Mathematical Discovery on Understanding Learning and Teaching Problem Solving

Mathematical Discovery on Understanding  Learning  and Teaching Problem Solving

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 ...

Author: George Pólya

Publisher:

ISBN: 4871878325

Category: Mathematics

Page: 218

View: 568

"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
Categories: Mathematics

Mathematical Discovery on Understanding Learning and Teaching Problem Solving

Mathematical Discovery on Understanding  Learning  and Teaching Problem Solving

Born in Budapest on 13 December 1887, his original name was Pólya Györg. He wrote perhaps the most famous book of mathematics ever written, namely "How to Solve It". However, "How to Solve It" is not strictly speaking a math book.

Author: George Pólya

Publisher:

ISBN: 4871878317

Category: Mathematics

Page: 236

View: 567

George Polya was a Hungarian mathematician. Born in Budapest on 13 December 1887, his original name was Polya Gyorg. He wrote perhaps the most famous book of mathematics ever written, namely "How to Solve It." However, "How to Solve It" is not strictly speaking a math book. It is a book about how to solve problems of any kind, of which math is just one type of problem. The same techniques could in principle be used to solve any problem one encounters in life (such as how to choose the best wife ). Therefore, Polya wrote the current volume to explain how the techniques set forth in "How to Solve It" can be applied to specific areas such as geometry.
Categories: Mathematics

Mathematical Discovery

Mathematical Discovery

Author: George Pólya

Publisher: John Wiley & Sons

ISBN: 0471693332

Category: Mathematics

Page: 216

View: 429

Categories: Mathematics

Pedagogy for Creative Problem Solving

Pedagogy for Creative Problem Solving

SPELT (Strategies Program for Effective Learning/Thinking): A description and
analysis of instructional procedures. Instructional ... Mathematical discovery: On
understanding, learning and teaching problem solving [Volume II]. New York, NY:
 ...

Author: Peter Merrotsy

Publisher: Taylor & Francis

ISBN: 9781351771733

Category: Education

Page: 254

View: 260

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.
Categories: Education

Philosophical Dimensions in Mathematics Education

Philosophical Dimensions in Mathematics Education

Philosophical Papers Volume II in 1978, posthumously edited by John Worrall
and Gregory Currie, 1978, 24-42.) Larvor ... Philosophia Mathematica (III), 9 (2),
212-29. Laudan, Larry ... Mathematical Discovery. On Understanding, Learning,
and Teaching Problem Solving. Volume II. John Wiley and Sons, New York.
Pólya ...

Author: Karen Francois

Publisher: Springer Science & Business Media

ISBN: 9780387715759

Category: Education

Page: 242

View: 321

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.
Categories: Education

Essays on the Foundations of Mathematics and Logic

Essays on the Foundations of Mathematics and Logic

[115] Pólya, G. [1962] Mathematical Discovery. On Understanding ... [116] Pólya,
G. [1965] Mathematical Discovery. On Understanding, Learning, and Teaching
Problem Solving. Volume II. John Wiley & Sons. New York. ... Volume II: Patterns
of Plausible Inference. Princeton ... Electronic Research Announcements of The
American Mathematical Society. 2, no1, 17-25. [126] Robertson, N. et al. [1997]
The ...

Author: Giandomenico Sica

Publisher: Polimetrica s.a.s.

ISBN: 9788876990144

Category: Mathematics

Page: 351

View: 975

Categories: Mathematics

International Handbook of Research in History Philosophy and Science Teaching

International Handbook of Research in History  Philosophy and Science Teaching

... To Solve It, Princeton University Press Pólya, G. (1962) Mathematical
Discovery: On Understanding, Learning, and Teaching Problem Solving, 2 vols,
John Wiley and Sons Pólya, G. (1968) Mathematics and Plausible Reasoning
Volume II: ...

Author: Michael R. Matthews

Publisher: Springer

ISBN: 9789400776548

Category: Education

Page: 2532

View: 288

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
Categories: Education

Collected Papers

Collected Papers

Author: George Pólya

Publisher:

ISBN: UCAL:B5159547

Category: Analytic functions

Page: 808

View: 238

Categories: Analytic functions

Models of Simon

Models of Simon

Polya, George (1954b), Mathematics and Plausible Reasoning: Volume II
Patterns of Plausible Inference, Princeton University Press, Princeton, NJ. Polya,
George (1962), Mathematical Discovery: On Understanding, Learning, and
Teaching Problem Solving, John Wiley ... Wang, Hao (1960), Toward Mechanical
Mathematics, IBM Journal for Research and Development, Vol. 4, No. 1, January,
pp. 2–22.

Author: Kumaraswamy Vela Velupillai

Publisher: Routledge

ISBN: 9781134385454

Category: Business & Economics

Page: 200

View: 907

Herbert Simon (1916-2001) is mostly celebrated for the theory of bounded rationality and satisficing. This book of essays on Models of Simon tackles these topics that the he broached in a professional career spanning more than 60 years. Expository material on the fundamental concepts he introduced are re-interpreted in terms of the theory of computability. This volume frames the behavioural issues of concern for economists, such as: hierarchy, causality, near-diagonal linear dynamical systems, discovery, the contrasts between the notion of heuristics, and the Church-Turing Thesis of Computability Theory. There is, consistently, an emphasis on the historical origins of the concepts Simon worked with, in emphasising Human Problem Solving and Decision Making – by rational individuals and institutions (like Organizations). The main feature of the results in the book are its emphasis on the procedural aspects of human problem solving, decision making and the remarkable way Simon harnessed many tools of mathematical logic, mathematics, cognitive sciences, economics and econometrics. This long-awaited volume is an important read for those who study economic theory and philosophy, microeconomics and political economy, as well as those interested in the great Herbert Simon’s work.
Categories: Business & Economics

Teaching Mathematics through Problem Solving in K 12 Classrooms

Teaching Mathematics through Problem Solving in K   12 Classrooms

This book shows how problems can be the vehicle for learning mathematics itself, and presents a comprehensive pedagogy based on classroom discourse, assessment, critical and creative thinking.

Author: Matthew Oldridge

Publisher: Rowman & Littlefield

ISBN: 9781475843347

Category: Education

Page: 134

View: 791

This book shows how problems can be the vehicle for learning mathematics itself, and presents a comprehensive pedagogy based on classroom discourse, assessment, critical and creative thinking.
Categories: Education

Catalog of Copyright Entries Third Series

Catalog of Copyright Entries  Third Series

... Bd.19–20) Appl. author: Ferdinand Springer, employer for hire. c springer-
Verlag; 27 Nov64; AF22365. POLYA, GEORGE. Mathematical discovery, on
understanding, learning, and teaching problem solving. Vol.2. New York, J. Wiley
. 191 p.

Author: Library of Congress. Copyright Office

Publisher: Copyright Office, Library of Congress

ISBN: STANFORD:36105006357474

Category: Copyright

Page: 1394

View: 445

Includes Part 1, Number 1: Books and Pamphlets, Including Serials and Contributions to Periodicals (January - June)
Categories: Copyright

Mathematica Scandinavica

Mathematica Scandinavica

Introduction 1-2 * Convex polyhedra with given values of a monotonic function of
finite faces and with given support numbers for infinite faces 3–8 ... George Pólya
: Mathematical discovery . On understanding , learning , and teaching problem
solving II . New York · London Sydney · John Wiley & Sons , Inc. , 1965. 22 + 191
pp . sh . 42 / - , Preface * From the preface to volume I * Hints to the reader . Part 2
 ...

Author:

Publisher:

ISBN: UCSD:31822005592936

Category: Mathematics

Page:

View: 541

Categories: Mathematics

Exploring Mathematics

Exploring Mathematics

Or perhaps you had an idea but got stuck halfway through? This book guides you in developing your creativity, as it takes you on a voyage of discovery into mathematics.

Author: Daniel Grieser

Publisher: Springer

ISBN: 9783319903217

Category: Mathematics

Page: 298

View: 364

Have you ever faced a mathematical problem and had no idea how to approach it? Or perhaps you had an idea but got stuck halfway through? This book guides you in developing your creativity, as it takes you on a voyage of discovery into mathematics. Readers will not only learn strategies for solving problems and logical reasoning, but they will also learn about the importance of proofs and various proof techniques. Other topics covered include recursion, mathematical induction, graphs, counting, elementary number theory, and the pigeonhole, extremal and invariance principles. Designed to help students make the transition from secondary school to university level, this book provides readers with a refreshing look at mathematics and deep insights into universal principles that are valuable far beyond the scope of this book. Aimed especially at undergraduate and secondary school students as well as teachers, this book will appeal to anyone interested in mathematics. Only basic secondary school mathematics is required, including an understanding of numbers and elementary geometry, but no calculus. Including numerous exercises, with hints provided, this textbook is suitable for self-study and use alongside lecture courses.
Categories: Mathematics

Mathematics by Experiment

Mathematics by Experiment

George Polya, Mathematical Discovery: On Understanding, Learning and
Teaching Problem Solving, 1968 The authors first met in 1985, when Bailey used
the Borwein quartic algorithm for π as part of a suite of tests on the new Cray-2
then ...

Author: Jonathan Borwein

Publisher: CRC Press

ISBN: 9781439865361

Category: Mathematics

Page: 393

View: 440

This revised and updated second edition maintains the content and spirit of the first edition and includes a new chapter, "Recent Experiences", that provides examples of experimental mathematics that have come to light since the publication of the first edition in 2003. For more examples and insights, Experimentation in Mathematics: Computational P
Categories: Mathematics

A Decade of the Berkeley Math Circle

A Decade of the Berkeley Math Circle

Based on a dozen of these sessions, this book encompasses a wide variety of enticing mathematical topics: from inversion in the plane to circle geometry; from combinatorics to Rubik's cube and abstract algebra; from number theory to mass ...

Author: Zvezdelina Stankova

Publisher: American Mathematical Soc.

ISBN: 9780821846834

Category: Mathematics

Page: 326

View: 694

Many mathematicians have been drawn to mathematics through their experience with math circles: extracurricular programs exposing teenage students to advanced mathematical topics and a myriad of problem solving techniques and inspiring in them a lifelong love for mathematics. Founded in 1998, the Berkeley Math Circle (BMC) is a pioneering model of a U.S. math circle, aspiring to prepare our best young minds for their future roles as mathematics leaders. Over the last decade, 50 instructors--from university professors to high school teachers to business tycoons--have shared their passion for mathematics by delivering more than 320 BMC sessions full of mathematical challenges and wonders. Based on a dozen of these sessions, this book encompasses a wide variety of enticing mathematical topics: from inversion in the plane to circle geometry; from combinatorics to Rubik's cube and abstract algebra; from number theory to mass point theory; from complex numbers to game theory via invariants and monovariants. The treatments of these subjects encompass every significant method of proof and emphasize ways of thinking and reasoning via 100 problem solving techniques. Also featured are 300 problems, ranging from beginner to intermediate level, with occasional peaks of advanced problems and even some open questions. The book presents possible paths to studying mathematics and inevitably falling in love with it, via teaching two important skills: thinking creatively while still ``obeying the rules,'' and making connections between problems, ideas, and theories. The book encourages you to apply the newly acquired knowledge to problems and guides you along the way, but rarely gives you ready answers. ``Learning from our own mistakes'' often occurs through discussions of non-proofs and common problem solving pitfalls. The reader has to commit to mastering the new theories and techniques by ``getting your hands dirty'' with the problems, going back and reviewing necessary problem solving techniques and theory, and persistently moving forward in the book. The mathematical world is huge: you'll never know everything, but you'll learn where to find things, how to connect and use them. The rewards will be substantial. 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.
Categories: Mathematics

Location of Zeros

Location of Zeros

Author: George Pólya

Publisher:

ISBN: UVA:X001445827

Category: Analytic functions

Page: 444

View: 543

Categories: Analytic functions

Cooperative Learning in Mathematics

Cooperative Learning in Mathematics

Grade level: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, p, e, i, s, t.

Author: Neil Davidson

Publisher: Addison-Wesley

ISBN: UOM:39015029742072

Category: Mathematics

Page: 409

View: 318

Top leaders in education provide practical strategies for using cooperative learning in all major topic areas and all levels of mathematics.
Categories: Mathematics

What s Next

What s Next

Contains life-related problems which address concepts from every area of mathematics.

Author: Wilbert Reimer

Publisher:

ISBN: PSU:000043942527

Category: Mathematics

Page: 60

View: 536

Contains life-related problems which address concepts from every area of mathematics.
Categories: Mathematics

Amongst Mathematicians

Amongst Mathematicians

The main part of this book, Chapters 3-8, consists of dialogues between two
characters M, a mathematician, and RME, ... These dialogues focus on a range of
issues regarding the learning and teaching of mathematics at university level. ...
In Chapter 2 I outline the processing that the data collected in these previous
studies has gone through in order to reach the ... the mathematics in the Episode
(problem, solution and examples of student response); reflect on the learning/
teaching ...

Author: Elena Nardi

Publisher: Springer Science & Business Media

ISBN: 9780387371412

Category: Education

Page: 340

View: 391

Offers a perspective on ways in which mathematicians perceive their students' learning and reflection by mathematicians on their teaching practice This book demonstrates the feasibility and potential of collaboration between practicing mathematicians and researchers in mathematics education by engaging mathematicians as educational co-researchers.
Categories: Education

Model Centered Learning

Model Centered Learning

This book should be of interest to mathematics educators, mathematicians, and graduate students in STEM education and instructional technologies.

Author: Lingguo Bu

Publisher: Springer Science & Business Media

ISBN: 9789460916182

Category: Education

Page: 247

View: 851

Model-Centered Learning: Pathways to Mathematical Understanding Using GeoGebra is the first book to report on the international use of GeoGebra and its growing impact on mathematics teaching and learning. Supported by new developments in model-centered learning and instruction, the chapters in this book move beyond the traditional views of mathematics and mathematics teaching, providing theoretical perspectives and examples of practice for enhancing students’ mathematical understanding through mathematical and didactical modeling. Designed specifically for teaching mathematics, GeoGebra integrates dynamic multiple representations in a conceptually rich learning environment that supports the exploration, construction, and evaluation of mathematical models and simulations. The open source nature of GeoGebra has led to a growing international community of mathematicians, teacher educators, and classroom teachers who seek to tackle the challenges and complexity of mathematics education through a grassroots initiative using instructional innovations. The chapters cover six themes: 1) the history, philosophy, and theory behind GeoGebra, 2) dynamic models and simulations, 3) problem solving and attitude change, 4) GeoGebra as a cognitive and didactical tool, 5) curricular challenges and initiatives, 6) equity and sustainability in technology use. This book should be of interest to mathematics educators, mathematicians, and graduate students in STEM education and instructional technologies.
Categories: Education