Piaget’s Genetic Epistemology for Mathematics Education Research
Piaget’s Genetic Epistemology for Mathematics Education Research

Author: Paul Christian Dawkins

Publisher: Springer Nature

Published: 2024-01-22

Total Pages: 620

ISBN-13: 3031473868

DOWNLOAD EBOOK

The book provides an entry point for graduate students and other scholars interested in using the constructs of Piaget’s genetic epistemology in mathematics education research. Constructs comprising genetic epistemology form the basis for some of the most well-developed theoretical frameworks available for characterizing learning, particularly in mathematics. The depth and complexity of Piaget’s work can make it challenging to find adequate entry points for learners, not least because it requires a reorientation regarding the nature of mathematical knowledge itself. This volume gathers leading scholars to help address that challenge. The main section of the book presents key Piagetian constructs for mathematics education research such as schemes and operations, figurative and operative thought, images and meanings, and decentering. The chapters that discuss these constructs include examples from research and address how these constructs can be used in research. There are two chapters on various types of reflective abstraction, because this construct is Piaget’s primary tool for characterizing the advancement of knowledge. The later sections of the book contain commentaries reflecting on the contributions of the body of theory developed in the first section. They connect genetic epistemology to current research domains such as equity and the latest in educational psychology. Finally, the book closes with short chapters portraying how scholars are using these tools in specific arenas of mathematics education research, including in special education, early childhood education, and statistics education.

Mathematical Epistemology and Psychology
Mathematical Epistemology and Psychology

Author: E.W. Beth

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 391

ISBN-13: 9401721939

DOWNLOAD EBOOK

One of the controversial philosophical issues of recent years has been the question of the nature of logical and mathematical entities. Platonist or linguistic modes of explanation have become fashionable, whilst abstrac tionist and constructionist theories have ceased to be so. Beth and Piaget approach this problem in their book from two somewhat different points of view. Beth's approach is largely historico-critical, although he discusses the nature of heuristic thinking in mathematics, whilst that of Piaget is psycho-genetic. The major purpose of this introduction is to summarise some of the main points of their respective arguments. In the first part of this book Beth makes a detailed study of the history of philosophical thinking about mathematics, and draws our attention to the important role played by the Aristotelian methodology of the demon strative sciences. This, he tells us, is characterised by three postulates: (a) deductivity, (b) self-evidence, and (c) reality. The last postulate asserts that the primitive notions of a demonstrative science must have reference to a domain of real entities in order to have significance. On the Aristote lian view discursive reasoning plays a major role in mathematics, whilst pure intuition plays a somewhat subordinate one.

Piaget's Theory
Piaget's Theory

Author: Harry Beilin

Publisher: Psychology Press

Published: 2013-04-15

Total Pages: 357

ISBN-13: 1134994214

DOWNLOAD EBOOK

This volume marks the 20th Anniversary Symposium of the Jean Piaget Society. Some of the American contributors were among the first to introduce Piaget to developmental and educational psychology in the United States, while some of the international contributors worked with Piaget to develop his program of genetic epistemology and continue to make significant contributions to it. Within this volume the possibility of Piaget's paradigm is reviewed not only as the stuff of normal science, yielding fascinating empirical questions that linger within it, but also, and more importantly, as the stuff of revolutionary science, with continuing potential to comprehensively structure our thinking about developmental theory. The constructive contribution Piaget's theory has for developmental theory emerges as four central themes in the volume: understanding the intentional or semantic aspect of mental life without abandoning the Piagetian assumption that is rational and committed to truth testing; examining mental life and its development as a dialectical relation of function and structure--a relation Piaget introduced in his study of the developmental relation between procedural and operational knowledge; exploring new and interdisciplinary perspectives on equilibration as the driving force of constructive adaptive processes; understanding social and historical forces in individual and cultural development--not necessarily as forces antithetical to Piaget's perspective but as forces that take on new meaning within his framework which avoids erroneous dichotomies such as the distinction between subjective and objective knowledge.

Conceptual Development
Conceptual Development

Author: Ellin Kofsky Scholnick

Publisher: Psychology Press

Published: 1999-04-01

Total Pages: 387

ISBN-13: 1135686920

DOWNLOAD EBOOK

This book examines a key issue in current cognitive theories - the nature of representation. Each chapter is characterized by attempts to frame hot topics in cognitive development within the landscape of current developmental theorizing and the past legacy of genetic epistemology. The chapters address four questions that are fundamental to any developmental line of inquiry: How should we represent the workings and contents of the mind? How does the child construct mental models during the course of development? What are the origins of these models? and What accounts for the novelties that are the products and producers of developmental change? These questions are situated in a historical context, Piagetian theory, and contemporary researchers attempt to trace how they draw upon, depart from, and transform the Piagetian legacy to revisit classic issues such as the child's awareness of the workings of mental life, the child's ability to represent the world, and the child's growing ability to process and learn from experience. The theoretical perspectives covered include constructivism, connectionism, theory-theory, information processing, dynamical systems, and social constructivist approaches. The research areas span imitation, mathematical reasoning, biological knowledge, language development, and theory of mind. Written by major contributors to the field, this work will be of interest to students and researchers wanting a brief but in-depth overview of the contemporary field of cognitive development.

Piaget’s Genetic Epistemology for Mathematics Education Research
Piaget’s Genetic Epistemology for Mathematics Education Research

Author: Paul Christian Dawkins

Publisher: Springer

Published: 2024-01-17

Total Pages: 0

ISBN-13: 9783031473852

DOWNLOAD EBOOK

The book provides an entry point for graduate students and other scholars interested in using the constructs of Piaget’s genetic epistemology in mathematics education research. Constructs comprising genetic epistemology form the basis for some of the most well-developed theoretical frameworks available for characterizing learning, particularly in mathematics. The depth and complexity of Piaget’s work can make it challenging to find adequate entry points for learners, not least because it requires a reorientation regarding the nature of mathematical knowledge itself. This volume gathers leading scholars to help address that challenge. The main section of the book presents key Piagetian constructs for mathematics education research such as schemes and operations, figurative and operative thought, images and meanings, and decentering. The chapters that discuss these constructs include examples from research and address how these constructs can be used in research. There are two chapters on various types of reflective abstraction, because this construct is Piaget’s primary tool for characterizing the advancement of knowledge. The later sections of the book contain commentaries reflecting on the contributions of the body of theory developed in the first section. They connect genetic epistemology to current research domains such as equity and the latest in educational psychology. Finally, the book closes with short chapters portraying how scholars are using these tools in specific arenas of mathematics education research, including in special education, early childhood education, and statistics education.

Mathematics for Tomorrow’s Young Children
Mathematics for Tomorrow’s Young Children

Author: C.S. Mansfield

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 335

ISBN-13: 9401722110

DOWNLOAD EBOOK

Social constructivism is just one view of learning that places emphasis on the social aspects of learning. Other theoretical positions, such as activity theory, also emphasise the importance of social interactions. Along with social constructivism, Vygotsky's writings on children's learning have recently also undergone close scru tiny and researchers are attempting a synthesis of aspects ofVygotskian theory and social constructivism. This re-examination of Vygotsky's work is taking place in many other subject fields besides mathematics, such as language learning by young children. It is interesting to speculate why Vygotsky's writings have appealed to so many researchers in different cultures and decades later than his own times. Given the recent increased emphasis on the social nature of learning and on the interactions between student, teacher and context factors, a finer grained analysis of the nature of different theories of learning now seems to be critical, and it was considered that different views of students' learning of mathematics needed to be acknowledged in the discussions of the Working Group.

Personal Epistemology
Personal Epistemology

Author: Barbara K. Hofer

Publisher: Routledge

Published: 2012-08-21

Total Pages: 429

ISBN-13: 113660863X

DOWNLOAD EBOOK

This is the first book to provide a comprehensive overview of the theoretical and methodological approaches to the study of personal epistemology from a psychological and educational perspective. Both theory building and empirical research have grown dramatically in the past decade but, until now, this work has not been pulled together in a single volume. That is the mission of this volume whose state-of-the-art theory and research are likely to define the field for the next 20 years. Key features of this important new book include: *Pioneering Contributors--The book provides current perspectives of each of the major theoreticians and researchers who pioneered this growing field, as well as contributions from new researchers. *Diverse Perspectives--The contributors represent a variety of perspectives, including education, educational psychology, developmental psychology, higher education, and science and mathematics education. *Editorial Integration--Opening and closing chapters by the editors set out key issues confronting the field.

Parallel Paths to Constructivism
Parallel Paths to Constructivism

Author: Susan Pass

Publisher: IAP

Published: 2004-11-01

Total Pages: 161

ISBN-13: 1607529289

DOWNLOAD EBOOK

No two people were more responsible for the current way lessons are taught worldwide than Jean Piaget and Lev Vygotsky. Both men had an important impact worldwide on how a person should be taught--starting in the last century and continuing today. Jean Piaget's Genetic Epistemology concentrated on the individual in learning. Lev Vygotsky's Cultural–Historical Theory concentrated on the social in learning. All over the world, teachers today use each man's ideas. Some use them at different times in their classrooms and others have learned to use them combined into the same lesson--bringing us to the crux of this book; namely, there are many lessons to learn by discovering the dynamics in the lives of both men. While both were from very different countries, there are many similarities in their lives. While most professors teaching introductory educational psychology courses focus on the difference in their lesson strategies, there are some remarkable similarities between their respective pedagogies. While differences in their families and countries were obviously significant, the two men differed surprisingly little in their pedagogical views and their basic ideas. Their similarities in views and ideas are due to the similarities in their lives. Chapter 1 looks at those similarities by looking at influences in their childhood. Chapter 2 observes their adolescence. Chapter 3 concentrates on young adulthood. Chapter 4 covers their postgraduate work. Chapter 5 traces the origins of their major ideas. For Jean Piaget, we look at the origin of chronological stages of development, the role of language, the role of the teacher, optimal mismatch, equilibration, error, and play. For Lev Vygotsky, we look at the origin of zone of proximal development, internalization, stage of development, "the social other," role of language, error, sociohistorical context of learning, scaffolding and play. Chapter 6 deals with how Jean Piaget and Lev Vygotsky were able to overcome adversity and the lessons that can be learned by such overcoming. Chapter 7 provides a new pedagogy based on the communications that Jean Piaget and Lev Vygotsky had with each other, noting the influence such communications had on their mutual ideas.