A Systemic Perspective on Cognition and Mathematics
A Systemic Perspective on Cognition and Mathematics

Author: Jeffrey Yi-Lin Forrest

Publisher: CRC Press

Published: 2013-02-28

Total Pages: 444

ISBN-13: 1138000167

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This book is devoted to the study of human thought, its systemic structure, and the historical development of mathematics both as a product of thought and as a fascinating case analysis. After demonstrating that systems research constitutes the second dimension of modern science, the monograph discusses the yoyo model, a recent ground-breaking development of systems research, which has brought forward revolutionary applications of systems research in various areas of the traditional disciplines, the first dimension of science. After the systemic structure of thought is factually revealed, mathematics, as a product of thought, is analyzed by using the age-old concepts of actual and potential infinities. In an attempt to rebuild the system of mathematics, this volume first provides a new look at some of the most important paradoxes, which have played a crucial role in the development of mathematics, in proving what these paradoxes really entail. Attention is then turned to constructing the logical foundation of two different systems of mathematics, one assuming that actual infinity is different than potential infinity, and the other that these infinities are the same. This volume will be of interest to academic researchers, students and professionals in the areas of systems science, mathematics, philosophy of mathematics, and philosophy of science.

A Systemic Perspective on Cognition and Mathematics
A Systemic Perspective on Cognition and Mathematics

Author: Jeffrey Yi-Lin Forrest

Publisher: CRC Press

Published: 2013-02-28

Total Pages: 434

ISBN-13: 020348732X

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This book is devoted to the study of human thought, its systemic structure, and the historical development of mathematics both as a product of thought and as a fascinating case analysis. After demonstrating that systems research constitutes the second dimension of modern science, the monograph discusses the yoyo model, a recent ground-breaking deve

General Systems Theory
General Systems Theory

Author: Jeffrey Yi-Lin Forrest

Publisher: Springer

Published: 2018-12-19

Total Pages: 378

ISBN-13: 3030045587

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This book demonstrates the theoretical value and practical significance of systems science and its logic of thinking by presenting a rigorously developed foundation—a tool for intuitive reasoning, which is supported by both theory and empirical evidence, as well as practical applications in business decision making. Following a foundation of general systems theory, the book presents an applied method to intuitively learn system-sciences fundamentals. The third and final part examines applications of the yoyo model and the theoretical results developed earlier within the context of problems facing business decision makers by organically combining methods of traditional science, the first dimension of science, with those of systems science, the second dimension, as argued by George Klir in the 1990s. This text would benefit graduate students, researchers, or practitioners in the areas of mathematics, systems science or engineering, economics, and business decision science.

Understanding Emotions in Mathematical Thinking and Learning
Understanding Emotions in Mathematical Thinking and Learning

Author: Ulises Xolocotzin

Publisher: Academic Press

Published: 2017-05-12

Total Pages: 476

ISBN-13: 0128024895

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Emotions play a critical role in mathematical cognition and learning. Understanding Emotions in Mathematical Thinking and Learning offers a multidisciplinary approach to the role of emotions in numerical cognition, mathematics education, learning sciences, and affective sciences. It addresses ways in which emotions relate to cognitive processes involved in learning and doing mathematics, including processing of numerical and physical magnitudes (e.g. time and space), performance in arithmetic and algebra, problem solving and reasoning attitudes, learning technologies, and mathematics achievement. Additionally, it covers social and affective issues such as identity and attitudes toward mathematics. - Covers methodologies in studying emotion in mathematical knowledge - Reflects the diverse and innovative nature of the methodological approaches and theoretical frameworks proposed by current investigations of emotions and mathematical cognition - Includes perspectives from cognitive experimental psychology, neuroscience, and from sociocultural, semiotic, and discursive approaches - Explores the role of anxiety in mathematical learning - Synthesizes unifies the work of multiple sub-disciplines in one place

Mathematics Learning in Early Childhood
Mathematics Learning in Early Childhood

Author: National Research Council

Publisher: National Academies Press

Published: 2009-11-13

Total Pages: 399

ISBN-13: 0309147433

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Early childhood mathematics is vitally important for young children's present and future educational success. Research demonstrates that virtually all young children have the capability to learn and become competent in mathematics. Furthermore, young children enjoy their early informal experiences with mathematics. Unfortunately, many children's potential in mathematics is not fully realized, especially those children who are economically disadvantaged. This is due, in part, to a lack of opportunities to learn mathematics in early childhood settings or through everyday experiences in the home and in their communities. Improvements in early childhood mathematics education can provide young children with the foundation for school success. Relying on a comprehensive review of the research, Mathematics Learning in Early Childhood lays out the critical areas that should be the focus of young children's early mathematics education, explores the extent to which they are currently being incorporated in early childhood settings, and identifies the changes needed to improve the quality of mathematics experiences for young children. This book serves as a call to action to improve the state of early childhood mathematics. It will be especially useful for policy makers and practitioners-those who work directly with children and their families in shaping the policies that affect the education of young children.

Cognition in Practice
Cognition in Practice

Author: Jean Lave

Publisher: Cambridge University Press

Published: 1988-07-29

Total Pages: 236

ISBN-13: 9780521357340

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Most previous research on human cognition has focused on problem-solving, and has confined its investigations to the laboratory. As a result, it has been difficult to account for complex mental processes and their place in culture and history. In this startling - indeed, disco in forting - study, Jean Lave moves the analysis of one particular form of cognitive activity, - arithmetic problem-solving - out of the laboratory into the domain of everyday life. In so doing, she shows how mathematics in the 'real world', like all thinking, is shaped by the dynamic encounter between the culturally endowed mind and its total context, a subtle interaction that shapes 1) Both tile human subject and the world within which it acts. The study is focused on mundane daily, activities, such as grocery shopping for 'best buys' in the supermarket, dieting, and so on. Innovative in its method, fascinating in its findings, the research is above all significant in its theoretical contributions. Have offers a cogent critique of conventional cognitive theory, turning for an alternative to recent social theory, and weaving a compelling synthesis from elements of culture theory, theories of practice, and Marxist discourse. The result is a new way of understanding human thought processes, a vision of cognition as the dialectic between persons-acting, and the settings in which their activity is constituted. The book will appeal to anthropologists, for its novel theory of the relation of cognition to culture and context; to cognitive scientists and educational theorists; and to the 'plain folks' who form its subject, and who will recognize themselves in it, a rare accomplishment in the modern social sciences.

Handbook of Cognitive Mathematics
Handbook of Cognitive Mathematics

Author: Marcel Danesi

Publisher: Springer Nature

Published: 2022-10-31

Total Pages: 1392

ISBN-13: 3031039459

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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.

Mathematical and Statistics Anxiety: Educational, Social, Developmental and Cognitive Perspectives
Mathematical and Statistics Anxiety: Educational, Social, Developmental and Cognitive Perspectives

Author: Kinga Morsanyi

Publisher: Frontiers Media SA

Published: 2017-01-19

Total Pages: 196

ISBN-13: 2889450767

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Mathematical anxiety is a feeling of tension, apprehension or fear which arises when a person is faced with mathematical content. The negative consequences of mathematical anxiety are well-documented. Students with high levels of mathematical anxiety might underperform in important test situations, they tend to hold negative attitudes towards mathematics, and they are likely to opt out of elective mathematics courses, which also affects their career opportunities. Although at the university level many students do not continue to study mathematics, social science students are confronted with the fact that their disciplines involve learning about statistics - another potential source of anxiety for students who are uncomfortable with dealing with numerical content. Research on mathematical anxiety is a truly interdisciplinary field with contributions from educational, developmental, cognitive, social and neuroscience researchers. The current collection of papers demonstrates the diversity of the field, offering both new empirical contributions and reviews of existing studies. The contributors also outline future directions for this line of research.

Collected Papers. Volume XIV
Collected Papers. Volume XIV

Author: Florentin Smarandache

Publisher: Infinite Study

Published: 2022-11-01

Total Pages: 970

ISBN-13:

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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.

Learning Mathematics
Learning Mathematics

Author: Prof Leone Burton

Publisher: Routledge

Published: 2012-10-12

Total Pages: 281

ISBN-13: 1135698473

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Learning Mathematics brings together a collection of interrelated and forward-looking chapters by internationally recognized experts that explores changes in the theories and practices of learning (and teaching) mathematics. The authors reject a traditional, transmission view of the teaching of mathematics which has proved so ineffective for learning. In its place they offer information gathered from research and from practice about effects on the learners seeking to create and negotiate meaning. Learners are presented as actively attempting to make sense of the mathematics they encounter, and learners, teachers and researchers are offered examples of ho such sense-making activities, incorporated into mathematics classrooms, impact on coming to know. The book celebrates both diversity, in the range of different perspectives, contributions and topics, and unity, in the linking chapters and themes, It will be fascinating reading for those mathematics educators who are eager to engage with a socio-cultural perspective in order to better understand the complexity of learning mathematics.