Mathematics For The Imagination

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Poetic Logic and the Origins of the Mathematical Imagination

Author : Marcel Danesi
Publisher : Springer Nature
ISBN 13 : 3031315820
Total Pages : 180 pages
Book Rating : 4.0/5 (313 download)

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Book Synopsis Poetic Logic and the Origins of the Mathematical Imagination by : Marcel Danesi

Download or read book Poetic Logic and the Origins of the Mathematical Imagination written by Marcel Danesi and published by Springer Nature. This book was released on 2023-09-02 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book treats eighteenth-century Italian philosopher Giambattista Vico’s theory of poetic logic for the first time as the originating force in mathematics, transforming instinctive counting and spatial perception into poetic (metaphorical) symbolism that dovetails with the origin of language. It looks at current work on mathematical cognition (from Lakoff and Núñez to Butterworth, Dehaene, and beyond), matching it against the poetic logic paradigm. In a sense, it continues from where Kasner and Newman left off, connecting contemporary research on the mathematical mind to the idea that the products of early mathematics were virtually identical to the first forms of poetic language. As such, this book informs the current research on mathematical cognition from a different angle, by looking back at a still relatively unknown philosopher within mathematics. The aim of this volume is to look broadly at what constitutes the mathematical mind through the Vichian lens of poetic logic. Vico was among the first to suggest that the essential nature of mind could be unraveled indirectly by reconstructing the sources of its “modifications” (his term for “creations”); that is, by examining the creation and function of symbols, words, and all the other uniquely human artifacts—including mathematics—the mind has allowed humans to establish “the world of civil society,” Vico’s term for culture and civilization. The book is of interest to cognitive scientists working on math cognition. It presents the theory of poetic logic as Vico articulated it in his book The New Science, examining its main premises and then applying it to an interpretation of the ongoing work in math cognition. It will also be of interest to the general public, since it presents a history of early mathematics through the lens of an idea that has borne fruit in understanding the origin of language and symbols more broadly.

The Mathematical Imagination

Author : Matthew Handelman
Publisher : Fordham Univ Press
ISBN 13 : 0823283852
Total Pages : 287 pages
Book Rating : 4.8/5 (232 download)

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Book Synopsis The Mathematical Imagination by : Matthew Handelman

Download or read book The Mathematical Imagination written by Matthew Handelman and published by Fordham Univ Press. This book was released on 2019-03-05 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an archeology of the undeveloped potential of mathematics for critical theory. As Max Horkheimer and Theodor W. Adorno first conceived of the critical project in the 1930s, critical theory steadfastly opposed the mathematization of thought. Mathematics flattened thought into a dangerous positivism that led reason to the barbarism of World War II. The Mathematical Imagination challenges this narrative, showing how for other German-Jewish thinkers, such as Gershom Scholem, Franz Rosenzweig, and Siegfried Kracauer, mathematics offered metaphors to negotiate the crises of modernity during the Weimar Republic. Influential theories of poetry, messianism, and cultural critique, Handelman shows, borrowed from the philosophy of mathematics, infinitesimal calculus, and geometry in order to refashion cultural and aesthetic discourse. Drawn to the austerity and muteness of mathematics, these friends and forerunners of the Frankfurt School found in mathematical approaches to negativity strategies to capture the marginalized experiences and perspectives of Jews in Germany. Their vocabulary, in which theory could be both mathematical and critical, is missing from the intellectual history of critical theory, whether in the work of second generation critical theorists such as Jürgen Habermas or in contemporary critiques of technology. The Mathematical Imagination shows how Scholem, Rosenzweig, and Kracauer’s engagement with mathematics uncovers a more capacious vision of the critical project, one with tools that can help us intervene in our digital and increasingly mathematical present. The Mathematical Imagination is available from the publisher on an open-access basis.

Mathematics and the Imagination

Author : Edward Kasner
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (14 download)

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Book Synopsis Mathematics and the Imagination by : Edward Kasner

Download or read book Mathematics and the Imagination written by Edward Kasner and published by . This book was released on 1979 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Classical Mathematics from Al-Khwarizmi to Descartes

Author : Roshdi Rashed
Publisher : Routledge
ISBN 13 : 1317622383
Total Pages : 621 pages
Book Rating : 4.3/5 (176 download)

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Book Synopsis Classical Mathematics from Al-Khwarizmi to Descartes by : Roshdi Rashed

Download or read book Classical Mathematics from Al-Khwarizmi to Descartes written by Roshdi Rashed and published by Routledge. This book was released on 2014-08-21 with total page 621 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book follows the development of classical mathematics and the relation between work done in the Arab and Islamic worlds and that undertaken by the likes of Descartes and Fermat. ‘Early modern,’ mathematics is a term widely used to refer to the mathematics which developed in the West during the sixteenth and seventeenth century. For many historians and philosophers this is the watershed which marks a radical departure from ‘classical mathematics,’ to more modern mathematics; heralding the arrival of algebra, geometrical algebra, and the mathematics of the continuous. In this book, Roshdi Rashed demonstrates that ‘early modern,’ mathematics is actually far more composite than previously assumed, with each branch having different traceable origins which span the millennium. Going back to the beginning of these parts, the aim of this book is to identify the concepts and practices of key figures in their development, thereby presenting a fuller reality of these mathematics. This book will be of interest to students and scholars specialising in Islamic science and mathematics, as well as to those with an interest in the more general history of science and mathematics and the transmission of ideas and culture.

Imagine Math 7

Author : Michele Emmer
Publisher : Springer Nature
ISBN 13 : 303042653X
Total Pages : 471 pages
Book Rating : 4.0/5 (34 download)

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Book Synopsis Imagine Math 7 by : Michele Emmer

Download or read book Imagine Math 7 written by Michele Emmer and published by Springer Nature. This book was released on 2020-10-07 with total page 471 pages. Available in PDF, EPUB and Kindle. Book excerpt: Imagine mathematics, imagine with the help of mathematics, imagine new worlds, new geometries, new forms. Imagine building mathematical models that make it possible to manage our world better, imagine solving great problems, imagine new problems never before thought of, imagine combining music, art, poetry, literature, architecture, theatre and cinema with mathematics. Imagine the unpredictable and sometimes counterintuitive applications of mathematics in all areas of human endeavour. This seventh volume starts with a homage to the Italian artist Mimmo Paladino who created exclusively for the Venice Conference 2019 ten original and unique works of art paper dedicated to the themes of the meeting. A large section is dedicated to the most recent Fields Medals including a Homage to Maryam Mirzakhani including a presentation of the exhibition on soap bubbles in art and science that took place in 2019. A section is dedicated to cinema and theatre including the performances by Claire Bardainne & Adrien Mondot. A part of the conference focused on the community of mathematicians, their role in literature and even in politics with the extraordinary example of Antanas Mockus Major of Bogotá. Mathematics in the constructions of bridges, in particular in Italy in the Sixties was presented by Tullia Iori. A very particular contribution on Origami by a mathematician, Marco Abate and an artist, Alessandro Beber. And many other topics. As usual the topics are treated in a way that is rigorous but captivating, detailed and full of evocations. This is an all-embracing look at the world of mathematics and culture. The world, life, culture, everything has changed in a few weeks with the Coronavirus. Culture, science are the main ways to safeguard people's physical and social life. Trust in humanity's creativity and ability. The motto today in Italy is Everything will be fine. This work is addressed to all those who have an interest in Mathematics.

Imagine Math 3

Author : Michele Emmer
Publisher : Springer
ISBN 13 : 3319012312
Total Pages : 468 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Imagine Math 3 by : Michele Emmer

Download or read book Imagine Math 3 written by Michele Emmer and published by Springer. This book was released on 2015-03-04 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: Imagine mathematics, imagine with the help of mathematics, imagine new worlds, new geometries, new forms. This volume in the series “Imagine Math” casts light on what is new and interesting in the relationships between mathematics, imagination and culture. The book opens by examining the connections between modern and contemporary art and mathematics, including Linda D. Henderson’s contribution. Several further papers are devoted to mathematical models and their influence on modern and contemporary art, including the work of Henry Moore and Hiroshi Sugimoto. Among the many other interesting contributions are an homage to Benoît Mandelbrot with reference to the exhibition held in New York in 2013 and the thoughts of Jean-Pierre Bourguignon on the art and math exhibition at the Fondation Cartier in Paris. An interesting part is dedicated to the connections between math, computer science and theatre with the papers by C. Bardainne and A. Mondot. The topics are treated in a way that is rigorous but captivating, detailed but very evocative. This is an all-embracing look at the world of mathematics and culture.

Descartes's Imagination

Author : Dennis L. Sepper
Publisher : Univ of California Press
ISBN 13 : 9780520200500
Total Pages : 344 pages
Book Rating : 4.2/5 (5 download)

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Book Synopsis Descartes's Imagination by : Dennis L. Sepper

Download or read book Descartes's Imagination written by Dennis L. Sepper and published by Univ of California Press. This book was released on 1996-01-01 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: "A work of major importance for the interpretation of Descartes's development and for the understanding of the function of the imagination in Descartes's early works. Descartes's Imagination will be a must in Descartes and imagination studies. It is long overdue."--Eva T. H. Brann, author of The World of Imagination: Sum and Substance "A significant contribution to our understanding of the development of Descartes's philosophy."--William R. Shea, author of The Magic of Numbers and Motion: The Scientific Career of Rene Descartes

Mathematics and the Imagination

Author : Edward Kasner
Publisher :
ISBN 13 :
Total Pages : 380 pages
Book Rating : 4.:/5 (638 download)

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Book Synopsis Mathematics and the Imagination by : Edward Kasner

Download or read book Mathematics and the Imagination written by Edward Kasner and published by . This book was released on 1949 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Teaching 360°: Effective Learning Through the Imagination

Author :
Publisher : BRILL
ISBN 13 : 9087903782
Total Pages : 156 pages
Book Rating : 4.0/5 (879 download)

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Book Synopsis Teaching 360°: Effective Learning Through the Imagination by :

Download or read book Teaching 360°: Effective Learning Through the Imagination written by and published by BRILL. This book was released on 2008-01-01 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a detailed examination of imagination in learning. Teachers working with the ideas of Imaginative Education in their classrooms provide examples that cover multiple curricular areas and span elementary through secondary school contexts.

Handbook of Cognitive Mathematics

Author : Marcel Danesi
Publisher : Springer Nature
ISBN 13 : 3031039459
Total Pages : 1392 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Handbook of Cognitive Mathematics by : Marcel Danesi

Download or read book Handbook of Cognitive Mathematics written by Marcel Danesi and published by Springer Nature. This book was released on 2022-10-31 with total page 1392 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cognitive mathematics provides insights into how mathematics works inside the brain and how it is interconnected with other faculties through so-called blending and other associative processes. This handbook is the first large collection of various aspects of cognitive mathematics to be amassed into a single title, covering decades of connection between mathematics and other figurative processes as they manifest themselves in language, art, and even algorithms. It will be of use to anyone working in math cognition and education, with each section of the handbook edited by an international leader in that field.

Handbook of Abductive Cognition

Author : Lorenzo Magnani
Publisher : Springer Nature
ISBN 13 : 3031101359
Total Pages : 1921 pages
Book Rating : 4.0/5 (311 download)

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Book Synopsis Handbook of Abductive Cognition by : Lorenzo Magnani

Download or read book Handbook of Abductive Cognition written by Lorenzo Magnani and published by Springer Nature. This book was released on 2023-03-31 with total page 1921 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Handbook offers the first comprehensive reference guide to the interdisciplinary field of abductive cognition, providing readers with extensive information on the process of reasoning to hypotheses in humans, animals, and in computational machines. It highlights the role of abduction in both theory practice: in generating and testing hypotheses and explanatory functions for various purposes and as an educational device. It merges logical, cognitive, epistemological and philosophical perspectives with more practical needs relating to the application of abduction across various disciplines and practices, such as in diagnosis, creative reasoning, scientific discovery, diagrammatic and ignorance-based cognition, and adversarial strategies. It also discusses the inferential role of models in hypothetical reasoning, abduction and creativity, including the process of development, implementation and manipulation for different scientific and technological purposes. Written by a group of internationally renowned experts in philosophy, logic, general epistemology, mathematics, cognitive, and computer science, as well as life sciences, engineering, architecture, and economics, the Handbook of Abductive Cognition offers a unique reference guide for readers approaching the process of reasoning to hypotheses from different perspectives and for various theoretical and practical purposes. Numerous diagrams, schemes and other visual representations are included to promote a better understanding of the relevant concepts and to make concepts highly accessible to an audience of scholars and students with different scientific backgrounds.

Mathematical Reasoning

Author : Lyn D. English
Publisher : Routledge
ISBN 13 : 1136491147
Total Pages : 407 pages
Book Rating : 4.1/5 (364 download)

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Book Synopsis Mathematical Reasoning by : Lyn D. English

Download or read book Mathematical Reasoning written by Lyn D. English and published by Routledge. This book was released on 2013-04-03 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: How we reason with mathematical ideas continues to be a fascinating and challenging topic of research--particularly with the rapid and diverse developments in the field of cognitive science that have taken place in recent years. Because it draws on multiple disciplines, including psychology, philosophy, computer science, linguistics, and anthropology, cognitive science provides rich scope for addressing issues that are at the core of mathematical learning. Drawing upon the interdisciplinary nature of cognitive science, this book presents a broadened perspective on mathematics and mathematical reasoning. It represents a move away from the traditional notion of reasoning as "abstract" and "disembodied", to the contemporary view that it is "embodied" and "imaginative." From this perspective, mathematical reasoning involves reasoning with structures that emerge from our bodily experiences as we interact with the environment; these structures extend beyond finitary propositional representations. Mathematical reasoning is imaginative in the sense that it utilizes a number of powerful, illuminating devices that structure these concrete experiences and transform them into models for abstract thought. These "thinking tools"--analogy, metaphor, metonymy, and imagery--play an important role in mathematical reasoning, as the chapters in this book demonstrate, yet their potential for enhancing learning in the domain has received little recognition. This book is an attempt to fill this void. Drawing upon backgrounds in mathematics education, educational psychology, philosophy, linguistics, and cognitive science, the chapter authors provide a rich and comprehensive analysis of mathematical reasoning. New and exciting perspectives are presented on the nature of mathematics (e.g., "mind-based mathematics"), on the array of powerful cognitive tools for reasoning (e.g., "analogy and metaphor"), and on the different ways these tools can facilitate mathematical reasoning. Examples are drawn from the reasoning of the preschool child to that of the adult learner.

Mindmatics

Author : Yair Neuman
Publisher : Springer Nature
ISBN 13 : 3031749553
Total Pages : 107 pages
Book Rating : 4.0/5 (317 download)

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Book Synopsis Mindmatics by : Yair Neuman

Download or read book Mindmatics written by Yair Neuman and published by Springer Nature. This book was released on with total page 107 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Toward a Visually-Oriented School Mathematics Curriculum

Author : Ferdinand Rivera
Publisher : Springer Science & Business Media
ISBN 13 : 9400700148
Total Pages : 319 pages
Book Rating : 4.4/5 (7 download)

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Book Synopsis Toward a Visually-Oriented School Mathematics Curriculum by : Ferdinand Rivera

Download or read book Toward a Visually-Oriented School Mathematics Curriculum written by Ferdinand Rivera and published by Springer Science & Business Media. This book was released on 2011-01-06 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: What does it mean to have a visual representation of a mathematical object, concept, or process? What visualization strategies support growth in mathematical thinking, reasoning, generalization, and knowledge? Is mathematical seeing culture-free? How can information drawn from studies in blind subjects help us understand the significance of a multimodal approach to learning mathematics? Toward a Visually-Oriented School Mathematics Curriculum explores a unified theory of visualization in school mathematical learning via the notion of progressive modeling. Based on the author’s longitudinal research investigations in elementary and middle school classrooms, the book provides a compelling empirical account of ways in which instruction can effectively orchestrate the transition from personally-constructed visuals, both externally-drawn and internally-derived, into more structured visual representations within the context of a socioculturally grounded mathematical activity. Both for teachers and researchers, a discussion of this topic is relevant in the history of the present. The ubiquity of technological tools and virtual spaces for learning and doing mathematics has aroused interest among concerned stakeholders about the role of mathematics in these contexts. The book begins with a prolegomenon on the author’s reflections on past and present visual studies in mathematics education. In the remaining seven chapters, visualization is pursued in terms of its role in bringing about progressions in mathematical symbolization, abduction, pattern generalization, and diagrammatization. Toward a Visually-Oriented School Mathematics Curriculum views issues surrounding visualization through the eyes of a classroom teacher-researcher; it draws on findings within and outside of mathematics education that help practitioners and scholars gain a better understanding of what it means to pleasurably experience the symmetric visual/symbolic reversal phenomenon – that is, seeing the visual in the symbolic and the symbolic in the visual."

Intercultural Pedagogical Reflections on Taiwan’s Education

Author : Jason C. Chan
Publisher : 政大出版社
ISBN 13 : 9869630456
Total Pages : 344 pages
Book Rating : 4.8/5 (696 download)

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Book Synopsis Intercultural Pedagogical Reflections on Taiwan’s Education by : Jason C. Chan

Download or read book Intercultural Pedagogical Reflections on Taiwan’s Education written by Jason C. Chan and published by 政大出版社. This book was released on 2018-12-01 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a product of intercultural dialogues between Rainer Kokemohr from Germany and educational scholars from Taiwan, during a period of more than 15 years. When professor Kokemohr served as a part-time chair professor at the College of Education, NCCU, he had the opportunity to observe different schools and to dialogue with many scholars. Section One of the book presents discussions on pedagogical norms and goals. Section Two brings together articles that discuss educational goals in relation to concrete social interactions or special, pedagogically significant phenomena and structures that determine teaching-learning processes within educational institutions. In Section Three, the authors discuss the challenge of modern education in view of historical or life-historical educational conditions.

Learning to Imagine

Author : Andrew Shtulman
Publisher : Harvard University Press
ISBN 13 : 0674294785
Total Pages : 353 pages
Book Rating : 4.6/5 (742 download)

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Book Synopsis Learning to Imagine by : Andrew Shtulman

Download or read book Learning to Imagine written by Andrew Shtulman and published by Harvard University Press. This book was released on 2023-11-14 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: An award-winning cognitive scientist offers a counterintuitive guide to cultivating imagination. Imagination is commonly thought to be the special province of youth—the natural companion of free play and the unrestrained vistas of childhood. Then come the deadening routines and stifling regimentation of the adult world, dulling our imaginative powers. In fact, Andrew Shtulman argues, the opposite is true. Imagination is not something we inherit at birth, nor does it diminish with age. Instead, imagination grows as we do, through education and reflection. The science of cognitive development shows that young children are wired to be imitators. When confronted with novel challenges, they struggle to think outside the box, and their creativity is rigidly constrained by what they deem probable, typical, or normal. Of course, children love to “play pretend,” but they are far more likely to simulate real life than to invent fantasy worlds of their own. And they generally prefer the mundane and the tried-and-true to the fanciful or the whimsical. Children’s imaginations are not yet fully formed because they necessarily lack knowledge, and it is precisely knowledge of what is real that provides a foundation for contemplating what might be possible. The more we know, the farther our imaginations can roam. As Learning to Imagine demonstrates, the key to expanding the imagination is not forgetting what you know but learning something new. By building upon the examples of creative minds across diverse fields, from mathematics to religion, we can consciously develop our capacities for innovation and imagination at any age.

Understanding Children's Mathematical Graphics: Beginnings in Play

Author : Elizabeth Carruthers
Publisher : McGraw-Hill Education (UK)
ISBN 13 : 0335240798
Total Pages : 234 pages
Book Rating : 4.3/5 (352 download)

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Book Synopsis Understanding Children's Mathematical Graphics: Beginnings in Play by : Elizabeth Carruthers

Download or read book Understanding Children's Mathematical Graphics: Beginnings in Play written by Elizabeth Carruthers and published by McGraw-Hill Education (UK). This book was released on 2011-04-16 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book challenges traditional beliefs and practices of teaching 'written' mathematics in early childhood. It gives theoretical underpinnings and offers exciting insights and context to children's early mathematical thinking and in particular into children's mathematical graphics, showing how this supports their understanding of the abstract symbolic language of mathematics. Drawing on a wide range of examples, it illustrates and explains how children explore and communicate their mathematical thinking through their mathematical graphics, and how this begins in play. The book looks at the power of children's own marks, symbols and other graphical representations to convey meanings, exploring how they support complex thinking. The authors explore the relationship between children's play and meaning making. Rather than viewing mathematics as a separate subject or as a set of basic 'skills' to be transmitted, they demonstrate that in supportive learning cultures children develop their own mathematical thinking to solve problems. Key features include: Numerous new examples and case studies of children from birth to 8 years,highlighting the complexity and richness of children's thinking Explanation of pedagogical issues - showing how they can support rich play and mathematics Draws on the authors' latest research This book is valuable reading for students, teachers, primary mathematics coordinators' and all early years' professionals working in the Early Years Foundation Stage and Key Stage One.