problem solving strategies in mathematics from common approaches to exemplary strategies

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Problem-Solving Strategies in Mathematics: From Common Approaches to Exemplary Strategies

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SIMILAR ITEMS (based on metadata)

• DOI: 10.1142/9478
• Corpus ID: 117837265

Problem-Solving Strategies in Mathematics: From Common Approaches to Exemplary Strategies

• Alfred S. Posamentier , Stephen Krulik
• Published 5 March 2015
• Mathematics

3 Citations

Analysis of contextual problem solutions, mathematical sentences, and misconceptions of pre-service mathematics teachers, invited paper: teaching critical thinking, problem solving, and design thinking: preparing is students for the future, the cops model for collaborative problem-solving in mathematics, related papers.

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Problem-Solving Strategies In Mathematics: From Common Approaches To Exemplary Strategies: 1 (Problem Solving in Mathematics and Beyond) Paperback – 5 Mar. 2015

• ISBN-10 9789814651639
• ISBN-13 978-9814651639
• Publisher Wspc
• Publication date 5 Mar. 2015
• Part of series Problem Solving In Mathematics And Beyond
• Language English
• Dimensions 15.24 x 1.09 x 22.86 cm
• Print length 188 pages
• See all details

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• ASIN ‏ : ‎ 981465163X
• Publisher ‏ : ‎ Wspc (5 Mar. 2015)
• Language ‏ : ‎ English
• Paperback ‏ : ‎ 188 pages
• ISBN-10 ‏ : ‎ 9789814651639
• ISBN-13 ‏ : ‎ 978-9814651639
• Dimensions ‏ : ‎ 15.24 x 1.09 x 22.86 cm
• 583 in History of Mathematics
• 751 in Mathematical Foundations
• 2,299 in Popular Science Maths

About the author

Alfred s. posamentier.

Alfred S. Posamentier (River Vale, NJ)is currently Chief Liaison for International Academic Affairs at Long Island University, New York, and was former Dean of the School of Education and Professor of Mathematics Education at Mercy College (2010-2015), New York, and previously (2010) Distinguished Lecturer at New York City College of Technology of the City University of New York. He is Professor Emeritus of Mathematics Education at The City College of the City University of New York, and former Dean of the School of Education, where he was for 40 years (1970-2010). He is the author and co-author of more than 60 mathematics books for teachers, secondary and elementary school students, and the general readership. Dr. Posamentier is also a frequent commentator in newspapers and journals on topics relating to education.

Dr. Posamentier has a B.A. (Hunter College/CUNY), M.A. (CCNY/CUNY), Ph.D. (Fordham University) and hold Educational Administrative certification from NY and NJ. He has been visiting professor at several European universities in Austria, England, Germany, Czech Republic, and Poland, while at the University of Vienna he was Fulbright Professor (1990).

In 1989 he was awarded an Honorary Fellow at the South Bank University (London, England). In recognition of his outstanding teaching, the City College Alumni Association named him Educator of the Year in 1994, and in 2009. New York City had the day, May 1, 1994, named in his honor by the President of the New York City Council. In 1994, he was also awarded the Grand Medal of Honor from the Republic of Austria, and in 1999, upon approval of Parliament, the President of the Republic of Austria awarded him the title of University Professor of Austria. In 2003 he was awarded the title of Ehrenbürger (Honorary Fellow) of the Vienna University of Technology, and in 2004 was awarded the Austrian Cross of Honor for Arts and Science, First Class from the President of the Republic of Austria. In 2005 he was inducted into the Hunter College Alumni Hall of Fame, and in 2006 he was awarded the prestigious Townsend Harris Medal by the City College Alumni Association. He was inducted into the New York State Mathematics Educator’s Hall of Fame in 2009, and in 2010 he was awarded the coveted Christian-Peter-Beuth Prize in Berlin.

He has taken on numerous important leadership positions in mathematics education locally. He was a member of the New York State Education Commissioner’s Blue Ribbon Panel on the Math-A Regents Exams, and the Commissioner’s Mathematics Standards Committee, which redefined the Standards for New York State, and he also served on the New York City schools Chancellor’s Math Advisory Panel.

Dr. Posamentier is a leading commentator on educational issues and continues his long-time passion of seeking ways to make mathematics interesting to both teachers, students and the general public – as can be seen from some of his more recent books: Strategy Games to Enhance Problem-Solving Ability in Mathematics (World Scientific Publishing, 2017) The Circle: A Mathematical Exploration Beyond the Line (Prometheus, 2016)

Effective Techniques to Motivate Mathematics Instruction (Routledge, 2016); Numbers: Their Tales, Types and Treasures (Prometheus, 2015), Problem-Solving Strategies in Mathematics (World Scientific, 2015), Teaching Secondary Mathematics: Techniques and Enrichment Units, 9th Ed. (Pearson, 2015), Mathematical Curiosities: A Treasure Trove of Unexpected Entertainments (Prometheus, 2014), Geometry: Its Elements and Structure, (Dover, 2014), Magnificent Mistakes in Mathematics (Prometheus Books, 2013), 100 Commonly Asked Questions in Math Class: Answers that Promote Mathematical Understanding, Grades 6-12 (Corwin, 2013), What successful Math Teacher Do: Grades 6-12 (Corwin 2006, 2013),The Secrets of Triangles: A Mathematical Journey (Prometheus Books, 2012), The Glorious Golden Ratio (Prometheus Books, 2012), The Art of Motivating Students for Mathematics Instruction (McGraw-Hill, 2011), The Pythagorean Theorem : Its Power and Glory (Prometheus, 2010), Mathematical Amazements and Surprises: Fascinating Figures and Noteworthy Numbers (Prometheus, 2009), Problem Solving in Mathematics: Grades 3-6: Powerful Strategies to Deepen Understanding (Corwin, 2009), Problem-Solving Strategies for Efficient and Elegant Solutions, Grades 6-12 (Corwin, 2008), The Fabulous Fibonacci Numbers (Prometheus Books, 2007), Progress in Mathematics K-9 textbook series (Sadlier-Oxford, 2006-2009), What successful Math Teacher Do: Grades K-5 (Corwin 2007), Exemplary Practices for Secondary Math Teachers (ASCD, 2007), 101+ Great Ideas to Introduce Key Concepts in Mathematics (Corwin, 2006), , A Biography of the World’s Most Mysterious Number (Prometheus Books, 2004), Math Wonders: To Inspire Teachers and Students (ASCD, 2003), and Math Charmers: Tantalizing Tidbits for the Mind (Prometheus Books, 2003).

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PROBLEM-SOLVING STRATEGIES IN MATHEMATICS From Common Approaches to Exemplary Strategies

• Author(s) Alfred S Posamentier; Stephen Krulik
• Publisher World Scientific

Print ISBN 9789814651622, 9814651621

Etext isbn 9789814651653, 9814651656.

• Copyright 2015
• Available from $ 19.00 USD SKU: 9789814651653

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PROBLEM-SOLVING STRATEGIES IN MATHEMATICS: From Common Approaches to Exemplary Strategies is written by Alfred S Posamentier; Stephen Krulik and published by World Scientific. The Digital and eTextbook ISBNs for PROBLEM-SOLVING STRATEGIES IN MATHEMATICS are 9789814651653, 9814651656 and the print ISBNs are 9789814651622, 9814651621. Save up to 80% versus print by going digital with VitalSource. Additional ISBNs for this eTextbook include 9789814651639.

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ebook ∣ From Common Approaches To Exemplary Strategies · Problem Solving In Mathematics and Beyond

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Problem Solving In Mathematics and Beyond

Alfred S Posamentier

World Scientific Publishing Company

05 March 2015

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• Introduction
• Working Backwards
• Adopting a Different Point of View
• Finding a Pattern
• Solving a Simpler Analogous Problem
• Accounting for All Possibilities
• Considering Extreme Cases
• Making a Drawing
• Intelligent Guessing and Testing
• Accounting for all Possibilities
• Organizing Data
• Logical Reasoning--.
• (source: Nielsen Book Data)

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Problem Solving in Mathematics and Beyond: Volume 1

Problem-solving strategies in mathematics.

• By (author): 
• Alfred S Posamentier ( Mercy College New York, USA )  and 
• Stephen Krulik ( Temple University, USA )
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"This is a wonderful book, filled with problems and witty solutions, addressed to anyone interested in problem-solving. Elementary mathematics is used so that the reader can focus on the strategy. The reader will enjoy reading this book and trying to find their own strategies to arrive at the solution of the problems proposed."

This book introduces ten problem-solving strategies by first presenting the strategy and then applying it to problems in elementary mathematics. In doing so, first the common approach is shown, and then a more elegant strategy is provided. Elementary mathematics is used so that the reader can focus on the strategy and not be distracted by some more sophisticated mathematics.

Errata(s) Errata

Sample Chapter(s) Introduction (71 KB) Chapter 1: Logical Reasoning (79 KB)

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• Logical Reasoning
• Pattern Recognition
• Working Backwards
• Adopting a Different Point of View
• Considering Extreme Cases
• Solving a Simpler Analgous Problem
• Organizing Data
• Making a Drawing or Visual Representation
• Accounting for All Possibilities
• Intelligent Guessing and Testing

FRONT MATTER

• Pages: i–xxiii

https://doi.org/10.1142/9789814651646_fmatter

• About the Authors
• Introduction

Chapter 1: Logical Reasoning

• Pages: 1–12

https://doi.org/10.1142/9789814651646_0001

It must seem rather redundant to have a chapter entirely devoted to a strategy referred to as logical reasoning. Regardless of the strategy being used to solve a problem, it would seem that some logical thinking must permeate the use of all the strategies. After all, to many people, problem solving is almost synonymous with logical reasoning, or logical thought. So, why have this chapter and why isolate this strategy…

Chapter 2: Pattern Recognition

• Pages: 13–28

https://doi.org/10.1142/9789814651646_0002

Some of the most inherent beauties of mathematics are the many patterns that occur in problems as we try to resolve them. The famous mathematician, W.W. Sawyer once said that mathematics could be thought of as a search for patterns. One of the major uses of mathematics is to predict things that occur in a regular manner. For example, how many scones will I need for 3 people? For 4 people? For 10 people? For n people…

Chapter 3: Working Backwards

• Pages: 29–43

https://doi.org/10.1142/9789814651646_0003

The very name of this strategy sounds confusing to most people. It is a very unnatural way of doing things. When most of us went to school, we were taught to solve mathematical problems in a direct, straightforward manner. And yet, working backwards is the way many real-life problems are often resolved. As a simple example, suppose you had to pick up your child from football practice at exactly 5:00 p.m. At what time should you leave? Well, let us say it take 30 minutes to get to the ballpark. We would better leave a 5-minute safety valve. Okay, then we need to leave 35 minutes earlier, or not later than 4:25 p.m. Without even thinking about it, we were working backwards! Of course, this is a very simple example of this strategy…

Chapter 4: Adopting a Different Point of View

• Pages: 45–63

https://doi.org/10.1142/9789814651646_0004

Of the many strategies that exist and that are available to us to solve mathematical problems, the one that allows us to avoid “running into a brick wall” — namely avoiding frustration — is that of approaching the problem from a different point of view. Perhaps one of the classic examples — because of its simplicity and dramatic difference in solution method — is the following. This is an example where the common method leads to a correct answer, but is cumbersome and can often provide an opportunity for some arithmetic mistakes. As an example, consider the following problem…

Chapter 5: Considering Extreme Cases

• Pages: 65–82

https://doi.org/10.1142/9789814651646_0005

In order to obtain some help with solving a particular problem, we may consider some variables at their extremes, while holding others constant. If no specificity for the variable has been prescribed, the extreme case might just provide us with some helpful insight. Most of us have used this strategy in real life, without consciously realizing that we were even doing so. We say to ourselves, “What is the worst that can happen?” — for a particular, situation up for a decision. This “worst-case scenario” is an example of using an extreme case that can sometimes help resolve a problem situation in a very clever way. Similarly, suppose you were asked to test a new product, say, laundry soap. You would have to test it in very cold water as well as very hot water — clearly a consideration of two extreme cases that makes the testing worthwhile. If it does well in these two extreme temperatures, it should do well in the temperatures in between…

Chapter 6: Solving a Simpler Analgous Problem

• Pages: 83–95

https://doi.org/10.1142/9789814651646_0006

There are problems that appear to be extremely complex when we first approach them. The numbers in the problem might be extremely large, and thus confusing or possibly distracting. Perhaps there is an excessive amount of data given, some of which may not even be necessary to solve the given problem. Even the way the problem has been presented can sometimes confuse the reader. Regardless of the reason, an excellent approach is to convert the problem into a simpler form, but as an equivalent version of the original. Change the numbers, modify the original drawing, or try another approach to simply alter the form of the problem. By solving this simplified version of the problem, the problem solver can possibly gain some insight into how to approach the original problem…

Chapter 7: Organizing Data

• Pages: 97–113

https://doi.org/10.1142/9789814651646_0007

The strategy of organizing data is one of the most important strategies, even though at first glance we might assume it to be axiomatic. That is, everyone should automatically organize the data that appears in a problem without giving it a moment's thought. It is what we often do in real life without consciously thinking about it…

Chapter 8: Making a Drawing or Visual Representation

• Pages: 115–130

https://doi.org/10.1142/9789814651646_0008

When a problem asks questions about a particular given geometric figure or drawing, it goes without saying that the drawing or visual representation is an integral part of the solution method. It is necessary, and helps to solve the problem. In that sense it is hard to imagine that some mathematicians in ancient times often derived geometric concepts without drawings — or at least they presented their geometric findings without the appropriate sketch. However, there are many problems where a drawing is not implicit in the statement of the problem; yet, actually seeing what is being considered can be of great help. Many people are visual learners; they need a picture rather than merely words to understand what is taking place. And no, it is not a case of daydreaming. Contrary to what some people believe, visualization has nothing to do with daydreaming. While daydreaming is often a waste of time, visualization is a very powerful method that can help you become more familiar with a given situation…

Chapter 9: Accounting for All Possibilities

• Pages: 131–143

https://doi.org/10.1142/9789814651646_0009

We know that organizing the data in a problem can sometimes be very revealing. When we look for a pattern, for example, carefully organized data in a list or table can aid in the search and help us discover the pattern. However, one particular type of list that is extremely important is the exhaustive list. In this kind of organized list, all the possibilities are listed in some systematic way. Somewhere included on this list will be what we are looking for. Constructing an exhaustive list enables us to examine all the possibilities in a carefully-organized manner…

Chapter 10: Intelligent Guessing and Testing

• Pages: 145–159

https://doi.org/10.1142/9789814651646_0010

Somehow, the very idea of guessing as a problem-solving strategy raises some eyebrows. Indeed, many of us can recall a teacher saying to someone who had volunteered an unusual answer, “Do you know , or are you just guessing? ” In some books, this method of guessing and testing is sometimes referred to as the method of “trial and error,” which is sometimes considered a more negative expression. The added adjective, intelligent guessing and testing should put your mind at ease, and reassure you that this is, indeed, a viable, and even an often useful strategy…

BACK MATTER

• Pages: 161–163

https://doi.org/10.1142/9789814651646_bmatter

"I recommend this book to anyone interested in furthering his or her understanding of problem-solving strategies. I would encourage those individuals to read the book, become familiar with the ten strategies, and then spend some time working through the given problems before reviewing the solutions provided because it will most likely offer some new insight and thinking into the problem."

"The problems presented here could be used by teachers to help their students develop problem-solving skills, by students interested in developing their own skills, or by anybody intrigued by mathematics."

"Many of the problems or problem types will be familiar to Gazette readers and some are quite similar to one another. They are attractively presented in a clear, unfussy manner."

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Problem-solving strategies in mathematics: from common approaches to exemplary strategies (problem solving in mathematics and beyond) - softcover, posamentier, alfred s.

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"I recommend this book to anyone interested in furthering his or her understanding of problemsolving strategies. I would encourage those individuals to read the book, become familiar with the ten strategies, and then spend some time working through the given problems before reviewing the solutions provided because it will most likely offer some new insight and thinking into the problem." Mathematics Teaching in the Middle School "The problems presented here could be used by teachers to help their students develop problemsolving skills, by students interested in developing their own skills, or by anybody intrigued by mathematics." Mathematics Teacher This book introduces ten problemsolving strategies by first presenting the strategy and then applying it to problems in elementary mathematics. In doing so, first the common approach is shown, and then a more elegant strategy is provided. Elementary mathematics is used so that the reader can focus on the strategy and not be distracted by some more sophisticated mathematics.

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This book introduces ten problem-solving strategies by first presenting the strategy and then applying it to problems in elementary mathematics. In so doing, the common less efficient approach is first mentioned and then the effective strategy is shown. Elementary mathematics is used so that the reader can focus on the strategy and not be distracted by some more sophisticated mathematics.

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• Publisher Wspc
• Publication date 2015
• ISBN 10  981465163X
• ISBN 13  9789814651639
• Binding Paperback
• Number of pages 188

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Paperback. Condition: Very Good. Problem-Solving Strategies In Mathematics: From Common Approaches To Exemplary Strategies: 1 (Problem Solving in Mathematics and Beyond) This book is in very good condition and will be shipped within 24 hours of ordering. The cover may have some limited signs of wear but the pages are clean, intact and the spine remains undamaged. This book has clearly been well maintained and looked after thus far. Money back guarantee if you are not satisfied. See all our books here, order more than 1 book and get discounted shipping. . Seller Inventory # 7719-9789814651639

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Problem-Solving Strategies In Mathematics: From Common Approaches To Exemplary Strategies (Problem Solving in Mathematics and Beyond)

Seller: HPB-Red , Dallas, TX, U.S.A.

paperback. Condition: Good. Connecting readers with great books since 1972! Used textbooks may not include companion materials such as access codes, etc. May have some wear or writing/highlighting. We ship orders daily and Customer Service is our top priority!. Seller Inventory # S_344388719

Problem-Solving Strategies in Mathematics: From Common Approaches to Exemplary Strategies

Seller: ThriftBooks-Dallas , Dallas, TX, U.S.A.

Paperback. Condition: Good. No Jacket. Pages can have notes/highlighting. Spine may show signs of wear. ~ ThriftBooks: Read More, Spend Less 0.7. Seller Inventory # G981465163XI3N00

Seller: Bahamut Media , Reading, United Kingdom

(4-star seller) Seller rating 4 out of 5 stars

Paperback. Condition: Very Good. Shipped within 24 hours from our UK warehouse. Clean, undamaged book with no damage to pages and minimal wear to the cover. Spine still tight, in very good condition. Remember if you are not happy, you are covered by our 100% money back guarantee. Seller Inventory # 6545-9789814651639

Seller: Solr Books , Skokie, IL, U.S.A.

Condition: VeryGood. Pages are clean! Minor shelf wear Fast Shipping - Each order powers our free bookstore in Chicago and sending books to Africa!. Seller Inventory # 5D4WH70004W0_ns

Seller: GF Books, Inc. , Hawthorne, CA, U.S.A.

Condition: Very Good. Book is in Used-VeryGood condition. Pages and cover are clean and intact. Used items may not include supplementary materials such as CDs or access codes. May show signs of minor shelf wear and contain very limited notes and highlighting. 0.75. Seller Inventory # 981465163X-2-3

Seller: Book Deals , Tucson, AZ, U.S.A.

Condition: Fair. Acceptable/Fair condition. Book is worn, but the pages are complete, and the text is legible. Has wear to binding and pages, may be ex-library. 0.75. Seller Inventory # 353-981465163X-acp

Seller: Books Unplugged , Amherst, NY, U.S.A.

Condition: Good. Buy with confidence! Book is in good condition with minor wear to the pages, binding, and minor marks within 0.75. Seller Inventory # bk981465163Xxvz189zvxgdd

Seller: Irish Booksellers , Portland, ME, U.S.A.

Condition: Good. SHIPS FROM USA. Used books have different signs of use and do not include supplemental materials such as CDs, Dvds, Access Codes, charts or any other extra material. All used books might have various degrees of writing, highliting and wear and tear and possibly be an ex-library with the usual stickers and stamps. Dust Jackets are not guaranteed and when still present, they will have various degrees of tear and damage. All images are Stock Photos, not of the actual item. book. Seller Inventory # 24-981465163X-G

Condition: New. Book is in NEW condition. 0.75. Seller Inventory # 981465163X-2-1

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