Mathematical Thinking And Problem Solving

Author : Alan H. Schoenfeld,Alan H. Sloane
Publisher : Routledge
Page : 303 pages
File Size : 55,8 Mb
Release : 2016-05-06
Category : Education
ISBN : 9781135440930

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Mathematical Thinking and Problem Solving by Alan H. Schoenfeld,Alan H. Sloane Pdf

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.

Author : John P. D'Angelo,Douglas Brent West
Publisher : Unknown
Page : 0 pages
File Size : 48,8 Mb
Release : 2018
Category : Mathematics
ISBN : 0134689577

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Mathematical Thinking by John P. D'Angelo,Douglas Brent West Pdf

For one/two-term courses in Transition to Advanced Mathematics or Introduction to Proofs. Also suitable for courses in Analysis or Discrete Math. This title is part of the Pearson Modern Classics series. Pearson Modern Classics are acclaimed titles at a value price. Please visit www.pearsonhighered.com/math-classics-series for a complete list of titles. This text is designed to prepare students thoroughly in the logical thinking skills necessary to understand and communicate fundamental ideas and proofs in mathematics-skills vital for success throughout the upperclass mathematics curriculum. The text offers both discrete and continuous mathematics, allowing instructors to emphasize one or to present the fundamentals of both. It begins by discussing mathematical language and proof techniques (including induction), applies them to easily-understood questions in elementary number theory and counting, and then develops additional techniques of proof via important topics in discrete and continuous mathematics. The stimulating exercises are acclaimed for their exceptional quality.

Author : Marilyn A. Reba,Douglas R. Shier
Publisher : CRC Press
Page : 605 pages
File Size : 49,7 Mb
Release : 2014-12-15
Category : Mathematics
ISBN : 9781482297935

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Puzzles, Paradoxes, and Problem Solving by Marilyn A. Reba,Douglas R. Shier Pdf

A Classroom-Tested, Alternative Approach to Teaching Math for Liberal Arts Puzzles, Paradoxes, and Problem Solving: An Introduction to Mathematical Thinking uses puzzles and paradoxes to introduce basic principles of mathematical thought. The text is designed for students in liberal arts mathematics courses. Decision-making situations that progress

Author : Sanjoy Mahajan
Publisher : MIT Press
Page : 152 pages
File Size : 47,6 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 : Paul Zeitz
Publisher : John Wiley & Sons
Page : 389 pages
File Size : 55,6 Mb
Release : 2017
Category : Problem solving
ISBN : 9781119239901

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The Art and Craft of Problem Solving by Paul Zeitz Pdf

This text on mathematical problem solving provides a comprehensive outline of "problemsolving-ology," concentrating on strategy and tactics. It discusses a number of standard mathematical subjects such as combinatorics and calculus from a problem solver's perspective.

Author : John Mason,Joy Davis
Publisher : Deakin University Press
Page : 120 pages
File Size : 47,8 Mb
Release : 1991
Category : Mathematics
ISBN : UOM:39015024965488

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Fostering and Sustaining Mathematics Thinking Through Problem Solving by John Mason,Joy Davis Pdf

Prepared for courses ECT405, ECT705 offered by the Faculty of Education in Deakin University's Open Campus Program.

Author : Arthur A. Hyde,Pamela R. Hyde
Publisher : Heinemann Educational Publishers
Page : 232 pages
File Size : 47,6 Mb
Release : 1991
Category : Education
ISBN : 0435083112

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Mathwise by Arthur A. Hyde,Pamela R. Hyde Pdf

Mathwise, written especially for teachers in grades three through six, introduces teachers to a broad view of what it means for students to do mathematics. Arthur and Pamela Hyde explore the powerful kinds of mathematical thinking that students are capable of doing and offer exciting approaches, methods, and strategies for teaching that will foster this capability. By building a bridge between students' lives and the key concepts of the curriculum, Mathwise helps teachers make mathematics a meaningful part of their students' world.

Author : Peter Liljedahl,Manuel Santos-Trigo
Publisher : Springer
Page : 362 pages
File Size : 54,6 Mb
Release : 2019-02-12
Category : Education
ISBN : 9783030104726

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Mathematical Problem Solving by Peter Liljedahl,Manuel Santos-Trigo Pdf

This book contributes to the field of mathematical problem solving by exploring current themes, trends and research perspectives. It does so by addressing five broad and related dimensions: problem solving heuristics, problem solving and technology, inquiry and problem posing in mathematics education, assessment of and through problem solving, and the problem solving environment. Mathematical problem solving has long been recognized as an important aspect of mathematics, teaching mathematics, and learning mathematics. It has influenced mathematics curricula around the world, with calls for the teaching of problem solving as well as the teaching of mathematics through problem solving. And as such, it has been of interest to mathematics education researchers for as long as the field has existed. Research in this area has generally aimed at understanding and relating the processes involved in solving problems to students’ development of mathematical knowledge and problem solving skills. The accumulated knowledge and field developments have included conceptual frameworks for characterizing learners’ success in problem solving activities, cognitive, metacognitive, social and affective analysis, curriculum proposals, and ways to promote problem solving approaches.

Author : Jordan Ellenberg
Publisher : Penguin Press
Page : 480 pages
File Size : 54,7 Mb
Release : 2014-05-29
Category : Mathematics
ISBN : 9781594205224

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How Not to Be Wrong by Jordan Ellenberg Pdf

A brilliant tour of mathematical thought and a guide to becoming a better thinker, How Not to Be Wrong shows that math is not just a long list of rules to be learned and carried out by rote. Math touches everything we do; It's what makes the world make sense. Using the mathematician's methods and hard-won insights-minus the jargon-professor and popular columnist Jordan Ellenberg guides general readers through his ideas with rigor and lively irreverence, infusing everything from election results to baseball to the existence of God and the psychology of slime molds with a heightened sense of clarity and wonder. Armed with the tools of mathematics, we can see the hidden structures beneath the messy and chaotic surface of our daily lives. How Not to Be Wrong shows us how--Publisher's description.

Author : George Polya,Jeremy Kilpatrick
Publisher : Courier Corporation
Page : 80 pages
File Size : 50,9 Mb
Release : 2013-04-09
Category : Mathematics
ISBN : 9780486318325

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The Stanford Mathematics Problem Book by George Polya,Jeremy Kilpatrick Pdf

Based on Stanford University's well-known competitive exam, this excellent mathematics workbook offers students at both high school and college levels a complete set of problems, hints, and solutions. 1974 edition.

Author : ALAN H. SCHOENFELD
Publisher : Elsevier
Page : 409 pages
File Size : 45,5 Mb
Release : 2014-06-28
Category : Mathematics
ISBN : 9781483295480

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Mathematical Problem Solving by ALAN H. SCHOENFELD Pdf

This book is addressed to people with research interests in the nature of mathematical thinking at any level, to people with an interest in "higher-order thinking skills" in any domain, and to all mathematics teachers. The focal point of the book is a framework for the analysis of complex problem-solving behavior. That framework is presented in Part One, which consists of Chapters 1 through 5. It describes four qualitatively different aspects of complex intellectual activity: cognitive resources, the body of facts and procedures at one's disposal; heuristics, "rules of thumb" for making progress in difficult situations; control, having to do with the efficiency with which individuals utilize the knowledge at their disposal; and belief systems, one's perspectives regarding the nature of a discipline and how one goes about working in it. Part Two of the book, consisting of Chapters 6 through 10, presents a series of empirical studies that flesh out the analytical framework. These studies document the ways that competent problem solvers make the most of the knowledge at their disposal. They include observations of students, indicating some typical roadblocks to success. Data taken from students before and after a series of intensive problem-solving courses document the kinds of learning that can result from carefully designed instruction. Finally, observations made in typical high school classrooms serve to indicate some of the sources of students' (often counterproductive) mathematical behavior.

Author : Keith J. Devlin
Publisher : Unknown
Page : 0 pages
File Size : 51,6 Mb
Release : 2012
Category : Mathematics
ISBN : 0615653634

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Introduction to Mathematical Thinking by Keith J. Devlin Pdf

"Mathematical thinking is not the same as 'doing math'--unless you are a professional mathematician. For most people, 'doing math' means the application of procedures and symbolic manipulations. Mathematical thinking, in contrast, is what the name reflects, a way of thinking about things in the world that humans have developed over three thousand years. It does not have to be about mathematics at all, which means that many people can benefit from learning this powerful way of thinking, not just mathematicians and scientists."--Back cover.

Author : Terence Tao
Publisher : OUP Oxford
Page : 116 pages
File Size : 54,6 Mb
Release : 2006-07-28
Category : Mathematics
ISBN : 9780191568695

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Solving Mathematical Problems by Terence Tao Pdf

Authored by a leading name in mathematics, this engaging and clearly presented text leads the reader through the tactics involved in solving mathematical problems at the Mathematical Olympiad level. With numerous exercises and assuming only basic mathematics, this text is ideal for students of 14 years and above in pure mathematics.

Author : Kaye Christine Stacey,Susie Groves
Publisher : Unknown
Page : 136 pages
File Size : 44,9 Mb
Release : 1985
Category : Mathematics
ISBN : 095899921X

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Strategies for Problem Solving by Kaye Christine Stacey,Susie Groves Pdf

Author : J Mason,L. Burton,K. Stacey
Publisher : Pearson Higher Ed
Page : 266 pages
File Size : 54,7 Mb
Release : 2011-01-10
Category : Mathematics
ISBN : 9780273728924

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Thnking Mathematically by J Mason,L. Burton,K. Stacey Pdf

Thinking Mathematically is perfect for anyone who wants to develop their powers to think mathematically, whether at school, at university or just out of interest. This book is invaluable for anyone who wishes to promote mathematical thinking in others or for anyone who has always wondered what lies at the core of mathematics. Thinking Mathematically reveals the processes at the heart of mathematics and demonstrates how to encourage and develop them. Extremely practical, it involves the reader in questions so that subsequent discussions speak to immediate experience.