Piaget S Genetic Epistemology For Mathematics Education Research

Author : Paul Christian Dawkins,Amy J. Hackenberg,Anderson Norton
Publisher : Springer
Page : 0 pages
File Size : 46,7 Mb
Release : 2024-01-17
Category : Education
ISBN : 303147385X

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Piaget’s Genetic Epistemology for Mathematics Education Research by Paul Christian Dawkins,Amy J. Hackenberg,Anderson Norton Pdf

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.

Author : Paul Christian Dawkins,Amy J. Hackenberg,Anderson Norton
Publisher : Springer Nature
Page : 620 pages
File Size : 51,6 Mb
Release : 2024-01-22
Category : Education
ISBN : 9783031473869

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Piaget’s Genetic Epistemology for Mathematics Education Research by Paul Christian Dawkins,Amy J. Hackenberg,Anderson Norton Pdf

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.

Author : Richard W. Copeland
Publisher : Macmillan College
Page : 472 pages
File Size : 40,5 Mb
Release : 1984
Category : Education
ISBN : STANFORD:36105032803764

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How Children Learn Mathematics by Richard W. Copeland Pdf

This text has two major purposes. One is diagnostic-to aid in discerning a child's stage of development as a basic for determining the type of mathematics for which he is ready. The second major purpose is to serve the "methods of teaching mathematics" courses in teacher education.l The reader will find this book very different from other methods texts because it is based on how children learn, not how to teach, and it should enable readers to see mathematics from the standpoint of the child as he progresses through the various stages of development.

Author : E.W. Beth,J. Piaget
Publisher : Springer Science & Business Media
Page : 326 pages
File Size : 40,9 Mb
Release : 2013-03-09
Category : Language Arts & Disciplines
ISBN : 9789401721936

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Mathematical Epistemology and Psychology by E.W. Beth,J. Piaget Pdf

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.

Author : Leslie P. Steffe
Publisher : Springer Science & Business Media
Page : 312 pages
File Size : 53,8 Mb
Release : 2012-12-06
Category : Psychology
ISBN : 9781461231783

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Epistemological Foundations of Mathematical Experience by Leslie P. Steffe Pdf

On the 26th, 27th, and 28th of February of 1988, a conference was held on the epistemological foundations of mathematical experience as part of the activities of NSF Grant No. MDR-8550463, Child Generated Multiplying and Dividing Algorithms: A Teaching Experiment. I had just completed work on the book Construction of Arithmetical Meanings and Strategies with Paul Cobb and Ernst von Glasersfeld and felt that substantial progress had been made in understanding the early numerical experiences of the six children who were the subjects of study in that book. While the book was in preparation, I was also engaged in the teaching experiment on mUltiplying and dividing algorithms. My focus in this teaching experiment was on investigating the mathematical experiences of the involved children and on developing a language through which those experiences might be expressed. However, prior to immersing myself in the conceptual analysis of the mathematical experiences of the children, I felt that it was crucial to critically evaluate the progress that we felt we had made in our earlier work. It was toward achieving this goal that I organized the conference. When trying to understand the mathematical experiences of a child, one can do no better than to interact with the child in a mathematical context guided by the intention to specify the child's current knowledge and the progress the child might make.

Author : Muriel Seltman
Publisher : Routledge
Page : 372 pages
File Size : 47,8 Mb
Release : 2013-01-11
Category : Psychology
ISBN : 9781135660994

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Piaget's Logic by Muriel Seltman Pdf

The literature relating to the work of Piaget is large and still growing. Some of it is Piagetian; some of it is critical. Most of this has been directed towards his experimental methodology and the conclusions drawn from it. The justification for the present contribution lies in what the authors believe to be the special embodiment in Piagetian thought of a central theme of our time. This theme is that the only possibility of truth lies in measurability and that knowledge is not recognisable unless it satisfies this criterion. This work is concentrated in the first instance on Piaget's claims that mental structures are exclusively logical mathematical in form, especially since this part of his work has received least attention. This book was first published in 1985.

Author : Jean Piaget
Publisher : Routledge
Page : 112 pages
File Size : 54,7 Mb
Release : 2013-07-04
Category : Medical
ISBN : 9781136221088

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Principles of Genetic Epistemology by Jean Piaget Pdf

First published in 1997. Routledge is an imprint of Taylor & Francis, an informa company.

Author : Angelika Bikner-Ahsbahs,Christine Knipping,Norma Presmeg
Publisher : Springer
Page : 592 pages
File Size : 41,5 Mb
Release : 2014-11-26
Category : Education
ISBN : 9789401791816

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Approaches to Qualitative Research in Mathematics Education by Angelika Bikner-Ahsbahs,Christine Knipping,Norma Presmeg Pdf

This volume documents a range of qualitative research approaches emerged within mathematics education over the last three decades, whilst at the same time revealing their underlying methodologies. Continuing the discussion as begun in the two 2003 ZDM issues dedicated to qualitative empirical methods, this book presents astate of the art overview on qualitative research in mathematics education and beyond. The structure of the book allows the reader to use it as an actual guide for the selection of an appropriate methodology, on a basis of both theoretical depth and practical implications. The methods and examples illustrate how different methodologies come to life when applied to a specific question in a specific context. Many of the methodologies described are also applicable outside mathematics education, but the examples provided are chosen so as to situate the approach in a mathematical context.

Author : Jürgen Maasz,Wolfgang Schlöglmann
Publisher : Sense Publishers
Page : 323 pages
File Size : 52,8 Mb
Release : 2006
Category : Mathematics
ISBN : 9789077874745

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New Mathematics Education Research and Practice by Jürgen Maasz,Wolfgang Schlöglmann Pdf

Mathematics education research has blossomed into many different areas which we can see in the programmes of the ICME conferences as well as in the various survey articles in the Handbooks. However, all of these lines of research are trying to grapple with a common problem, the complexity of the process of learning mathematics. Although our knowledge of the process is more extensive and deeper despite the fragmented nature of research in this area, there is still a need to overcome this fragmentation and to see learning as one process with different aspects. To overcome this fragmentation, this book identifies six themes: (1) mathematics, culture and society, (2) the structure of mathematics and its influence on the learning process, (3) mathematics learning as a cognitive process, (4) mathematics learning as a social process, (5) affective conditions of the mathematics learning process, (6) new technologies and mathematics learning. This book is addressed to all researchers in mathematic education. It gives an orientation and overview by addressing some carefully chosen questions on what is going on and what are the main results and questions what are important books or papers if further information is needed.

Author : E. Glasersfeld
Publisher : Springer Science & Business Media
Page : 264 pages
File Size : 43,9 Mb
Release : 2006-04-11
Category : Education
ISBN : 9780306472015

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Radical Constructivism in Mathematics Education by E. Glasersfeld Pdf

Mathematics is the science of acts without things - and through this, of things one can define by acts. 1 Paul Valéry The essays collected in this volume form a mosaik of theory, research, and practice directed at the task of spreading mathematical knowledge. They address questions raised by the recurrent observation that, all too frequently, the present ways and means of teaching mathematics generate in the student a lasting aversion against numbers, rather than an understanding of the useful and sometimes enchanting things one can do with them. Parents, teachers, and researchers in the field of education are well aware of this dismal situation, but their views about what causes the wide-spread failure and what steps should be taken to correct it have so far not come anywhere near a practicable consensus. The authors of the chapters in this book have all had extensive experience in teaching as well as in educational research. They approach the problems they have isolated from their own individual perspectives. Yet, they share both an overall goal and a specific fundamental conviction that characterized the efforts about which they write here. The common goal is to find a better way to teach mathematics. The common conviction is that knowledge cannot simply be transferred ready-made from parent to child or from teacher to student but has to be actively built up by each learner in his or her own mind.

Author : Myron Frederick Rosskopf,Leslie P. Steffe,Stanley Taback
Publisher : Unknown
Page : 266 pages
File Size : 46,8 Mb
Release : 1971
Category : Cognition in children
ISBN : UOM:39015002563651

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Piagetian Cognitive-development Research and Mathematical Education by Myron Frederick Rosskopf,Leslie P. Steffe,Stanley Taback Pdf

Author : Roza Leikin,Rina Zazkis
Publisher : Springer Science & Business Media
Page : 300 pages
File Size : 51,6 Mb
Release : 2010-04-10
Category : Science
ISBN : 9789048139903

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Learning Through Teaching Mathematics by Roza Leikin,Rina Zazkis Pdf

The idea of teachers Learning through Teaching (LTT) – when presented to a naïve bystander – appears as an oxymoron. Are we not supposed to learn before we teach? After all, under the usual circumstances, learning is the task for those who are being taught, not of those who teach. However, this book is about the learning of teachers, not the learning of students. It is an ancient wisdom that the best way to “truly learn” something is to teach it to others. Nevertheless, once a teacher has taught a particular topic or concept and, consequently, “truly learned” it, what is left for this teacher to learn? As evident in this book, the experience of teaching presents teachers with an exciting opp- tunity for learning throughout their entire career. This means acquiring a “better” understanding of what is being taught, and, moreover, learning a variety of new things. What these new things may be and how they are learned is addressed in the collection of chapters in this volume. LTT is acknowledged by multiple researchers and mathematics educators. In the rst chapter, Leikin and Zazkis review literature that recognizes this phenomenon and stress that only a small number of studies attend systematically to LTT p- cesses. The authors in this volume purposefully analyze the teaching of mathematics as a source for teachers’ own learning.

Author : Leslie Smith
Publisher : Routledge
Page : 568 pages
File Size : 44,6 Mb
Release : 2002-09-26
Category : Psychology
ISBN : 9781134786138

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Critical Readings on Piaget by Leslie Smith Pdf

First published in 1996. Routledge is an imprint of Taylor & Francis, an informa company.

Author : Anonim
Publisher : BRILL
Page : 371 pages
File Size : 55,7 Mb
Release : 2008-01-01
Category : Education
ISBN : 9789087905521

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The Handbook of Mathematics Teacher Education: Volume 4 by Anonim Pdf

The Handbook of Mathematics Teacher Education, the first of its kind, addresses the learning of mathematics teachers at all levels of schooling to teach mathematics, and the provision of activity and programmes in which this learning can take place. It consists of four volumes. Volume 4 of this handbook has the title The Mathematics Teacher Educator as a Developing Professional.

Author : Edward Silver,Christine Keitel-Kreidt
Publisher : Springer
Page : 185 pages
File Size : 41,8 Mb
Release : 2014-11-26
Category : Education
ISBN : 9783319119526

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Pursuing Excellence in Mathematics Education by Edward Silver,Christine Keitel-Kreidt Pdf

​Chapters in this book recognize the more than forty years of sustained and distinguished lifetime achievement in mathematics education research and development of Jeremy Kilpatrick. Including contributions from a variety of skilled mathematics educators, this text honors Jeremy Kilpatrick, reflecting on his groundbreaking papers, book chapters, and books - many of which are now standard references in the literature - on mathematical problem solving, the history of mathematics education, mathematical ability and proficiency, curriculum change and its history, global perspectives on mathematics education, and mathematics assessment. Many chapters also offer substantial contributions of their own on important themes, including mathematical problem solving, mathematics curriculum, the role of theory in mathematics education, the democratization of mathematics, and international perspectives on the professional field of mathematics education.​