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Author: H. Fischbein Publisher: Springer Science & Business Media ISBN: 0306472376 Category : Education Languages : en Pages : 298
Book Description
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: Springer Science & Business Media ISBN: 0306472376 Category : Education Languages : en Pages : 298
Book Description
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: Ronny Desmet Publisher: ISBN: 9781940447131 Category : Languages : en Pages : 246
Book Description
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: R.L. Tieszen Publisher: Springer Science & Business Media ISBN: 9400922930 Category : Philosophy Languages : en Pages : 223
Book Description
"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: Ruth Stavy Publisher: Teachers College Press ISBN: 9780807770412 Category : Education Languages : en Pages : 148
Book Description
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: Matt A. Bernstein Publisher: John Wiley & Sons ISBN: 1118210646 Category : Mathematics Languages : en Pages : 189
Book Description
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: Stephen Lerman Publisher: Springer ISBN: 9783030157883 Category : Education Languages : en Pages : 916
Book Description
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: David Wilson Henderson Publisher: Prentice Hall ISBN: Category : Mathematics Languages : en Pages : 438
Book Description
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 ISBN: 0128141093 Category : Psychology Languages : en Pages : 244
Book Description
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
Author: Edric Cane Publisher: Dog Ear Publishing ISBN: 9781457518652 Category : Education Languages : en Pages : 194
Book Description
Edric's book is absolutely outstanding. His insight into kids' mental processes, and his techniques for building bridges between real-world experience and math processing are something pretty close to a paradigm shift. AND he knows how to write clearly, simply, conversationally. Howard and Marion Brady, educators, authors, What's Worth Learning. "I have never actually been thanked after a lesson, but today I was. Many times." A teacher tries a strategy based on teaching to her students' intuition, and a topic that had frustrated them no longer seems such a hurdle. Through very practical strategies that teachers can immediately borrow for their classes, Teaching to Intuition seeks to address the widespread estrangement from mathematics displayed by many. Focusing on essential elementary and middle school topics, at that early stage where gaps begin and where too many children lose ground and lose hope, Teaching to Intuition seeks to reconcile students with mathematics itself. It proposes strategies to connect the facts and processes of mathematics to our children's intimate sense of understanding and helps them see mathematics as an emanation of realities and thinking structures that are already theirs. Edric Cane has taught in Europe, in Africa, and at Oberlin College (Ohio) and Occidental College (Los Angeles). He taught math in a 95 percent minority school in the Los Angeles Unified School District. He has a PhD from the University of Michigan and spent two years as a Besse Scholar at Saint Antony's College (Oxford University, England). He now lives near Sacramento, California. The originality of Teaching to Intuition reflects to some degree the variety of his experiences and interests.
Author: H. Fischbein
Author: H. Fischbein
Author: Ronny Desmet
Author: R.L. Tieszen
Author: H. Fischbein
Author: Ruth Stavy
Author: Matt A. Bernstein
Author: Stephen Lerman
Author: David Wilson Henderson
Author: Lois Isenman
Author: Edric Cane