A Systemic Perspective on Cognition and Mathematics

A Systemic Perspective on Cognition and Mathematics
Author: Jeffrey Yi-Lin Forrest
Publisher: CRC Press
Total Pages: 434
Release: 2013-02-28
Genre: Computers
ISBN: 020348732X

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

A Systemic Perspective on Cognition and Mathematics

A Systemic Perspective on Cognition and Mathematics
Author: Jeffrey Yi-Lin Forrest
Publisher: CRC Press
Total Pages: 444
Release: 2013-02-28
Genre: Computers
ISBN: 1138000167

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.

The Nature and Development of Mathematics

The Nature and Development of Mathematics
Author: John Adams
Publisher: Routledge
Total Pages: 348
Release: 2017-04-21
Genre: Education
ISBN: 1317300181

From an infant’s first grasp of quantity to Einstein’s theory of relativity, the human experience of number has intrigued researchers for centuries. Numeracy and mathematics have played fundamental roles in the development of societies and civilisations, and yet there is an essential mystery to these concepts, evidenced by the fear many people still feel when confronted by apparently simple sums. Including perspectives from anthropology, education and psychology, The Nature and Development of Mathematics addresses three core questions: Is maths natural? What is the impact of our culture and environment on mathematical thinking? And how can we improve our mathematical ability? Examining the cognitive processes that we use, the origins of these skills and their cultural context, and how learning and teaching can be supported in the classroom, the book contextualises each issue within the wider field, arguing that only by taking a cross-disciplinary perspective can we fully understand what it means to be numerate, as well as how we become numerate in our modern world. This is a unique collection including contributions from a range of renowned international researchers. It will be of interest to students and researchers across cognitive psychology, cultural anthropology and educational research.

An Introduction to Mathematical Cognition

An Introduction to Mathematical Cognition
Author: Camilla Gilmore
Publisher: Routledge
Total Pages: 406
Release: 2018-06-13
Genre: Psychology
ISBN: 1317410106

The last decade has seen a rapid growth in our understanding of the cognitive systems that underlie mathematical learning and performance, and an increased recognition of the importance of this topic. This book showcases international research on the most important cognitive issues that affect mathematical performance across a wide age range, from early childhood to adulthood. The book considers the foundational competencies of nonsymbolic and symbolic number processing before discussing arithmetic, conceptual understanding, individual differences and dyscalculia, algebra, number systems, reasoning and higher-level mathematics such as formal proof. Drawing on diverse methodology from behavioural experiments to brain imaging, each chapter discusses key theories and empirical findings and introduces key tasks used by researchers. The final chapter discusses challenges facing the future development of the field of mathematical cognition and reviews a set of open questions that mathematical cognition researchers should address to move the field forward. This book is ideal for undergraduate or graduate students of psychology, education, cognitive sciences, cognitive neuroscience and other academic and clinical audiences including mathematics educators and educational psychologists.

Development of Mathematical Cognition

Development of Mathematical Cognition
Author: Daniel B. Berch
Publisher: Academic Press
Total Pages: 418
Release: 2015-10-03
Genre: Psychology
ISBN: 0128019093

Development of Mathematical Cognition: Neural Substrates and Genetic Influences reviews advances in extant imaging modalities and the application of brain stimulation techniques for improving mathematical learning. It goes on to explore the role genetics and environmental influences have in the development of math abilities and disabilities. Focusing on the neural substrates and genetic factors associated with both the typical and atypical development of mathematical thinking and learning, this second volume in the Mathematical Cognition and Learning series integrates the latest in innovative measures and methodological advances from the top researchers in the field. Provides details about new progress made in the study of neural correlates of numerical and arithmetic cognition Addresses recent work in quantitative and molecular genetics Works to improve instruction in numerical, arithmetical, and algebraic thinking and learning Informs policy to help increase the level of mathematical proficiency among the general public

Situated Cognition

Situated Cognition
Author: David Kirshner
Publisher: Taylor & Francis
Total Pages: 334
Release: 2021-12-16
Genre: Psychology
ISBN: 1000106047

This book is a result of a symposium at a recent annual meeting of the American Educational Research Association that explored foundational issues relative to situated cognition theory. Its chapters contribute to discourse about repositioning situated cognition theory within the broader supporting disciplines and to resolving the problematics addressed within the book. There is a cumulative vision to the book -- its theme is that the notion of the individual in situated cognition theory needs to be fundamentally reformulated. No theoretical reconfiguration of the social world or of social practices can overcome an individual cast in the dualist tradition. This reformulation probes the physiological, psychoanalytic, and semiotic constitution of persons. Chapters authors cover a wide range of topics including: * transfer of training -- arguing that traditional cognitive psychology has found precious little evidence of people's ability to apply knowledge gained in one context to the problems encountered in another; * ecosocial systems -- a new object of inquiry for situated cognition theory in which the primary units of analysis are not things or people, but processes and practices; * how linkages between discursive practices are manifested as semiotic chaining of signifiers for individuals engaged in everyday activities at home or at school; * how the ability to function in ways that are consistent with logic emerges not through reflective abstraction on actions, but through an enhanced sense of agency as more responsible roles are adopted in daily life practices; * the mutual constitution of social and individual knowledge -- familiar terms and concepts normally available through linguistic labels are cultural models, to be distinguished from the variegated and hidden mid-level meanings that reflect their situated uses in social activity; * the material (neurological) substrate through which cultural models and mid-level meanings emerge; and * how learning environments can be structured to take advantage of the perceptual underpinnings of cognition.

Affect and Mathematical Problem Solving

Affect and Mathematical Problem Solving
Author: Douglas B. McLeod
Publisher: Springer Science & Business Media
Total Pages: 246
Release: 2012-12-06
Genre: Mathematics
ISBN: 1461236142

Research on cognitive aspects of mathematical problem solving has made great progress in recent years, but the relationship of affective factors to problem-solving performance has been a neglected research area. The purpose of Affect and Mathematical Problem Solving: A New Perspective is to show how the theories and methods of cognitive science can be extended to include the role of affect in mathematical problem solving. The book presents Mandler's theory of emotion and explores its implications for the learning and teaching of mathematical problem solving. Also, leading researchers from mathematics, education, and psychology report how they have integrated affect into their own cognitive research. The studies focus on metacognitive processes, aesthetic influences on expert problem solvers, teacher decision-making, technology and teaching problem solving, and beliefs about mathematics. The results suggest how emotional factors like anxiety, frustration, joy, and satisfaction can help or hinder performance in problem solving.

Semantic Cognition

Semantic Cognition
Author: Timothy T. Rogers
Publisher: MIT Press
Total Pages: 446
Release: 2004
Genre: Computers
ISBN: 9780262182393

A mechanistic theory of the representation and use of semantic knowledge that uses distributed connectionist networks as a starting point for a psychological theory of semantic cognition.

Understanding Emotions in Mathematical Thinking and Learning

Understanding Emotions in Mathematical Thinking and Learning
Author: Ulises Xolocotzin
Publisher: Academic Press
Total Pages: 476
Release: 2017-05-12
Genre: Psychology
ISBN: 0128024895

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