The Number Sense

How the Mind Creates Mathematics, Revised and Updated Edition

Author: Stanislas Dehaene

Publisher: OUP USA

ISBN: 0199753873

Category: Mathematics

Page: 316

View: 9251

"Our understanding of how the human brain performs mathematical calculations is far from complete. In The Number Sense, Stanislas Dehaene offers readers an enlightening exploration of the mathematical mind. Using research showing that human infants have a rudimentary number sense, Dehaene suggests that this sense is as basic as our perception of color, and that it is wired into the brain. But how then did we leap from this basic number ability to trigonometry, calculus, and beyond? Dehaene shows that it was the invention of symbolic systems of numerals that started us on the climb to higher mathematics. Tracing the history of numbers, we learn that in early times, people indicated numbers by pointing to part of their bodies, and how Roman numerals were replaced by modern numbers. On the way, we also discover many fascinating facts: for example, because Chinese names for numbers are short, Chinese people can remember up to nine or ten digits at a time, while English-speaking people can only remember seven. A fascinating look at the crossroads where numbers and neurons intersect, The Number Sense offers an intriguing tour of how the structure of the brain shapes our mathematical abilities, and how math can open up a window on the human mind"--Provided by publisher.

The Number Sense : How the Mind Creates Mathematics

How the Mind Creates Mathematics

Author: Stanislas Dehaene Research Affiliate Institut National de la Sante et de la Recherche Medicale

Publisher: Oxford University Press, USA

ISBN: 0199723095

Category: Mathematics

Page: 288

View: 9320

Our understanding of how the human brain performs mathematical calculations is far from complete. But in recent years there have been many exciting scientific discoveries, some aided by new imaging techniques--which allow us for the first time to watch the living mind at work--and others by ingenious experiments conducted by researchers all over the world. There are still perplexing mysteries--how, for instance, do idiot savants perform almost miraculous mathematical feats?--but the picture is growing steadily clearer. In The Number Sense, Stanislas Dehaene offers general readers a first look at these recent stunning discoveries, in an enlightening exploration of the mathematical mind. Dehaene, a mathematician turned cognitive neuropsychologist, begins with the eye-opening discovery that animals--including rats, pigeons, raccoons, and chimpanzees--can perform simple mathematical calculations, and he describes ingenious experiments that show that human infants also have a rudimentary number sense (American scientist Karen Wynn, for instance, using just a few Mickey Mouse toys and a small puppet theater, proved that five-month-old infants already have the ability to add and subtract). Further, Dehaene suggests that this rudimentary number sense is as basic to the way the brain understands the world as our perception of color or of objects in space, and, like these other abilities, our number sense is wired into the brain. But how then did the brain leap from this basic number ability to trigonometry, calculus, and beyond? Dehaene shows that it was the invention of symbolic systems of numerals that started us on the climb to higher mathematics, and in a marvelous chapter he traces the history of numbers, from early times when people indicated a number by pointing to a part of their body (even today, in many societies in New Guinea, the word for six is "wrist"), to early abstract numbers such as Roman numerals (chosen for the ease with which they could be carved into wooden sticks), to modern numbers. On our way, we also discover many fascinating facts: for example, because Chinese names for numbers are so short, Chinese people can remember up to nine or ten digits at a time--English-speaking people can only remember seven. Dehaene also explores the unique abilities of idiot savants and mathematical geniuses, asking what might explain their special mathematical talent. And we meet people whose minute brain lesions render their mathematical ability useless--one man, in fact, who is certain that two and two is three. Using modern imaging techniques (PET scans and MRI), Dehaene reveals exactly where in the brain numerical calculation takes place. But perhaps most important, The Number Sense reaches many provocative conclusions that will intrigue anyone interested in mathematics or the mind. Dehaene argues, for instance, that many of the difficulties that children face when learning math, and which may turn into a full-blown adult "innumeracy," stem from the architecture of our primate brain, which has not evolved for the purpose of doing mathematics. He also shows why the human brain does not work like a computer, and that the physical world is not based on mathematics--rather, mathematics evolved to explain the physical world the way that the eye evolved to provide sight. A truly fascinating look at the crossroads where numbers and neurons intersect, The Number Sense offers an intriguing tour of how the structure of the brain shapes our mathematical abilities, and how our mathematics opens up a window on the human mind.

Der Zahlensinn oder Warum wir rechnen können

Author: Stanislas Dehaene

Publisher: Springer-Verlag

ISBN: 3034878257

Category: Science

Page: 311

View: 4166

Wir sind umgeben von Zahlen. Ob auf Kreditkarten gestanzt oder auf Münzen geprägt, ob auf Schecks gedruckt oder in den Spalten computerisierter Tabellen aufgelistet, überall beherrschen Zahlen unser Leben. Sie sind auch der Kern unserer Technologie. Ohne Zahlen könnten wir weder Raketen starten, die das Sonnensystem erkunden, noch Brücken bauen, Güter austauschen oder Rech nungen bezahlen. In gewissem Sinn sind Zahlen also kulturelle Erfindungen, die sich ihrer Bedeutung nach nur mit der Landwirtschaft oder mit dem Rad vergleichen lassen. Aber sie könnten sogar noch tiefere Wurzeln haben. Tausende von Jahren vor Christus benutzten babylonische Wissenschaftler Zahlzeichen, um erstaun lich genaueastronomische Tabellen zu berechnen. Zehntausende von Jahren zuvor hatten Menschen der Steinzeit die ersten geschriebenen Zahlenreihen geschaffen, indem sie Knochen einkerbten oder Punkte auf Höhlenwände malten. Und, wie ich später überzeugend darzustellen hoffe, schon vor weiteren Millionen von Jahren, lange bevor es Menschen gab, nahmen Tiere aller Arten Zahlen zur Kenntnis und stellten mit ihnen einfache Kopfrechnungen an. Sind Zahlen also fast so alt wie das Leben selbst? Sind sie in der Struktur unseres Gehirns verankert? Besitzen wir einen Zahlensinn, eine spezielle Intuition, die uns hilft, Zahlen und Mathematik mit Sinn zu erfüllen? Ich wurde vor fünfzehn Jahren, während meiner Ausbildung zum Mathema tiker, fasziniert von den abstrakten Objekten, mit denen ich umzugehen lernte, vor allem von den einfachsten von ihnen- den Zahlen.

Mind & Body

Wie Gehirn und Psyche die Gesundheit beeinflussen - Wissen & Leben Herausgegeben von Wulf Bertram

Author: Rüegg, Johann Caspar

Publisher: Schattauer Verlag

ISBN: 379453204X

Category:

Page: 224

View: 3668

Ein Buch aus der Reihe "Wissen & Leben" „Es ist der Geist, der sich den Körper baut“ (Friedrich Schiller) Welche Zusammenhänge bestehen zwischen Gehirn, Emotionen und Körper? Wie werden traumatische Erfahrungen erinnert; kann man sie löschen oder „überschreiben“? Wie beeinflussen frühkindliche Erlebnisse die Gesundheit? Und wie kann Meditation das Gehirn verändern? Die aktuellen Erkenntnisse der Hirnforschung, Immunologie und Genetik werfen zahlreiche spannende Fragen auf. Wissenschaftlich fundiert, anschaulich und unterhaltsam erklärt der bekannte Heidelberger Physiologe Johann Caspar Rüegg die komplexen Wechselwirkungen zwischen „mind“ und „body“ und wie man sie gezielt nutzen kann. Neue Denk- und Verhaltensweisen, aber auch spirituelle Erfahrungen können Veränderungen hervorrufen, die über unsere Psyche auf den Körper wirken – denn: Gesundheit beginnt im Kopf! In der 3. Auflage ergänzt ein Kapitel zur „sprechenden Medizin“ das breitgefächerte Themenspektrum. Rüegg zeigt auf, wie Worte nachhaltig die Funktionsweise des Gehirns verändern: Sie können die Wirkung von Medikamenten verstärken und sogar wie ein Medikament wirken. Ein neues Glossar erklärt kurz und präzise über 50 Fachbegriffe. Ein geist- und lehrreiches Lesevergnügen für alle, die mehr über die Wechselwirkungen zwischen Gehirn, Psyche und Körper wissen möchten!

(K)ein Gespür für Zahlen

So bekommt man den Durchblick in Mathe

Author: Barbara Oakley

Publisher: MVG Verlag

ISBN: 3864157811

Category: Mathematics

Page: 352

View: 4760

Mathematik versteht man oder eben nicht. Der eine ist dafür natürlich begabt, dem anderen bleibt dieses Fach für immer ein Rätsel. Stimmt nicht, sagt nun Barbara Oakley und zeigt mit ihrem Buch, dass wirklich jeder ein Gespür für Zahlen hat. Mathematik braucht nämlich nicht nur analytisches Denken, sondern auch den kreativen Geist. Denn noch mehr als um Formeln geht es um die Freiheit, einen der vielen möglichen Lösungsansätze zu finden. Der Weg ist das Ziel. Und wie man zum richtigen Ergebnis kommt, ist eine Kunst, die man entwickeln, entdecken und in sich wecken kann. Die Autorin vermittelt eine Vielfalt an Techniken und Werkzeugen, die das Verständnis von Mathematik und Naturwissenschaft grundlegend verbessern. (K)ein Gespür für Zahlen nimmt Ihnen — vor allem wenn Sie sich in Schule, Uni oder Beruf mathematisch oder naturwissenschaftlich beweisen müssen — nicht nur die Grundangst, sondern stärkt Ihren Mut, Ihren mathematischen Fähigkeiten zu vertrauen. So macht Mathe Spaß!

Kognitive Neurowissenschaften

Author: Hans-Otto Karnath,Peter Thier

Publisher: Springer-Verlag

ISBN: 3642255264

Category: Psychology

Page: 800

View: 1062

Das Lehrbuch präsentiert eine Betrachtung sämtlicher kognitiver Leistungen: von Wahrnehmung, Aufmerksamkeit, Orientierung über Sprache, Denken, Vorstellung, Gedächtnis, Handeln, Reaktion bis zu Motorik und Emotion. Dafür werden Beiträge aus den Bereichen Psychologie, Biologie und Medizin hinzugezogen. Merksätze und Zusammenfassungen erleichtern das Lernen, Fallbeispiele und Exkurse dienen der Vertiefung. Die 3. Auflage des Lehrbuchs (zuvor:„Neuropsychologie“) bietet viele neue Kapitel und eine begleitende Website mit Lern-Tools und Lehrmaterialien.

Förderung der Zahlbegriffsentwicklung bei sehenden und blinden Kindern

Empirische Grundlagen und didaktische Konzepte

Author: Juliane Leuders

Publisher: Springer-Verlag

ISBN: 3834825492

Category: Mathematics

Page: 384

View: 3645

Die wissenschaftliche Kenntnislage zur Entwicklung mathematischer Kompetenzen bei blinden Kindern ist lückenhaft, heterogen und teilweise widersprüchlich. Auch für sehende Kinder wurden psychologische Forschungsergebnisse bisher nur teilweise aus didaktischer Perspektive ausgewertet. Juliane Leuders bietet einen umfassenden Überblick über den deutschen und englischsprachigen Forschungsstand zu den Grundlagen des Arithmetiklernens von sehenden und blinden Vorschulkindern und Schulanfängern. Sie thematisiert neuro- und wahrnehmungspsychologische Grundlagen des Hörens und Tastens und erörtert kognitive Prozesse und die Entwicklung des zahlbezogenen Denkens. Im didaktischen Teil beschreibt sie den Kompetenzerwerb im inklusiven Unterricht, die Qualität von Veranschaulichungen und erarbeitet konkrete Vorschläge für die Adaption von Unterrichtsmaterialien.

Das neue Lexikon des Unwissens

Worauf es bisher keine Antwort gibt

Author: Kathrin Passig,Aleks Scholz,Kai Schreiber

Publisher: Rowohlt Verlag GmbH

ISBN: 3644110115

Category: Fiction

Page: 304

View: 7313

Ist unsere Welt nicht allmählich komplett erforscht, alles vermessen und geklärt? Von wegen. Es gibt erstaunlich viele weiße Flecken auf der Landkarte des menschlichen Wissens. Warum es Links- und Rechtshänder gibt, ist ebenso ungeklärt wie die Entstehung von Braunen Zwergen, das Gewicht eines Kilogramms oder die Frage, woher die seltsamen Geräusche aus der Tiefsee stammen. Ob Dunkle Energie, weiblicher Orgasmus oder Erdbebenvorhersage: Die Welt ist voller Rätsel. Ein faszinierender Blick auf Dinge, von denen wir lediglich wissen, dass wir sie nicht wissen. «Unterhaltsam, geistreich, witzig.» Süddeutsche Zeitung über «Lexikon des Unwissens»

Planting the Seeds of Algebra, 3-5

Explorations for the Upper Elementary Grades

Author: Monica Neagoy

Publisher: Corwin Press

ISBN: 1483379760

Category: Education

Page: 248

View: 1256

Give your students a foundation of algebra for math success – now and in the future! Students and teachers must become friendly with algebraic foundations, as they have increasingly become the gateway to careers in the STEM fields. Monica Neagoy empowers teachers to embrace algebra and connect it to higher math concepts, tuning you and your students to algebraic thinking, reasoning, and doing. You’ll discover: ?Four explorations to help you weave key algebraic ideas into everyday mathematics Step-by-step lessons from real classrooms that will guide you in teaching concepts and in establishing their relevance and applicability New methods that break down difficult algebraic concepts and build a critical foundation for higher math

Das lebendige Theorem

Author: Cédric Villani

Publisher: S. Fischer Verlag

ISBN: 3104025665

Category: Mathematics

Page: 304

View: 4830

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.

Metaphor and Analogy in the Sciences

Author: F. Hallyn

Publisher: Springer Science & Business Media

ISBN: 9401594422

Category: Philosophy

Page: 244

View: 1852

This collection of papers contains historical case studies, systematic contributions of a general nature, and applications to specific sciences. The bibliographies of the contributions contain references to all central items from the traditions that are relevant today. While providing access to contemporary views on the issue, the papers illustrate the wide variety of functions of metaphors and analogies, as well as the many connections between the study of some of these functions and other subjects and disciplines.

Modelling and Mathematics Education

ICTMA 9 - Applications in Science and Technology

Author: J F Matos,S K Houston,W Blum,S P Carreira

Publisher: Elsevier

ISBN: 0857099655

Category: Mathematics

Page: 432

View: 3715

The articles included in this book are from the ICTMA 9 conference held in Lisbon, attended by delegates from about 30 countries. This work records the 1999 Lisbon Conference of ICTMA. It contains the selected and edited content of the conference and makes a significant contribution to mathematical modelling which is the significant investigative preliminary to all scientific and technological applications from machinery to satellites and docking of space-ships. Contains the selected and edited content of the 1999 Lisbon Conference of ICTMA Makes a significant contribution to mathematical modelling, which is the significant investigative preliminary to all scientific and technological applications from machinery to satellites and docking of space-ships

Cognition in Education

Author: Jose P. Mestre,Brian H. Ross

Publisher: Academic Press

ISBN: 0123876915

Category: Psychology

Page: 313

View: 6233

Education and cognitive psychology are natural companions-they both are focused on how people think and learn. Although collaborations have occurred for many years, recently there has been a much greater interest in collaborations that bring cognitive principles into classroom settings. This renewed collaborative research has led both to new evidence-based instructional practices and to a better understanding of cognitive principles. This volume contains overviews of research projects at the intersection of cognitive science and education. The prominent contributors-cognitive psychologists, developmental psychologists, educational psychologists, and science educators-were chosen both for the quality of their work and the variety of their contributions-general principles; influence of affect and motivation; and focus on math and science education. This volume contains overviews of research projects at the intersection of cognitive science and education The prominent contributors were chosen both for the quality of their work and the variety of their contributions general principles; influence of affect and motivation; and focus on math and science education.

Sociocultural Research on Mathematics Education

An International Perspective

Author: Bill Atweh,Helen Forgasz,Ben Nebres

Publisher: Routledge

ISBN: 1135653119

Category: Education

Page: 480

View: 6884

This volume--the first to bring together research on sociocultural aspects of mathematics education--presents contemporary and international perspectives on social justice and equity issues that impact mathematics education. In particular, it highlights the importance of three interacting and powerful factors--gender, social, and cultural dimensions. Sociocultural Research on Mathematics Education: An International Perspective is distinguished in several ways: * It is research based. Chapters report on significant research projects; present a comprehensive and critical summary of the research findings; and offer a critical discussion of research methods and theoretical perspectives undertaken in the area. * It is future oriented, presenting recommendations for practice and policy and identifying areas for further research. * It deals with all aspects of formal and informal mathematics education and applications and all levels of formal schooling. As the context of mathematics education rapidly changes-- with an increased demand for mathematically literate citizenship; an increased awareness of issues of equity, inclusivity, and accountability; and increased efforts for globalization of curriculum development and research-- questions are being raised more than ever before about the problems of teaching and learning mathematics from a non-cognitive science perspective. This book contributes significantly to addressing such issues and answering such questions. It is especially relevant for researchers, graduate students, and policymakers in the field of mathematics education.

Russell's Unknown Logicism

A Study in the History and Philosophy of Mathematics

Author: S. Gandon

Publisher: Springer

ISBN: 1137024658

Category: Mathematics

Page: 263

View: 2595

In this excellent book Sebastien Gandon focuses mainly on Russell's two major texts, Principa Mathematica and Principle of Mathematics , meticulously unpicking the details of these texts and bringing a new interpretation of both the mathematical and the philosophical content. Winner of The Bertrand Russell Society Book Award 2013.

Teaching Deaf Learners

Psychological and Developmental Foundations

Author: Harry Knoors PhD,Marc Marschark

Publisher: Oxford University Press

ISBN: 0190213841

Category: Psychology

Page: 304

View: 4449

Teaching Deaf Learners: Psychological and Developmental Foundations explores how deaf students (children and adolescents) learn and the conditions that support their reaching their full cognitive potential -- or not. Beginning with an introduction to teaching and learning of both deaf and hearing students, Knoors and Marschark take an ecological approach to deaf education, emphasizing the need to take into account characteristics of learners and of the educational context. Building on the evidence base with respect to developmental and psychological factors in teaching and learning, they describe characteristics of deaf learners which indicate that teaching deaf learners is not, or should not, be the same as teaching hearing learners. In this volume, Knoors and Marschark explore factors that influence the teaching of deaf learners, including their language proficiencies, literacy and numeracy skills, cognitive abilities, and social-emotional factors. These issues are addressed in separate chapters, with a focus on the importance to all of them of communication and language. Separate chapters are devoted to the promise of multimedia enhanced education and the possible influences of contextual aspects of the classroom and the school on learning by deaf students. The book concludes by pointing out the importance of appropriate education of teachers of deaf learners, given the increasing diversity of those students and the contexts in which they are educated. It bridges the gap between research and practice in teaching and outlines ways to improve teacher education.

Naturalizing Badiou

Mathematical Ontology and Structural Realism

Author: Fabio Gironi

Publisher: Springer

ISBN: 1137463473

Category: Philosophy

Page: 236

View: 3980

Crossing the boundaries between 'continental' and 'analytic' philosophical approaches, this book proposes a naturalistic revision of the mathematical ontology of Alain Badiou, establishing links with structuralist projects in the philosophy of science and mathematics.

Cognitive Remediation Therapy for Schizophrenia

Theory and Practice

Author: Professor Til Wykes,Dr Clare Reeder

Publisher: Routledge

ISBN: 1135444099

Category: Psychology

Page: 328

View: 2972

Could CRT provide the first structured method of alleviating cognitive deficits associated with schizophrenia? Cognitive Remediation Therapy for Schizophrenia describes the background and development of this new psychological therapy and demonstrates how it provides the first structured help to overcome the thinking problems associated with schizophrenia. In three sections, the book covers the theoretical and empirical underpinning of cognitive remediation therapy and explores its application. Part I, 'The Development of Therapy', provides the historical context and theoretical background to the therapy and emphasizes the value of rehabilitating cognitive deficits. In Part II, 'Improving Cognitive Processes', the process and effects of changing cognition are examined. Finally, in Part III, 'The Process of Therapy', the authors provide a clinical guide to the delivery of cognitive remediation therapy and use case examples to support its efficacy. This book is the first to describe an individual cognitive remediation therapy programme based on a clear model of the relationship between thinking and behaviour. It will be of both academic and clinical value to all those health professionals and clinical academics who want not only to understand the relationships between thought and action but also to intervene to improve therapy.

Developmental Disorders of Language Learning and Cognition

Author: Charles Hulme,Margaret J. Snowling

Publisher: John Wiley & Sons

ISBN: 1118697308

Category: Psychology

Page: 448

View: 7114

This important new text is a comprehensive survey of currentthinking and research on a wide range of developmental disorders. Highlights key research on normal and typical development Includes clinical case studies and diagrams to illustrate keyconcepts A reader-friendly writing style

Educational Neuroscience

Initiatives and Emerging Issues

Author: Kathryn E. Patten,Stephen R. Campbell

Publisher: John Wiley & Sons

ISBN: 144434580X

Category: Education

Page: 120

View: 6592

Educational Neuroscience provides an overview of the wide range of recent initiatives in educational neuroscience, examining a variety of methodological concerns, issues, and directions. Encourages interdisciplinary perspectives in educational neuroscience Contributions from leading researchers examine key issues relating to educational neuroscience and mind, brain, and education more generally Promotes a theoretical and empirical base for the subject area Explores a range of methods available to researchers Identifies agencies, organizations, and associations facilitating development in the field Reveals a variety of on-going efforts to establish theories, models, methods, ethics, and a common language