Exploring Investigating And Discovering In Mathematics
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Exploring Investigating And Discovering In Mathematics
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Author : Vasile Berinde
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Exploring Investigating And Discovering In Mathematics written by Vasile Berinde and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This book offers creative problem solving techniques designed to develop and inspire inventive skills in students. It presents an array of selected elementary themes from arithmetic, algebra, geometry, analysis and applied mathematics. Includes solutions to over 100 problems and hints for over 150 further problems and exercises.
Discovering Mathematics
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Author : A. Gardiner
language : en
Publisher: Courier Corporation
Release Date : 2006-01-26
Discovering Mathematics written by A. Gardiner and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-26 with Mathematics categories.
The term "mathematics" usually suggests an array of familiar problems with solutions derived from well-known techniques. Discovering Mathematics: The Art of Investigation takes a different approach, exploring how new ideas and chance observations can be pursued, and focusing on how the process invariably leads to interesting questions that would never have otherwise arisen. With puzzles involving coins, postage stamps, and other commonplace items, students are challenged to account for the simple explanations behind perplexing mathematical phenomena. Elementary methods and solutions allow readers to concentrate on the way in which the material is explored, as well as on strategies for answers that aren't immediately obvious. The problems don't require the kind of sophistication that would put them out of reach of ordinary students, but they're sufficiently complex to capture the essential features of mathematical discovery. Complete solutions appear at the end.
Exploring Mathematics
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Author : Daniel Grieser
language : en
Publisher: Springer
Release Date : 2018-05-21
Exploring Mathematics written by Daniel Grieser and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-21 with Mathematics categories.
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.
Exploring Mathematics
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Author : John Meier
language : en
Publisher: Cambridge University Press
Release Date : 2017-08-07
Exploring Mathematics written by John Meier and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-07 with Mathematics categories.
With exercises and projects, Exploring Mathematics supports an active approach to the transition to upper-level theoretical math courses.
Values And Valuing In Mathematics Education
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Author : Philip Clarkson
language : en
Publisher: Springer
Release Date : 2019-04-24
Values And Valuing In Mathematics Education written by Philip Clarkson and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-24 with Education categories.
This engaging open access book discusses how a values and valuing perspective can facilitate a more effective mathematics pedagogical experience, and allows readers to explore multiple applications of the values perspective across different education systems. It also clearly shows that teaching mathematics involves not only reasoning and feelings, but also students’ interactions with their cultural setting and each other. The book brings together the work of world leaders and new thinkers in mathematics educational research to improve the learning and teaching of mathematics. Addressing themes such as discovering hidden cultural values, a multicultural society and methodological issues in the investigation of values in mathematics, it stimulates readers to consider these topics in cross-cultural ways, and offers suggestions for research and classroom practice. It is a valuable resource for scholars of mathematics education, from early childhood through to higher education and an inspiring read for all mathematics teachers.
Discovering Patterns In Mathematics And Poetry
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Author : Marcia Birken
language : en
Publisher: Rodopi
Release Date : 2008
Discovering Patterns In Mathematics And Poetry written by Marcia Birken and has been published by Rodopi this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Literary Criticism categories.
You are invited to join a fascinating journey of discovery, as Marcia Birken and Anne C. Coon explore the intersecting patterns of mathematics and poetry -- bringing the two fields together in a new way. Setting the tone with humor and illustrating each chapter with countless examples, Birken and Coon begin with patterns we can see, hear, and feel and then move to more complex patterns. Number systems and nursery rhymes lead to the Golden Mean and sestinas. Simple patterns of shape introduce tessellations and concrete poetry. Fractal geometry makes fractal poetry possible. Ultimately, patterns for the mind lead to questions: How do mathematicians and poets conceive of proof, paradox, and infinity? What role does analogy play in mathematical discovery and poetic expression? The book will be of special interest to readers who enjoy looking for connections across traditional disciplinary boundaries.Discovering Patterns in Mathematics and Poetry features centuries of creative work by mathematicians, poets, and artists, including Fibonacci, Albrecht Dürer, M. C. Escher, David Hilbert, Benoit Mandelbrot, William Shakespeare, Edna St. Vincent Millay, Langston Hughes, E.E. Cummings, and many contemporary experimental poets. Original illustrations include digital photographs, mathematical and poetic models, and fractal imagery.
Monthly Problem Gems
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Author : Hongwei Chen
language : en
Publisher: CRC Press
Release Date : 2021-07-06
Monthly Problem Gems written by Hongwei Chen and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-06 with Mathematics categories.
This book is an outgrowth of a collection of sixty-two problems offered in the The American Mathematical Monthly (AMM) the author has worked over the last two decades. Each selected problem has a central theme, contains gems of sophisticated ideas connected to important current research, and opens new vistas in the understanding of mathematics. The AMM problem section provides one of the most challenging and interesting problem sections among the various journals and online sources currently available. The published problems and solutions have become a treasure trove rife with mathematical gems. The author presents either his published solution in the AMM or an alternative solution to the published one to present and develop problem-solving techniques. A rich glossary of important theorems and formulas is included for easy reference. The reader may regard this book as a starter set for AMM problems, providing a jumping of point to new ideas, and extending their personal lexicon of problems and solutions. This collection is intended to encourage the reader to move away from routine exercises toward creative solutions, as well as offering the reader a systematic illustration of how to organize the transition from problem solving to exploring, investigating and discovering new results.
Investigating Science With Young Children
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Author : Rosemary Althouse
language : en
Publisher: Teachers College Press
Release Date : 1988
Investigating Science With Young Children written by Rosemary Althouse and has been published by Teachers College Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Education categories.
Teaching science to young children has long been an area of intense interest and concern to educators. Investigating Science with Young Children is specifically designed to address this concern in a practical, timely, and enjoyable way. Originally planned as an extension of the ten-booklet series, Science Experiences for Young Children (Teachers College Press, 1975), this book outlines 85 lively activities the teacher can use in guiding three-, four-, and five-year-olds in a fruitful exploration of science. The first part of the book presents a theoretical explanation of the process approach advocated by the author; the second, the activities themselves: Exploring Water, Mixing Colors, Setting Objects in Motion, to name a few. Investigating Science with Young Children offers an informed guide to resources necessary to implement an effective and productive science program. The book will help teachers fully understand the process approach and encourage them to develop their own science activities for the classroom. As the author states, “It is not enough to read about process science; you must use it to find out how much children enjoy and learn from this method.” This book will serve as a supplemental text for early childhood and primary science curriculum courses and as an invaluable resource for teachers. “There is much of value here.” —School Science & Mathematics “Teaching science by a process approach is an exciting adventure for both teachers and children. There is neither a predetermined sequence of events for children nor a specific set of directions for the teacher. Process science is an open-ended approach, and the direction learning will take is determined, for the most part, by the children.” —From the Preface
Mathematical Discovery On Understanding Learning And Teaching Problem Solving
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Author : George Pólya
language : en
Publisher:
Release Date : 2009
Mathematical Discovery On Understanding Learning And Teaching Problem Solving written by George Pólya and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
George Polya was a Hungarian mathematician. Born in Budapest on 13 December 1887, his original name was Polya Gyorg. He wrote perhaps the most famous book of mathematics ever written, namely "How to Solve It." However, "How to Solve It" is not strictly speaking a math book. It is a book about how to solve problems of any kind, of which math is just one type of problem. The same techniques could in principle be used to solve any problem one encounters in life (such as how to choose the best wife ). Therefore, Polya wrote the current volume to explain how the techniques set forth in "How to Solve It" can be applied to specific areas such as geometry.
Teaching Mathematics In Elementary And Middle School
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Author : Joseph G. R. Martinez
language : en
Publisher: Prentice Hall
Release Date : 2007
Teaching Mathematics In Elementary And Middle School written by Joseph G. R. Martinez and has been published by Prentice Hall this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Education categories.
With an emphasis on inquiry and process, "Teaching Mathematics in Elementary and Middle School "embraces active mathematics instruction and the development of mathematical thinking through problem solving. The text challenges future teachers to prepare their K-8 students for a world that requires a higher level of mathematical literacy and enables them to compete in a global society.Teachers will develop their own mathematical abilities, allowing them to help students discover a rich combination of thinking processes and problem-solving strategies, raising the learning expectations for all. Unique text features "TIE-Thought, Investigation and Exploration "features ask pre-service teachers to develop their own thinking and learning abilities, preparing them to better challenge their students. "Mathematics in the Real World," "Idea Files," and "Teacher Profiles "model best practices and supply readers with concrete teaching tools and strategies. "Mathematical Thinking," "Mathematical Games" and "Mathematics and Technology" features detail activities to engage and develop students' mathematical thinking. Accompanying student artifacts illustrate the progression of students' conceptual understanding. [CD logo replaces bullet] "Math Activities CD-ROM" provides an outstanding text component containing more than 100 activities that use a three-step process-explore, invent, discover-to foster the development of mathematical thinking through guided inquiry. Aligned with the NCTM standards, each activity is integrated within the text and designed to help develop students' conceptual understanding of mathematics. "Mathematics in Literature" offers thoroughly developed ideas for using children's literature to create meaningful contexts for mathematics learning. An extensive bibliography that can be used for this purpose appears on the CD-Rom. "I think the text is an excellent resource for elementary and middle school methods courses. In particular, I like how the textbook handles the 'bigger issues' such as geometric reasoning rather than just 'geometry.' I also like the excellent foundation in educational research that the textbook provides, as well as some very careful attention and consistent referencing to the NCTM standards and principles. The incorporation of classroom vignettes, teacher illustrations, and samples of student work also all add to the excellent grounding of the text in real world classroom work." Dr. Neal Grandgenett, University of Nebraska at Omaha