Download or read book Numerical Thinking written by Charles Phillips and published by Connections Book Publishing. This book was released on 2013 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offers a collection of mathematical puzzles to help develop confidence with numbers and productive thinking.
Download or read book Thinking as Communicating written by Anna Sfard and published by Cambridge University Press. This book was released on 2008-01-21 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an attempt to change our thinking about thinking. Anna Sfard undertakes this task convinced that many long-standing, seemingly irresolvable quandaries regarding human development originate in ambiguities of the existing discourses on thinking. Standing on the shoulders of Vygotsky and Wittgenstein, the author defines thinking as a form of communication. The disappearance of the time-honoured thinking-communicating dichotomy is epitomised by Sfard's term, commognition, which combines communication with cognition. The commognitive tenet implies that verbal communication with its distinctive property of recursive self-reference may be the primary source of humans' unique ability to accumulate the complexity of their action from one generation to another. The explanatory power of the commognitive framework and the manner in which it contributes to our understanding of human development is illustrated through commognitive analysis of mathematical discourse accompanied by vignettes from mathematics classrooms.
Download or read book The Roots Of Thinking written by Maxine Sheets-Johnstone and published by Temple University Press. This book was released on 2010-04-29 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: A ground-breaking interdisciplinary study about conceptual origins linking hominid thinking with hominid evolution.
Download or read book Talking About Nothing written by Jody Azzouni and published by Oxford University Press. This book was released on 2010-09-30 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ordinary language and scientific language enable us to speak about, in a singular way (using demonstratives and names), what we recognize not to exist: fictions, the contents of our hallucinations, abstract objects, and various idealized but nonexistent objects that our scientific theories are often couched in terms of. Indeed, references to such nonexistent items-especially in the case of the application of mathematics to the sciences-are indispensable. We cannot avoid talking about such things. Scientific and ordinary languages thus enable us to say things about Pegasus or about hallucinated objects that are true (or false), such as "Pegasus was believed by the ancient Greeks to be a flying horse," or "That elf I'm now hallucinating over there is wearing blue shoes." Standard contemporary metaphysical views and semantic analyses of singular idioms on offer in contemporary philosophy of language have not successfully accommodated these routine practices of saying true and false things about the nonexistent while simultaneously honoring the insight that such things do not exist in any way at all (and have no properties). That is, philosophers often feel driven to claim that such objects do exist, or they claim that all our talk isn't genuine truth-apt talk, but only pretence. This book reconfigures metaphysics (and the role of metaphysics in semantics) in radical ways that allow the accommodation of our ordinary ways of speaking of what does not exist while retaining the absolutely crucial presupposition that such objects exist in no way at all, have no properties, and so are not the truth-makers for the truths and falsities that are about them.
Download or read book Developing Numerical Fluency written by Patsy Kanter and published by Heinemann Educational Books. This book was released on 2018 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This is a must-read book for any teachers of math." -Jo Boaler, Professor of Mathematics Education at Stanford University and author of Mathematical Mindsets Numerical fluency is about understanding Numerical fluency is about understanding, not memorization. It comes over time as students engage in active thinking and doing, not endless worksheets and timed tests. Classroom instruction and materials, however, often don't feel aligned with these realities. In Developing Numerical Fluency, Patsy Kanter and Steven Leinwand take a fresh look at a commonly-asked question: "How do I teach number facts so my students know them fluently?" They apply their decades of experience teaching mathematics to rethinking effective fluency instruction. Classroom-tested ideas you can use right away Each chapter introduces ideas, techniques, and strategies that contribute to meaningful fluency for all students. You'll find: pivotal understandings that illuminate what contributes to real numerical fluency six instructional processes that support lasting fluency development classroom structures and activities for building fluency in addition, subtraction, multiplication, and division suggestions for creating a school-wide culture of numerical fluency. Patsy and Steve remind us that, "Students do not develop numerical fluency by memorizing and regurgitating rules." But many of us learned mathematics in exactly this way, making shifting our instruction challenging. Developing Numerical Fluency provides just the right support, offering big ideas for rethinking instruction paired with classroom-tested activities you can use right away.
Download or read book Train Your Brain Teach Yourself written by Simon Wootton and published by Teach Yourself. This book was released on 2010-01-29 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: Train your brain to be quicker, fitter and brighter than it's ever been! This book gives you everything you need to get a mental edge, featuring hundreds of puzzles, quizzes and problem-solving games. It also gives you some great advice on how to maximise your mental agility through diet, exercise and the right lifestyle choices, as well as showing you how to put your new, more powerful brain to the test at work, home and play. NOT GOT MUCH TIME? One, five and ten-minute introductions to key principles to get you started. AUTHOR INSIGHTS Lots of instant help with common problems and quick tips for success, based on the authors' many years of experience. TEST YOURSELF Tests in the book and online to keep track of your progress. EXTEND YOUR KNOWLEDGE Extra online articles at www.teachyourself.com to give you a richer understanding of how to train your brain. FIVE THINGS TO REMEMBER Quick refreshers to help you remember the key facts. TRY THIS Innovative exercises illustrate what you've learnt and how to use it.
Download or read book Build Your Brain Power written by Simon Wootton and published by Teach Yourself. This book was released on 2015-06-18 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new edition of a popular guide to improving your mental agility will help you improve your performance at work and sharpen your thinking skills in all areas. Based on the latest scientific findings and including up-to-date coverage of how meditative skills such as mindfulness can enhance your brain power, this book gives you everything you need to get a mental edge. It challenges you to think on your feet with hundreds of puzzles, quizzes and problem-solving games, while giving you lifestyle advice on diet, exercise and lifestyle choices. Showing you how to put your new, more powerful brain to the test at work, home and play, this is a smart guide for any smart professional who wants to be brighter, quicker and in the lead at all times.
Download or read book Number Talks written by Sherry Parrish and published by Math Solutions. This book was released on 2010 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: "A multimedia professional learning resource"--Cover.
Download or read book How Not to Be Wrong written by Jordan Ellenberg and published by Penguin Press. This book was released on 2014-05-29 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: A brilliant tour of mathematical thought and a guide to becoming a better thinker, How Not to Be Wrong shows that math is not just a long list of rules to be learned and carried out by rote. Math touches everything we do; It's what makes the world make sense. Using the mathematician's methods and hard-won insights-minus the jargon-professor and popular columnist Jordan Ellenberg guides general readers through his ideas with rigor and lively irreverence, infusing everything from election results to baseball to the existence of God and the psychology of slime molds with a heightened sense of clarity and wonder. Armed with the tools of mathematics, we can see the hidden structures beneath the messy and chaotic surface of our daily lives. How Not to Be Wrong shows us how--Publisher's description.
Download or read book Space Time and Number in the Brain written by Stanislas Dehaene and published by Academic Press. This book was released on 2011-07-13 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of mathematical cognition and the ways in which the ideas of space, time and number are encoded in brain circuitry has become a fundamental issue for neuroscience. How such encoding differs across cultures and educational level is of further interest in education and neuropsychology. This rapidly expanding field of research is overdue for an interdisciplinary volume such as this, which deals with the neurological and psychological foundations of human numeric capacity. A uniquely integrative work, this volume provides a much needed compilation of primary source material to researchers from basic neuroscience, psychology, developmental science, neuroimaging, neuropsychology and theoretical biology. - The first comprehensive and authoritative volume dealing with neurological and psychological foundations of mathematical cognition - Uniquely integrative volume at the frontier of a rapidly expanding interdisciplinary field - Features outstanding and truly international scholarship, with chapters written by leading experts in a variety of fields
Download or read book The Oxford Handbook of Numerical Cognition written by Roi Cohen Kadosh and published by Oxford Library of Psychology. This book was released on 2015 with total page 1217 pages. Available in PDF, EPUB and Kindle. Book excerpt: How do we understand numbers? Do animals and babies have numerical abilities? Why do some people fail to grasp numbers, and how we can improve numerical understanding? Numbers are vital to so many areas of life: in science, economics, sports, education, and many aspects of everyday life from infancy onwards. Numerical cognition is a vibrant area that brings together scientists from different and diverse research areas (e.g., neuropsychology, cognitive psychology, developmental psychology, comparative psychology, anthropology, education, and neuroscience) using different methodological approaches (e.g., behavioral studies of healthy children and adults and of patients; electrophysiology and brain imaging studies in humans; single-cell neurophysiology in non-human primates, habituation studies in human infants and animals, and computer modeling). While the study of numerical cognition had been relatively neglected for a long time, during the last decade there has been an explosion of studies and new findings. This has resulted in an enormous advance in our understanding of the neural and cognitive mechanisms of numerical cognition. In addition, there has recently been increasing interest and concern about pupils' mathematical achievement in many countries, resulting in attempts to use research to guide mathematics instruction in schools, and to develop interventions for children with mathematical difficulties. This handbook brings together the different research areas that make up the field of numerical cognition in one comprehensive and authoritative volume. The chapters provide a broad and extensive review that is written in an accessible form for scholars and students, as well as educationalists, clinicians, and policy makers. The book covers the most important aspects of research on numerical cognition from the areas of development psychology, cognitive psychology, neuropsychology and rehabilitation, learning disabilities, human and animal cognition and neuroscience, computational modeling, education and individual differences, and philosophy. Containing more than 60 chapters by leading specialists in their fields, the Oxford Handbook of Numerical Cognition is a state-of-the-art review of the current literature.
Download or read book Calculated Values written by William Deringer and published by Harvard University Press. This book was released on 2018-02-19 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern political culture features a deep-seated faith in the power of numbers to find answers, settle disputes, and explain how the world works. Whether evaluating economic trends, measuring the success of institutions, or divining public opinion, we are told that numbers don’t lie. But numbers have not always been so revered. Calculated Values traces how numbers first gained widespread public authority in one nation, Great Britain. Into the seventeenth century, numerical reasoning bore no special weight in political life. Complex calculations were often regarded with suspicion, seen as the narrow province of navigators, bookkeepers, and astrologers, not gentlemen. This changed in the decades following the Glorious Revolution of 1688. Though Britons’ new quantitative enthusiasm coincided with major advances in natural science, financial capitalism, and the power of the British state, it was no automatic consequence of those developments, William Deringer argues. Rather, it was a product of politics—ugly, antagonistic, partisan politics. From parliamentary debates to cheap pamphlets, disputes over taxes, trade, and national debt were increasingly conducted through calculations. Some of the era’s most pivotal political moments, like the 1707 Union of England and Scotland and the 1720 South Sea Bubble, turned upon calculative conflicts. As Britons learned to fight by the numbers, they came to believe, as one calculator wrote in 1727, that “facts and figures are the most stubborn evidences.” Yet the authority of numbers arose not from efforts to find objective truths that transcended politics, but from the turmoil of politics itself.
Download or read book Cognitive Biology written by Luca Tommasi and published by MIT Press. This book was released on 2024-04-30 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: An overview of current research at the intersection of psychology and biology, integrating evolutionary and developmental data and explanations. In the past few decades, sources of inspiration in the multidisciplinary field of cognitive science have widened. In addition to ongoing vital work in cognitive and affective neuroscience, important new work is being conducted at the intersection of psychology and the biological sciences in general. This volume offers an overview of the cross-disciplinary integration of evolutionary and developmental approaches to cognition in light of these exciting new contributions from the life sciences. This research has explored many cognitive abilities in a wide range of organisms and developmental stages, and results have revealed the nature and origin of many instances of the cognitive life of organisms. Each section of Cognitive Biology deals with a key domain of cognition: spatial cognition; the relationships among attention, perception, and learning; representations of numbers and economic values; and social cognition. Contributors discuss each topic from the perspectives of psychology and neuroscience, brain theory and modeling, evolutionary theory, ecology, genetics, and developmental science. Contributors Chris M. Bird, Elizabeth M. Brannon, Neil Burgess, Jessica F. Cantlon, Stanislas Dehaene, Christian F. Doeller, Reuven Dukas, Rochel Gelman, Alexander Gerganov, Paul W. Glimcher, Robert L. Goldstone, Edward M. Hubbard, Lucia F. Jacobs, Mark H. Johnson, Annette Karmiloff-Smith, David Landy, Lynn Nadel, Nora S. Newcombe, Daniel Osorio, Mary A. Peterson, Manuela Piazza, Philippe Pinel, Michael L. Platt, Kristin R. Ratliff, Michael E. Roberts, Wendy S. Shallcross, Stephen V. Shepherd, Sylvain Sirois, Luca Tommasi, Alessandro Treves, Alexandra Twyman, Giorgio Vallortigara
Download or read book The Archaeology of Measurement written by Iain Morley and published by Cambridge University Press. This book was released on 2010-04-26 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explores the archaeological evidence for the development of measuring activities in numerous ancient societies and the implications of these discoveries.
Download or read book Emerging Research in Intelligent Systems written by Miguel Botto-Tobar and published by Springer Nature. This book was released on 2022-02-02 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the XVI Multidisciplinary International Congress on Science and Technology (CIT 2021), held in Quito, Ecuador, on June 14–18, 2021, proudly organized by Universidad de las Fuerzas Armadas ESPE in collaboration with GDEON. CIT is an international event with a multidisciplinary approach that promotes the dissemination of advances in science and technology research through the presentation of keynote conferences. In CIT, theoretical, technical, or application works that are research products are presented to discuss and debate ideas, experiences, and challenges. Presenting high-quality, peer-reviewed papers, the book discusses the following topics: Artificial Intelligence Computational Modeling Data Communications Defense Engineering Innovation, Technology, and Society Managing Technology & Sustained Innovation, and Business Development Security and Cryptography Software Engineering
Download or read book Numbers Language and the Human Mind written by Heike Wiese and published by Cambridge University Press. This book was released on 2003-12-11 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: What constitutes our number concept? What makes it possible for us to employ numbers the way we do; which mental faculties contribute to our grasp of numbers? What do we share with other species, and what is specific to humans? How does our language faculty come into the picture? This 2003 book addresses these questions and discusses the relationship between numerical thinking and the human language faculty, providing psychological, linguistic and philosophical perspectives on number, its evolution and its development in children. Heike Wiese argues that language as a human faculty plays a crucial role in the emergence of systematic numerical thinking. She characterises number sequences as powerful and highly flexible mental tools that are unique to humans and shows that it is language that enables us to go beyond the perception of numerosity and to develop such mental tools.
Download or read book Teaching Mathematics in Grades 6 12 written by Randall E. Groth and published by SAGE Publications. This book was released on 2012-08-10 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: A journey into the vibrant and intriguing world of mathematics education Teaching Mathematics in Grades 6 - 12 explores how research in mathematics education can inform teaching practice in grades 6-12. The author shows secondary mathematics teachers the value of being a researcher in the classroom by constantly experimenting with methods for developing students′ mathematical thinking and then connecting this research to practices that enhance students′ understanding of the material. The chapters in Part I introduce secondary teachers to the field of mathematics education with cross-cutting issues that apply to teaching and learning in all mathematics content areas. The chapters in Part II are devoted to specific mathematics content strands and describe how students think about mathematical concepts. The goal of the text is to have secondary math teachers gain a deeper understanding of the types of mathematical knowledge their students bring to grade 6 – 12 classrooms, and how students′ thinking may develop in response to different teaching strategies.
