 4.3/5 (194 download)

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Book Synopsis The Philosophy of Mathematics Education by : Paul Ernest

Download or read book The Philosophy of Mathematics Education written by Paul Ernest and published by Springer. This book was released on 2016-07-15 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Philosophical Dimensions in Mathematics Education

Author : Karen Francois
Publisher : Springer Science & Business Media
ISBN 13 : 0387715754
Total Pages : 235 pages
Book Rating : 4.3/5 (877 download)

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Book Synopsis Philosophical Dimensions in Mathematics Education by : Karen Francois

Download or read book Philosophical Dimensions in Mathematics Education written by Karen Francois and published by Springer Science & Business Media. This book was released on 2007-11-15 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together diverse recent developments exploring the philosophy of mathematics in education. The unique combination of ethnomathematics, philosophy, history, education, statistics and mathematics offers a variety of different perspectives from which existing boundaries in mathematics education can be extended. The ten chapters in this book offer a balance between philosophy of and philosophy in mathematics education. Attention is paid to the implementation of a philosophy of mathematics within the mathematics curriculum.

The Philosophy of Mathematics Education Today

Author : Paul Ernest
Publisher : Springer
ISBN 13 : 3319777602
Total Pages : 375 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis The Philosophy of Mathematics Education Today by : Paul Ernest

Download or read book The Philosophy of Mathematics Education Today written by Paul Ernest and published by Springer. This book was released on 2018-06-09 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an up-to-date overview of the research on philosophy of mathematics education, one of the most important and relevant areas of theory. The contributions analyse, question, challenge, and critique the claims of mathematics education practice, policy, theory and research, offering ways forward for new and better solutions. The book poses basic questions, including: What are our aims of teaching and learning mathematics? What is mathematics anyway? How is mathematics related to society in the 21st century? How do students learn mathematics? What have we learnt about mathematics teaching? Applied philosophy can help to answer these and other fundamental questions, and only through an in-depth analysis can the practice of the teaching and learning of mathematics be improved. The book addresses important themes, such as critical mathematics education, the traditional role of mathematics in schools during the current unprecedented political, social, and environmental crises, and the way in which the teaching and learning of mathematics can better serve social justice and make the world a better place for the future.

Lectures on the Philosophy of Mathematics

Author : Joel David Hamkins
Publisher : MIT Press
ISBN 13 : 0262542234
Total Pages : 350 pages
Book Rating : 4.2/5 (625 download)

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Book Synopsis Lectures on the Philosophy of Mathematics by : Joel David Hamkins

Download or read book Lectures on the Philosophy of Mathematics written by Joel David Hamkins and published by MIT Press. This book was released on 2021-03-09 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to the philosophy of mathematics grounded in mathematics and motivated by mathematical inquiry and practice. In this book, Joel David Hamkins offers an introduction to the philosophy of mathematics that is grounded in mathematics and motivated by mathematical inquiry and practice. He treats philosophical issues as they arise organically in mathematics, discussing such topics as platonism, realism, logicism, structuralism, formalism, infinity, and intuitionism in mathematical contexts. He organizes the book by mathematical themes--numbers, rigor, geometry, proof, computability, incompleteness, and set theory--that give rise again and again to philosophical considerations.

Towards a Philosophy of Critical Mathematics Education

Author : Ole Skovsmose
Publisher : Springer Science & Business Media
ISBN 13 : 9401735565
Total Pages : 312 pages
Book Rating : 4.4/5 (17 download)

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Book Synopsis Towards a Philosophy of Critical Mathematics Education by : Ole Skovsmose

Download or read book Towards a Philosophy of Critical Mathematics Education written by Ole Skovsmose and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Levels of Infinity

Author : Hermann Weyl
Publisher : Courier Corporation
ISBN 13 : 0486266931
Total Pages : 258 pages
Book Rating : 4.4/5 (862 download)

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Book Synopsis Levels of Infinity by : Hermann Weyl

Download or read book Levels of Infinity written by Hermann Weyl and published by Courier Corporation. This book was released on 2013-09-26 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: Original anthology features less-technical essays discussing logic, topology, abstract algebra, relativity theory, and the works of David Hilbert. Most have been long unavailable or previously unpublished in book form. 2012 edition.

Philosophy for Children Through the Secondary Curriculum

Author : Lizzy Lewis
Publisher : A&C Black
ISBN 13 : 1441196617
Total Pages : 322 pages
Book Rating : 4.4/5 (411 download)

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Book Synopsis Philosophy for Children Through the Secondary Curriculum by : Lizzy Lewis

Download or read book Philosophy for Children Through the Secondary Curriculum written by Lizzy Lewis and published by A&C Black. This book was released on 2012-05-17 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Philosophy for Children (P4C) is an approach to learning and teaching that aims to develop reasoning and judgement. Students learn to listen to and respect their peers' opinions, think creatively and work together to develop a deeper understanding of concepts central to their own lives and the subjects they are studying. With the teacher adopting the role of facilitator, a true community develops in which rich and meaningful dialogue results in enquiry of the highest order. Each chapter is written by a leading P4C expert and provides an introduction to the relationship between P4C and the subject area, lesson stimuli and activities for extending and deepening students' thinking. The book includes: • guidance on how to embed P4C in curriculum subjects in a crowded and demanding secondary curriculum timetable • troubleshooting advice for the teacher-turned-facilitator • a companion website containing useful links, downloadable resources and material to display on your interactive whiteboard. Edited and collated by the UK's leading P4C organisation, this book introduces a rationale for using and adapting P4C in the secondary curriculum.

History and Philosophy of Modern Mathematics

Author : William Aspray
Publisher : U of Minnesota Press
ISBN 13 : 0816615675
Total Pages : 396 pages
Book Rating : 4.8/5 (166 download)

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Book Synopsis History and Philosophy of Modern Mathematics by : William Aspray

Download or read book History and Philosophy of Modern Mathematics written by William Aspray and published by U of Minnesota Press. This book was released on 1988 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: History and Philosophy of Modern Mathematics was first published in 1988. Minnesota Archive Editions uses digital technology to make long-unavailable books once again accessible, and are published unaltered from the original University of Minnesota Press editions. The fourteen essays in this volume build on the pioneering effort of Garrett Birkhoff, professor of mathematics at Harvard University, who in 1974 organized a conference of mathematicians and historians of modern mathematics to examine how the two disciplines approach the history of mathematics. In History and Philosophy of Modern Mathematics, William Aspray and Philip Kitcher bring together distinguished scholars from mathematics, history, and philosophy to assess the current state of the field. Their essays, which grow out of a 1985 conference at the University of Minnesota, develop the basic premise that mathematical thought needs to be studied from an interdisciplinary perspective. The opening essays study issues arising within logic and the foundations of mathematics, a traditional area of interest to historians and philosophers. The second section examines issues in the history of mathematics within the framework of established historical periods and questions. Next come case studies that illustrate the power of an interdisciplinary approach to the study of mathematics. The collection closes with a look at mathematics from a sociohistorical perspective, including the way institutions affect what constitutes mathematical knowledge.

Philosophy, Learning and the Mathematics Curriculum

Author : Xuehui Xie
Publisher : BRILL
ISBN 13 : 9087902573
Total Pages : 412 pages
Book Rating : 4.0/5 (879 download)

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Book Synopsis Philosophy, Learning and the Mathematics Curriculum by : Xuehui Xie

Download or read book Philosophy, Learning and the Mathematics Curriculum written by Xuehui Xie and published by BRILL. This book was released on 2019-02-18 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics curriculums used in progressive classrooms of the United States and in classrooms of the People’s Republic of China presuppose markedly different philosophies. Xie and Carspecken reconstruct different assumptions operating implicitly within mathematics curriculums developed by the Ministry of Education in China and NCTM in the United States. Each curriculum is constructed upon a deep structure holistically integrating presuppositions about the nature of the human self, society, learning processes, language, concepts, human development, freedom, authority and the epistemology and ontology of mathematical knowledge. Xie and Carspecken next present an extended discussion of the two main philosophical traditions informing these curriculums: dialectical materialism in the case of the Chinese mathematics curriculum, and Dewey’s instrumental pragmatism in the case of NCTM. Both philosophies were developed as movements out of Hegelian idealism while retaining the anti-dualist and anti-empiricist insights of Hegel’s thought. The history of dialectical materialism and Dewey’s instrumentalism is carefully examined by the authors to identify both similarities and sharp differences in the resulting mature philosophies. Drawing upon more recent philosophies of intersubjectivity (Brandom, Habermas) and dialectical materialist psychologies (Vygotsky, Luria), the authors conclude this book with arguments for overcoming the limitations of a purely instrumentalist framework and for expanding potentialities implicit within dialectical philosophies. This book will be of value to a broad audience, including mathematics educators, philosophers, curriculum theorists, social theorists, and those who work in comparative education and learning science.

Critical Mathematics Education

Author : Paul Ernest
Publisher : IAP
ISBN 13 : 1681232618
Total Pages : 361 pages
Book Rating : 4.6/5 (812 download)

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Book Synopsis Critical Mathematics Education by : Paul Ernest

Download or read book Critical Mathematics Education written by Paul Ernest and published by IAP. This book was released on 2016-01-01 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics is traditionally seen as the most neutral of disciplines, the furthest removed from the arguments and controversy of politics and social life. However, critical mathematics challenges these assumptions and actively attacks the idea that mathematics is pure, objective, and value?neutral. It argues that history, society, and politics have shaped mathematics—not only through its applications and uses but also through molding its concepts, methods, and even mathematical truth and proof, the very means of establishing truth. Critical mathematics education also attacks the neutrality of the teaching and learning of mathematics, showing how these are value?laden activities indissolubly linked to social and political life. Instead, it argues that the values of openness, dialogicality, criticality towards received opinion, empowerment of the learner, and social/political engagement and citizenship are necessary dimensions of the teaching and learning of mathematics, if it is to contribute towards democracy and social justice. This book draws together critical theoretic contributions on mathematics and mathematics education from leading researchers in the field. Recurring themes include: The natures of mathematics and critical mathematics education, issues of epistemology and ethics; Ideology, the hegemony of mathematics, ethnomathematics, and real?life education; Capitalism, globalization, politics, social class, habitus, citizenship and equity. The book demonstrates the links between these themes and the discipline of mathematics, and its critical teaching and learning. The outcome is a groundbreaking collection unified by a shared concern with critical perspectives of mathematics and education, and of the ways they impact on practice.

The Philosophy of the Christian Curriculum

Author : R. J. Rushdoony
Publisher : Chalcedon Foundation
ISBN 13 : 1879998750
Total Pages : pages
Book Rating : 4.8/5 (799 download)

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Book Synopsis The Philosophy of the Christian Curriculum by : R. J. Rushdoony

Download or read book The Philosophy of the Christian Curriculum written by R. J. Rushdoony and published by Chalcedon Foundation. This book was released on 2012-10-17 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The Christian School represents a break with humanistic education, but, too often in leaving the state school, the Christian educator has carried the state's humanism with him. A curriculum is not neutral: it is either a course in humanism or training in a God-centered faith and life. The liberal arts curriculum means literally that course which trains students in the arts of freedom. This raises the key question: is freedom in and of man or Christ? The Christian art of freedom, that is, the Christian liberal arts curriculum, is emphatically not the same as the humanistic one. It is urgently necessary for Christian educators to rethink the meaning and nature of the curriculum. It should be clear then that whether history, science, mathematics, grammar, literature, ecology, civic duty, or law, every aspect of curriculum must be reconstructed along Biblical lines. The overall objective is for Christian families to prepare and equip themselves for service in the Kingdom of God, and this cannot be done without a rethinking of the philosophy of the Christian curriculum. In this study, Rousas John Rushdoony develops the philosophy of the Christian curriculum. It is the pioneering study in this field, and it is important reading for all Christian educators.

Humanizing Mathematics and its Philosophy

Author : Bharath Sriraman
Publisher : Birkhäuser
ISBN 13 : 331961231X
Total Pages : 357 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Humanizing Mathematics and its Philosophy by : Bharath Sriraman

Download or read book Humanizing Mathematics and its Philosophy written by Bharath Sriraman and published by Birkhäuser. This book was released on 2017-11-07 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Festschrift contains numerous colorful and eclectic essays from well-known mathematicians, philosophers, logicians, and linguists celebrating the 90th birthday of Reuben Hersh. The essays offer, in part, attempts to answer the following questions set forth by Reuben himself as a focus for this volume: Can practicing mathematicians, as such, contribute anything to the philosophy of math? Can or should philosophers of math, as such, say anything to practicing mathematicians? Twenty or fifty years from now, what will be similar, and what will, or could, or should be altogether different: About the philosophy of math? About math education? About math research institutions? About data processing and scientific computing? The essays also offer glimpses into Reuben’s fertile mind and his lasting influence on the mathematical community, as well as revealing the diverse roots, obstacles and philosophical dispositions that characterize the working lives of mathematicians. With contributions from a veritable “who’s who” list of 20th century luminaries from mathematics and philosophy, as well as from Reuben himself, this volume will appeal to a wide variety of readers from curious undergraduates to prominent mathematicians.

The Nature of Mathematical Knowledge

Author : Philip Kitcher
Publisher : Oxford University Press, USA
ISBN 13 : 0195035410
Total Pages : 300 pages
Book Rating : 4.1/5 (95 download)

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Book Synopsis The Nature of Mathematical Knowledge by : Philip Kitcher

Download or read book The Nature of Mathematical Knowledge written by Philip Kitcher and published by Oxford University Press, USA. This book was released on 1984 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book argues against the view that mathematical knowledge is a priori, contending that mathematics is an empirical science and develops historically, just as natural sciences do. Kitcher presents a complete, systematic, and richly detailed account of the nature of mathematical knowledge and its historical development, focusing on such neglected issues as how and why mathematical language changes, why certain questions assume overriding importance, and how standards of proof are modified.

Synthetic Philosophy of Contemporary Mathematics

Author : Fernando Zalamea
Publisher : National Geographic Books
ISBN 13 : 0956775012
Total Pages : 0 pages
Book Rating : 4.9/5 (567 download)

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Book Synopsis Synthetic Philosophy of Contemporary Mathematics by : Fernando Zalamea

Download or read book Synthetic Philosophy of Contemporary Mathematics written by Fernando Zalamea and published by National Geographic Books. This book was released on 2012-09-01 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: A panoramic survey of the vast spectrum of modern and contemporary mathematics and the new philosophical possibilities they suggest. A panoramic survey of the vast spectrum of modern and contemporary mathematics and the new philosophical possibilities they suggest, this book gives the inquisitive non-specialist an insight into the conceptual transformations and intellectual orientations of modern and contemporary mathematics. The predominant analytic approach, with its focus on the formal, the elementary and the foundational, has effectively divorced philosophy from the real practice of mathematics and the profound conceptual shifts in the discipline over the last century. The first part discusses the specificity of modern (1830–1950) and contemporary (1950 to the present) mathematics, and reviews the failure of mainstream philosophy of mathematics to address this specificity. Building on the work of the few exceptional thinkers to have engaged with the “real mathematics” of their era (including Lautman, Deleuze, Badiou, de Lorenzo and Châtelet), Zalamea challenges philosophy's self-imposed ignorance of the “making of mathematics.” In the second part, thirteen detailed case studies examine the greatest creators in the field, mapping the central advances accomplished in mathematics over the last half-century, exploring in vivid detail the characteristic creative gestures of modern master Grothendieck and contemporary creators including Lawvere, Shelah, Connes, and Freyd. Drawing on these concrete examples, and oriented by a unique philosophical constellation (Peirce, Lautman, Merleau-Ponty), in the third part Zalamea sets out the program for a sophisticated new epistemology, one that will avail itself of the powerful conceptual instruments forged by the mathematical mind, but which have until now remained largely neglected by philosophers.

Curriculum Philosophy and Theory for Music Education Praxis

Author : Thomas A. Regelski
Publisher : Oxford University Press
ISBN 13 : 0197558690
Total Pages : 201 pages
Book Rating : 4.1/5 (975 download)

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Book Synopsis Curriculum Philosophy and Theory for Music Education Praxis by : Thomas A. Regelski

Download or read book Curriculum Philosophy and Theory for Music Education Praxis written by Thomas A. Regelski and published by Oxford University Press. This book was released on 2021 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: Basics of Curriculum -- Traditional Philosophical Foundations of Curriculum -- Twentieth-Century Philosophical Foundations of Curriculum -- Contemporary Perspectives for Curriculum Theory. -- Curriculum Models from Educational Theory -- Curriculum as and for Music as Praxis.

The Math Pact, Middle School

Author : Sarah B. Bush
Publisher : Corwin
ISBN 13 : 154439957X
Total Pages : 209 pages
Book Rating : 4.5/5 (443 download)

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Book Synopsis The Math Pact, Middle School by : Sarah B. Bush

Download or read book The Math Pact, Middle School written by Sarah B. Bush and published by Corwin. This book was released on 2020-09-19 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: A schoolwide solution for students’ mathematics success! Do you sometimes start to teach a mathematics concept and feel like you’re staring at a sea of bewildered faces? What happens when you discover students previously learned a calculation trick or a mnemonic that has muddied their long-term understanding? When "rules" seem to change from year to year, teacher to teacher, or school to school, mathematics can seem like a disconnected mystery for students. Clear up the confusion with a Mathematics Whole-School Agreement! Expanded from the highly popular "Rules that Expire" series of NCTM articles, this essential guide leads educators through the collaborative step-by-step process of establishing a coherent and consistent learner-centered and equitable approach to mathematics instruction. Through this work, you will identify, streamline, and become passionate about using clear and consistent mathematical language, notations, representations, rules, and generalizations within and across classrooms and grades. Importantly, you’ll learn to avoid "rules that expire"—tricks that may seem to help students in one grade but hurt in the long run. Features of this book include · Abundant grade-specific examples · Effective working plans for sustainability · Barrier-busting tips, to-dos, and try-it-outs · Practical templates and checklists · PLC prompts and discussion points When teachers unite across grades, students hit the ground running every year. Take the next step together as a team and help all your students build on existing understanding to find new success and most importantly, love learning and doing mathematics!

Thinking about Mathematics

Author : Stewart Shapiro
Publisher : OUP Oxford
ISBN 13 : 0192893068
Total Pages : 323 pages
Book Rating : 4.1/5 (928 download)

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Book Synopsis Thinking about Mathematics by : Stewart Shapiro

Download or read book Thinking about Mathematics written by Stewart Shapiro and published by OUP Oxford. This book was released on 2000-07-13 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: Thinking about Mathematics covers the range of philosophical issues and positions concerning mathematics. The text describes the questions about mathematics that motivated philosophers throughout history and covers historical figures such as Plato, Aristotle, Kant, and Mill. It also presents the major positions and arguments concerning mathematics throughout the twentieth century, bringing the reader up to the present positions and battle lines.