Mathematical Essays On Embodied Cognition
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Mathematical Essays On Embodied Cognition
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Author : Rodrick Wallace
language : en
Publisher: Springer Nature
Release Date : 2025-05-13
Mathematical Essays On Embodied Cognition written by Rodrick Wallace and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-13 with Technology & Engineering categories.
This book provides a unique formal foundation for the development of statistical tools useful in the exploration of observational and experimental data related to embodied cognition. The asymptotic limit theorems of information and control theories can be used to construct statistical tools analogous to -- but different from -- regression models for the study of the often highly punctuated cognitive phenomena embedded in and hence influenced by a surrounding ecosystem of which the phenomena are themselves part. The book builds probability models based on those theorems that incorporate embodiment at a number of scales and levels of organization, ranging from the effects of stress on the immune system within a higher organism, through institutional (and machine) cognition under challenge from adversaries, to the failure of public health institutions under pathogen challenge. In distinct contrast to the existing literature, many detailed, worked-out examples provide templates for sophisticated readers to build their own model/tool constructs.
The Body In Mathematics
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Author :
language : en
Publisher: BRILL
Release Date : 2024-12-30
The Body In Mathematics 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 2024-12-30 with Education categories.
An embodied perspective on mathematical thinking, teaching and learning has grown from early theoretical and empirical work in the 90’s to a diverse and productive collection of approaches today. The aim of this book is to survey the landscape of these approaches and to provide empirical examples of research and an in-depth analysis of the most influential perspectives on embodiment and mathematics. More particularly, the book clarifies differences and points of contact among several theoretical and methodological frameworks that all take embodiment as a core construct in understanding mathematical thinking, and illustrates in a concrete way the affordances of each of these frameworks. Contributors are: Dor Abrahamson, Martha W. Alibali, Corey Brady, James A. Dixon, Laurie Edwards, Virginia J. Flood, Susan Gerofsky, Christina Krause, Ricardo Nemirovsky, Matthew Petersen, Luis Radford, Wolff-Michael Roth, Anna Shvarts, and Ashwin Vaidya.
18 Unconventional Essays On The Nature Of Mathematics
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Author : Reuben Hersh
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-01-16
18 Unconventional Essays On The Nature Of Mathematics written by Reuben Hersh and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-16 with Mathematics categories.
Collection of the most interesting recent writings on the philosophy of mathematics written by highly respected researchers from philosophy, mathematics, physics, and chemistry Interdisciplinary book that will be useful in several fields—with a cross-disciplinary subject area, and contributions from researchers of various disciplines
Interdisciplinary Perspectives On Math Cognition
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Author : Marcel Danesi
language : en
Publisher: Springer Nature
Release Date : 2019-09-14
Interdisciplinary Perspectives On Math Cognition written by Marcel Danesi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-14 with Mathematics categories.
This is an anthology of contemporary studies from various disciplinary perspectives written by some of the world's most renowned experts in each of the areas of mathematics, neuroscience, psychology, linguistics, semiotics, education, and more. Its purpose is not to add merely to the accumulation of studies, but to show that math cognition is best approached from various disciplinary angles, with the goal of broadening the general understanding of mathematical cognition through the different theoretical threads that can be woven into an overall understanding. This volume will be of interest to mathematicians, cognitive scientists, educators of mathematics, philosophers of mathematics, semioticians, psychologists, linguists, anthropologists, and all other kinds of scholars who are interested in the nature, origin, and development of mathematical cognition.
Emerging Perspectives On Gesture And Embodiment In Mathematics
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Author : Laurie D. Edwards
language : en
Publisher: IAP
Release Date : 2014-07-01
Emerging Perspectives On Gesture And Embodiment In Mathematics written by Laurie D. Edwards and has been published by IAP this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-01 with Education categories.
The purpose of the book is to establish a common language for, and understanding of, embodiment as it applies to mathematical thinking, and to link mathematics education research to recent work in gesture studies, cognitive linguistics and the theory of embodied cognition. Just as in past decades, mathematics education experienced a "turn to the social" in which socio-cultural factors were explored, in recent years there has been a nascent "turn to the body." An increasing number of researchers and theorists in mathematics education have become interested in the fact that, although mathematics may be socially constructed, this construction is not arbitrary or unconstrained, but rather is rooted in, and shaped by, the body. All those who engage with mathematics, whether at an elementary or advanced level, share the same basic biological and cognitive capabilities, as well as certain common physical experiences that come with being humans living in a material world. In addition, the doing and communicating of mathematics is never a purely intellectual activity: it involves a wide range of bodily actions, from committing inscriptions to paper or whiteboard, to speaking, listening, gesturing and gazing. This volume will present recent research on gesture and mathematics, within a framework that addresses several levels of mathematical development. The chapters will begin with contributions that examine early mathematical and proto-mathematical knowledge, for example, the conservation of volume and counting. The role of gesture in teaching and learning arithmetic procedures will be addressed. Core concepts and tools from secondary level mathematics will be investigated, including algebra, functions and graphing. And finally, research into the embodied understanding of advanced topics in geometry and calculus will be presented. The overall goal for the volume is to acknowledge the multimodal nature of mathematical knowing, and to contribute to the creation of a model of the interactions and mutual influences of bodily motion, spatial thinking, gesture, speech and external inscriptions on mathematical thinking, communication and learning. The intended audience is researchers and theorists in mathematics education as well as graduate students in the field.
Handbook Of Cognitive Mathematics
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Author : Marcel Danesi
language : en
Publisher: Springer Nature
Release Date : 2022-10-31
Handbook Of Cognitive Mathematics written by Marcel Danesi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-31 with Mathematics categories.
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.
Image Schema Theory And Mathematical Cognition
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Author : Marcel Danesi
language : en
Publisher: Springer Nature
Release Date : 2025-04-10
Image Schema Theory And Mathematical Cognition written by Marcel Danesi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-04-10 with Mathematics categories.
This book uses blending theory in math cognition, and assesses the main aspect of this theory, called image schema theory. Applied work in math pedagogy has used this theory, but no work has assessed its validity. This book provides an overall assessment of the theory with regard to its validity in the study of math cognition. Overall, this book presents image schema theory as it has evolved today to mathematicians, cognitive scientists, and math educators, deriving from it any concrete implications for modeling math in computer science and, on the other side, for making math pedagogy more effective.
Mathematical Representation At The Interface Of Body And Culture
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Author : Wolff-Michael Roth
language : en
Publisher: IAP
Release Date : 2009-06-01
Mathematical Representation At The Interface Of Body And Culture written by Wolff-Michael Roth 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 Education categories.
Over the past two decades, the theoretical interests of mathematics educators have changed substantially—as any brief look at the titles and abstracts of articles shows. Largely through the work of Paul Cobb and his various collaborators, mathematics educators came to be attuned to the intricate relationship between individual and the social configuration of which she or he is part. That is, this body of work, running alongside more traditional constructivist and psychological approaches, showed that what happens at the collective level in a classroom both constrains and affords opportunities for what individuals do (their practices). Increasingly, researchers focused on the mediational role of sociomathematical norms and how these emerged from the enacted lessons. A second major shift in mathematical theorizing occurred during the past decade: there is an increasing focus on the embodied and bodily manifestation of mathematical knowing (e.g., Lakoff & Núñez, 2000). Mathematics educators now working from this perspective have come to their position from quite different bodies of literatures: for some, linguistic concerns and mathematics as material praxis lay at the origin for their concerns; others came to their position through the literature on the situated nature of cognition; and yet another line of thinking emerged from the work on embodiment that Humberto Maturana and Francisco Varela advanced. Whatever the historical origins of their thinking, mathematics educators taking an embodiment perspective presuppose that it is of little use to think of mathematical knowing in terms of transcendental concepts somehow recorded in the brain, but rather, that we need to conceptual knowing as mediated by the human body, which, because of its senses, is at the origin of sense. One of the question seldom asked is how the two perspectives, one that focuses on the bodily, embodied nature of mathematical cognition and the other that focuses on its social nature, can be thought together. This edited volume situates itself at the intersection of theoretical and focal concerns of both of these lines of work. In all chapters, the current culture both at the classroom and at the societal level comes to be expressed and provides opportunities for expressing oneself in particular ways; and these expressions always are bodily expressions of body-minds. As a collective, the chapters focus on mathematical knowledge as an aspect or attribute of mathematical performance; that is, mathematical knowing is in the doing rather than attributable to some mental substrate structured in particular ways as conceived by conceptual change theorists or traditional cognitive psychologists. The collection as a whole shows readers important aspects of mathematical cognition that are produced and observable at the interface between the body (both human and those of [inherently material] inscriptions) and culture. Drawing on cultural-historical activity theory, the editor develops an integrative perspective that serves as a background to a narrative that runs through and pulls together the book into an integrated whole.
Visualisation And Epistemological Access To Mathematics Education In Southern Africa
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Author : Marc Schäfer
language : en
Publisher: Taylor & Francis
Release Date : 2023-04-27
Visualisation And Epistemological Access To Mathematics Education In Southern Africa written by Marc Schäfer and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-27 with Education categories.
This book demonstrates that using visualisation processes in mathematics education can help to enhance teaching and learning and bridge the inequality gap that exists between well-resourced and under-resourced schools in Southern Africa. Drawing on classroom research conducted in the Southern African region, it examines how epistemological access in a context of gross inequality can be constructively addressed by providing research-based solutions and recommendations. The book outlines the visualisation process as an integral but often overlooked process of mathematics teaching and learning. It goes beyond the traditional understanding of visualisation processes such as picture forming and using tools and considers visualisation processes that are semiotic in nature and includes actions such as gestures in combination with language. It adds value to the visualisation in mathematics education research discourse and deliberation in Africa. With a unique focus on Southern Africa and open avenues for further research and collaboration in the region, it will be a highly relevant reading for researchers, academics and post-graduate students of mathematics education, comparative education and social justice education.
Collected Papers Volume Xiv
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Author : Florentin Smarandache
language : en
Publisher: Infinite Study
Release Date : 2022-11-01
Collected Papers Volume Xiv written by Florentin Smarandache and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-01 with Mathematics categories.
This fourteenth volume of Collected Papers is an eclectic tome of 87 papers in Neutrosophics and other fields, such as mathematics, fuzzy sets, intuitionistic fuzzy sets, picture fuzzy sets, information fusion, robotics, statistics, or extenics, comprising 936 pages, published between 2008-2022 in different scientific journals or currently in press, by the author alone or in collaboration with the following 99 co-authors (alphabetically ordered) from 26 countries: Ahmed B. Al-Nafee, Adesina Abdul Akeem Agboola, Akbar Rezaei, Shariful Alam, Marina Alonso, Fran Andujar, Toshinori Asai, Assia Bakali, Azmat Hussain, Daniela Baran, Bijan Davvaz, Bilal Hadjadji, Carlos Díaz Bohorquez, Robert N. Boyd, M. Caldas, Cenap Özel, Pankaj Chauhan, Victor Christianto, Salvador Coll, Shyamal Dalapati, Irfan Deli, Balasubramanian Elavarasan, Fahad Alsharari, Yonfei Feng, Daniela Gîfu, Rafael Rojas Gualdrón, Haipeng Wang, Hemant Kumar Gianey, Noel Batista Hernández, Abdel-Nasser Hussein, Ibrahim M. Hezam, Ilanthenral Kandasamy, W.B. Vasantha Kandasamy, Muthusamy Karthika, Nour Eldeen M. Khalifa, Madad Khan, Kifayat Ullah, Valeri Kroumov, Tapan Kumar Roy, Deepesh Kunwar, Le Thi Nhung, Pedro López, Mai Mohamed, Manh Van Vu, Miguel A. Quiroz-Martínez, Marcel Migdalovici, Kritika Mishra, Mohamed Abdel-Basset, Mohamed Talea, Mohammad Hamidi, Mohammed Alshumrani, Mohamed Loey, Muhammad Akram, Muhammad Shabir, Mumtaz Ali, Nassim Abbas, Munazza Naz, Ngan Thi Roan, Nguyen Xuan Thao, Rishwanth Mani Parimala, Ion Pătrașcu, Surapati Pramanik, Quek Shio Gai, Qiang Guo, Rajab Ali Borzooei, Nimitha Rajesh, Jesús Estupiñan Ricardo, Juan Miguel Martínez Rubio, Saeed Mirvakili, Arsham Borumand Saeid, Saeid Jafari, Said Broumi, Ahmed A. Salama, Nirmala Sawan, Gheorghe Săvoiu, Ganeshsree Selvachandran, Seok-Zun Song, Shahzaib Ashraf, Jayant Singh, Rajesh Singh, Son Hoang Le, Tahir Mahmood, Kenta Takaya, Mirela Teodorescu, Ramalingam Udhayakumar, Maikel Y. Leyva Vázquez, V. Venkateswara Rao, Luige Vlădăreanu, Victor Vlădăreanu, Gabriela Vlădeanu, Michael Voskoglou, Yaser Saber, Yong Deng, You He, Youcef Chibani, Young Bae Jun, Wadei F. Al-Omeri, Hongbo Wang, Zayen Azzouz Omar.