Mathematical Knowledge And The Interplay Of Practices

Author : José Ferreirós
Publisher : Princeton University Press
Page : 358 pages
File Size : 53,6 Mb
Release : 2015-12-22
Category : Science
ISBN : 9781400874002

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Mathematical Knowledge and the Interplay of Practices by José Ferreirós Pdf

This book presents a new approach to the epistemology of mathematics by viewing mathematics as a human activity whose knowledge is intimately linked with practice. Charting an exciting new direction in the philosophy of mathematics, José Ferreirós uses the crucial idea of a continuum to provide an account of the development of mathematical knowledge that reflects the actual experience of doing math and makes sense of the perceived objectivity of mathematical results. Describing a historically oriented, agent-based philosophy of mathematics, Ferreirós shows how the mathematical tradition evolved from Euclidean geometry to the real numbers and set-theoretic structures. He argues for the need to take into account a whole web of mathematical and other practices that are learned and linked by agents, and whose interplay acts as a constraint. Ferreirós demonstrates how advanced mathematics, far from being a priori, is based on hypotheses, in contrast to elementary math, which has strong cognitive and practical roots and therefore enjoys certainty. Offering a wealth of philosophical and historical insights, Mathematical Knowledge and the Interplay of Practices challenges us to rethink some of our most basic assumptions about mathematics, its objectivity, and its relationship to culture and science.

Author : José Ferreirós
Publisher : Princeton University Press
Page : 357 pages
File Size : 54,9 Mb
Release : 2015-12-22
Category : Science
ISBN : 9780691167510

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Mathematical Knowledge and the Interplay of Practices by José Ferreirós Pdf

This book presents a new approach to the epistemology of mathematics by viewing mathematics as a human activity whose knowledge is intimately linked with practice. Charting an exciting new direction in the philosophy of mathematics, José Ferreirós uses the crucial idea of a continuum to provide an account of the development of mathematical knowledge that reflects the actual experience of doing math and makes sense of the perceived objectivity of mathematical results. Describing a historically oriented, agent-based philosophy of mathematics, Ferreirós shows how the mathematical tradition evolved from Euclidean geometry to the real numbers and set-theoretic structures. He argues for the need to take into account a whole web of mathematical and other practices that are learned and linked by agents, and whose interplay acts as a constraint. Ferreirós demonstrates how advanced mathematics, far from being a priori, is based on hypotheses, in contrast to elementary math, which has strong cognitive and practical roots and therefore enjoys certainty. Offering a wealth of philosophical and historical insights, Mathematical Knowledge and the Interplay of Practices challenges us to rethink some of our most basic assumptions about mathematics, its objectivity, and its relationship to culture and science.

Author : Bindu Elizabeth Pothen
Publisher : Stanford University
Page : 253 pages
File Size : 52,8 Mb
Release : 2011
Category : Electronic
ISBN : STANFORD:ck171qs7892

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Refining the Mathematics Knowledge Base by Bindu Elizabeth Pothen Pdf

Understanding the knowledge that teachers must bring to their classrooms is critical to the advancement of the field of teacher education. Understanding how teacher knowledge impacts various aspects of teacher practice is also critical. Understanding the interplay between teacher knowledge and practice, and consequently the result that this relationship has on student learning is most important. This dissertation attempts to advance our collective understanding of the complex relationship between teacher knowledge, teacher practice, and student learning in the field of elementary mathematics. Four third-grade teachers were followed as they taught a subset of lessons in a unit on fractions. The study first investigates the types of knowledge that the teachers brought to their classrooms. Then, an examination is conducted of the way in which these types of knowledge impacted their teaching practice. Finally, the student learning that resulted over the course of these lessons is discussed. This study supports the widespread belief that teacher knowledge is important to instruction. The descriptions of the case study teachers highlight that their varying levels of knowledge resulted in unique aspects of practice being emphasized in their classrooms. This dissertation documents the differences in teaching practice and the trade-offs that produce differences in student learning. Interesting student learning patterns emerged, based on qualitative student interviews. Medium students from classrooms in which teachers focused for more sustained periods on mathematical concepts seemed to demonstrate greater procedural fluency and deeper conceptual understanding than their peers in the other classrooms. Low students in classrooms where fluency was the focus seemed to show slightly greater procedural fluency, though less conceptual understanding, than their peers in the classrooms that spent more time on concepts. High students showed no appreciable difference across all classrooms. This study adds to the field by introducing a new construct, the conceptual threshold, to offer an explanation of these student learning trends.

Author : Mauricio Suárez,Mauro Dorato,Miklós Rédei
Publisher : Springer Science & Business Media
Page : 332 pages
File Size : 49,8 Mb
Release : 2010-07-17
Category : Science
ISBN : 9789048132522

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EPSA Philosophical Issues in the Sciences by Mauricio Suárez,Mauro Dorato,Miklós Rédei Pdf

This volume collects papers presented at the Founding Conference of the European Philosophy of Science Association meeting, held November 2007. It provides an excellent overview of the state of the art in philosophy of science in different European countries.

Author : Bharath Sriraman
Publisher : Springer Nature
Page : 3221 pages
File Size : 42,8 Mb
Release : 2024-05-05
Category : Electronic
ISBN : 9783031408465

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Handbook of the History and Philosophy of Mathematical Practice by Bharath Sriraman Pdf

Author : Apostolos Doxiadis,Barry Mazur
Publisher : Princeton University Press
Page : 593 pages
File Size : 53,8 Mb
Release : 2012-03-18
Category : Mathematics
ISBN : 9781400842681

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Circles Disturbed by Apostolos Doxiadis,Barry Mazur Pdf

Why narrative is essential to mathematics Circles Disturbed brings together important thinkers in mathematics, history, and philosophy to explore the relationship between mathematics and narrative. The book's title recalls the last words of the great Greek mathematician Archimedes before he was slain by a Roman soldier—"Don't disturb my circles"—words that seem to refer to two radically different concerns: that of the practical person living in the concrete world of reality, and that of the theoretician lost in a world of abstraction. Stories and theorems are, in a sense, the natural languages of these two worlds—stories representing the way we act and interact, and theorems giving us pure thought, distilled from the hustle and bustle of reality. Yet, though the voices of stories and theorems seem totally different, they share profound connections and similarities. A book unlike any other, Circles Disturbed delves into topics such as the way in which historical and biographical narratives shape our understanding of mathematics and mathematicians, the development of "myths of origins" in mathematics, the structure and importance of mathematical dreams, the role of storytelling in the formation of mathematical intuitions, the ways mathematics helps us organize the way we think about narrative structure, and much more. In addition to the editors, the contributors are Amir Alexander, David Corfield, Peter Galison, Timothy Gowers, Michael Harris, David Herman, Federica La Nave, G.E.R. Lloyd, Uri Margolin, Colin McLarty, Jan Christoph Meister, Arkady Plotnitsky, and Bernard Teissier.

Author : Shier Ju,Benedikt Löwe,Thomas Müller,Yun Xie
Publisher : Birkhäuser
Page : 123 pages
File Size : 42,5 Mb
Release : 2016-08-10
Category : Mathematics
ISBN : 9783319315027

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Cultures of Mathematics and Logic by Shier Ju,Benedikt Löwe,Thomas Müller,Yun Xie Pdf

This book gathers the proceedings of the conference "Cultures of Mathematics and Logic," held in Guangzhou, China. The event was the third in a series of interdisciplinary, international conferences emphasizing the cultural components of philosophy of mathematics and logic. It brought together researchers from many disciplines whose work sheds new light on the diversity of mathematical and logical cultures and practices. In this context, the cultural diversity can be diachronical (different cultures in different historical periods), geographical (different cultures in different regions), or sociological in nature.

Author : Paul Ernest
Publisher : Routledge
Page : 328 pages
File Size : 53,8 Mb
Release : 2003-09-02
Category : Education
ISBN : 9781135716196

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Constructing Mathematical Knowledge by Paul Ernest Pdf

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.

Author : Bindu Elizabeth Pothen
Publisher : Unknown
Page : 128 pages
File Size : 43,5 Mb
Release : 2011
Category : Electronic
ISBN : OCLC:745374775

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Refining the Mathematics Knowledge Base by Bindu Elizabeth Pothen Pdf

Understanding the knowledge that teachers must bring to their classrooms is critical to the advancement of the field of teacher education. Understanding how teacher knowledge impacts various aspects of teacher practice is also critical. Understanding the interplay between teacher knowledge and practice, and consequently the result that this relationship has on student learning is most important. This dissertation attempts to advance our collective understanding of the complex relationship between teacher knowledge, teacher practice, and student learning in the field of elementary mathematics. Four third-grade teachers were followed as they taught a subset of lessons in a unit on fractions. The study first investigates the types of knowledge that the teachers brought to their classrooms. Then, an examination is conducted of the way in which these types of knowledge impacted their teaching practice. Finally, the student learning that resulted over the course of these lessons is discussed. This study supports the widespread belief that teacher knowledge is important to instruction. The descriptions of the case study teachers highlight that their varying levels of knowledge resulted in unique aspects of practice being emphasized in their classrooms. This dissertation documents the differences in teaching practice and the trade-offs that produce differences in student learning. Interesting student learning patterns emerged, based on qualitative student interviews. Medium students from classrooms in which teachers focused for more sustained periods on mathematical concepts seemed to demonstrate greater procedural fluency and deeper conceptual understanding than their peers in the other classrooms. Low students in classrooms where fluency was the focus seemed to show slightly greater procedural fluency, though less conceptual understanding, than their peers in the classrooms that spent more time on concepts. High students showed no appreciable difference across all classrooms. This study adds to the field by introducing a new construct, the conceptual threshold, to offer an explanation of these student learning trends.

Author : Lorenzo Magnani,Tommaso Bertolotti
Publisher : Springer
Page : 1180 pages
File Size : 49,9 Mb
Release : 2017-05-22
Category : Technology & Engineering
ISBN : 9783319305264

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Springer Handbook of Model-Based Science by Lorenzo Magnani,Tommaso Bertolotti Pdf

This handbook offers the first comprehensive reference guide to the interdisciplinary field of model-based reasoning. It highlights the role of models as mediators between theory and experimentation, and as educational devices, as well as their relevance in testing hypotheses and explanatory functions. The Springer Handbook merges philosophical, cognitive and epistemological perspectives on models with the more practical needs related to the application of this tool across various disciplines and practices. The result is a unique, reliable source of information that guides readers toward an understanding of different aspects of model-based science, such as the theoretical and cognitive nature of models, as well as their practical and logical aspects. The inferential role of models in hypothetical reasoning, abduction and creativity once they are constructed, adopted, and manipulated for different scientific and technological purposes is also discussed. Written by a group of internationally renowned experts in philosophy, the history of science, general epistemology, mathematics, cognitive and computer science, physics and life sciences, as well as engineering, architecture, and economics, this Handbook uses numerous diagrams, schemes and other visual representations to promote a better understanding of the concepts. This also makes it highly accessible to an audience of scholars and students with different scientific backgrounds. All in all, the Springer Handbook of Model-Based Science represents the definitive application-oriented reference guide to the interdisciplinary field of model-based reasoning.

Author : Bart van Kerkhove
Publisher : World Scientific
Page : 248 pages
File Size : 40,7 Mb
Release : 2009
Category : Mathematics
ISBN : 9789812812223

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New Perspectives on Mathematical Practices by Bart van Kerkhove Pdf

This volume focuses on the importance of historical enquiry for the appreciation of philosophical problems concerning mathematics. It contains a well-balanced mixture of contributions by internationally established experts, such as Jeremy Gray and Jens Hoyrup; upcoming scholars, such as Erich Reck and Dirk Schlimm; and young, promising researchers at the beginning of their careers. The book is situated within a relatively new and broadly naturalistic tradition in the philosophy of mathematics. In this alternative philosophical current, which has been dramatically growing in importance in the last few decades, unlike in the traditional schools, proper attention is paid to scientific practices as informing for philosophical accounts.

Author : Geoffrey B. Saxe
Publisher : Psychology Press
Page : 259 pages
File Size : 40,6 Mb
Release : 2015-01-28
Category : Psychology
ISBN : 9781317728085

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Culture and Cognitive Development by Geoffrey B. Saxe Pdf

Researchers examining children's mathematics acquisition are now questioning the belief that children learn mathematics principally through formalized, in-school mathematics education. There is increasing evidence that children gain mathematical understanding through their participation in out-of-school cultural practices and that their mathematics only occasionally resembles what they learn in the classroom. Culture and Cognitive Development presents the latest research by Dr. Geoffrey Saxe on this issue. In examinations of the mathematical understandings of child candy sellers in an urban center in northeastern Brazil, Dr. Saxe finds sharp contrasts between mathematics as practiced in school and in real-world settings. In this unique research project he presents a penetrating conceptual treatment of the interplay between culture and cognitive development, filling a void in current research literature. Subjects examined include: the interplay between sociocultural and cognitive developmental processes the differences between math knowledge learned in and out of the classroom the ways math learning in the classroom is modified by children's out-of-school mathematics and, correspondingly, how practical out-of-school mathematics use is modified by formal education

Author : Alan Bishop,Stieg Mellin-Olsen,Joop van Dormolen
Publisher : Springer Science & Business Media
Page : 214 pages
File Size : 54,6 Mb
Release : 2013-11-27
Category : Education
ISBN : 9789401721950

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Mathematical Knowledge: Its Growth Through Teaching by Alan Bishop,Stieg Mellin-Olsen,Joop van Dormolen Pdf

In the first BACOMET volume different perspectives on issues concerning teacher education in mathematics were presented (B. Christiansen, A. G. Howson and M. Otte, Perspectives on Mathematics Education, Reidel, Dordrecht, 1986). Underlying all of them was the fundamental problem area of the relationships between mathematical knowledge and the teaching and learning processes. The subsequent project BACOMET 2, whose outcomes are presented in this book, continued this work, especially by focusing on the genesis of mathematical knowledge in the classroom. The book developed over the period 1985-9 through several meetings, much discussion and considerable writing and redrafting. Our major concern was to try to analyse what we considered to be the most significant aspects of the relationships in order to enable mathematics educators to be better able to handle the kinds of complex issues facing all mathematics educators as we approach the end of the twentieth century. With access to mathematics education widening all the time, with a multi tude of new materials and resources being available each year, with complex cultural and social interactions creating a fluctuating context of education, with all manner of technology becoming more and more significant, and with both informal education (through media of different kinds) and non formal education (courses of training etc. ) growing apace, the nature of formal mathematical education is increasingly needing analysis.

Author : Lyn D. English,David Kirshner
Publisher : Routledge
Page : 726 pages
File Size : 43,9 Mb
Release : 2015-07-30
Category : Education
ISBN : 9781134626649

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Handbook of International Research in Mathematics Education by Lyn D. English,David Kirshner Pdf

This third edition of the Handbook of International Research in Mathematics Education provides a comprehensive overview of the most recent theoretical and practical developments in the field of mathematics education. Authored by an array of internationally recognized scholars and edited by Lyn English and David Kirshner, this collection brings together overviews and advances in mathematics education research spanning established and emerging topics, diverse workplace and school environments, and globally representative research priorities. New perspectives are presented on a range of critical topics including embodied learning, the theory-practice divide, new developments in the early years, educating future mathematics education professors, problem solving in a 21st century curriculum, culture and mathematics learning, complex systems, critical analysis of design-based research, multimodal technologies, and e-textbooks. Comprised of 12 revised and 17 new chapters, this edition extends the Handbook’s original themes for international research in mathematics education and remains in the process a definitive resource for the field.

Author : Anonim
Publisher : Unknown
Page : 252 pages
File Size : 40,7 Mb
Release : 1999
Category : Electronic
ISBN : OCLC:247385653

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Forms of Mathematical Knowledge by Anonim Pdf