Epistemological Foundations Of Mathematical Experience
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Author | : Leslie P. Steffe |
Publisher | : Springer Science & Business Media |
Total Pages | : 257 |
Release | : 2012-12-06 |
Genre | : Psychology |
ISBN | : 1461231787 |
Download Epistemological Foundations of Mathematical Experience Book in PDF, Epub and Kindle
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 | : Leslie P Steffe |
Publisher | : |
Total Pages | : 332 |
Release | : 1991-09-17 |
Genre | : |
ISBN | : 9781461231790 |
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Author | : Paul Christian Dawkins |
Publisher | : Springer Nature |
Total Pages | : 620 |
Release | : 2024-01-22 |
Genre | : Education |
ISBN | : 3031473868 |
Download Piaget’s Genetic Epistemology for Mathematics Education Research Book in PDF, Epub and Kindle
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 | : Philip J. Davis |
Publisher | : Houghton Mifflin Harcourt |
Total Pages | : 470 |
Release | : 1998 |
Genre | : Mathematics |
ISBN | : 9780395929681 |
Download The Mathematical Experience Book in PDF, Epub and Kindle
Explores the foundations of mathematics, looking at the history and philosophy of the field, and includes biographical sketches of people who have made mathematics their life's work
Author | : Paul Cobb |
Publisher | : Springer Science & Business Media |
Total Pages | : 204 |
Release | : 2013-03-09 |
Genre | : Education |
ISBN | : 9401720576 |
Download Learning Mathematics Book in PDF, Epub and Kindle
This volume emphasizes students' inferred mathematical experiences as the starting point in the theory-building process. The book addresses conceptual constructions, including multiplicative notions, fractions, algebra, and the fundamental theorem of calculus, and theoretical constructs such as the crucial role of language and symbols, and the importance of dynamic imagery.
Author | : Paul Ernest |
Publisher | : Routledge |
Total Pages | : 295 |
Release | : 2012-10-12 |
Genre | : Education |
ISBN | : 1136364722 |
Download Constructing Mathematical Knowledge Book in PDF, Epub and Kindle
First published in 1994. This book and its companion volume, Mathematics, Education and Philosophy: An International Perspective are edited collections. Instead of the sharply focused concerns of the research monograph, the books offer a panorama of complementary and forward-looking perspectives. They illustrate the breadth of theoretical and philosophical perspectives that can fruitfully be brough to bear on the mathematics and education. The empathise of this book is on epistemological issues, encompassing multiple perspectives on the learning of mathematics, as well as broader philosophical reflections on the genesis of knowledge. It explores constructivist and social theories of learning and discusses the rile of the computer in light of these theories.
Author | : Philipp Berghofer |
Publisher | : Springer Nature |
Total Pages | : 382 |
Release | : 2022-03-24 |
Genre | : Science |
ISBN | : 3030961133 |
Download The Justificatory Force of Experiences Book in PDF, Epub and Kindle
This book offers a phenomenological conception of experiential justification that seeks to clarify why certain experiences are a source of immediate justification and what role experiences play in gaining (scientific) knowledge. Based on the author's account of experiential justification, this book exemplifies how a phenomenological experience-first epistemology can epistemically ground the individual sciences. More precisely, it delivers a comprehensive picture of how we get from epistemology to the foundations of mathematics and physics. The book is unique as it utilizes methods and insights from the phenomenological tradition in order to make progress in current analytic epistemology. It serves as a starting point for re-evaluating the relevance of Husserlian phenomenology to current analytic epistemology and making an important step towards paving the way for future mutually beneficial discussions. This is achieved by exemplifying how current debates can benefit from ideas, insights, and methods we find in the phenomenological tradition.
Author | : Leslie P. Steffe |
Publisher | : Routledge |
Total Pages | : 539 |
Release | : 2013-04-03 |
Genre | : Education |
ISBN | : 1136485473 |
Download Theories of Mathematical Learning Book in PDF, Epub and Kindle
Chemists, working with only mortars and pestles, could not get very far unless they had mathematical models to explain what was happening "inside" of their elements of experience -- an example of what could be termed mathematical learning. This volume contains the proceedings of Work Group 4: Theories of Mathematics, a subgroup of the Seventh International Congress on Mathematical Education held at Université Laval in Québec. Bringing together multiple perspectives on mathematical thinking, this volume presents elaborations on principles reflecting the progress made in the field over the past 20 years and represents starting points for understanding mathematical learning today. This volume will be of importance to educational researchers, math educators, graduate students of mathematical learning, and anyone interested in the enterprise of improving mathematical learning worldwide.
Author | : James J. Kaput |
Publisher | : American Mathematical Soc. |
Total Pages | : 330 |
Release | : 1998 |
Genre | : Education |
ISBN | : 0821808826 |
Download Research in Collegiate Mathematics Education III Book in PDF, Epub and Kindle
Volume 3 of Research in Collegiate Mathematics Education (RCME) presents state-of-the-art research on understanding, teaching and learning mathematics at the post-secondary level. This volume contains information on methodology and research concentrating on these areas of student learning: Problem Solving; Understanding Concepts; and Understanding Proofs.
Author | : Paul Ernest |
Publisher | : Routledge |
Total Pages | : 328 |
Release | : 2003-09-02 |
Genre | : Education |
ISBN | : 1135716196 |
Download Constructing Mathematical Knowledge Book in PDF, Epub and Kindle
Provides perspectives on the learning of mathematics and epistemology. The book explores constructivist and social theories of learning, and discusses the role of the computer in the light of these theories.