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: 8779


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.

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: 3460


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.

Deep Thinking

What Mathematics Can Teach Us About the Mind

Author: William Byers

Publisher: World Scientific

ISBN: 9814618055

Category: Education

Page: 264

View: 3194


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

The Origins of Creativity

Author: Bruce Adolphe

Publisher: Oxford University Press, USA

ISBN: 9780198507154

Category: Psychology

Page: 268

View: 8010


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 giftfor 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 thesingle, 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 isthe 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 contributorsfrom 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 imagesand 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 bookoffers 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.

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: 9728


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.

Selected Regular Lectures from the 12th International Congress on Mathematical Education

Author: Sung Je Cho

Publisher: Springer

ISBN: 3319171879

Category: Education

Page: 932

View: 7341


This book comprises the full selected Regular Lectures from the Proceedings of the 12th International Congress on Mathematical Education (ICME-12), which was held at COEX in Seoul, Korea, from July 8th to 15th, 2012. ICME-12 brought together 4700 experts from 100 countries, working to understand all of the intellectual and attitudinal challenges in the subject of mathematics education as a multidisciplinary research and practice. These selected Regular Lectures present the work of fifty-one prominent mathematics educators from all over the globe. The Lectures cover a wide spectrum of topics, themes and issues and aim to give direction to future research towards educational improvement in the teaching and learning of mathematics education. This book is of particular interest to researchers, teachers and curriculum developers in mathematics education.

Affect and Mathematics Education

Fresh Perspectives on Motivation, Engagement, and Identity

Author: Markku S. Hannula,Gilah C. Leder,Francesca Morselli,Maike Vollstedt,Qiaoping Zhang

Publisher: Springer

ISBN: 3030137619

Category: Education

Page: 437

View: 685


This open access book, inspired by the ICME 13 topic study group “Affect, beliefs and identity in mathematics education”, presents the latest trends in research in the area. Following an introduction and a survey chapter providing a concise overview of the state-of-art in the field of mathematics-related affect, the book is divided into three main sections: motivation and values, engagement, and identity in mathematics education. Each section comprises several independent chapters based on original research, as well as a reflective commentary by an expert in the area. Collectively, the chapters present a rich methodological spectrum, from narrative analysis to structural equation modelling. In the final chapter, the editors look ahead to future directions in the area of mathematics-education-related affect. It is a timely resource for all those interested in the interaction between affect and mathematics education.

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: 7910


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.