Mathematical Creativity and Mathematical Giftedness

Enhancing Creative Capacities in Mathematically Promising Students


Author: Florence Mihaela Singer

Publisher: Springer

ISBN: 3319731564

Category: Education

Page: 428

View: 6964

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.

Leadership and Creativity

A History of the Cavendish Laboratory, 1871–1919


Author: Dong-Won Kim

Publisher: Springer Science & Business Media

ISBN: 940172055X

Category: Science

Page: 226

View: 3891

Historical accounts of successful laboratories often consist primarily of reminiscences by their directors and the eminent people who studied or worked in these laboratories. Such recollections customarily are delivered at the celebration of a milestone in the history of the laboratory, such as the institution's fiftieth or one hundredth anniversary. Three such accounts of the Cavendish Laboratory at the University of Cambridge have been recorded. The first of these, A History of the Cavendish Laboratory, 1871-1910, was published in 1910 in honor of the twenty fifth anniversary of Joseph John Thomson's professorship there. The second, The Cavendish Laboratory, 1874-1974, was published in 1974 to commemorate the one hundredth anniversary of the Cavendish. The third, A Hundred Years and More of Cambridge Physics, is a short pamphlet, also published at the centennial of the 1 Cavendish. These accounts are filled with the names of great physicists (such as James Clerk Maxwell, Lord Rayleigh, J. J. Thomson, Ernest Rutherford, and William Lawrence Bragg), their glorious achievements (for example, the discoveries of the electron, the neutron, and DNA) and interesting anecdotes about how these achievements were reached. But surely a narrative that does justice to the history of a laboratory must recount more than past events. Such a narrative should describe a living entity and provide not only details of the laboratory's personnel, organization, tools, and tool kits, but should also explain how these components interacted within 2 their wider historical, cultural, and social contexts.

How Quantum Activism Can Save Civilization

A Few People Can Change Human Evolution


Author: Amit Goswami

Publisher: Hampton Roads Publishing

ISBN: 9781612830520

Category: Health & Fitness

Page: 320

View: 3824

Beginning with Taking the Quantum Leap by Fred Alan Wolf, there have been a number of books that have created new paradigms for integrating science and spirituality. These books have been long on theory and short on application. This work represents something completely different for this genre. In his previous book, God is Not Dead, Goswami proved that not only are science and religion compatible, but that quantum physics proves the existence of God. In this new book, Goswami moves beyond theory into the realm of action. He asserts that quantum thinking is striking the death blow to scientific materialism; that quantum thinking allows us to break from past bad habits and bring us into free will and possibilities. Beginning with the question: “God is here, so what are you going to do about it?” Goswami calls for a plan of action that involves applying “quantum thinking” to a variety of societal issues. He issues a call for a spiritual economics that is concerned with our well-being rather than only our material needs; democracy that uses power to serve, instead of dominating others; education that liberates rather than shackles; and new healthy practices that restore wholeness.

Deep Thinking

What Mathematics Can Teach Us About the Mind


Author: William Byers

Publisher: World Scientific

ISBN: 9814618055

Category: Education

Page: 264

View: 5413

There is more than one way to think. Most people are familiar with the systematic, rule-based thinking that one finds in a mathematical proof or a computer program. But such thinking does not produce breakthroughs in mathematics and science nor is it the kind of thinking that results in significant learning. Deep thinking is a different and more basic way of using the mind. It results in the discontinuous “aha!” experience, which is the essence of creativity. It is at the heart of every paradigm shift or reframing of a problematic situation. The identification of deep thinking as the default state of the mind has the potential to reframe our current approach to technological change, education, and the nature of mathematics and science. For example, there is an unbridgeable gap between deep thinking and computer simulations of thinking. Many people suspect that such a gap exists, but find it difficult to make this intuition precise. This book identifies the way in which the authentic intelligence of deep thinking differs from the artificial intelligence of “big data” and “analytics”. Deep thinking is the essential ingredient in every significant learning experience, which leads to a new way to think about education. It is also essential to the construction of conceptual systems that are at the heart of mathematics and science, and of the technologies that shape the modern world. Deep thinking can be found whenever one conceptual system morphs into another. The sources of this study include the cognitive development of numbers in children, neuropsychology, the study of creativity, and the historical development of mathematics and science. The approach is unusual and original. It comes out of the author's lengthy experience as a mathematician, teacher, and writer of books about mathematics and science, such as How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create Mathematics and The Blind Spot: Science and the Crisis of Uncertainty. Contents:What is Deep Thinking?Conceptual SystemsDeep Thinking in Mathematics and ScienceDeep Thinking in the Mind and the BrainDeep Thinking and CreativityDeep LearningGood TeachingUndergraduate MathematicsWhat the Mind Can Teach Us About MathematicsWhat Mathematics Can Teach Us About the MindReferences Readership: Students, graduate students and researchers with an interest in mathematics, mathematicians, scientists, philosophers, psychologists, and readers who use mathematics in their work. Key Features:In this book, the author, a mathematician, demonstrates the specific difference between creative mathematical thought and the analytic thought of logic and the artificial intelligence of computersThis book shows why learning is a creative activity and demonstrates how teaching and learning must undergo radical changes in this age of rapid technological changeMathematics is a model for how people think and it reveals the essence of intelligenceThe author, a mathematician, demonstrates that creativity is a basic feature of the world. The same phenomenon of creative intelligence underlies the theory of evolution, child development, learning, and scientific and mathematical research. Creativity is so natural that even babies are capable of it but so difficult that adults have great trouble with it. This book explains the reasons behind this apparent paradoxKeywords:Mathematics;Cognitive Development;Thinking;Education;Mathematics Education;Conceptual Systems

Autism Spectrum Disorders: Building Foundation Skills in Mathematics


Author: Leslie Broun

Publisher: National Professional Resources Inc./Dude Publishing

ISBN: 1935609610

Category: Education

Page: 6

View: 3890

Designed for educators who work with students with autism spectrum disorders (ASD) and/or other developmental disabilities, this reference guide provides a greater understanding of the preparatory role that visual performance skills play in the learning of mathematics. Practical instructional strategies required to build the foundational skills needed to master the common core state standards (CCSS) in Mathematics are presented.

The Origins of Creativity


Author: Bruce Adolphe

Publisher: Oxford University Press, USA

ISBN: 9780198507154

Category: Psychology

Page: 268

View: 9051

After Newton died in 1727, a monument was erected in the Scientist's Corner of Westminster Abbey. It was decorated with a pile of four books and adorned with cherubs holding a prism, a telescope and newly minted coins. The implication is clear. Newton's towering intellect and god-given gift for creative thinking was the origin of his inspiration. Not far away, at the front of the monument to Newton, is the tomb of Charles Darwin, who published On the Origin of Species, which first discussed the evolution of man. The proximity of the monuments is telling. If we are to define the single, most unique human attribute evolution has produced, it must be our ability to think creatively. Thinking is the ultimate human resource. Breaking through the barriers posed by dogma, and reaching beyond the limits of established patterns of thinking to discover what is new and useful is the engine that drives society. This book, which had its genesis in a conference organized by Karl Pfenninger, and held at Aspen, Colorado, entitled 'Higher brain function, art and science: an interdisciplinary examination of the creative process', brings together articles by thirteen contributors from the fields of science, art and music. Two of the contributors have been awarded Nobel prizes, and all are distinguished representatives of their fields. The Origins of Creativity is organized around four central themes of creativity: the creative experience in art and science; the biologicalbasis of imagination, emotion and reason; creative powers and the environment; and the mind's perception of patterns. The views of artists, who couch their ideas in more metaphorical language, mingle with the analytical thoughts of scientists who strive to understand how the brain generates images and ideas. The voices of creators - artist, scientist, mathematician - and of those who study creative activity - neuroscientist, psychologist, philosopher - generate a broad spectrum of views on creativity whose integration offers new insights and becomes a creative act in itself. This book offers insights into the origins of human creativity to scientists, artists, and general readers. Its inter-disciplinary authorship presents a uniquely broad perspective on current research, and the style throughout is accessible and engaging.

Creative Minds, Charmed Lives

Interviews at Institute for Mathematical Sciences, National University of Singapore


Author: Yu Kiang Leong

Publisher: World Scientific

ISBN: 9814317594

Category: Biography & Autobiography

Page: 352

View: 5683

This book features interviews of 38 eminent mathematicians and mathematical scientists who were invited to participate in the programs of the Institute for Mathematical Sciences, National University of Singapore. Originally published in its newsletter Imprints from 2003 to 2009, these interviews give a fascinating and insightful glimpse into the passion driving some of the most creative minds in modern research in pure mathematics, applied mathematics, statistics, economics and engineering. The reader is drawn into a panorama of the past and present development of some of the ideas that have revolutionized modern science and mathematics. This book should be relevant to those who are interested in the history and psychology of ideas. It should provide motivation, inspiration and guidance to students who aspire to do research and to beginning researchers who are looking for career niches. For those who wish to be broadly educated, it is informative without delving into excessive technical details and is, at the same time, thought provoking enough to arouse their curiosity to learn more about the world around them.

Genius and Eminence


Author: Robert S. Albert

Publisher: Psychology Press

ISBN: 9780080377643

Category: Psychology

Page: 410

View: 3419

A fascinating introduction to the research into, and theories, of exceptional achievement. Topics covered include the arguments around personal dynamics and biological processes, the IQ issue, and how family and learning experiences are related to achievement.

Fourteenth School on Operators in Functional Spaces

Spectral Theory of Operators : Novgorod State Pedagogical Institute, 1989


Author: Semen G. Gindikin

Publisher: American Mathematical Soc.

ISBN: 0821875000

Category: Mathematics

Page: 176

View: 1274

Containing the proceedings of the Fourteenth School on Operators in Functional Spaces, held in Novgorod, USSR, in the summer of 1989, this volume focuses on the spectral theory of differential operators. The emphasis is on estimates of the number of negative eigenvalues of elliptic differential operators and on the analysis of asymptotical distribution of eigenvalues. Three of the papers discuss distribution of eigenvalues, while the fourth studies scattering theory. The authors rank among the leading Soviet specialists in this area of research. Aimed at researchers in spectral theory of differential operators, scattering theory, and related problems in mathematical physics, this collection provides an excellent overview of some of the major problems in the field.

Advanced Mathematical Thinking


Author: David Tall

Publisher: Springer Science & Business Media

ISBN: 0306472031

Category: Education

Page: 292

View: 4836

This book is the first major study of advanced mathematical thinking as performed by mathematicians and taught to students in senior high school and university. Topics covered include the psychology of advanced mathematical thinking, the processes involved, mathematical creativity, proof, the role of definitions, symbols, and reflective abstraction. It is highly appropriate for the college professor in mathematics or the general mathematics educator.

Lectures on Entire Functions


Author: B. Ya Levin

Publisher: American Mathematical Soc.

ISBN: 0821808974

Category: Mathematics

Page: 248

View: 1319

As a brilliant university lecturer, B. Ya. Levin attracted a large audience of working mathematicians and of students from various levels and backgrounds. For approximately 40 years, his Kharkov University seminar was a school for mathematicians working in analysis and a center for active research. This monograph aims to expose the main facts of the theory of entire functions and to give their applications in real and functional analysis. The general theory starts with the fundamental results on the growth of entire functions of finite order, their factorization according to the Hadamard theorem, properties of indicator and theorems of Phragmen-Lindelof type.

U.S. Research Institutes in the Mathematical Sciences

Assessment and Perspectives


Author: National Research Council,Division on Engineering and Physical Sciences,Commission on Physical Sciences, Mathematics, and Applications,Committee on U.S. Mathematical Sciences Research Institutes

Publisher: National Academies Press

ISBN: 9780309184618

Category: Mathematics

Page: 42

View: 8011

This report is the result of a fast-track study of U.S. mathematical sciences research institutes done in response to a request from the National Science Foundation (NSF). The task of the Committee on U.S. Mathematical Sciences Research Institutes was to address the following three questions: 1. What are the characteristic features of effective mathematical sciences research institutes in the ways that they further mathematical research in the United States, and are there ways that the current configuration can be improved? 2. What kinds of institutes should there be in the United States, and how many does the nation need? 3. How should U.S. mathematical sciences research institutes be configured (with regard to, for example, diversity of operating formats, distribution of mathematical fields, and interinstitute cooperation or coordination) in order to have the nation's mathematical research enterprise continue to be most productive and successful?

Creative Motion Graphic Titling

Titling with Motion Graphics for Film, Video, and the Web


Author: Bill Byrne,Yael Braha

Publisher: Taylor & Francis

ISBN: 1136132139

Category: Art

Page: 410

View: 4532

The book features genre-based tutorial sections, with step by step instructions for creating effective horror, comedy, drama, and suspense titling sequences. Tutorials for creating some of the most popular title sequences in blockbuster movies are included (Se7en, The Sopranos, 24, The Matrix). Other tutorials teach you how to effectively use sound and VFX in your titles, and also included is instruction on editing your title sequence. These techniques, as well as chapters on the essentials of typography allow you to apply these lessons to your title sequence regardless of whether it's for TV, the web, or digital signage. Also included is a DVD with sample clips, as well as project files that allow you to refine the techniques you learned in the book. As an added bonus we've included 3 titling chapters from other Focal books, with specific instructions on titling within certain software applications. Cover images provided by MK12, from The Alphabet Conspiracy. Learn more at

Mathematical Understanding 5-11

A Practical Guide to Creative Communication in Maths


Author: Anne D Cockburn

Publisher: SAGE

ISBN: 1848605285

Category: Education

Page: 128

View: 4985

Sam - a young and enthusiastic trainee teacher - asked the class, 'What is the difference between 7 and 6?'. Jo's hand shot up and he immediately responded, 'Well seven is all straight lines and sixes are all curly.' How can you help children to make progress in mathematical understanding? Children's mathematical misconceptions very often arise as a result of poor communication. This practical and innovative book presents a range of creative strategies to help teachers communicate effectively in the mathematics classroom, offering some new ways of presenting the fundamental concepts and principles of mathematics, and clearly demonstrating that the most effective form of communication is not always verbal. Each chapter focuses on a theme or concept central to the numeracy strategy, such as subtraction, shape and space, constructing and connecting 2D and 3D shapes, data-logging and graph interpretation, and mathematical reasoning. Each chapter supports teachers' subject knowledge as well as suggesting a range of communication strategies (e.g. speaking, listening, drawing, role play, and visual methods such as posters and ICT work) to help teachers and children to share and build on their understanding. All of the activities have been tried and tested in classrooms across Europe. Written by a team of highly experienced teachers, the book will be valuable reading for pre- and in-service teachers, teacher educators and anyone who has an interest in extending the ways children actively engage with mathematics. Teachers with EAL pupils in their class may find it of particular value in communicating mathematical concepts to those who find English difficult. The book is accompanied by a DVD which includes video clips of children at work in mathematics classrooms, software used in the project, copies of material from the book and additional activities.

Flow, Gesture, and Spaces in Free Jazz

Towards a Theory of Collaboration


Author: Guerino Mazzola,Paul B. Cherlin

Publisher: Springer Science & Business Media

ISBN: 3540921958

Category: Music

Page: 141

View: 2940

Free jazz, as performed by such artists as John Coltrone and Archie Shepp, is a creative, collaborative art form. This book examines free jazz and develops geometric theories of gestures and distributed identities, also known as swarm intelligence.

Handbook of Creativity


Author: Robert J. Sternberg

Publisher: Cambridge University Press

ISBN: 9780521576048

Category: Psychology

Page: 490

View: 5960

The goal of this handbook is to provide the most comprehensive, definitive, and authoritative single-volume review available in the field of creativity. The book contains twenty-two chapters covering a wide range of issues and topics in the field of creativity, all written by distinguished leaders in the field. The volume is divided into six parts. The introduction sets out the major themes and reviews the history of thinking about creativity. Subsequent parts deal with methods, origins, self and environment, special topics and conclusions. All educated readers with an interest in creative thinking will find this volume to be accessible and engrossing.