The Mathematical Experience Study Edition

The Mathematical Experience  Study Edition PDF
Author: Philip Davis
Publisher: Springer Science & Business Media
ISBN: 0817682945
Size: 69.37 MB
Format: PDF
Category : Mathematics
Languages : en
Pages : 500
View: 4599

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Winner of the 1983 National Book Award! "...a perfectly marvelous book about the Queen of Sciences, from which one will get a real feeling for what mathematicians do and who they are. The exposition is clear and full of wit and humor..." - The New Yorker (1983 National Book Award edition) Mathematics has been a human activity for thousands of years. Yet only a few people from the vast population of users are professional mathematicians, who create, teach, foster, and apply it in a variety of situations. The authors of this book believe that it should be possible for these professional mathematicians to explain to non-professionals what they do, what they say they are doing, and why the world should support them at it. They also believe that mathematics should be taught to non-mathematics majors in such a way as to instill an appreciation of the power and beauty of mathematics. Many people from around the world have told the authors that they have done precisely that with the first edition and they have encouraged publication of this revised edition complete with exercises for helping students to demonstrate their understanding. This edition of the book should find a new generation of general readers and students who would like to know what mathematics is all about. It will prove invaluable as a course text for a general mathematics appreciation course, one in which the student can combine an appreciation for the esthetics with some satisfying and revealing applications. The text is ideal for 1) a GE course for Liberal Arts students 2) a Capstone course for perspective teachers 3) a writing course for mathematics teachers. A wealth of customizable online course materials for the book can be obtained from Elena Anne Marchisotto ([email protected]) upon request.

The Mathematical Experience Study Edition

The Mathematical Experience  Study Edition PDF
Author: Philip Davis
Publisher: Birkhäuser
ISBN: 9780817682965
Size: 71.82 MB
Format: PDF, Mobi
Category : Mathematics
Languages : en
Pages : 500
View: 4772

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Winner of the 1983 National Book Award! "...a perfectly marvelous book about the Queen of Sciences, from which one will get a real feeling for what mathematicians do and who they are. The exposition is clear and full of wit and humor..." - The New Yorker (1983 National Book Award edition) Mathematics has been a human activity for thousands of years. Yet only a few people from the vast population of users are professional mathematicians, who create, teach, foster, and apply it in a variety of situations. The authors of this book believe that it should be possible for these professional mathematicians to explain to non-professionals what they do, what they say they are doing, and why the world should support them at it. They also believe that mathematics should be taught to non-mathematics majors in such a way as to instill an appreciation of the power and beauty of mathematics. Many people from around the world have told the authors that they have done precisely that with the first edition and they have encouraged publication of this revised edition complete with exercises for helping students to demonstrate their understanding. This edition of the book should find a new generation of general readers and students who would like to know what mathematics is all about. It will prove invaluable as a course text for a general mathematics appreciation course, one in which the student can combine an appreciation for the esthetics with some satisfying and revealing applications. The text is ideal for 1) a GE course for Liberal Arts students 2) a Capstone course for perspective teachers 3) a writing course for mathematics teachers. A wealth of customizable online course materials for the book can be obtained from Elena Anne Marchisotto ([email protected]) upon request.

The Mathematical Experience Study Edition

The Mathematical Experience  Study Edition PDF
Author: Philip Davis
Publisher: Birkhäuser
ISBN: 9780817682965
Size: 64.27 MB
Format: PDF, ePub, Docs
Category : Mathematics
Languages : en
Pages : 500
View: 4510

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Winner of the 1983 National Book Award! "...a perfectly marvelous book about the Queen of Sciences, from which one will get a real feeling for what mathematicians do and who they are. The exposition is clear and full of wit and humor..." - The New Yorker (1983 National Book Award edition) Mathematics has been a human activity for thousands of years. Yet only a few people from the vast population of users are professional mathematicians, who create, teach, foster, and apply it in a variety of situations. The authors of this book believe that it should be possible for these professional mathematicians to explain to non-professionals what they do, what they say they are doing, and why the world should support them at it. They also believe that mathematics should be taught to non-mathematics majors in such a way as to instill an appreciation of the power and beauty of mathematics. Many people from around the world have told the authors that they have done precisely that with the first edition and they have encouraged publication of this revised edition complete with exercises for helping students to demonstrate their understanding. This edition of the book should find a new generation of general readers and students who would like to know what mathematics is all about. It will prove invaluable as a course text for a general mathematics appreciation course, one in which the student can combine an appreciation for the esthetics with some satisfying and revealing applications. The text is ideal for 1) a GE course for Liberal Arts students 2) a Capstone course for perspective teachers 3) a writing course for mathematics teachers. A wealth of customizable online course materials for the book can be obtained from Elena Anne Marchisotto ([email protected]) upon request.

Erfahrung Mathematik

Erfahrung Mathematik PDF
Author: P.J. Davis
Publisher: Springer-Verlag
ISBN: 3034850409
Size: 39.26 MB
Format: PDF
Category : Science
Languages : de
Pages : 466
View: 3480

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ie ältesten uns bekannten mathematischen Schriftta D feln stammen aus der Zeit um 2400 v. ehr. ; aber wir dürfen davon ausgehen, daß das Bedürfnis, Mathematik zu schaffen, ein Ausdruck der menschlichen Zivilisation an sich ist. In vier bis fünf Jahrtausenden hat sich ein gewalti ges System von Praktiken und Begriffen - die Mathematik herangebildet, die in vielfältiger Weise mit unserem Alltag verknüpft ist. Was ist Mathematik? Was bedeutet sie? Wo mit befaßt sie sich? Was sind ihre Methoden? Wie wird sie geschaffen und benützt? Wo ist ihr Platz in der Vielgestalt der menschlichen Erfahrung? Welchen Nutzen bringt sie? Was für Schaden richtet sie an? Welches Gewicht kommt ihr zu? Diese schwierigen Fragen werden noch zusätzlich kompliziert durch die Fülle des Materials und die weitver zweigten Querverbindungen, die es dem einzelnen verun möglichen, alles zu begreifen, geschweige denn, es in seiner Gesamtheit zu erfassen und zwischen den Deckeln eines normalen Buches unterzubringen. Um von dieser Material fülle nicht erdrückt zu werden, haben sich die Autoren für eine andere Betrachtungsweise entschieden. Die Mathema tik ist seit Tausenden von Jahren ein Feld menschlicher Ak tivität. In begrenztem Rahmen ist jeder von uns ein Mathe matiker und betreibt bewußt Mathematik, wenn er zum Beispiel auf dem Markt einkauft, Tapeten ausmißt oder ei nen Keramiktopf mit einem regelmäßigen Muster verziert. In bescheidenem Ausmaß versucht sich auch jeder von uns als mathematischer Denker. Schon mit dem Ausruf «Aber Zahlen lügen nicht!» befinden wir uns in der Gesellschaft von Plato oder Lakatos.

Epistemological Foundations Of Mathematical Experience

Epistemological Foundations of Mathematical Experience PDF
Author: Leslie P. Steffe
Publisher: Springer Science & Business Media
ISBN: 1461231787
Size: 53.22 MB
Format: PDF, Docs
Category : Psychology
Languages : en
Pages : 312
View: 1600

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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.

What Is Mathematics Really

What is Mathematics  Really  PDF
Author: Reuben Hersh
Publisher: Oxford University Press, USA
ISBN: 9780195130874
Size: 63.59 MB
Format: PDF, ePub, Docs
Category : Medical
Languages : en
Pages : 343
View: 6415

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Tries to refine the philosophy of mathematics to reflect what mathematicians really do, and argues that mathematics must be understood in a social context.

Bilder Der Mathematik

Bilder der Mathematik PDF
Author: Georg Glaeser
Publisher: Springer Spektrum
ISBN: 9783662434161
Size: 45.18 MB
Format: PDF
Category : Mathematics
Languages : de
Pages : 340
View: 1616

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Wie sieht eine Kurve aus, die die ganze Ebene oder den Raum vollständig ausfüllt? Kann man einen Polyeder flexibel bewegen, ja sogar umstülpen? Was ist die projektive Ebene oder der vierdimensionale Raum? Gibt es Seifenblasen, die keine runden Kugel sind? Wie kann man die komplizierte Struktur von Strömungen besser verstehen? In diesem Buch erleben Sie die Mathematik von ihrer anschaulichen Seite und finden faszinierende und bisher nie gesehene Bilder, die Ihnen illustrative Antworten zu all diesen Fragestellungen geben. Zu allen Bildern gibt es kurze Erklärungstexte, viele Literaturhinweise und jede Menge Web-Links. Das Buch ist für alle Freunde der Mathematik, die nicht nur trockenen Text und endlose Formeln sehen wollen. Vom Schüler zum Lehrer, vom Studenten zum Professor. Es soll sie alle inspirieren und anregen, sich mit diesem oder jenem vermeintlich nur Insidern vorbehaltenem Thema zu beschäftigen. Lernen Sie die Mathematik von einer ganz neuen und bunten Seite kennen. Die Neuauflage ist vollständig durchgesehen und um acht Doppelseiten mit neuen und spektakulären Bildern ergänzt. Stimmen zur 1. Auflage: „Die durchweg exzellenten grafischen Veranschaulichungen geben gute Beispiele, wie man elegant und sauber argumentiert. Möge dieses Buch viele Leserinnen und Leser zur Mathematik verführen." c't 17/09 „In den ‚Bildern der Mathematik‘ kann man nach Herzenslust schmökern. Denn die einzelnen Mathematik-Häppchen und kleinen Geschichten sind zwar thematisch geordnet, bauen aber nicht aufeinander auf. So ist dieses Buch – für ein mathematisches Sachbuch sicher erstaunlich – sogar für den Nachttisch geeignet." Deutschlandradio Kultur

Loving And Hating Mathematics

Loving and Hating Mathematics PDF
Author: Reuben Hersh
Publisher: Princeton University Press
ISBN: 9781400836116
Size: 64.49 MB
Format: PDF, ePub, Docs
Category : Mathematics
Languages : en
Pages : 432
View: 1206

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Mathematics is often thought of as the coldest expression of pure reason. But few subjects provoke hotter emotions--and inspire more love and hatred--than mathematics. And although math is frequently idealized as floating above the messiness of human life, its story is nothing if not human; often, it is all too human. Loving and Hating Mathematics is about the hidden human, emotional, and social forces that shape mathematics and affect the experiences of students and mathematicians. Written in a lively, accessible style, and filled with gripping stories and anecdotes, Loving and Hating Mathematics brings home the intense pleasures and pains of mathematical life. These stories challenge many myths, including the notions that mathematics is a solitary pursuit and a "young man's game," the belief that mathematicians are emotionally different from other people, and even the idea that to be a great mathematician it helps to be a little bit crazy. Reuben Hersh and Vera John-Steiner tell stories of lives in math from their very beginnings through old age, including accounts of teaching and mentoring, friendships and rivalries, love affairs and marriages, and the experiences of women and minorities in a field that has traditionally been unfriendly to both. Included here are also stories of people for whom mathematics has been an immense solace during times of crisis, war, and even imprisonment--as well as of those rare individuals driven to insanity and even murder by an obsession with math. This is a book for anyone who wants to understand why the most rational of human endeavors is at the same time one of the most emotional.

Descartes Dream

Descartes  Dream PDF
Author: Philip J. Davis
Publisher: Courier Corporation
ISBN: 0486442527
Size: 22.26 MB
Format: PDF, ePub, Mobi
Category : Mathematics
Languages : en
Pages : 321
View: 4693

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These provocative essays take a modern look at the 17th-century thinker's dream, examining the influences of mathematics on society, particularly in light of technological advances. They survey the conditions that elicit the application of mathematic principles; the applications' effectiveness; and how applied mathematics transform perceptions of reality. 1987 edition.

Experiencing Mathematics

Experiencing Mathematics PDF
Author: Reuben Hersh
Publisher: American Mathematical Soc.
ISBN: 082189420X
Size: 10.58 MB
Format: PDF, ePub, Mobi
Category : Mathematics
Languages : en
Pages : 282
View: 7573

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The question ``What am I doing?'' haunts many creative people, researchers, and teachers. Mathematics, poetry, and philosophy can look from the outside sometimes as ballet en pointe, and at other times as the flight of the bumblebee. Reuben Hersh looks at mathematics from the inside; he collects his papers written over several decades, their edited versions, and new chapters in his book Experiencing Mathematics, which is practical, philosophical, and in some places as intensely personal as Swann's madeleine. --Yuri Manin, Max Planck Institute, Bonn, Germany What happens when mid-career a mathematician unexpectedly becomes philosophical? These lively and eloquent essays address the questions that arise from a crisis of reflectiveness: What is a mathematical proof and why does it come after, not before, mathematical revelation? Can mathematics be both real and a human artifact? Do mathematicians produce eternal truths, or are the judgments of the mathematical community quasi-empirical and historically framed? How can we be sure that an infinite series that seems to converge really does converge? This collection of essays by Reuben Hersh makes an important contribution. His lively and eloquent essays bring the reality of mathematical research to the page. He argues that the search for foundations is misleading, and that philosophers should shift from focusing narrowly on the deductive structure of proof, to tracing the broader forms of quasi-empirical reasoning that star the history of mathematics, as well as examining the nature of mathematical communities and how and why their collective judgments evolve from one generation to the next. If these questions keep you up at night, then you should read this book. And if they don't, then you should read this book anyway, because afterwards, they will! --Emily Grosholz, Department of Philosophy, Penn State, Pennsylvania, USA Most mathematicians, when asked about the nature and meaning of mathematics, vacillate between the two unrealistic poles of Platonism and formalism. By looking carefully at what mathematicians really do when they are doing mathematics, Reuben Hersh offers an escape from this trap. This book of selected articles and essays provides an honest, coherent, and clearly understandable account of mathematicians' proof as it really is, and of the existence and reality of mathematical entities. It follows in the footsteps of Poincare, Hadamard, and Polya. The pragmatism of John Dewey is a better fit for mathematical practice than the dominant ``analytic philosophy''. Dialogue, satire, and fantasy enliven the philosophical and methodological analysis. Reuben Hersh has written extensively on mathematics, often from the point of view of a philosopher of science. His book with Philip Davis, The Mathematical Experience, won the National Book Award in science. Hersh is emeritus professor of mathematics at the University of New Mexico.

Discipline And Experience

Discipline and Experience PDF
Author: Peter Dear
Publisher: University of Chicago Press
ISBN: 9780226139432
Size: 68.72 MB
Format: PDF, Kindle
Category : Science
Languages : en
Pages : 290
View: 980

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Although the Scientific Revolution has long been regarded as the beginning of modern science, there has been little consensus about its true character. While the application of mathematics to the study of the natural world has always been recognized as an important factor, the role of experiment has been less clearly understood. Peter Dear investigates the nature of the change that occurred during this period, focusing particular attention on evolving notions of experience and how these developed into the experimental work that is at the center of modern science. He examines seventeenth-century mathematical sciences—astronomy, optics, and mechanics—not as abstract ideas, but as vital enterprises that involved practices related to both experience and experiment. Dear illuminates how mathematicians and natural philosophers of the period—Mersenne, Descartes, Pascal, Barrow, Newton, Boyle, and the Jesuits—used experience in their argumentation, and how and why these approaches changed over the course of a century. Drawing on mathematical texts and works of natural philosophy from all over Europe, he describes a process of change that was gradual, halting, sometimes contradictory—far from the sharp break with intellectual tradition implied by the term "revolution."

The Mathematics Experience

The Mathematics Experience PDF
Author: Mary Ann Haubner
Publisher: Houghton Mifflin School
ISBN: 9780395494080
Size: 25.24 MB
Format: PDF, Docs
Category : Juvenile Nonfiction
Languages : en
Pages : 528
View: 2595

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Developing 21st Century Competencies In The Mathematics Classroom

Developing 21st Century Competencies in the Mathematics Classroom PDF
Author: Pee Choon Toh
Publisher: World Scientific
ISBN: 9813143630
Size: 23.76 MB
Format: PDF, ePub, Docs
Category : Mathematics
Languages : en
Pages : 292
View: 1766

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The aim of this book is to contribute towards literature in the field of mathematics education, specifically the development of 21st century competencies amongst learners of mathematics. The book comprising fourteen chapters, written by renowned researchers in mathematics education, provides readers with approaches and applicable classroom strategies to foster skills and dispositions that will enable learners to thrive in the fast-changing and complex world that we live in today. The chapters in the book can be classified into three broad themes. The first is an examination of what is meant by 21st century competencies and how they can be developed within the context of the mathematics curriculum. The second is an in-depth discussion of evidence-based practices aimed at fostering specific competencies like metacognition and reflective thinking, critical thinking and communication skills. The last and third theme is about teaching approaches that are likely to feature increasingly in the 21st century classroom, for example flipped learning or the use of comics and storytelling. Contents:21st Century Competencies in Mathematics Classrooms (Pee Choon TOH & Berinderjeet KAUR)Mathematics Education, Virtues and 21st Century Competencies (Stephen THORNTON)Enriching Secondary Mathematics Education with 21st Century Competencies (WONG Khoon Yoong)Mathematics in 21st Century Life (Barry KISSANE)Mathematics Subject Mastery — A Must for Developing 21st Century Skills (Berinderjeet KAUR, WONG Lai Fong & Divya BHARDWAJ)Teaching in the 21st Century Mathematics Classroom: Metacognitive Questioning (Cynthia SETO)Listening and Responding to Children's Reflective Thinking: Two Case Studies on the Use of the National Assessment in Japan (Keiko HINO)Using Open-Ended Tasks to Foster 21st Century Learners at the Primary Level (YEO Kai Kow Joseph)Productive Talk in the Primary Mathematics Classroom (KOAY Phong Lee)Justification in Singapore Secondary Mathematics (CHUA Boon Liang)Examples in the Teaching of Mathematics: Teachers' Perceptions (Lay Keow NG & Jaguthsing DINDYAL)On the Efficacy of Flipped Classroom: Motivation and Cognitive Load (Weng Kin HO & Puay San CHAN)Use of Comics and Storytelling in Teaching Mathematics (TOH Tin Lam, CHENG Lu Pien, JIANG Heng & LIM Kam Ming)Game Theory: An Alternative Mathematical Experience (Ein-Ya GURA) Readership: Graduate students, researchers, practitioners and teachers in mathematics.