Making and Breaking Mathematical Sense

Histories and Philosophies of Mathematical Practice

Author: Roi Wagner

Publisher: Princeton University Press

ISBN: 1400883784

Category: Mathematics

Page: 256

View: 9817

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In line with the emerging field of philosophy of mathematical practice, this book pushes the philosophy of mathematics away from questions about the reality and truth of mathematical entities and statements and toward a focus on what mathematicians actually do—and how that evolves and changes over time. How do new mathematical entities come to be? What internal, natural, cognitive, and social constraints shape mathematical cultures? How do mathematical signs form and reform their meanings? How can we model the cognitive processes at play in mathematical evolution? And how does mathematics tie together ideas, reality, and applications? Roi Wagner uniquely combines philosophical, historical, and cognitive studies to paint a fully rounded image of mathematics not as an absolute ideal but as a human endeavor that takes shape in specific social and institutional contexts. The book builds on ancient, medieval, and modern case studies to confront philosophical reconstructions and cutting-edge cognitive theories. It focuses on the contingent semiotic and interpretive dimensions of mathematical practice, rather than on mathematics' claim to universal or fundamental truths, in order to explore not only what mathematics is, but also what it could be. Along the way, Wagner challenges conventional views that mathematical signs represent fixed, ideal entities; that mathematical cognition is a rigid transfer of inferences between formal domains; and that mathematics’ exceptional consensus is due to the subject’s underlying reality. The result is a revisionist account of mathematical philosophy that will interest mathematicians, philosophers, and historians of science alike.

Erfindung des Computers, Elektronenrechner, Entwicklungen in Deutschland, England und der Schweiz

Author: Herbert Bruderer

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 3110599317

Category: Computers

Page: 849

View: 9806

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Das preisgekrönte Werk „Meilensteine der Rechentechnik" liegt in der 2., völlig neu bearbeiteten und stark erweiterten Auflage vor. Die beiden Bände, die im Ganzen rund 1600 Seiten umfassen, sind ein Gesamtwerk, lassen sich aber auch einzeln nutzen. Diese Schrift behandelt sowohl analoge wie digitale Geräte und geht auf benachbarte Bereiche wie Automatenbau (z.B. Figuren- und Musikautomaten) sowie wissenschaftliche Instrumente (z.B. Himmelskunde, Vermessungswesen, Uhrmacherkunst) ein. Gestreift werden zudem frühe Schreibmaschinen und programmgesteuerte mechanische Webstühle. Schwerpunkte des ersten Bandes sind: Grundlagen, mechanische Rechenmaschinen, Rechenschieber, historische Automaten, Entwicklung der Rechenkunst, Schritt-für-Schritt-Anleitungen für analoge und digitale Rechengeräte. Alle wichtigen Fachbegriffe werden erklärt. Die weltweit prachtvollsten Rundbaurechenmaschinen und Androiden werden in Wort und Bild vorgestellt. Das Buch enthält ferner grundsätzliche Betrachtungen zu Themen wie Digitalisierung und künstliche Intelligenz sowie zur Rolle der Technikgeschichte und der Erhaltung des technischen Kulturguts. Der zweite Band widmet sich überwiegend den Elektronenrechnern: Erfindung des Computers, weltweite Entwicklung der Rechentechnik, insbesondere in Deutschland, England und der Schweiz. Er schließt überdies je ein Fachwörterbuch Deutsch-Englisch und Englisch-Deutsch ein. Die sollen das Lesen anspruchsvoller fremdsprachiger Texte und Übersetzungen fördern. Hinzu kommt eine umfassende weltweite Bibliografie. Beide Bände berichten über aufsehenerregende neue Funde von Dokumenten und Gegenständen (u.a. weltgrößte serienmäßig gefertigte Rechenwalze, weltweit kleinster mechanischer Parallelrechner, erster mechanischer Prozessrechner), sie eignen sich auch als Nachschlagewerke. Sie sind allgemein verständlich und richten sich an alle, die Freude haben an Technik-, Mathematik-, Informatik- und Kunstgeschichte. Mehrsprachige Bibliografie zur Mathematik-, Informatik, Technik- und Naturwissenschaftsgeschichte mit über 5000 Einträgen, Fachwörterbuch Deutsch-Englisch und Englisch-Deutsch mit je 4000 Einträgen, 18 Schritt-für-Schritt-Anleitungen für die Bedienung historischer analoger und digitaler Geräte, 100 tabellarische Übersichten, zahlreiche Zeittafeln, ausführliches Personen-, Orts- und Sachverzeichnis. Herbert Bruderer ist Dozent i.R. am Departement für Informatik der Eidgenössischen Technischen Hochschule (ETH) Zürich und Technikhistoriker. Er hat zahlreiche Bücher zur Informatik verfasst und ist mehrfacher Preisträger.

Sourcebook in the Mathematics of Medieval Europe and North Africa

Author: Victor J. Katz,Menso Folkerts,Barnabas Hughes,Roi Wagner,J. Lennart Berggren

Publisher: Princeton University Press

ISBN: 1400883202

Category: Mathematics

Page: 592

View: 1864

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Medieval Europe was a meeting place for the Christian, Jewish, and Islamic civilizations, and the fertile intellectual exchange of these cultures can be seen in the mathematical developments of the time. This sourcebook presents original Latin, Hebrew, and Arabic sources of medieval mathematics, and shows their cross-cultural influences. Most of the Hebrew and Arabic sources appear here in translation for the first time. Readers will discover key mathematical revelations, foundational texts, and sophisticated writings by Latin, Hebrew, and Arabic-speaking mathematicians, including Abner of Burgos's elegant arguments proving results on the conchoid—a curve previously unknown in medieval Europe; Levi ben Gershon’s use of mathematical induction in combinatorial proofs; Al-Mu’taman Ibn Hūd’s extensive survey of mathematics, which included proofs of Heron’s Theorem and Ceva’s Theorem; and Muhyī al-Dīn al-Maghribī’s interesting proof of Euclid’s parallel postulate. The book includes a general introduction, section introductions, footnotes, and references. The Sourcebook in the Mathematics of Medieval Europe and North Africa will be indispensable to anyone seeking out the important historical sources of premodern mathematics.

Starry Reckoning: Reference and Analysis in Mathematics and Cosmology

Author: Emily Rolfe Grosholz

Publisher: Springer

ISBN: 3319466909

Category: Philosophy

Page: 187

View: 6567

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This book deals with a topic that has been largely neglected by philosophers of science to date: the ability to refer and analyze in tandem. On the basis of a set of philosophical case studies involving both problems in number theory and issues concerning time and cosmology from the era of Galileo, Newton and Leibniz up through the present day, the author argues that scientific knowledge is a combination of accurate reference and analytical interpretation. In order to think well, we must be able to refer successfully, so that we can show publicly and clearly what we are talking about. And we must be able to analyze well, that is, to discover productive and explanatory conditions of intelligibility for the things we are thinking about. The book’s central claim is that the kinds of representations that make successful reference possible and those that make successful analysis possible are not the same, so that significant scientific and mathematical work typically proceeds by means of a heterogeneous discourse that juxtaposes and often superimposes a variety of kinds of representation, including formal and natural languages as well as more iconic modes. It demonstrates the virtues and necessity of heterogeneity in historically central reasoning, thus filling an important gap in the literature and fostering a new, timely discussion on the epistemology of science and mathematics.

Das lebendige Theorem

Author: Cédric Villani

Publisher: S. Fischer Verlag

ISBN: 3104025665

Category: Mathematics

Page: 304

View: 5173

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Im Kopf eines Genies – der Bericht von einem mathematischen Abenteuer und der Roman eines sehr erfolgreichen Forschers Cédric Villani gilt als Kandidat für die begehrte Fields-Medaille, eine Art Nobelpreis für Mathematiker. Sie wird aber nur alle vier Jahre vergeben, und man muss unter 40 sein. Er hat also nur eine Chance. Unmöglich! Unmöglich? Fieberhaft macht er sich an die Arbeit. Jetzt erzählt er seine Geschichte, und ihm gelingt das Unglaubliche: Wir werden direkte Zeugen der Denkprozesse eines Mathematikers, und das, ohne die dazugehörigen Formeln verstehen zu müssen. Ein Buch, so einzigartig wie sein Autor.

CCSS and UDL: Common Core State Standards and Universal Design for Learning

Author: Joseph Casbarro

Publisher: National Professional Resources Inc./Dude Publishing

ISBN: 1935609777

Category: Education

Page: 6

View: 3560

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Given the prevalence of student diversity, schools are struggling to find ways to help with the implementation of CCSS. With the wide range of student learning styles, socioeconomic backgrounds and life experiences, one key to meeting this challenge is the use of Universal Design for Learning (UDL). Originally developed to address the instructional needs of students with disabilities, UDL is now being embraced as an answer to creating learning environments where all students, regardless of their individual differences, can meet the CCSS. Designed for classroom teachers, this guide provides practical strategies and best practices for utilizing UDL as a means to help students successfully access and achieve the CCSS.

Das BUCH der Beweise

Author: Martin Aigner,Günter M. Ziegler

Publisher: Springer-Verlag

ISBN: 3662064545

Category: Mathematics

Page: 247

View: 7260

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Die elegantesten mathematischen Beweise, spannend und für jeden Interessierten verständlich. "Der Beweis selbst, seine Ästhetik, seine Pointe geht ins Geschichtsbuch der Königin der Wissenschaften ein. Ihre Anmut offenbart sich in dem gelungenen und geschickt illustrierten Buch." Die Zeit

Mathematics Success and Failure Among African-American Youth

The Roles of Sociohistorical Context, Community Forces, School Influence, and Individual Agency

Author: Danny Bernard Martin

Publisher: Routledge

ISBN: 1135676224

Category: Education

Page: 214

View: 1657

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No matter how mathematics achievement and persistence are measured, African Americans seem to lag behind their peers. This state of affairs is typically explained in terms of student ability, family background, differential treatment by teachers, and biased curricula. But what can explain disproportionately poor performance and persistence of African-American students who clearly possess the ability to do well, who come from varied family and socioeconomic backgrounds, who are taught by caring and concerned teachers, and who learn mathematics in the context of a reform-oriented mathematics curriculum? And, why do some African-American students succeed in mathematics when underachievement is the norm among their fellow students? Danny Martin addresses these questions in Mathematics Success and Failure Among African-American Youth, the results of a year-long ethnographic and observational study of African-American students and their parents and teachers. Mathematics Success and Failure Among African-American Youth goes beyond the conventional explanations of ability, socioeconomic status, differential treatment, and biased curricula to consider the effects of history, community, and peers--and the individual agency that allows some students to succeed despite these influences. Martin's analysis suggests that prior studies of mathematics achievement and persistence among African Americans have failed to link sociohistorical, community, school, and intrapersonal forces in sufficiently meaningful ways, and that they suffer from theoretical and methodological limitations that hinder the ability of mathematics educators to reverse the negative achievement and persistence trends that continue to afflict African-American students. The analyses and findings offered in Martin's book lead to exciting implications for future research and intervention efforts concerning African-American students--and other students for whom history and context play an important role. This book will be useful and informative to many groups: mathematics education researchers, education researchers interested in the social context of learning and teaching, policymakers, preservice and in-service teachers, students, parents, and community advocates. It will also be of interest to readers concerned with multicultural education, cross-cultural studies of mathematics learning, sociology of education, Black Studies, and issues of underrepresentation in science and mathematics.

Making Number Talks Matter

Developing Mathematical Practices and Deepening Understanding, Grades 4-10

Author: Cathy Humphreys,Ruth Parker

Publisher: Stenhouse Publishers

ISBN: 1571109986

Category: Education

Page: 200

View: 8700

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Making Number Talks Matter is about the myriad decisions facing teachers as they make this fifteen-minute daily routine a vibrant and vital part of their mathematics instruction. Throughout the book, Cathy Humphreys and Ruth Parker offer practical ideas for using Number Talks to help students learn to reason numerically and build a solid foundation for the study of mathematics. This book will be an invaluable resource whether you are already using Number Talks or not; whether you are an elementary, middle school, high school, or college teacher; or even if you are a parent wanting to support your child with mathematics. Using insight gained from many years of doing Number Talks with students of all ages, Cathy and Ruth address questions to ask during Number Talks, teacher moves that turn the thinking over to students, the mathematics behind the various strategies, and ways to overcome bumps in the road. If you've been looking for ways to transform your mathematics classroom--to bring sense-making and divergent thinking to the foreground, to bring the Standards for Mathematical Practice to life, and to bring joy back into your instruction--this book is for you.

Eine Naturgeschichte der menschlichen Moral

Author: Michael Tomasello

Publisher: Suhrkamp Verlag

ISBN: 351874822X

Category: Psychology

Page: 282

View: 6540

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Die Evolution des menschlichen Moralbewusstseins gehört zu den großen Rätseln der Wissenschaft. Es hat die Phantasie von Generationen von Forschern beflügelt, zahlreiche Theorien liegen auf dem Tisch, aber die Frage »Woher kommt die Moral?« ist nach wie vor offen. In Fortschreibung seiner faszinierenden Naturgeschichte des Menschen legt nun Michael Tomasello eine Antwort vor. Gestützt auf jahrzehntelange empirische Forschungen, rekonstruiert er die Entstehung des einzigartigen menschlichen Sinns für Werte und Normen als einen zweistufigen Prozess. Dieser beginnt vor einigen hunderttausend Jahren, als die frühen Menschen gemeinsame Sache machen mussten, um zu überleben; und er endet beim modernen, ultrakooperativen homo sapiens sapiens, der beides besitzt: Eine Moralität der zweiten Person, die unseren Umgang mit dem je einzelnen Gegenüber prägt, und eine gruppenbezogene »objektive« Moral, die sagt, was hier bei »uns« als gut oder gerecht gilt. In der Tradition von Mead, Kohlberg und Piaget zeigt Tomasello außerdem, wie sich die individuelle Moralentwicklung in einer bereits normengesättigten Welt vollzieht. Und so ist Eine Naturgeschichte der menschlichen Moral der derzeit wohl umfassendste Versuch zu verstehen, wie wir das geworden sind, was nur wir sind: genuin moralische Wesen.

Mathematics and Modern Art

Proceedings of the First ESMA Conference, held in Paris, July 19-22, 2010

Author: Claude Bruter

Publisher: Springer Science & Business Media

ISBN: 3642244971

Category: Mathematics

Page: 178

View: 7201

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The link between mathematics and art remains as strong today as it was in the earliest instances of decorative and ritual art. Arts, architecture, music and painting have for a long time been sources of new developments in mathematics, and vice versa. Many great painters have seen no contradiction between artistic and mathematical endeavors, contributing to the progress of both, using mathematical principles to guide their visual creativity, enriching their visual environment with the new objects created by the mathematical science. Owing to the recent development of the so nice techniques for visualization, while mathematicians can better explore these new mathematical objects, artists can use them to emphasize their intrinsic beauty, and create quite new sceneries. This volume, the content of the first conference of the European Society for Mathematics and the Arts (ESMA), held in Paris in 2010, gives an overview on some significant and beautiful recent works where maths and art, including architecture and music, are interwoven. The book includes a wealth of mathematical illustrations from several basic mathematical fields including classical geometry, topology, differential geometry, dynamical systems. Here, artists and mathematicians alike elucidate the thought processes and the tools used to create their work

Strategies for Common Core Mathematics

Implementing the Standards for Mathematical Practice, 6-8

Author: Leslie Texas,Tammy Jones

Publisher: Routledge

ISBN: 1317921380

Category: Education

Page: 176

View: 9440

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This new, practical book provides an explanation of each of the eight mathematical practices and gives middle school educators specific instructional strategies that align with the Common Core State Standards for Mathematics. Math teachers, curriculum coordinators, and district math supervisors get practical ideas on how to engage middle school students in mathematical practices, develop problem-solving skills, and promote higher-order thinking. Learn how to scaffold activities across grades and get strategies you can implement immediately in your classroom. All middle school mathematics educators should have this book in their professional libraries!

The Design of Everyday Things

Psychologie und Design der alltäglichen Dinge

Author: Norman Don

Publisher: Vahlen

ISBN: 3800648105

Category: Business & Economics

Page: 320

View: 7927

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Apple, Audi, Braun oder Samsung machen es vor: Gutes Design ist heute eine kritische Voraussetzung für erfolgreiche Produkte. Dieser Klassiker beschreibt die fundamentalen Prinzipien, um Dinge des täglichen Gebrauchs umzuwandeln in unterhaltsame und zufriedenstellende Produkte. Don Norman fordert ein Zusammenspiel von Mensch und Technologie mit dem Ziel, dass Designer und Produktentwickler die Bedürfnisse, Fähigkeiten und Handlungsweisen der Nutzer in den Vordergrund stellen und Designs an diesen angepasst werden. The Design of Everyday Things ist eine informative und spannende Einführung für Designer, Marketer, Produktentwickler und für alle an gutem Design interessierten Menschen. Zum Autor Don Norman ist emeritierter Professor für Kognitionswissenschaften. Er lehrte an der University of California in San Diego und der Northwest University in Illinois. Mitte der Neunzigerjahre leitete Don Norman die Advanced Technology Group bei Apple. Dort prägte er den Begriff der User Experience, um über die reine Benutzbarkeit hinaus eine ganzheitliche Erfahrung der Anwender im Umgang mit Technik in den Vordergrund zu stellen. Norman ist Mitbegründer der Beratungsfirma Nielsen Norman Group und hat unter anderem Autohersteller von BMW bis Toyota beraten. „Keiner kommt an Don Norman vorbei, wenn es um Fragen zu einem Design geht, das sich am Menschen orientiert.“ Brand Eins 7/2013 „Design ist einer der wichtigsten Wettbewerbsvorteile. Dieses Buch macht Spaß zu lesen und ist von größter Bedeutung.” Tom Peters, Co-Autor von „Auf der Suche nach Spitzenleistungen“

Mathematics for Elementary School Teachers

Author: Tom Bassarear

Publisher: Cengage Learning

ISBN: 0840054637

Category: Mathematics

Page: 752

View: 5591

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Intended for the one- or two-semester course required of Education majors, MATHEMATICS FOR ELEMENTARY SCHOOL TEACHERS, 5E, offers future teachers a comprehensive mathematics course designed to foster concept development through examples, investigations, and explorations. Visual icons throughout the main text allow instructors to easily connect content to the hands-on activities in the corresponding Explorations Manual. Bassarear presents real-world problems, problems that require active learning in a method similar to how archaeologists explore an archaeological find: they carefully uncover the site, slowly revealing more and more of the structure. The author demonstrates that there are many paths to solving a problem, and that sometimes, problems have more than one solution. With this exposure, future teachers will be better able to assess student needs using diverse approaches. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

Beyond Formulas in Mathematics and Teaching

Dynamics of the High School Algebra Classroom

Author: Daniel Chazan

Publisher: Teachers College Press

ISBN: 9780807739181

Category: Education

Page: 200

View: 5053

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Based on the author’s experience as a researcher and teacher of lower-track students, Beyond Formulas in Mathematics and Teaching illuminates the complex dynamics of the algebra classroom. From within this setting, Daniel Chazan thoughtfully explores topics that concern all dedicated educators, how to really know one’s students, how to find engaging material, and how to inspire meaningful classroom conversations. Throughout, he addresses the predicaments that are central to the lives of teachers who work in standard educational settings. By highlighting teaching dilemmas, Chazan prompts readers to consider what their own responses would be in similar situations. With an eye to ways of restructuring roles and relationships, Beyond Formulas in Mathematics and Teaching is essential reading for educators seeking to enhance their teaching practices and understanding of students who may be estranged from school.

Teaching STEM and Common Core with Mentor Texts: Collaborative Lesson Plans, K–5

Collaborative Lesson Plans, K-5

Author: Anastasia Suen,Shirley L. Duke

Publisher: ABC-CLIO

ISBN: 1610695976

Category: Language Arts & Disciplines

Page: 237

View: 6571

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Librarians can use this book to become leaders in their schools, collaborating with teachers to keep them abreast of resources that will facilitate the inclusion of STEM in the curriculum. • Offers five library lessons for each STEM subject based on a mentor text and a lesson for the collaborating teacher • Provides a booktalk to interest the students and a "Book Time" section that allows for reading all or parts of the book accompanied by a general discussion • Shows the range of grades for which each lesson is most suited and how it can be adapted • Includes a graphic organizer (GO Chart) with each lesson, as well as two options for assessing the lesson

A New Mathematical and Philosophical Dictionary

Comprising an Explanation of Terms and Principles of Pure and Mixed Mathematics, and Such Branches of Natural Philosophy as are Susceptible of Mathematical Investigation. With Historical Sketches of the Rise, Progress and Present State of the Several Departments of These Sciences, and an Account of the Discoveries and Writings of the Most Celebrated Authors, Both Ancient and Modern

Author: Peter Barlow

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: 772

View: 9338

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Teaching by Design in Elementary Mathematics, Grades K–1

Author: Jennifer Stepanek,Melinda Leong,Linda Griffin,Lisa Lavelle

Publisher: Corwin Press

ISBN: 1452238839

Category: Education

Page: 256

View: 7267

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Strengthen mathematics lessons through collaborative learning with this research-based professional development program. Included are grade-appropriate number and operations topics aligned with the Common Core State Standards.

Teaching by Design in Elementary Mathematics, Grades 2–3

Author: Jennifer Stepanek,Melinda Leong,Linda Griffin,Lisa Lavelle

Publisher: Corwin Press

ISBN: 1452238812

Category: Education

Page: 256

View: 1334

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Strengthen mathematics lessons through collaborative learning with this research-based professional development program. Included are grade-appropriate number and operations topics aligned with the Common Core State Standards.