Download or read book Epistemological Foundations of Mathematical Experience written by Leslie P. Steffe and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Epistemological Foundations of Mathematical Experience written by Leslie P Steffe and published by . This book was released on 1991-09-17 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Mathematical Experience written by Philip J. Davis and published by Houghton Mifflin Harcourt. This book was released on 1998 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Piaget s Genetic Epistemology for Mathematics Education Research written by Paul Christian Dawkins and published by Springer Nature. This book was released on 2024-01-22 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Constructing Mathematical Knowledge written by Paul Ernest and published by Routledge. This book was released on 2012-10-12 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Constructing Mathematical Knowledge written by Paul Ernest and published by Routledge. This book was released on 2003-09-02 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Holomorphic Vector Fields on Compact K hler Manifolds written by Yoz_ Matsushima and published by American Mathematical Soc.. This book was released on 1971-12-31 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Learning Mathematics written by Paul Cobb and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Theories of Mathematical Learning written by Leslie P. Steffe and published by Routledge. This book was released on 2013-04-03 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Justificatory Force of Experiences written by Philipp Berghofer and published by Springer Nature. This book was released on 2022-03-24 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Research in Collegiate Mathematics Education III written by James J. Kaput and published by American Mathematical Soc.. This book was released on 1998 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Development of Multiplicative Reasoning in the Learning of Mathematics written by Guershon Harel and published by SUNY Press. This book was released on 1994-01-01 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: Two of the most important concepts children develop progressively throughout their mathematics education years are additivity and multiplicativity. Additivity is associated with situations that involve adding, joining, affixing, subtracting, separating and removing. Multiplicativity is associated with situations that involve duplicating, shrinking, stressing, sharing equally, multiplying, dividing, and exponentiating. This book presents multiplicativity in terms of a multiplicative conceptual field (MCF), not as individual concepts. It is presented in terms of interrelations and dependencies within, between, and among multiplicative concepts. The authors share the view that research on the mathematical, cognitive, and instructional aspects of multiplicative concepts must be situated in an MCF framework.
Download or read book Experience and Prediction written by Hans Reichenbach and published by Forgotten Books. This book was released on 2017-09-12 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from Experience and Prediction: An Analysis of the Foundations and the Structure of Knowledge The conviction that the key to an understanding of sci entific method is contained within the probability problem grew stronger and stronger with me in the face of such basic mistakes. This is the reason why, for a long time, I renounced a comprehensive report of my epistemological views, although my special investigations into different problems of epistemology demanded a construction of foundations different from those constructed by some of my philosophical friends. I concentrated my inquiry on the problem of probability which demanded at the same time a mathematical and a logical analysis. It is only after having traced out a logistic theory of probability, includ ing a solution of the problem of induction, that I turn now to an application of these ideas to questions of a more gen eral epistemological character. As my theory of probabil ity has been published for some years, it was not necessary to present it with all mathematical details once more in the present book; the fifth chapter, however, gives an ah breviated report of this theory - a report which seemed necessary as the probability book has been published in German only. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Download or read book Ongoing Advancements in Philosophy of Mathematics Education written by Maria Aparecida Viggiani Bicudo and published by Springer Nature. This book was released on 2023-11-01 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ongoing Advancements in Philosophy of Mathematics Education approaches the philosophy of mathematics education in a forward movement, analyzing, reflecting, and proposing significant contemporary themes in the field of mathematics education. The theme that gives life to the book is philosophy of mathematics education understood as arising from the intertwining between philosophy of mathematics and philosophy of education which, through constant analytical and reflective work regarding teaching and learning practices in mathematics, is materialized in its own discipline, philosophy of mathematics education. This is the field of investigation of the chapters in the book. The chapters are written by an international cohort of authors, from a variety of countries, regions, and continents. Some of these authors work with philosophical and psychological foundations traditionally accepted by Western civilization. Others expose theoretical foundations based on a new vision and comprising innovative approaches to historical and present-day issues in educational philosophy. The final third of the book is devoted to these unique and innovative research stances towards important and change resistant societal topics such as racism, technology gaps, or the promotion of creativity in the field of mathematics education.
Download or read book Foundational Issues in Artificial Intelligence and Cognitive Science written by M.H. Bickhard and published by Elsevier. This book was released on 1996-10-15 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book focuses on a conceptual flaw in contemporary artificial intelligence and cognitive science. Many people have discovered diverse manifestations and facets of this flaw, but the central conceptual impasse is at best only partially perceived. Its consequences, nevertheless, visit themselves as distortions and failures of multiple research projects - and make impossible the ultimate aspirations of the fields. The impasse concerns a presupposition concerning the nature of representation - that all representation has the nature of encodings: encodingism. Encodings certainly exist, but encodingism is at root logically incoherent; any programmatic research predicted on it is doomed too distortion and ultimate failure. The impasse and its consequences - and steps away from that impasse - are explored in a large number of projects and approaches. These include SOAR, CYC, PDP, situated cognition, subsumption architecture robotics, and the frame problems - a general survey of the current research in AI and Cognitive Science emerges. Interactivism, an alternative model of representation, is proposed and examined.
Download or read book Foundations for the Future in Mathematics Education written by Richard A. Lesh and published by Routledge. This book was released on 2020-10-07 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: The central question addressed in Foundations for the Future in Mathematics Education is this: What kind of understandings and abilities should be emphasized to decrease mismatches between the narrow band of mathematical understandings and abilities that are emphasized in mathematics classrooms and tests, and those that are needed for success beyond school in the 21st century? This is an urgent question. In fields ranging from aeronautical engineering to agriculture, and from biotechnologies to business administration, outside advisors to future-oriented university programs increasingly emphasize the fact that, beyond school, the nature of problem-solving activities has changed dramatically during the past twenty years, as powerful tools for computation, conceptualization, and communication have led to fundamental changes in the levels and types of mathematical understandings and abilities that are needed for success in such fields. For K-12 students and teachers, questions about the changing nature of mathematics (and mathematical thinking beyond school) might be rephrased to ask: If the goal is to create a mathematics curriculum that will be adequate to prepare students for informed citizenship—as well as preparing them for career opportunities in learning organizations, in knowledge economies, in an age of increasing globalization—how should traditional conceptions of the 3Rs be extended or reconceived? Overall, this book suggests that it is not enough to simply make incremental changes in the existing curriculum whose traditions developed out of the needs of industrial societies. The authors, beyond simply stating conclusions from their research, use results from it to describe promising directions for a research agenda related to this question. The volume is organized in three sections: *Part I focuses on naturalistic observations aimed at clarifying what kind of “mathematical thinking” people really do when they are engaged in “real life” problem solving or decision making situations beyond school. *Part II shifts attention toward changes that have occurred in kinds of elementary-but-powerful mathematical concepts, topics, and tools that have evolved recently—and that could replace past notions of “basics” by providing new foundations for the future. This section also initiates discussions about what it means to “understand” the preceding ideas and abilities. *Part III extends these discussions about meaning and understanding—and emphasizes teaching experiments aimed at investigating how instructional activities can be designed to facilitate the development of the preceding ideas and abilities. Foundations for the Future in Mathematics Education is an essential reference for researchers, curriculum developers, assessment experts, and teacher educators across the fields of mathematics and science education.
Download or read book How Chinese Learn Mathematics written by Lianghuo Fan and published by World Scientific. This book was released on 2004 with total page 591 pages. Available in PDF, EPUB and Kindle. Book excerpt: - Represents a concerted research effort in mathematics education of Chinese learners, the first of its kind - Contains contributions from the world's leading scholars and most active researchers in this area and beyond - Provides comprehensive coverage and insiders' perspectives on relevant issues
