Solving Mathematical Problems

With numerous exercises and assuming only basic mathematics, this text is ideal for students of 14 years and above in pure mathematics.

Solving Mathematical Problems

Author: Terence Tao

Publisher: Oxford University Press on Demand

ISBN: 9780199205608

Page: 103

View: 768

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.

How to Solve Mathematical Problems

Seven problem-solving techniques include inference, classification of action sequences, subgoals, contradiction, working backward, relations between problems, and mathematical representation.

How to Solve Mathematical Problems

Author: Wayne A. Wickelgren

Publisher: Courier Corporation

ISBN: 0486152685

Page: 288

View: 785

Seven problem-solving techniques include inference, classification of action sequences, subgoals, contradiction, working backward, relations between problems, and mathematical representation. Also, problems from mathematics, science, and engineering with complete solutions.

Mathematics as Problem Solving

Various elementary techniques for solving problems in algebra, geometry, and combinatorics are explored in this second edition of Mathematics as Problem Solving.

Mathematics as Problem Solving

Author: Alexander Soifer

Publisher: Springer Science & Business Media

ISBN: 0387746463

Page: 106

View: 367

Various elementary techniques for solving problems in algebra, geometry, and combinatorics are explored in this second edition of Mathematics as Problem Solving. Each new chapter builds on the previous one, allowing the reader to uncover new methods for using logic to solve problems. Topics are presented in self-contained chapters, with classical solutions as well as Soifer's own discoveries. With roughly 200 different problems, the reader is challenged to approach problems from different angles. Mathematics as Problem Solving is aimed at students from high school through undergraduate levels and beyond, educators, and the general reader interested in the methods of mathematical problem solving.

Mathematical Problem Solving

This book contributes to the field of mathematical problem solving by exploring current themes, trends and research perspectives.

Mathematical Problem Solving

Author: Peter Liljedahl

Publisher: Springer

ISBN: 9783030104719

Page: 362

View: 499

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.

Problem Solving in Mathematics Education

This survey book reviews four interrelated areas: (i) the relevance of heuristics in problem-solving approaches – why they are important and what research tells us about their use; (ii) the need to characterize and foster creative problem ...

Problem Solving in Mathematics Education

Author: Peter Liljedahl

Publisher: Springer

ISBN: 9783319407296

Page: 39

View: 765

This survey book reviews four interrelated areas: (i) the relevance of heuristics in problem-solving approaches – why they are important and what research tells us about their use; (ii) the need to characterize and foster creative problem-solving approaches – what type of heuristics helps learners devise and practice creative solutions; (iii) the importance that learners formulate and pursue their own problems; and iv) the role played by the use of both multiple-purpose and ad hoc mathematical action types of technologies in problem-solving contexts – what ways of reasoning learners construct when they rely on the use of digital technologies, and how technology and technology approaches can be reconciled.

Problem Solving Strategies

Equally, this is a must-have for individuals interested in solving difficult and challenging problems.

Problem Solving Strategies

Author: Arthur Engel

Publisher: Springer Science & Business Media

ISBN: 0387982191

Page: 403

View: 507

A unique collection of competition problems from over twenty major national and international mathematical competitions for high school students. Written for trainers and participants of contests of all levels up to the highest level, this will appeal to high school teachers conducting a mathematics club who need a range of simple to complex problems and to those instructors wishing to pose a "problem of the week", thus bringing a creative atmosphere into the classrooms. Equally, this is a must-have for individuals interested in solving difficult and challenging problems. Each chapter starts with typical examples illustrating the central concepts and is followed by a number of carefully selected problems and their solutions. Most of the solutions are complete, but some merely point to the road leading to the final solution. In addition to being a valuable resource of mathematical problems and solution strategies, this is the most complete training book on the market.

Mathematics Problem Solving Challenges for Secondary School Students and Beyond

This book is a rare resource consisting of problems and solutions similar to those seen in mathematics contests from around the world.

Mathematics Problem Solving Challenges for Secondary School Students and Beyond

Author: David Linker

Publisher: World Scientific

ISBN: 981473005X

Page: 196

View: 539

This book is a rare resource consisting of problems and solutions similar to those seen in mathematics contests from around the world. It is an excellent training resource for high school students who plan to participate in mathematics contests, and a wonderful collection of problems that can be used by teachers who wish to offer their advanced students some challenging nontraditional problems to work on to build their problem solving skills. It is also an excellent source of problems for the mathematical hobbyist who enjoys solving problems on various levels. Problems are organized by topic and level of difficulty and are cross-referenced by type, making finding many problems of a similar genre easy. An appendix with the mathematical formulas needed to solve the problems has been included for the reader's convenience. We expect that this book will expand the mathematical knowledge and help sharpen the skills of students in high schools, universities and beyond. Contents:Arithmetic and LogicAlgebraGeometryTrigonometryLogarithmsCountingNumber TheoryProbabilityFunctional Equations Readership: High school students, teachers and general public interested in exciting mathematics problems.

Principles of Mathematical Problem Solving

This book presents the principles and specific problem-solving methods that can be used to solve a variety of mathematical problems.

Principles of Mathematical Problem Solving

Author: Martin J. Erickson

Publisher: Pearson College Division

ISBN: 9780130964458

Page: 252

View: 372

This book presents the principles and specific problem-solving methods that can be used to solve a variety of mathematical problems. The book provides clear examples of various problem-solving methods accompanied by numerous exercises and their solutions. Principles of Mathematical Problem Solving introduces and explains specific problem-solving methods (with examples), and gives a set of exercises and complete solutions for each method. The idea is that by studying the principles and applying them to the exercises, the reader will gain problem-solving ability as well as general mathematical insight. Eventually, the reader should be able to produce results that have "the whole air of intuition." Organized according to specific techniques in separate chapters, techniques include induction and the pigeonhole principle, among others. Arranged in order of increasing difficulty, the book presents a wide variety of problem sets designed to illustrate significant mathematical ideas. Each chapter also includes a moderate amount of the "theory" behind each problem-solving principle it presents. An essential resource for every student of mathematics and every professional who needs to solve mathematical problems.

Mathematical Problem Solving

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.

Mathematical Problem Solving

Author: ALAN H. SCHOENFELD

Publisher: Elsevier

ISBN: 1483295486

Page: 409

View: 428

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.

Youngsters Solving Mathematical Problems with Technology

This book contributes to both mathematical problem solving and the communication of mathematics by students, and the role of personal and home technologies in learning beyond school.

Youngsters Solving Mathematical Problems with Technology

Author: Susana Carreira

Publisher: Springer

ISBN: 331924910X

Page: 255

View: 887

This book contributes to both mathematical problem solving and the communication of mathematics by students, and the role of personal and home technologies in learning beyond school. It does this by reporting on major results and implications of the [email protected] project that investigated youngsters’ mathematical problem solving and, in particular, their use of digital technologies in tackling, and communicating the results of their problem solving, in environments beyond school. The book has two focuses: Mathematical problem solving skills and strategies, forms of representing and expressing mathematical thinking, technological-based solutions; and students ́ and teachers ́ perspectives on mathematics learning, especially school compared to beyond-school mathematics.

The Art of Mathematical Problem Solving

Mathematics is a fine art, like painting, sculpture, or music. This book teaches the art of solving challenging mathematics problems. Part I presents a general process for solving problems.

The Art of Mathematical Problem Solving

Author: Richard M. Beekman

Publisher: Lulu.com

ISBN: 1329428900

Page: 266

View: 689

Mathematics is a fine art, like painting, sculpture, or music. This book teaches the art of solving challenging mathematics problems. Part I presents a general process for solving problems. Part II contains 35 difficult and challenging mathematics problems with complete solutions. The goal is to teach the reader how to proceed from an initial state of "panic and fear" to finding a beautiful and elegant solution to a problem.

Posing and Solving Mathematical Problems

The book is divided in three parts, one directed to new research perspectives and the other two directed to teachers and students, respectively. This book collects recent research on posing and solving mathematical problems.

Posing and Solving Mathematical Problems

Author: Patricio Felmer

Publisher: Springer

ISBN: 3319280236

Page: 402

View: 156

This book collects recent research on posing and solving mathematical problems. Rather than treating these two crucial aspects of school mathematics as separate areas of study, the authors approach them as a unit where both areas are measured on equal grounds in relation to each other. The contributors are from a vast variety of countries and with a wide range of experience; it includes the work from many of the leading researchers in the area and an important number of young researchers. The book is divided in three parts, one directed to new research perspectives and the other two directed to teachers and students, respectively.

Problem Solving Through Problems

This is a practical anthology of some of the best elementary problems in different branches of mathematics.

Problem Solving Through Problems

Author: Loren C. Larson

Publisher: Springer

ISBN: 0387961712

Page: 352

View: 764

This is a practical anthology of some of the best elementary problems in different branches of mathematics. Arranged by subject, the problems highlight the most common problem-solving techniques encountered in undergraduate mathematics. This book teaches the important principles and broad strategies for coping with the experience of solving problems. It has been found very helpful for students preparing for the Putnam exam.

Methods for Solving Mathematical Physics Problems

The book is of the handbook-teaching type. On the one hand, the book describes the main definitions, the concepts of the examined methods and approaches used in them, and also the results and claims obtained in every specific case.

Methods for Solving Mathematical Physics Problems

Author: V. I. Agoshkov

Publisher: Cambridge Int Science Publishing

ISBN: 1904602053

Page: 320

View: 845

The book examines the classic and generally accepted methods for solving mathematical physics problems (method of the potential theory, the eigenfunction method, integral transformation methods, discretisation characterisation methods, splitting methods). A separate chapter is devoted to methods for solving nonlinear equations. The book offers a large number of examples of how these methods are applied to the solution of specific mathematical physics problems, applied in the areas of science and social activities, such as energy, environmental protection, hydrodynamics, theory of elasticity, etc.

The Hard Mathematical Olympiad Problems and Their Solutions

The approaches in the book build understanding and not just methods in solving problems. This book is a must read for many math students and is useful for many teachers around the world.

The Hard Mathematical Olympiad Problems and Their Solutions

Author: Steve Dinh

Publisher:

ISBN: 9781463444907

Page: 320

View: 311

This book shows the approaches to solving many difficult Mathematical Olympiad and other international problems posted at the www.mathlinks.ro, the largest mathematical webpage that has most of the problems used to select the talented students of the world. At the time of this book's publication, the solutions to many of these problems are not yet available. This book is not only as much about methods of solving mathematical problems as it is about various approaches to solving the difficult problems in general. It is a first step in examining the creativity that goes into problem-solving. The real points of the book are the enumeration of problem-solving strategies and the tricks applied to solve the problems. The approaches in the book build understanding and not just methods in solving problems. This book is a must read for many math students and is useful for many teachers around the world.

Mathematical Problem Solving The Bar Model Method

This professional learning workbook introduces teachers to the fundamentals of using the Bar Model Method, providing the basis and process of understanding different types of word problems and deriving the bar models to solve them.

Mathematical Problem Solving   The Bar Model Method

Author: Liu Yueh Mei

Publisher: Teaching Resources

ISBN: 9789810781972

Page: 90

View: 243

This professional learning workbook introduces teachers to the fundamentals of using the Bar Model Method, providing the basis and process of understanding different types of word problems and deriving the bar models to solve them. The Bar Model Method is a key problem solving strategy consistently taught to primary school students in Singapore, a nation acknowledged as a global top performer in mathematics based on its performance in benchmarking studies such as the Trends in International Mathematics and Science Study (TIMSS). The Bar Model Method is acknowledged as an effective problem solving heuristic that enables students to understand, visualize and represent conceptually complex problems and their solutions simply and elegantly, and in doing so, further reinforces and builds their conceptual and procedural knowledge, making them more effective problem solvers. The visual representation of the problem and the solution constructed by the student enables the teacher to understand the student's thought process and allows them to correct misconceptions immediately and appropriately. This professional learning workbook introduces teachers to the fundamentals of using the Bar Model Method, providing the basis and process of understanding different types of word problems and deriving the bar models to solve them. For use with Grades 1-6.

Challenging Mathematical Problems with Elementary Solutions

Volume I of a two-part series, this book features a broad spectrum of 100 challenging problems related to probability theory and combinatorial analysis.

Challenging Mathematical Problems with Elementary Solutions

Author: ?. ? ?????

Publisher: Courier Corporation

ISBN: 0486655369

Page: 214

View: 709

Volume I of a two-part series, this book features a broad spectrum of 100 challenging problems related to probability theory and combinatorial analysis. The problems, most of which can be solved with elementary mathematics, range from relatively simple to extremely difficult. Suitable for students, teachers, and any lover of mathematics. Complete solutions.

Youngsters Solving Mathematical Problems with Technology

This book investigates problem solving approaches to mathematical problems that youngsters use in the wake of the growing availability of digital technologies, and how these approaches can be effective and productive for their unique needs.

Youngsters Solving Mathematical Problems with Technology

Author: Susana Carreira

Publisher:

ISBN: 9783319249094

Page:

View: 647

This book investigates problem solving approaches to mathematical problems that youngsters use in the wake of the growing availability of digital technologies, and how these approaches can be effective and productive for their unique needs. The empirical research, conducted in the [email protected] project, delves into the many ways in which students can achieve the solution to a mathematical problem and communicate it with the technological tools they have at their disposal, either in their home environment or in their mathematics classroom. The researchers then address the implications for the future study of a broadened perspective on mathematical problem solving with technology. In addition to exploring how technology has changed mathematical problem solving, the book also provides: A well-developed theoretical framework that integrates the use of technology into mathematical problem-solving Insightful analysis of the young participants' methods of mathematical problem solving, in addition to their teachers and families Examples of student solutions, together with the students' explanations of how they achieved their solution Youngsters Solving Mathematical Problems with Technology is an extremely valuable resource for any researcher or educator interested in mat hematics education, technology in education, or the intersection of both.>.

Comprehending Problem Solving

Look into the classrooms of some of these math teachers in this book, as they share their success stories illustrating the rewards of using these activities to foster deep mathematical understanding.

Comprehending Problem Solving

Author: Arthur Hyde

Publisher: Heinemann Educational Books

ISBN: 9780325049243

Page: 152

View: 537

Nationally recognized mathematics educator and author Art Hyde takes a culminating look at his thirty years of experience working with teachers and students to answer the question: In the Common Core era, what are the most successful practices for helping children solve mathematical problems with deep understanding? The key , he argues, is providing positive experiences with meaningful mathematics centered around rich activities. When students are given the opportunity to wrestle with appropriately difficult activities based on real life situations and intriguing contexts, they become excited about the math and willingly tackle problems with more zeal and accuracy than ever before. The result is deeper understanding of the content and greater skill at doing mathematics. Art draws on extensive research on how children learn and the relationship between reading and mathematical comprehension. His braided model of problem solving in which cognition, language, and mathematics are woven together intentionally forms the basis of math activities that he and numerous elementary teachers around the country have used. Look into the classrooms of some of these math teachers in this book, as they share their success stories illustrating the rewards of using these activities to foster deep mathematical understanding. Arthur Hyde is a professor of mathematics education at National Louis University, where he received its Excellence in Teaching award. While teaching high school mathematics in Philadelphia, he developed a variety of creative methods for teaching math. He also obtained a doctorate in curriculum and instruction from the University of Pennsylvania, where he later directed its teacher-education programs. He has worked frequently in elementary classrooms, conducting extensive professional development programs on teaching mathematics and math problem solving in Chicago and its surrounding school districts. His previous books include: Best Practice, Fourth Edition (coauthored with Steven Zemelman and Harvey Daniels), Understanding Middle School Math, and Comprehending Math.

Understanding Mathematics Through Problem Solving

This book will present a collection of mathematical problems — lighthearted in nature — intended to entertain the general readership.

Understanding Mathematics Through Problem Solving

Author: Posamentier Alfred S

Publisher: World Scientific

ISBN: 9814663697

Page: 532

View: 101

This book will present a collection of mathematical problems — lighthearted in nature — intended to entertain the general readership. Problems will be selected largely for the unusual and unexpected solutions to which they lend themselves. Some interesting contents included: All in all, the book is meant to entertain the general readership and to convince them about the power and beauty of mathematics.