Intuition In Science And Mathematics
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Intuition In Science And Mathematics
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Author : H. Fischbein
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-12-19
Intuition In Science And Mathematics written by H. Fischbein and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-12-19 with Education categories.
In writing the present book I have had in mind the following objectives: - To propose a theoretical, comprehensive view of the domain of intuition. - To identify and organize the experimental findings related to intuition scattered in a wide variety of research contexts. - To reveal the educational implications of the idea, developed for science and mathematics education. Most of the existing monographs in the field of intuition are mainly concerned with theoretical debates - definitions, philosophical attitudes, historical considerations. (See, especially the works of Wild (1938), of Bunge (1 962) and of Noddings and Shore (1 984).) A notable exception is the book by Westcott (1968), which combines theoretical analyses with the author’s own experimental studies. But, so far, no attempt has been made to identify systematically those findings, spread throughout the research literature, which could contribute to the deciphering of the mechanisms of intuition. Very often the relevant studies do not refer explicitly to intuition. Even when this term is used it occurs, usually, as a self-evident, common sense term.
Intuition In Science And Mathematics
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Author : H. Fischbein
language : en
Publisher:
Release Date : 2014-01-15
Intuition In Science And Mathematics written by H. Fischbein and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Intuition And Science
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Author : Mario Bunge
language : en
Publisher:
Release Date : 1962
Intuition And Science written by Mario Bunge and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1962 with Intuition categories.
How Students Mis Understand Science And Mathematics
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Author : Ruth Stavy
language : en
Publisher: Teachers College Press
Release Date : 2000-01-01
How Students Mis Understand Science And Mathematics written by Ruth Stavy and has been published by Teachers College Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-01-01 with Education categories.
In this long-awaited book, Timothy J. Lensmire examines the problems and promise of progressive literacy education. He does this by developing a series of striking metaphors in which, for example, he imagines the writing workshop as a carnival or popular festival and the teacher as a novelist who writes her student-characters into more and less desirable classroom stories. Grounded in Lensmire's own and others' work in schools, Powerful Writing, Responsible Teaching makes powerful use of Bakhtin's theories of language and writing and Dewey's vision of schooling and democracy. Lensmire's book is, at once, a defense, a criticism, and a reconstruction of progressive and critical literacy approaches.
Mathematical Intuition
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Author : R.L. Tieszen
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Mathematical Intuition written by R.L. Tieszen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Philosophy categories.
"Intuition" has perhaps been the least understood and the most abused term in philosophy. It is often the term used when one has no plausible explanation for the source of a given belief or opinion. According to some sceptics, it is understood only in terms of what it is not, and it is not any of the better understood means for acquiring knowledge. In mathematics the term has also unfortunately been used in this way. Thus, intuition is sometimes portrayed as if it were the Third Eye, something only mathematical "mystics", like Ramanujan, possess. In mathematics the notion has also been used in a host of other senses: by "intuitive" one might mean informal, or non-rigourous, or visual, or holistic, or incomplete, or perhaps even convincing in spite of lack of proof. My aim in this book is to sweep all of this aside, to argue that there is a perfectly coherent, philosophically respectable notion of mathematical intuition according to which intuition is a condition necessary for mathemati cal knowledge. I shall argue that mathematical intuition is not any special or mysterious kind of faculty, and that it is possible to make progress in the philosophical analysis of this notion. This kind of undertaking has a precedent in the philosophy of Kant. While I shall be mostly developing ideas about intuition due to Edmund Husser! there will be a kind of Kantian argument underlying the entire book.
Intuition In Mathematics And Physics
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Author : Ronny Desmet
language : en
Publisher:
Release Date : 2016-06-16
Intuition In Mathematics And Physics written by Ronny Desmet and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-16 with categories.
Despite the many revolutions in science and philosophy since Newton and Hume, the outdated idea of an inevitable war between the abstractions of science and the deep intuitions of humankind is reconfirmed, again and again. The history of science is interpreted and presented as a succession of victories over the army of our misleading intuitions, and each success of science is marketed as a defeat of intuition. Instead of endorsing the modern dogma that a truth cannot be scientific unless it hurts the deep intuitions of mankind, and that we cannot be scientific unless we tame the authority of our intuition, the authors of this collection highlight developments in 20th and early 21st century science and philosophy that have the potential to support, or even further, Whitehead's philosophical integration of the abstractions of mathematics and physics with the deep intuitions of humankind. Instead of accepting the authority of science-inspired philosophers to reduce and disenchant nature and humankind in the name of our most successful scientific theories, the authors stress the contemporary relevance of Whitehead's philosophical research program of thinking things together - science and intuition; facts and values - to promote the fundamental coherence that is required to start building an ecological civilization.
Intuition And Science
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Author : Mario Augusto Bunge
language : en
Publisher:
Release Date : 1975
Intuition And Science written by Mario Augusto Bunge and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with Intuition categories.
Intuition And The Axiomatic Method
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Author : Emily Carson
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-07-02
Intuition And The Axiomatic Method written by Emily Carson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-07-02 with Philosophy categories.
Following developments in modern geometry, logic and physics, many scientists and philosophers in the modern era considered Kant’s theory of intuition to be obsolete. But this only represents one side of the story concerning Kant, intuition and twentieth century science. Several prominent mathematicians and physicists were convinced that the formal tools of modern logic, set theory and the axiomatic method are not sufficient for providing mathematics and physics with satisfactory foundations. All of Hilbert, Gödel, Poincaré, Weyl and Bohr thought that intuition was an indispensable element in describing the foundations of science. They had very different reasons for thinking this, and they had very different accounts of what they called intuition. But they had in common that their views of mathematics and physics were significantly influenced by their readings of Kant. In the present volume, various views of intuition and the axiomatic method are explored, beginning with Kant’s own approach. By way of these investigations, we hope to understand better the rationale behind Kant’s theory of intuition, as well as to grasp many facets of the relations between theories of intuition and the axiomatic method, dealing with both their strengths and limitations; in short, the volume covers logical and non-logical, historical and systematic issues in both mathematics and physics.
Thinking About Equations
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Author : Matt A. Bernstein
language : en
Publisher: John Wiley & Sons
Release Date : 2011-09-20
Thinking About Equations written by Matt A. Bernstein and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-20 with Mathematics categories.
An accessible guide to developing intuition and skills for solving mathematical problems in the physical sciences and engineering Equations play a central role in problem solving across various fields of study. Understanding what an equation means is an essential step toward forming an effective strategy to solve it, and it also lays the foundation for a more successful and fulfilling work experience. Thinking About Equations provides an accessible guide to developing an intuitive understanding of mathematical methods and, at the same time, presents a number of practical mathematical tools for successfully solving problems that arise in engineering and the physical sciences. Equations form the basis for nearly all numerical solutions, and the authors illustrate how a firm understanding of problem solving can lead to improved strategies for computational approaches. Eight succinct chapters provide thorough topical coverage, including: Approximation and estimation Isolating important variables Generalization and special cases Dimensional analysis and scaling Pictorial methods and graphical solutions Symmetry to simplify equations Each chapter contains a general discussion that is integrated with worked-out problems from various fields of study, including physics, engineering, applied mathematics, and physical chemistry. These examples illustrate the mathematical concepts and techniques that are frequently encountered when solving problems. To accelerate learning, the worked example problems are grouped by the equation-related concepts that they illustrate as opposed to subfields within science and mathematics, as in conventional treatments. In addition, each problem is accompanied by a comprehensive solution, explanation, and commentary, and numerous exercises at the end of each chapter provide an opportunity to test comprehension. Requiring only a working knowledge of basic calculus and introductory physics, Thinking About Equations is an excellent supplement for courses in engineering and the physical sciences at the upper-undergraduate and graduate levels. It is also a valuable reference for researchers, practitioners, and educators in all branches of engineering, physics, chemistry, biophysics, and other related fields who encounter mathematical problems in their day-to-day work.
Chance Logic And Intuition An Introduction To The Counter Intuitive Logic Of Chance
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Author : Steven Tijms
language : en
Publisher: World Scientific
Release Date : 2021-02-18
Chance Logic And Intuition An Introduction To The Counter Intuitive Logic Of Chance written by Steven Tijms and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-18 with Mathematics categories.
Chance rules our daily lives in many different ways. From the outcomes of the lottery to the outcomes of medical tests, from the basketball court to the court of law. The ways of chance are capricious. Bizarre things happen all the time. Nevertheless, chance has a logic of its own. It obeys the rules of probability. But if you open a standard book on probability, you may very well feel far removed from everyday life. Abstract formulas and mathematical symbols stare back at you with almost every turn of the page.This book introduces you to the logic of chance without the use of mathematical formulas or symbols. In Part One, you will meet the fascinating pioneers of the mathematics of probability, including Galileo Galilei and Blaise Pascal. Their stories will introduce you, step by step, to the basics of probability. In Part Two, various examples in all areas of daily life will show you how chance defies our expectations time and again. But armed with the basic rules of probability and a good dose of inventiveness, you will be able to unravel the counter-intuitive logic of chance.