Mathematical Discovery on Understanding, Learning, and Teaching Problem Solving

Author: George Pólya,Sam Sloan

Publisher: N.A

ISBN: 9784871878326

Category: Mathematics

Page: 218

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"Solving problems," writes Polya, "is a practical art, like swimming, or skiing, or playing the piano: You can learn it only by imitation and practice. This book cannot offer you a magic key that opens all the doors and solves all the problems, but it offers you good examples for imitation and many opportunities for practice: If you wish to learn swimming you have to go into the water and if you wish to become a problem solver you have to solve problems." "In enough cases to allay . . . discouragement over not immediately discovering a solution, Professor Polya masterfully leads the reader down several unproductive paths. At the end of each chapter he provides examples for the render to solve. By means of these carefully selected and arranged problems, many of them directly related to others that precede, and guided by just the right suggestions at just the proper time, the reader's own ability is developed and extended. Solutions to the examples and, in many cases, outlines of procedures for discovering solutions. arc given at the back of the book. With striking promise for effectiveness, the entire book as a unit is one great experience in learning processes for problem solving through participation. The author has captured with great success the implication of his basic premise stated in the preface ..." The Mathematics Teacher
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Mathematical Discovery on Understanding, Learning and Teaching Problem Solving, Volumes I and II

Author: George Polya

Publisher: John Wiley & Sons Incorporated

ISBN: N.A

Category: Mathematics

Page: 220

View: 876

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A unique, heuristic approach to mathematical discovery and problem solving This combined edition of Mathematical Discovery: On Understanding, Learning and Teaching Problem Solving is unique among mathematics texts. Espousing a heuristic approach to mathematical problem solving, the text may be followed sequentially or according to instructors' individualized curricula. Beginning with a discussion of patterns and practical approaches to problem solving, the book then presents examples from various branches of math and science to help students discover how to solve problems on their own – an invaluable skill for the classroom and beyond.
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Philosophical Dimensions in Mathematics Education

Author: Karen Francois,Jean Paul Van Bendegem

Publisher: Springer Science & Business Media

ISBN: 0387715754

Category: Education

Page: 242

View: 5081

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This book brings together diverse recent developments exploring the philosophy of mathematics in education. The unique combination of ethnomathematics, philosophy, history, education, statistics and mathematics offers a variety of different perspectives from which existing boundaries in mathematics education can be extended. The ten chapters in this book offer a balance between philosophy of and philosophy in mathematics education. Attention is paid to the implementation of a philosophy of mathematics within the mathematics curriculum.
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Pedagogy for Creative Problem Solving

Author: Peter Merrotsy

Publisher: Taylor & Francis

ISBN: 1351771736

Category: Education

Page: 254

View: 1635

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This book provides students and practising teachers with a solid, research-based framework for understanding creative problem solving and its related pedagogy. Practical and accessible, it equips readers with the knowledge and skills to approach their own solutions to the creative problem of teaching for creative problem solving. First providing a firm grounding in the history of problem solving, the nature of a problem, and the history of creativity and its conceptualisation, the book then critically examines current educational practices, such as creativity and problem solving models and common classroom teaching strategies. This is followed by a detailed analysis of key pedagogical ideas important for creative problem solving: creativity and cognition, creative problem solving environments, and self regulated learning. Finally, the ideas debated and developed are drawn together to form a solid foundation for teaching for creative problem solving, and presented in a model called Middle C. Middle C is an evidence-based model of pedagogy for creative problem solving. It comprises 14 elements, each of which is necessary for quality teaching that will provide students with the knowledge, skills, structures and support to express their creative potential. As well as emphasis on the importance of self regulated learning, a new interpretation of Pólya's heuristic is presented.
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International Handbook of Research in History, Philosophy and Science Teaching

Author: Michael R. Matthews

Publisher: Springer

ISBN: 9400776543

Category: Education

Page: 2532

View: 1183

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This inaugural handbook documents the distinctive research field that utilizes history and philosophy in investigation of theoretical, curricular and pedagogical issues in the teaching of science and mathematics. It is contributed to by 130 researchers from 30 countries; it provides a logically structured, fully referenced guide to the ways in which science and mathematics education is, informed by the history and philosophy of these disciplines, as well as by the philosophy of education more generally. The first handbook to cover the field, it lays down a much-needed marker of progress to date and provides a platform for informed and coherent future analysis and research of the subject. The publication comes at a time of heightened worldwide concern over the standard of science and mathematics education, attended by fierce debate over how best to reform curricula and enliven student engagement in the subjects. There is a growing recognition among educators and policy makers that the learning of science must dovetail with learning about science; this handbook is uniquely positioned as a locus for the discussion. The handbook features sections on pedagogical, theoretical, national, and biographical research, setting the literature of each tradition in its historical context. It reminds readers at a crucial juncture that there has been a long and rich tradition of historical and philosophical engagements with science and mathematics teaching, and that lessons can be learnt from these engagements for the resolution of current theoretical, curricular and pedagogical questions that face teachers and administrators. Science educators will be grateful for this unique, encyclopaedic handbook, Gerald Holton, Physics Department, Harvard University This handbook gathers the fruits of over thirty years’ research by a growing international and cosmopolitan community Fabio Bevilacqua, Physics Department, University of Pavia
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Theories of Mathematics Education

Seeking New Frontiers

Author: Bharath Sriraman,Lyn English

Publisher: Springer Science & Business Media

ISBN: 3642007422

Category: Education

Page: 668

View: 8395

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Advances in Mathematics Education is a new and innovative book series published by Springer that builds on the success and the rich history of ZDM—The Inter- tional Journal on Mathematics Education (formerly known as Zentralblatt für - daktik der Mathematik). One characteristic of ZDM since its inception in 1969 has been the publication of themed issues that aim to bring the state-of-the-art on c- tral sub-domains within mathematics education. The published issues include a rich variety of topics and contributions that continue to be of relevance today. The newly established monograph series aims to integrate, synthesize and extend papers from previously published themed issues of importance today, by orienting these issues towards the future state of the art. The main idea is to move the ?eld forward with a book series that looks to the future by building on the past by carefully choosing viable ideas that can fruitfully mutate and inspire the next generations. Taking ins- ration from Henri Poincaré (1854–1912), who said “To create consists precisely in not making useless combinations and in making those which are useful and which are only a small minority.
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Catalog of Copyright Entries. Third Series

1965: January-June

Author: Library of Congress. Copyright Office

Publisher: Copyright Office, Library of Congress

ISBN: N.A

Category: Copyright

Page: 1394

View: 5805

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Includes Part 1, Number 1: Books and Pamphlets, Including Serials and Contributions to Periodicals (January - June)
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Mathematical Thinking and Problem Solving

Author: Alan H. Schoenfeld,Alan H. Sloane

Publisher: Routledge

ISBN: 1135440867

Category: Education

Page: 360

View: 6841

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In the early 1980s there was virtually no serious communication among the various groups that contribute to mathematics education -- mathematicians, mathematics educators, classroom teachers, and cognitive scientists. Members of these groups came from different traditions, had different perspectives, and rarely gathered in the same place to discuss issues of common interest. Part of the problem was that there was no common ground for the discussions -- given the disparate traditions and perspectives. As one way of addressing this problem, the Sloan Foundation funded two conferences in the mid-1980s, bringing together members of the different communities in a ground clearing effort, designed to establish a base for communication. In those conferences, interdisciplinary teams reviewed major topic areas and put together distillations of what was known about them.* A more recent conference -- upon which this volume is based -- offered a forum in which various people involved in education reform would present their work, and members of the broad communities gathered would comment on it. The focus was primarily on college mathematics, informed by developments in K-12 mathematics. The main issues of the conference were mathematical thinking and problem solving.
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Geometry in Problems

Author: Alexander Shen

Publisher: American Mathematical Soc.

ISBN: 1470419211

Category: Geometry

Page: 214

View: 1996

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Classical Euclidean geometry, with all its triangles, circles, and inscribed angles, remains an excellent playground for high-school mathematics students, even if it looks outdated from the professional mathematician's viewpoint. It provides an excellent choice of elegant and natural problems that can be used in a course based on problem solving. The book contains more than 750 (mostly) easy but nontrivial problems in all areas of plane geometry and solutions for most of them, as well as additional problems for self-study (some with hints). Each chapter also provides concise reminders of basic notions used in the chapter, so the book is almost self-contained (although a good textbook and competent teacher are always recommended). More than 450 figures illustrate the problems and their solutions. The book can be used by motivated high-school students, as well as their teachers and parents. After solving the problems in the book the student will have mastered the main notions and methods of plane geometry and, hopefully, will have had fun in the process. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession. What a joy! Shen's ``Geometry in Problems'' is a gift to the school teaching world. Beautifully organized by content topic, Shen has collated a vast collection of fresh, innovative, and highly classroom-relevant questions, problems, and challenges sure to enliven the minds and clever thinking of all those studying Euclidean geometry for the first time. This book is a spectacular resource for educators and students alike. Users will not only sharpen their mathematical understanding of specific topics but will also sharpen their problem-solving wits and come to truly own the mathematics explored. Also, Math Circle leaders can draw much inspiration for session ideas from the material presented in this book. --James Tanton, Mathematician-at-Large, Mathematical Association of America We learn mathematics best by doing mathematics. The author of this book recognizes this principle. He invites the reader to participate in learning plane geometry through carefully chosen problems, with brief explanations leading to much activity. The problems in the book are sometimes deep and subtle: almost everyone can do some of them, and almost no one can do all. The reader comes away with a view of geometry refreshed by experience. --Mark Saul, Director of Competitions, Mathematical Association of America
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