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: 7786

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"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.
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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: 6889

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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.
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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: 6708

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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
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Metaphor and Analogy in the Sciences

Author: F. Hallyn

Publisher: Springer Science & Business Media

ISBN: 9401594422

Category: Philosophy

Page: 244

View: 7808

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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.
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Sociocultural Research on Mathematics Education

An International Perspective

Author: Bill Atweh,Helen Forgasz,Ben Nebres

Publisher: Routledge

ISBN: 1135653119

Category: Education

Page: 480

View: 811

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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.
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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: 9223

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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
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Cognition in Education

Author: Jose P. Mestre,Brian H. Ross

Publisher: Academic Press

ISBN: 0123876915

Category: Psychology

Page: 313

View: 2297

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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.
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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: 9388

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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.
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Group Decision Making

Drawing Out and Reconciling Differences

Author: Thomas L. Saaty,Kirti Peniwati

Publisher: RWS Publications

ISBN: 1888603224

Category:

Page: 385

View: 1004

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When a group makes a decision, that decision carries a lot more weight than when just one person does it. Think of the founding fathers of the American constitution and how much power and influence their ideas have had in the entire world for more than two hundred years. Also think of gravity, a universal force brought about by an enormous number of minute particles that band together to make a universal law. Together, they create a massive force, a law of nature; alone they can barely be noticed. That is how our minds work by deciding together to create a power that transcends our individuality. Group decision making is a gift and an opportunity to create greater influence through the working together of many minds. This book shows how to use the Analytic Hierarchy Process for hierarchical decision making and the Analytic Network Process for decision making in networks with dependence and feedback in group decision making. Part I discusses the group and the decision and shows the importance of using a structured process, particularly for those high value decisions involving many powerful parties with different interests. It discusses how to facilitate a group decision, combine individual judgments and smooth differences to arrive at a decision that everyone can live with and get behind. Part II discusses the group in planning and how to draw out differences. Part III is about conflict resolution and Part IV is about how to address significant issues that come up in group decision making and shows that it is possible to construct an overall group preference.
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