Unlocking Creativity In Solving Novel Mathematics Problems

Author : Carol R. Aldous
Publisher : Routledge
Page : 318 pages
File Size : 45,6 Mb
Release : 2019-06-25
Category : Education
ISBN : 9780429684272

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Unlocking Creativity in Solving Novel Mathematics Problems by Carol R. Aldous Pdf

Unlocking Creativity in Solving Novel Mathematics Problems delivers a fascinating insight into thinking and feeling approaches used in creative problem solving and explores whether attending to ‘feeling’ makes any difference to solving novel problems successfully. With a focus on research throughout, this book reveals ways of identifying, describing and measuring ‘feeling’ (or ‘intuition’) in problem-solving processes. It details construction of a new creative problem-solving conceptual framework using cognitive and non-cognitive elements, including the brain’s visuo-spatial and linguistic circuits, conscious and non-conscious mental activity, and the generation of feeling in listening to the self, identified from verbal data. This framework becomes the process model for developing a comprehensive quantitative model of creative problem solving incorporating the Person, Product, Process and Environment dimensions of creativity. In a world constantly seeking new ideas and new approaches to solving complex problems, the application of this book’s findings will revolutionize the way students, teachers, businesses and industries approach novel problem solving, and mathematics learning and teaching.

Author : Carol R. Aldous
Publisher : Routledge
Page : 400 pages
File Size : 47,5 Mb
Release : 2019-06-25
Category : Education
ISBN : 9780429684265

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Unlocking Creativity in Solving Novel Mathematics Problems by Carol R. Aldous Pdf

Unlocking Creativity in Solving Novel Mathematics Problems delivers a fascinating insight into thinking and feeling approaches used in creative problem solving and explores whether attending to ‘feeling’ makes any difference to solving novel problems successfully. With a focus on research throughout, this book reveals ways of identifying, describing and measuring ‘feeling’ (or ‘intuition’) in problem-solving processes. It details construction of a new creative problem-solving conceptual framework using cognitive and non-cognitive elements, including the brain’s visuo-spatial and linguistic circuits, conscious and non-conscious mental activity, and the generation of feeling in listening to the self, identified from verbal data. This framework becomes the process model for developing a comprehensive quantitative model of creative problem solving incorporating the Person, Product, Process and Environment dimensions of creativity. In a world constantly seeking new ideas and new approaches to solving complex problems, the application of this book’s findings will revolutionize the way students, teachers, businesses and industries approach novel problem solving, and mathematics learning and teaching.

Author : George Lenchner
Publisher : Unknown
Page : 295 pages
File Size : 45,6 Mb
Release : 1983
Category : Mathematics
ISBN : 0395345464

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Creative Problem Solving in School Mathematics by George Lenchner Pdf

Author : Alexander A. Roytvarf
Publisher : Springer Science & Business Media
Page : 405 pages
File Size : 42,6 Mb
Release : 2013-01-04
Category : Mathematics
ISBN : 9780817684068

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Thinking in Problems by Alexander A. Roytvarf Pdf

This concise, self-contained textbook gives an in-depth look at problem-solving from a mathematician’s point-of-view. Each chapter builds off the previous one, while introducing a variety of methods that could be used when approaching any given problem. Creative thinking is the key to solving mathematical problems, and this book outlines the tools necessary to improve the reader’s technique. The text is divided into twelve chapters, each providing corresponding hints, explanations, and finalization of solutions for the problems in the given chapter. For the reader’s convenience, each exercise is marked with the required background level. This book implements a variety of strategies that can be used to solve mathematical problems in fields such as analysis, calculus, linear and multilinear algebra and combinatorics. It includes applications to mathematical physics, geometry, and other branches of mathematics. Also provided within the text are real-life problems in engineering and technology. Thinking in Problems is intended for advanced undergraduate and graduate students in the classroom or as a self-study guide. Prerequisites include linear algebra and analysis.

Author : Zhou, Chunfang
Publisher : IGI Global
Page : 252 pages
File Size : 45,6 Mb
Release : 2020-10-16
Category : Education
ISBN : 9781799835295

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Introducing Problem-Based Learning (PBL) for Creativity and Innovation in Chinese Universities: Emerging Research and Opportunities by Zhou, Chunfang Pdf

Chinese universities are striving to integrate new educational elements such as student-centered learning, group learning, active learning, and learning by doing into current traditional curriculum systems for creativity development among young generations. However, the concept of creativity by its very nature is a complex term of many perspectives. It is necessary to clarify what creativity is, how creativity can be fostered in learning environments, and what universities should do in order to foster creative young talents. Introducing Problem-Based Learning (PBL) for Creativity and Innovation in Chinese Universities: Emerging Research and Opportunities is a critical scholarly resource that provides a multidimensional understanding on both challenges and opportunities of fostering creativity and PBL in Chinese universities and particularly discusses this implementation in a Chinese cultural context. Though related to a Chinese cultural context, the book can inspire other universities in other cultures, particularly in Asian areas, to learn why PBL is a potential strategy for creativity development and to rethink how to facilitate the innovation capability of universities in the future. Featuring a wide range of topics such as course design, educational technology, and curriculum development, this book is ideal for education professionals, academicians, teaching professors, researchers, administrators, and students.

Author : Richard M. Beekman
Publisher : Lulu.com
Page : 268 pages
File Size : 44,7 Mb
Release : 2016-01-30
Category : Science
ISBN : 9781329428904

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The Art of Mathematical Problem Solving by Richard M. Beekman Pdf

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.

Author : Robert Kaplinsky
Publisher : Taylor & Francis
Page : 193 pages
File Size : 48,6 Mb
Release : 2023-10-10
Category : Education
ISBN : 9781003839880

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Open Middle Math by Robert Kaplinsky Pdf

This book is an amazing resource for teachers who are struggling to help students develop both procedural fluency and conceptual understanding.. --Dr. Margaret (Peg) Smith, co-author of5 Practices for Orchestrating Productive Mathematical Discussions Robert Kaplinsky, the co-creator of Open Middle math problems, brings hisnew class of tasks designed to stimulate deeper thinking and lively discussion among middle and high school students in Open Middle Math: Problems That Unlock Student Thinking, Grades 6-12. The problems are characterized by a closed beginning,- meaning all students start with the same initial problem, and a closed end,- meaning there is only one correct or optimal answer. The key is that the middle is open- in the sense that there are multiple ways to approach and ultimately solve the problem. These tasks have proven enormously popular with teachers looking to assess and deepen student understanding, build student stamina, and energize their classrooms. Professional Learning Resource for Teachers: Open Middle Math is an indispensable resource for educators interested in teaching student-centered mathematics in middle and high schools consistent with the national and state standards. Sample Problems at Each Grade: The book demonstrates the Open Middle concept with sample problems ranging from dividing fractions at 6th grade to algebra, trigonometry, and calculus. Teaching Tips for Student-Centered Math Classrooms: Kaplinsky shares guidance on choosing problems, designing your own math problems, and teaching for multiple purposes, including formative assessment, identifying misconceptions, procedural fluency, and conceptual understanding. Adaptable and Accessible Math: The tasks can be solved using various strategies at different levels of sophistication, which means all students can access the problems and participate in the conversation. Open Middle Math will help math teachers transform the 6th -12th grade classroom into an environment focused on problem solving, student dialogue, and critical thinking.

Author : Torsten Fritzlar,Daiela Assmus,Kerstin Bräuning,Ana Kuzle,Benjamin Rott
Publisher : WTM-Verlag Münster
Page : 250 pages
File Size : 44,9 Mb
Release : 2016-06-30
Category : Juvenile Nonfiction
ISBN : 9783959870139

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Problem Solving in Mathematics Education by Torsten Fritzlar,Daiela Assmus,Kerstin Bräuning,Ana Kuzle,Benjamin Rott Pdf

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.

Author : Titu Andreescu,Kathy Cordeiro,Alina Andreescu
Publisher : John Wiley & Sons
Page : 294 pages
File Size : 49,9 Mb
Release : 2019-12-17
Category : Education
ISBN : 9781119575733

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Awesome Math by Titu Andreescu,Kathy Cordeiro,Alina Andreescu Pdf

Help your students to think critically and creatively through team-based problem solving instead of focusing on testing and outcomes. Professionals throughout the education system are recognizing that standardized testing is holding students back. Schools tend to view children as outcomes rather than as individuals who require guidance on thinking critically and creatively. Awesome Math focuses on team-based problem solving to teach discrete mathematics, a subject essential for success in the STEM careers of the future. Built on the increasingly popular growth mindset, this timely book emphasizes a problem-solving approach for developing the skills necessary to think critically, creatively, and collaboratively. In its current form, math education is a series of exercises: straightforward problems with easily-obtained answers. Problem solving, however, involves multiple creative approaches to solving meaningful and interesting problems. The authors, co-founders of the multi-layered educational organization AwesomeMath, have developed an innovative approach to teaching mathematics that will enable educators to: Move their students beyond the calculus trap to study the areas of mathematics most of them will need in the modern world Show students how problem solving will help them achieve their educational and career goals and form lifelong communities of support and collaboration Encourage and reinforce curiosity, critical thinking, and creativity in their students Get students into the growth mindset, coach math teams, and make math fun again Create lesson plans built on problem based learning and identify and develop educational resources in their schools Awesome Math: Teaching Mathematics with Problem Based Learning is a must-have resource for general education teachers and math specialists in grades 6 to 12, and resource specialists, special education teachers, elementary educators, and other primary education professionals.

Author : Daniel Grieser
Publisher : Springer
Page : 308 pages
File Size : 43,5 Mb
Release : 2018-05-21
Category : Mathematics
ISBN : 9783319903217

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Exploring Mathematics by Daniel Grieser Pdf

Have you ever faced a mathematical problem and had no idea how to approach it? Or perhaps you had an idea but got stuck halfway through? This book guides you in developing your creativity, as it takes you on a voyage of discovery into mathematics. Readers will not only learn strategies for solving problems and logical reasoning, but they will also learn about the importance of proofs and various proof techniques. Other topics covered include recursion, mathematical induction, graphs, counting, elementary number theory, and the pigeonhole, extremal and invariance principles. Designed to help students make the transition from secondary school to university level, this book provides readers with a refreshing look at mathematics and deep insights into universal principles that are valuable far beyond the scope of this book. Aimed especially at undergraduate and secondary school students as well as teachers, this book will appeal to anyone interested in mathematics. Only basic secondary school mathematics is required, including an understanding of numbers and elementary geometry, but no calculus. Including numerous exercises, with hints provided, this textbook is suitable for self-study and use alongside lecture courses.

Author : George Lenchner
Publisher : Unknown
Page : 16 pages
File Size : 42,5 Mb
Release : 1983
Category : Mathematics
ISBN : 0395345472

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Creative Problem Solving in School Mathematics by George Lenchner Pdf

Author : Florence Mihaela Singer
Publisher : Springer
Page : 428 pages
File Size : 54,9 Mb
Release : 2018-03-07
Category : Education
ISBN : 9783319731568

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Mathematical Creativity and Mathematical Giftedness by Florence Mihaela Singer Pdf

This book discusses the relationships between mathematical creativity and mathematical giftedness. It gathers the results of a literature review comprising all papers addressing mathematical creativity and giftedness presented at the International Congress on Mathematical Education (ICME) conferences since 2000. How can mathematical creativity contribute to children’s balanced development? What are the characteristics of mathematical giftedness in early ages? What about these characteristics at university level? What teaching strategies can enhance creative learning? How can young children’s mathematical promise be preserved and cultivated, preparing them for a variety of professions? These are some of the questions addressed by this book. The book offers, among others: analyses of substantial learning environments that promote creativity in mathematics lessons; discussions of a variety of strategies for posing and solving problems; investigations of students’ progress throughout their schooling; and examinations of technological tools and virtual resources meant to enhance learning with understanding. Multiple perspectives in the interdisciplinary fields of mathematical creativity and giftedness are developed to offer a springboard for further research. The theoretical and empirical studies included in the book offer a valuable resource for researchers, as well as for teachers of gifted students in specialized or inclusive settings, at various levels of education.

Author : Florence Mihaela Singer,Nerida F. Ellerton,Jinfa Cai
Publisher : Springer
Page : 587 pages
File Size : 49,7 Mb
Release : 2015-06-12
Category : Education
ISBN : 9781461462583

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Mathematical Problem Posing by Florence Mihaela Singer,Nerida F. Ellerton,Jinfa Cai Pdf

The mathematics education community continues to contribute research-based ideas for developing and improving problem posing as an inquiry-based instructional strategy for enhancing students’ learning. A large number of studies have been conducted which have covered many research topics and methodological aspects of teaching and learning mathematics through problem posing. The Authors' groundwork has shown that many of these studies predict positive outcomes from implementing problem posing on: student knowledge, problem solving and posing skills, creativity and disposition toward mathematics. This book examines, in-depth, the contribution of a problem posing approach to teaching mathematics and discusses the impact of adopting this approach on the development of theoretical frameworks, teaching practices and research on mathematical problem posing over the last 50 years. ​​

Author : Scott A. Chamberlin,Eric L. Mann
Publisher : Routledge
Page : 147 pages
File Size : 49,5 Mb
Release : 2021-09-03
Category : Education
ISBN : 9781000489712

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The Relationship of Affect and Creativity in Mathematics by Scott A. Chamberlin,Eric L. Mann Pdf

The Relationship of Affect and Creativity in Mathematics explores the five legs of creativity—Iconoclasm, Impartiality, Investment, Intuition, and Inquisitiveness—as they relate to mathematical giftedness. This book: Discusses these affective components relevant to mathematical learning experiences. Shares how affective components impact students' creative processes and products. Shows the influence of learning facilitators, including teachers, afterschool mentors, and parents. Describes facilitating environments that may enhance the likelihood that creative process and ultimately product emerge. Utilizes the expertise of two young scholars to discuss the practical effects of affect and creativity in learning experiences. This practical, research-based book is a must-read for stakeholders in gifted education, as many advanced students are underidentified in the area of creativity in mathematics.

Author : Roza Leikin,Abraham Berman,Boris Koichu
Publisher : BRILL
Page : 419 pages
File Size : 48,5 Mb
Release : 2009-01-01
Category : Education
ISBN : 9789087909352

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Creativity in Mathematics and the Education of Gifted Students by Roza Leikin,Abraham Berman,Boris Koichu Pdf

This book breaks through in the field of mathematical creativity and giftedness. It suggests directions for closing the gap between research in the field of mathematics education and research in the field of creativity and giftedness. It also outlines a research agenda for further research and development in the field.