Critical Philosophy Of Mathematics
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Critical Philosophy Of Mathematics
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Author : Ole Skovsmose
language : en
Publisher: Springer Nature
Release Date : 2024-09-25
Critical Philosophy Of Mathematics written by Ole Skovsmose and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-25 with Education categories.
This book provides a philosophy of mathematics that resonates with critical mathematics education. It draws attention to the social complexities that characterise the period of Modernity including the extreme exploitation of manual workers and their families, brutal forms of colonisations, trading of slaves, and the formation of racist ideologies. It portrays Modernity as a period of contradictions and highlights that mathematics is a part of these contradictions. The text interprets mathematics as being indefinite, seeing that mathematics is a part of the ongoing human constructions. It outlines a performative interpretation of mathematics, portraying mathematics as intrinsically connected to actions. Any kind of action, including mathematics-based actions, calls for ethical considerations and this leads to any mathematical practice, either in research, application, or education, to face ethical challenges. It illustrates with examples how a critical philosophy of mathematics can come to be an integral part of classroom practices.
Critical Mathematics Education
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Author : Paul Ernest
language : en
Publisher: IAP
Release Date : 2016-01-01
Critical Mathematics Education written by Paul Ernest and has been published by IAP this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-01-01 with Education categories.
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.
Mathematics In Kant S Critical Philosophy
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Author : Lisa Shabel
language : en
Publisher: Routledge
Release Date : 2017-09-25
Mathematics In Kant S Critical Philosophy written by Lisa Shabel and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-25 with Mathematics categories.
Mathematics in Kant's Critical Philosophy provides a much needed reading (and re-reading) of Kant's theory of the construction of mathematical concepts through a fully contextualized analysis. In this work Lisa Shabel convincingly argues that it is only through an understanding of the relevant eighteenth century mathematics textbooks, and the related mathematical practice, can the material and context necessary for a successful interpretation of Kant's philosophy be provided. This is borne out through sustained readings of Euclid and Woolf in particular, which, when brought together with Kant's work, allows for the elucidation of several key issues and the reinterpretation of many hitherto opaque and long debated passages.
Kant Studies On Mathematics In The Critical Philosophy
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Author : Emily Carson
language : en
Publisher: Routledge
Release Date : 2017-12-22
Kant Studies On Mathematics In The Critical Philosophy written by Emily Carson and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-22 with Philosophy categories.
There is a long tradition, in the history and philosophy of science, of studying Kant’s philosophy of mathematics, but recently philosophers have begun to examine the way in which Kant’s reflections on mathematics play a role in his philosophy more generally, and in its development. For example, in the Critique of Pure Reason, Kant outlines the method of philosophy in general by contrasting it with the method of mathematics; in the Critique of Practical Reason, Kant compares the Formula of Universal Law, central to his theory of moral judgement, to a mathematical postulate; in the Critique of Judgement, where he considers aesthetic judgment, Kant distinguishes the mathematical sublime from the dynamical sublime. This last point rests on the distinction that shapes the Transcendental Analytic of Concepts at the heart of Kant’s Critical philosophy, that between the mathematical and the dynamical categories. These examples make it clear that Kant's transcendental philosophy is strongly influenced by the importance and special status of mathematics. The contributions to this book explore this theme of the centrality of mathematics to Kant’s philosophy as a whole. This book was originally published as a special issue of the Canadian Journal of Philosophy.
The Philosophy Of Mathematics Education
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Author : Paul Ernest
language : en
Publisher: Springer
Release Date : 2016-07-15
The Philosophy Of Mathematics Education written by Paul Ernest and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-15 with Education categories.
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.
Critical Mathematics Education Past Present And Future
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Author :
language : en
Publisher: BRILL
Release Date : 2010-01-01
Critical Mathematics Education Past Present And Future written by and has been published by BRILL this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-01-01 with Education categories.
Critical mathematics education brings together a series of concerns related to mathematics and its role in society, the practices of teaching and learning of mathematics in educational settings, and the practices of researching mathematics education. The work of Ole Skovsmose has provided a seminal contribution to the shaping of those concerns in the international community of mathematics educators and mathematics education researchers. This book gathers contributions of researchers from five continents, for whom critical mathematics education has been an inspiration to think about many different topics such as the dialogical and political dimensions of teacher education, mathematical modeling, the philosophy of mathematics from social and political perspectives, teaching practices in classrooms, the connection between mathematics and society, the scope and limits of critical thinking in relation to mathematics and mathematics education, and the political dimension of researching mathematics education. The book is not only a tribute to Ole Skovsmose’s long academic career; it is also a way of providing an overview of the roots of the critical mathematics education concerns, their current developments in different parts of the world, and their future directions. With a diversity of styles and forms of texts, this book is addressed to all those teachers and researchers who would like to be introduced or would like to go deeper into the types of insights that critical mathematics education offers.
Critical Issues In Mathematics Education
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Author : Bharath Sriraman
language : en
Publisher: IAP
Release Date : 2009-06-01
Critical Issues In Mathematics Education written by Bharath Sriraman and has been published by IAP this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-06-01 with Mathematics categories.
The word "critical" in the title of this collection has three meanings, all of which are relevant. One meaning, as applied to a situation or problem, is "at a point of crisis". A second meaning is "expressing adverse or disapproving comments or judgments". A third is related to the verb "to critique", meaning "to analyze the merits and faults of". The authors contributing to this book pose challenging questions, from multiple perspectives, about the roles of mathematics in society and the implications for education. Traditional reasons for teaching mathematics include: preparing a new generation of mathematics researchers and a cadre of technically competent users of mathematics; training students to think logically; and because mathematics is as much part of cultural heritage as literature or music. These reasons remain valid, though open to critique, but a deeper analysis is required that recognizes the roles of mathematics in framing many aspects of contemporary society, that will connect mathematics education to the lived experiences of students, their communities, and society in general, and that acknowledges the global ethical responsibilities of mathematicians and mathematics educators. The book is organized in four sections (1) Mathematics education: For what and why? (2) Globalization and cultural diversity, (3) Mathematics, education, and society and (4) Social justice in, and through, mathematics education The chapters address fundamental issues such as the relevance of school mathematics in people's lives; creating a sense of agency for the field of mathematics education, and redefining the relationship between mathematics as discipline, mathematics as school subject and mathematics as part of people's lives.
Levels Of Infinity
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Author : Hermann Weyl
language : en
Publisher: Courier Corporation
Release Date : 2013-09-26
Levels Of Infinity written by Hermann Weyl and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-26 with Mathematics categories.
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.
Applying Critical Mathematics Education
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Author :
language : en
Publisher: BRILL
Release Date : 2021-07-05
Applying Critical Mathematics Education written by and has been published by BRILL this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-05 with Education categories.
There is no shortage of urgent, complex problems that mathematics education can and should engage with. Pandemics, forest fires, pollution, Black Lives Matter protests, and fake news all involve mathematics, are matters of life and death, have a clear political dimension, and are interdisciplinary in nature. They demand a critical approach. The authors in this volume showcase new insights, teaching ideas and new and unique ways of applying critical mathematics education, in areas as diverse as climate change, obesity, decolonisation and ethnomathematics. This book demonstrates that there is plenty to be done with critical mathematics education. Contributors are: Annica Andersson, Tonya Gau Bartell, Richard Barwell, Lisa Lunney Borden, Sunghwan Byun, Anna Chronaki, Brian Greer, Jennifer Hall, Victoria Hand, Kjellrun Hiis Hauge, Beth Herbel-Eisenmann, Rune Herheim, Courtney Koestler, Kate le Roux, Swapna Mukhopadhyay, Aldo Parra, Anita Rampal, Sheena Rughubar-Reddy, Toril Eskeland Rangnes, Ulrika Ryan, Lisa Steffensen, Paola Valero and David Wagner.
Thinking About Mathematics
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Author : Stewart Shapiro
language : en
Publisher: OUP Oxford
Release Date : 2000-07-13
Thinking About Mathematics written by Stewart Shapiro and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-07-13 with Philosophy categories.
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.