Powerful Problem Solving

Powerful Problem Solving

Author: Max Ray

Publisher: Heinemann Educational Books

Published: 2013

Total Pages: 0

ISBN-13: 9780325050904

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How can we break the cycle of frustrated students who "drop out of math" because the procedures just don't make sense to them? Or who memorize the procedures for the test but don't really understand the mathematics? Max Ray-Riek and his colleagues at the Math Forum @ Drexel University say "problem solved," by offering their collective wisdom about how students become proficient problem solvers, through the lens of the CCSS for Mathematical Practices. They unpack the process of problem solving in fresh new ways and turn the Practices into activities that teachers can use to foster habits of mind required by the Common Core: communicating ideas and listening to the reflections of others estimating and reasoning to see the "big picture" of a problem organizing information to promote problem solving using modeling and representations to visualize abstract concepts reflecting on, revising, justifying, and extending the work. Powerful Problem Solving shows what's possible when students become active doers rather than passive consumers of mathematics. Max argues that the process of sense-making truly begins when we create questioning, curious classrooms full of students' own thoughts and ideas. By asking "What do you notice? What do you wonder?" we give students opportunities to see problems in big-picture ways, and discover multiple strategies for tackling a problem. Self-confidence, reflective skills, and engagement soar, and students discover that the goal is not to be "over and done," but to realize the many different ways to approach problems. Read a sample chapter.


Book Synopsis Powerful Problem Solving by : Max Ray

Download or read book Powerful Problem Solving written by Max Ray and published by Heinemann Educational Books. This book was released on 2013 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: How can we break the cycle of frustrated students who "drop out of math" because the procedures just don't make sense to them? Or who memorize the procedures for the test but don't really understand the mathematics? Max Ray-Riek and his colleagues at the Math Forum @ Drexel University say "problem solved," by offering their collective wisdom about how students become proficient problem solvers, through the lens of the CCSS for Mathematical Practices. They unpack the process of problem solving in fresh new ways and turn the Practices into activities that teachers can use to foster habits of mind required by the Common Core: communicating ideas and listening to the reflections of others estimating and reasoning to see the "big picture" of a problem organizing information to promote problem solving using modeling and representations to visualize abstract concepts reflecting on, revising, justifying, and extending the work. Powerful Problem Solving shows what's possible when students become active doers rather than passive consumers of mathematics. Max argues that the process of sense-making truly begins when we create questioning, curious classrooms full of students' own thoughts and ideas. By asking "What do you notice? What do you wonder?" we give students opportunities to see problems in big-picture ways, and discover multiple strategies for tackling a problem. Self-confidence, reflective skills, and engagement soar, and students discover that the goal is not to be "over and done," but to realize the many different ways to approach problems. Read a sample chapter.

Math Stories for Problem Solving Success

Math Stories for Problem Solving Success

Author: James L. Overholt

Publisher: Jossey-Bass

Published: 1989-11-13

Total Pages: 0

ISBN-13: 9780787966256

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Here are 51 interesting, true-to-life situations to motivate teenagers to apply math skills for solving everyday problems. For example, in the story "The Challenge" students use decimals and averages as they compare rival football teams' statistics. In "An Interesting Loan", they get practical experience working with money as they help Mike figure out how to pay for a new dirt bike. Each reproducible story is followed by three increasingly difficult groups of problems that focus on the same math topic, making it easy for students of all ability levels to develop the math skills being stressed in the lesson.


Book Synopsis Math Stories for Problem Solving Success by : James L. Overholt

Download or read book Math Stories for Problem Solving Success written by James L. Overholt and published by Jossey-Bass. This book was released on 1989-11-13 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here are 51 interesting, true-to-life situations to motivate teenagers to apply math skills for solving everyday problems. For example, in the story "The Challenge" students use decimals and averages as they compare rival football teams' statistics. In "An Interesting Loan", they get practical experience working with money as they help Mike figure out how to pay for a new dirt bike. Each reproducible story is followed by three increasingly difficult groups of problems that focus on the same math topic, making it easy for students of all ability levels to develop the math skills being stressed in the lesson.

Mathematical Problem Solving

Mathematical Problem Solving

Author: Peter Liljedahl

Publisher: Springer

Published: 2019-02-12

Total Pages: 362

ISBN-13: 3030104729

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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.


Book Synopsis Mathematical Problem Solving by : Peter Liljedahl

Download or read book Mathematical Problem Solving written by Peter Liljedahl and published by Springer. This book was released on 2019-02-12 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Problem Solving in Mathematics Education

Author: Peter Liljedahl

Publisher: Springer

Published: 2016-06-27

Total Pages: 46

ISBN-13: 3319407309

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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.


Book Synopsis Problem Solving in Mathematics Education by : Peter Liljedahl

Download or read book Problem Solving in Mathematics Education written by Peter Liljedahl and published by Springer. This book was released on 2016-06-27 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Experiences in Mathematics

Problem-Solving Experiences in Mathematics

Author: Randall I. Charles

Publisher:

Published: 2004-04

Total Pages:

ISBN-13: 9780769032511

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Book Synopsis Problem-Solving Experiences in Mathematics by : Randall I. Charles

Download or read book Problem-Solving Experiences in Mathematics written by Randall I. Charles and published by . This book was released on 2004-04 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Mathematical Problem Solving

Mathematical Problem Solving

Author: ALAN H. SCHOENFELD

Publisher: Elsevier

Published: 2014-06-28

Total Pages: 426

ISBN-13: 1483295486

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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.


Book Synopsis Mathematical Problem Solving by : ALAN H. SCHOENFELD

Download or read book Mathematical Problem Solving written by ALAN H. SCHOENFELD and published by Elsevier. This book was released on 2014-06-28 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Youngsters Solving Mathematical Problems with Technology

Youngsters Solving Mathematical Problems with Technology

Author: Susana Carreira

Publisher: Springer

Published: 2016-02-19

Total Pages: 269

ISBN-13: 331924910X

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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 Problem@Web 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.


Book Synopsis Youngsters Solving Mathematical Problems with Technology by : Susana Carreira

Download or read book Youngsters Solving Mathematical Problems with Technology written by Susana Carreira and published by Springer. This book was released on 2016-02-19 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Problem@Web 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.

Problem-Solving Experiences in Mathematics

Problem-Solving Experiences in Mathematics

Author: Randall I. Charles

Publisher: Addison-Wesley

Published: 1984-06-01

Total Pages:

ISBN-13: 9780201206845

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Now for grades K-8 with a new kindergarten level and newly revised editions of grades 1 and 2. These new editions of this popular program features: -- lessons that use manipulatives to emphasize hands-on learning at each grade level -- assessment guidelines The program enhances any math text, teaching students to: -- approach problems systematically -- identify various solution strategies -- realize that more than one strategy may be used on a single problem Teacher Sourcebooks feature easy-to-follow strategies, guidelines for multiple uses of the program, extension problems, and evaluation methods. Each Teacher Sourcebook includes blackline masters with problem clusters to reproduce intact or cut into individual problems. Use them as resources for problem-of-the-day, problem-of-the-week, homework activities, or in a problem-solving resource center. Available in Spanish for grades 1-6.


Book Synopsis Problem-Solving Experiences in Mathematics by : Randall I. Charles

Download or read book Problem-Solving Experiences in Mathematics written by Randall I. Charles and published by Addison-Wesley. This book was released on 1984-06-01 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Now for grades K-8 with a new kindergarten level and newly revised editions of grades 1 and 2. These new editions of this popular program features: -- lessons that use manipulatives to emphasize hands-on learning at each grade level -- assessment guidelines The program enhances any math text, teaching students to: -- approach problems systematically -- identify various solution strategies -- realize that more than one strategy may be used on a single problem Teacher Sourcebooks feature easy-to-follow strategies, guidelines for multiple uses of the program, extension problems, and evaluation methods. Each Teacher Sourcebook includes blackline masters with problem clusters to reproduce intact or cut into individual problems. Use them as resources for problem-of-the-day, problem-of-the-week, homework activities, or in a problem-solving resource center. Available in Spanish for grades 1-6.

Problem-solving Experiences in Mathematics

Problem-solving Experiences in Mathematics

Author: Anne M. Bloomer

Publisher:

Published: 1996

Total Pages: 58

ISBN-13:

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Book Synopsis Problem-solving Experiences in Mathematics by : Anne M. Bloomer

Download or read book Problem-solving Experiences in Mathematics written by Anne M. Bloomer and published by . This book was released on 1996 with total page 58 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Problem Solving in Mathematics Education

Problem Solving in Mathematics Education

Author: Torsten Fritzlar

Publisher: WTM-Verlag Münster

Published: 2016-06-30

Total Pages: 250

ISBN-13: 3959870132

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From 3rd to 5th of September 2015 the 17th international ProMath conference (Problem Solving in Mathematics Education) took place at the Faculty of Education of the Martin Luther University Halle-Wittenberg (Germany). For the first time, it was combined with the annual meeting of the working group “Problem Solving” of the Society of Didactics of Mathematics. This book contains 20 peer reviewed articles of researchers from five European countries. The topics of the papers evolved around different areas of learning and problem solving. There are some theoretical papers on problem oriented mathematics instruction and specific aspects of problem solving and creativity as well as reports on detailed studies of problem solving processes of pupils and preservice teachers. Authors also present experiences with “real” problem solving instruction in different countries, considerations and teaching experiments on didactic concepts to foster pupils’ problem solving abilities, and they describe mathematically rich problem fields and their potentials for mathematical investigations in class. ProMath is a group of experienced and early career researchers in the field of mathematics education who are interested in investigating and fostering mathematical problem solving and problem oriented mathematics teaching.


Book Synopsis Problem Solving in Mathematics Education by : Torsten Fritzlar

Download or read book Problem Solving in Mathematics Education written by Torsten Fritzlar and published by WTM-Verlag Münster. This book was released on 2016-06-30 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: From 3rd to 5th of September 2015 the 17th international ProMath conference (Problem Solving in Mathematics Education) took place at the Faculty of Education of the Martin Luther University Halle-Wittenberg (Germany). For the first time, it was combined with the annual meeting of the working group “Problem Solving” of the Society of Didactics of Mathematics. This book contains 20 peer reviewed articles of researchers from five European countries. The topics of the papers evolved around different areas of learning and problem solving. There are some theoretical papers on problem oriented mathematics instruction and specific aspects of problem solving and creativity as well as reports on detailed studies of problem solving processes of pupils and preservice teachers. Authors also present experiences with “real” problem solving instruction in different countries, considerations and teaching experiments on didactic concepts to foster pupils’ problem solving abilities, and they describe mathematically rich problem fields and their potentials for mathematical investigations in class. ProMath is a group of experienced and early career researchers in the field of mathematics education who are interested in investigating and fostering mathematical problem solving and problem oriented mathematics teaching.