Intuition In Science And Mathematics

Author : H. Fischbein
Publisher : Springer Science & Business Media
Page : 298 pages
File Size : 53,6 Mb
Release : 2005-12-19
Category : Education
ISBN : 9780306472374

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Intuition in Science and Mathematics by H. Fischbein Pdf

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.

Author : H. Fischbein
Publisher : Unknown
Page : 244 pages
File Size : 40,9 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 9401737371

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Intuition in Science and Mathematics by H. Fischbein Pdf

Author : R.L. Tieszen
Publisher : Springer Science & Business Media
Page : 223 pages
File Size : 53,9 Mb
Release : 2012-12-06
Category : Philosophy
ISBN : 9789400922938

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Mathematical Intuition by R.L. Tieszen Pdf

"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.

Author : Ronny Desmet
Publisher : Unknown
Page : 246 pages
File Size : 45,8 Mb
Release : 2016-06-16
Category : Electronic
ISBN : 1940447135

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Intuition in Mathematics and Physics by Ronny Desmet Pdf

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.

Author : Mario Bunge
Publisher : Unknown
Page : 176 pages
File Size : 42,8 Mb
Release : 1962
Category : Intuition
ISBN : UOM:39015072136792

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Intuition and Science by Mario Bunge Pdf

Author : Ruth Stavy,Dina Tirosh
Publisher : Teachers College Press
Page : 148 pages
File Size : 40,6 Mb
Release : 2000-01-01
Category : Education
ISBN : 0807770418

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How Students (mis-) Understand Science and Mathematics by Ruth Stavy,Dina Tirosh Pdf

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.

Author : Sanjoy Mahajan
Publisher : MIT Press
Page : 152 pages
File Size : 49,9 Mb
Release : 2010-03-05
Category : Education
ISBN : 9780262265591

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Street-Fighting Mathematics by Sanjoy Mahajan Pdf

An antidote to mathematical rigor mortis, teaching how to guess answers without needing a proof or an exact calculation. In problem solving, as in street fighting, rules are for fools: do whatever works—don't just stand there! Yet we often fear an unjustified leap even though it may land us on a correct result. Traditional mathematics teaching is largely about solving exactly stated problems exactly, yet life often hands us partly defined problems needing only moderately accurate solutions. This engaging book is an antidote to the rigor mortis brought on by too much mathematical rigor, teaching us how to guess answers without needing a proof or an exact calculation. In Street-Fighting Mathematics, Sanjoy Mahajan builds, sharpens, and demonstrates tools for educated guessing and down-and-dirty, opportunistic problem solving across diverse fields of knowledge—from mathematics to management. Mahajan describes six tools: dimensional analysis, easy cases, lumping, picture proofs, successive approximation, and reasoning by analogy. Illustrating each tool with numerous examples, he carefully separates the tool—the general principle—from the particular application so that the reader can most easily grasp the tool itself to use on problems of particular interest. Street-Fighting Mathematics grew out of a short course taught by the author at MIT for students ranging from first-year undergraduates to graduate students ready for careers in physics, mathematics, management, electrical engineering, computer science, and biology. They benefited from an approach that avoided rigor and taught them how to use mathematics to solve real problems. Street-Fighting Mathematics will appear in print and online under a Creative Commons Noncommercial Share Alike license.

Author : Steven Tijms
Publisher : World Scientific
Page : 254 pages
File Size : 52,9 Mb
Release : 2021-02-18
Category : Mathematics
ISBN : 9789811229206

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Chance, Logic And Intuition: An Introduction To The Counter-intuitive Logic Of Chance by Steven Tijms Pdf

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.

Author : Emily Carson,Renate Huber
Publisher : Springer Science & Business Media
Page : 356 pages
File Size : 53,7 Mb
Release : 2006-01-24
Category : Mathematics
ISBN : 1402040393

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Intuition and the Axiomatic Method by Emily Carson,Renate Huber Pdf

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.

Author : Stephen Lerman
Publisher : Springer
Page : 916 pages
File Size : 54,8 Mb
Release : 2020-02-07
Category : Education
ISBN : 3030157881

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Encyclopedia of Mathematics Education by Stephen Lerman Pdf

The Encyclopedia of Mathematics Education is a comprehensive reference text, covering every topic in the field with entries ranging from short descriptions to much longer pieces where the topic warrants more elaboration. The entries provide access to theories and to research in the area and refer to the leading publications for further reading. The Encyclopedia is aimed at graduate students, researchers, curriculum developers, policy makers, and others with interests in the field of mathematics education. It is planned to be 700 pages in length in its hard copy form but the text will subsequently be up-dated and developed on-line in a way that retains the integrity of the ideas, the responsibility for which will be in the hands of the Editor-in-Chief and the Editorial Board. This second edition will include additional entries on: new ideas in the politics of mathematics education, working with minority students, mathematics and art, other cross-disciplinary studies, studies in emotions and mathematics, new frameworks for analysis of mathematics classrooms, and using simulations in mathematics teacher education. Existing entries will be revised and new entries written. Members of the international mathematics education research community will be invited to propose new entries. Editorial Board: Bharath Sriraman Melony Graven Yoshinori Shimizu Ruhama Even Michele Artigue Eva Jablonka Wish to Become an Author? Springer's Encyclopedia of Mathematics Education's first edition was published in 2014. The Encyclopedia is a "living" project and will continue to accept articles online as part of an eventual second edition. Articles will be peer-reviewed in a timely manner and, if found acceptable, will be immediately published online. Suggested articles are, of course, welcome. Feel encouraged to think about additional topics that we overlooked the first time around, and to suggest colleagues (including yourself!) who will want to write them. Interested new authors should contact the editor in chief, Stephen Lerman, at [email protected], for more specific instructions.

Author : Matt A. Bernstein,William A. Friedman
Publisher : John Wiley & Sons
Page : 189 pages
File Size : 53,9 Mb
Release : 2011-09-20
Category : Mathematics
ISBN : 9781118210642

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Thinking About Equations by Matt A. Bernstein,William A. Friedman Pdf

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.

Author : Shlomo Vinner
Publisher : Springer
Page : 141 pages
File Size : 53,5 Mb
Release : 2019-04-26
Category : Mathematics
ISBN : 9783319900353

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Mathematics, Education, and Other Endangered Species by Shlomo Vinner Pdf

This book examines the critical roles and effects of mathematics education. The exposition draws from the author’s forty-year mathematics career, integrating his research in the psychology of mathematical thinking into an overview of the true definition of math. The intention for the reader is to undergo a “corrective” experience, obtaining a clear message on how mathematical thinking tools can help all people cope with everyday life. For those who have struggled with math in the past, the book also aims to clarify that math learning difficulties are likely a result of improper pedagogy as opposed to any lack of intelligence on the part of the student. This personal treatise will be of interest to a variety of readers, from mathematics teachers and those who train them to those with an interest in education but who may lack a solid math background.

Author : Kalid Azad
Publisher : Unknown
Page : 98 pages
File Size : 51,5 Mb
Release : 2015-12-04
Category : Electronic
ISBN : 1519711549

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Math, Better Explained by Kalid Azad Pdf

Math, Better Explained is an intuitive guide to the math fundamentals. Learn math the way your teachers always wanted.

Author : David Wilson Henderson,Daina Taimin̦a
Publisher : Prentice Hall
Page : 438 pages
File Size : 48,8 Mb
Release : 2005
Category : Mathematics
ISBN : STANFORD:36105114443091

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Experiencing Geometry by David Wilson Henderson,Daina Taimin̦a Pdf

The distinctive approach of Henderson and Taimina's volume stimulates readers to develop a broader, deeper, understanding of mathematics through active experience--including discovery, discussion, writing fundamental ideas and learning about the history of those ideas. A series of interesting, challenging problems encourage readers to gather and discuss their reasonings and understanding. The volume provides an understanding of the possible shapes of the physical universe. The authors provide extensive information on historical strands of geometry, straightness on cylinders and cones and hyperbolic planes, triangles and congruencies, area and holonomy, parallel transport, SSS, ASS, SAA, and AAA, parallel postulates, isometries and patterns, dissection theory, square roots, pythagoras and similar triangles, projections of a sphere onto a plane, inversions in circles, projections (models) of hyperbolic planes, trigonometry and duality, 3-spheres and hyperbolic 3-spaces and polyhedra. For mathematics educators and other who need to understand the meaning of geometry.

Author : Lois Isenman
Publisher : Academic Press
Page : 244 pages
File Size : 52,5 Mb
Release : 2018-04-12
Category : Psychology
ISBN : 9780128141090

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Understanding Intuition by Lois Isenman Pdf

Understanding Intuition: A Journey In and Out of Science explores the biological and cognitive mechanisms that account for intuition, and examines the first-person experience. The book integrates both scientific and personal perspectives on this important yet elusive mental capacity. It uses specific encounters to illustrate that intuition is enhanced when we can attend to the subtle aspects of our inner experiences, such as bodily sensations, images, and differing kinds of intuitive evaluative feelings, all of which may emerge no further than on the fringe of awareness. This awareness of subtle inner experiences helps forge a more fluid exchange between the unconscious and conscious minds, and allows readers to calibrate their own intuitions. Over the course of the book, readers will gain a deeper appreciation and respect for the unconscious mind and its potential sophistication, and even its potential wisdom. Understanding Intuition is a timely and critical resource for students and researchers in psychology, cognitive science, theology, women’s studies, and neuroscience. Stresses the powerful influence of the unconscious mind and its important adaptive role Frames intuition as significant and novel unconscious insight Presents a systematic framework for understanding different kinds of intuition Examines the emotional underpinnings of intuition, giving special emphasis to the role of somatic feelings and their derivatives