Creative Problem Solving in School Mathematics PDF Download

Author: George Lenchner
Publisher:
ISBN: 9780975731611
Category : Australian Primary Schools Mathematical Olympiad
Languages : en
Pages : 281

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Book Description

Author: Alan Sultan
Publisher: World Scientific
ISBN: 981473005X
Category : Mathematics
Languages : en
Pages : 196

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Book Description
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.

Author: Peter Liljedahl
Publisher: Springer
ISBN: 3319407309
Category : Education
Languages : en
Pages : 46

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Book Description
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.

Author: Arthur Engel
Publisher: Springer Science & Business Media
ISBN: 0387226419
Category : Mathematics
Languages : en
Pages : 404

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Book Description
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.

Author: Alexander Soifer
Publisher: Springer Science & Business Media
ISBN: 0387746463
Category : Education
Languages : en
Pages : 120

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Book Description
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.

Author: ALAN H. SCHOENFELD
Publisher: Elsevier
ISBN: 1483295486
Category : Mathematics
Languages : en
Pages : 426

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Book Description
This book is addressed to people with research interests in the nature of mathematical thinking at any level, topeople 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: Akihiko Takahashi
Publisher: Routledge
ISBN: 1000359867
Category : Education
Languages : en
Pages : 159

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Book Description
This engaging book offers an in-depth introduction to teaching mathematics through problem-solving, providing lessons and techniques that can be used in classrooms for both primary and lower secondary grades. Based on the innovative and successful Japanese approaches of Teaching Through Problem-solving (TTP) and Collaborative Lesson Research (CLR), renowned mathematics education scholar Akihiko Takahashi demonstrates how these teaching methods can be successfully adapted in schools outside of Japan. TTP encourages students to try and solve a problem independently, rather than relying on the format of lectures and walkthroughs provided in classrooms across the world. Teaching Mathematics Through Problem-Solving gives educators the tools to restructure their lesson and curriculum design to make creative and adaptive problem-solving the main way students learn new procedures. Takahashi showcases TTP lessons for elementary and secondary classrooms, showing how teachers can create their own TTP lessons and units using techniques adapted from Japanese educators through CLR. Examples are discussed in relation to the Common Core State Standards, though the methods and lessons offered can be used in any country. Teaching Mathematics Through Problem-Solving offers an innovative new approach to teaching mathematics written by a leading expert in Japanese mathematics education, suitable for pre-service and in-service primary and secondary math educators.

Author: Arthur Hyde
Publisher: Heinemann Educational Books
ISBN: 9780325049243
Category : Education
Languages : en
Pages : 0

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Book Description
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.

Author: Peter Liljedahl
Publisher: Springer
ISBN: 3030104729
Category : Education
Languages : en
Pages : 361

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Book Description
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: Matthew Oldridge
Publisher: Rowman & Littlefield
ISBN: 1475843348
Category : Education
Languages : en
Pages : 135

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Book Description
“Teaching through problem-solving” is a commonly used phrase for mathematics educators. This book shows how to use worthwhile and interesting mathematics tasks and problems to build a classroom culture based on students’ reasoning and thinking. It develops a set of axioms about problem-solving classrooms to show teachers that mathematics is playful and engaging. It presents an aspirational vision for school mathematics, one which all teachers can bring into being in their classrooms.