Download or read book Iconic Arithmetic Volume I written by william bricken and published by Unary Press. This book was released on 2019-04-10 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: Arithmetic evolves. Iconic arithmetic is built from icons that look and feel like what they mean, rather than from strings of symbols that must be memorized. The book explores the formal structure of two types of postsymbolic boundary arithmetic. Ensemble arithmetic modernizes tallies to provide forms that add together by being placed together and multiply by being placed inside one another. James algebra defines the concepts and operations of arithmetic as different ways of arranging containers. Three simple axioms are sufficient. Features of iconic arithmetic include (1) a void with no representation and no properties instead of the symbol zero; (2) void-equivalent forms that can be freely deleted; (3) meaning based on existence of structure rather than truth or numerical value; (4) only one relation (containment) to represent all forms; and (5) construction and deletion to implement all transformations. Iconic forms and transformations can be represented as two and three dimensional structures that can be directly viewed, manipulated, and even inhabited. Many different spatial interactive dialects are described. The author explores this new kind of arithmetic from the perspectives of historical evolution, formal mathematics, computer science and mathematics education. The overall objective is to provide proof of principle that our current universal approach to the arithmetic of numbers is a design choice rather than a truth embedded in numbers themselves. Iconic Arithmetic recognizes that knowledge is embodied, multidimensional, sensual, simple. It helps us to transition into a postsymbolic world of interactive information.
Download or read book Psychology and Mathematics Education written by Gila Hanna and published by Frontiers Media SA. This book was released on 2023-09-05 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern Mathematics is constructed rigorously through proofs, based on truths, which are either axioms or previously proven theorems. Thus, it is par excellence a model of rational inquiry. Links between Cognitive Psychology and Mathematics Education have been particularly strong during the last decades. Indeed, the Enlightenment view of the rational human mind that reasons, makes decisions and solves problems based on logic and probabilities, was shaken during the second half of the twentieth century. Cognitive psychologists discovered that humans' thoughts and actions often deviate from rules imposed by strict normative theories of inference. Yet, these deviations should not be called "errors": as Cognitive Psychologists have demonstrated, these deviations may be either valid heuristics that succeed in the environments in which humans have evolved, or biases that are caused by a lack of adaptation to abstract information formats. Humans, as the cognitive psychologist and economist Herbert Simon claimed, do not usually optimize, but rather satisfice, even when solving problem. This Research Topic aims at demonstrating that these insights have had a decisive impact on Mathematics Education. We want to stress that we are concerned with the view of bounded rationality that is different from the one espoused by the heuristics-and-biases program. In Simon’s bounded rationality and its direct descendant ecological rationality, rationality is understood in terms of cognitive success in the world (correspondence) rather than in terms of conformity to content-free norms of coherence (e.g., transitivity).
Download or read book Iconic Arithmetic Volume III written by William Bricken and published by . This book was released on 2021-02-28 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume III of this series applies the innovations of iconic arithmetic to several branches of elementary mathematics to yield new techniques and new insights that are not accessible to symbolic arithmetic. The rules of algebra are reduced to three simple patterns expressed as spatial containment relations. These patterns resurrect a discarded imaginary number that provides an additive foundation for the multiplicative i, replaces inverse operations by a single constant, and eliminates signed numbers by rendering polarity as an exponent. Postsymbolic arithmetic reduces trigonometry to reflection along a line, condenses calculus derivatives into a single generic pattern, and identifies and organizes infinite and indeterminate expressions. Other innovations include base-free logarithms, fractional polarity, bipolar numbers, and direct deletion of illusory structure introduced by typographic notation.The overall goal is to demonstrate a comprehensive formal system that can be interpreted as arithmetic but bears little resemblance to our current universally adopted symbolic arithmetic. Iconic Arithmetic provides a proof of concept that our understanding of arithmetic has been limited by the absence of formal techniques for sensory interaction with abstraction.
Download or read book A Dingo Ate My Math Book written by Burkard Polster and published by American Mathematical Soc.. This book was released on 2017-12-27 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Dingo Ate My Math Book presents ingenious, unusual, and beautiful nuggets of mathematics with a distinctly Australian flavor. It focuses, for example, on Australians' love of sports and gambling, and on Melbourne's iconic, mathematically inspired architecture. Written in a playful and humorous style, the book offers mathematical entertainment as well as a glimpse of Australian culture for the mathematically curious of all ages. This collection of engaging stories was extracted from the Maths Masters column that ran from 2007 to 2014 in Australia's Age newspaper. The maths masters in question are Burkard Polster and Marty Ross, two (immigrant) Aussie mathematicians, who each week would write about math in the news, providing a new look at old favorites, mathematical history, quirks of school mathematics—whatever took their fancy. All articles were written for a very general audience, with the intention of being as inviting as possible and assuming a minimum of mathematical background.
Download or read book Icons of Mathematics written by Claudi Alsina and published by MAA. This book was released on 2011-08-04 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: An exploration of the mathematics of twenty geometric diagrams that play a crucial role in visualizing mathematical proofs. Those teaching undergraduate mathematics will find material here for problem solving sessions, as well as enrichment material for courses on proofs and mathematical reasoning.
Download or read book Math Goes to the Movies written by Burkard Polster and published by JHU Press. This book was released on 2012-08-31 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mel Gibson teaching Euclidean geometry, Meg Ryan and Tim Robbins acting out Zeno's paradox, Michael Jackson proving in three different ways that 7 x 13 = 28. These are just a few of the intriguing mathematical snippets that occur in hundreds of movies. Burkard Polster and Marty Ross pored through the cinematic calculus to create this thorough and entertaining survey of the quirky, fun, and beautiful mathematics to be found on the big screen. Math Goes to the Movies is based on the authors' own collection of more than 700 mathematical movies and their many years using movie clips to inject moments of fun into their courses. With more than 200 illustrations, many of them screenshots from the movies themselves, this book provides an inviting way to explore math, featuring such movies as: • Good Will Hunting • A Beautiful Mind • Stand and Deliver • Pi • Die Hard • The Mirror Has Two Faces The authors use these iconic movies to introduce and explain important and famous mathematical ideas: higher dimensions, the golden ratio, infinity, and much more. Not all math in movies makes sense, however, and Polster and Ross talk about Hollywood's most absurd blunders and outrageous mathematical scenes. Interviews with mathematical consultants to movies round out this engaging journey into the realm of cinematic mathematics. This fascinating behind-the-scenes look at movie math shows how fun and illuminating equations can be.
Download or read book Laws Of Form A Fiftieth Anniversary written by Louis H Kauffman and published by World Scientific. This book was released on 2023-01-09 with total page 944 pages. Available in PDF, EPUB and Kindle. Book excerpt: Laws of Form is a seminal work in foundations of logic, mathematics and philosophy published by G Spencer-Brown in 1969. The book provides a new point of view on form and the role of distinction, markedness and the absence of distinction (the unmarked state) in the construction of any universe. A conference was held August 8-10, 2019 at the Old Library, Liverpool University, 19 Abercromby Square, L697ZN, UK to celebrate the 50th anniversary of the publication of Laws of Form and to remember George Spencer-Brown, its author. The book is a collection of papers introducing and extending Laws of Form written primarily by people who attended the conference in 2019.
Download or read book Enthusiastic Mathematics written by Bernie Lewin and published by . This book was released on 2018-11-19 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fifty years ago, a small sparse book came out under the pretentious title Laws of Form. Its author might have once fallen in with the logical philosophers of Cambridge, including Russell and Wittgenstein. But only later, while designing primitive switching circuits for British Rail, did George Spencer Brown come upon the arithmetic underlying Boolean algebra. Laws of Form flips the reduction of mathematics to logic, revealing simple laws of being and knowing that only reflect what great mystics, East and West, have been saying all along. Enthusiastic Mathematics offers the first thorough, philosophical introduction to Laws of Form. With no presumption for logic or mathematics, the reader is delivered into its philosophical vision via a colourful journey through the history of science.
Download or read book Darts on History of Mathematics Volume Ii written by Satish C. Bhatnagar and published by Balboa Press. This book was released on 2023-02-16 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: What is new in the book? Apart from its format, in brief, it has thought-provoking angles of observation and deductive conclusions on many topics, which may look ordinary or rare. Who will benefit from the book? Any lay person with an historical bent of mind on mathematical topics stands to gain from it. Both undergraduate and graduate students in history of mathematics courses would enjoy it. All reflections are independent—they are excellent bedtime reading too.
Download or read book The Handbook of Mathematics Teacher Education Volume 2 written by and published by BRILL. This book was released on 2008-01-01 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Mathematics Teacher Education, the first of its kind, addresses the learning of mathematics teachers at all levels of schooling to teach mathematics, and the provision of activity and programmes in which this learning can take place. It consists of four volumes. Volume 2, Tools and Processes in Mathematics Teacher Education, focuses on the “how” of mathematics teacher education.
Download or read book Visual and Spatial Analysis written by Boris Kovalerchuk and published by Springer Science & Business Media. This book was released on 2007-11-06 with total page 582 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advanced visual analysis and problem solving has been conducted successfully for millennia. The Pythagorean Theorem was proven using visual means more than 2000 years ago. In the 19th century, John Snow stopped a cholera epidemic in London by proposing that a specific water pump be shut down. He discovered that pump by visually correlating data on a city map. The goal of this book is to present the current trends in visual and spatial analysis for data mining, reasoning, problem solving and decision-making. This is the first book to focus on visual decision making and problem solving in general with specific applications in the geospatial domain - combining theory with real-world practice. The book is unique in its integration of modern symbolic and visual approaches to decision making and problem solving. As such, it ties together much of the monograph and textbook literature in these emerging areas. This book contains 21 chapters that have been grouped into five parts: (1) visual problem solving and decision making, (2) visual and heterogeneous reasoning, (3) visual correlation, (4) visual and spatial data mining, and (5) visual and spatial problem solving in geospatial domains. Each chapter ends with a summary and exercises. The book is intended for professionals and graduate students in computer science, applied mathematics, imaging science and Geospatial Information Systems (GIS). In addition to being a state-of-the-art research compilation, this book can be used a text for advanced courses on the subjects such as modeling, computer graphics, visualization, image processing, data mining, GIS, and algorithm analysis.
Download or read book Encyclopedia of Mathematics Education written by Louise Grinstein and published by Routledge. This book was released on 2001-03-15 with total page 912 pages. Available in PDF, EPUB and Kindle. Book excerpt: First published in 2001. Routledge is an imprint of Taylor & Francis, an informa company.
Download or read book A s in Algebra Clueless at Grocery Store written by Ameya and published by DigitalBuzzar. This book was released on with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt: Is your child a math whiz in the classroom but left scratching their head in the grocery store? You're not alone! Most textbooks teach equations, not everyday essentials. But fear not, frustrated parents and math-muddled youngsters! "A's in Algebra, Clueless at the Grocery Store?" is your secret weapon to bridge gap between real world math and textbook math. This Book is Packed with: 🔢 100 Engaging Challenges: Turn math into an adventure with real-world applications like campfire math, bank math mastery, and even math with emojis. From chessboard puzzles to fashion trend calculations, this book makes math exciting and relevant. ➕ Fascinating Add-Ons: Dive into sections like "Did You Know," "5 Tips to Overcome Math Anxiety," and "How to Become an Expert in Math." These informative tidbits keep learning interesting and provide valuable insights. ➗ Interactive Learning Experience: Keep your child motivated with virtual gifts, trophies, and reward coupons. Learning math has never been this interactive and fun! ✖️Celebrate Success: Upon completing the challenges, your child will earn a Certificate of Achievement, proudly recognizing their mathematical prowess and accomplishments. Don’t let their math skills stay confined to the classroom. Empower them to conquer any numerical challenge that comes their way! Buy A’s in Algebra, Clueless at Grocery Store? today and open the door to a world of mathematical proficiency and real-world application. 🌟
Download or read book Converging Perspectives on Conceptual Change written by Tamer G. Amin and published by Routledge. This book was released on 2017-11-13 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: Conceptual change, how conceptual understanding is transformed, has been investigated extensively since the 1970s. The field has now grown into a multifaceted, interdisciplinary effort with strands of research in cognitive and developmental psychology, education, educational psychology, and the learning sciences. Converging Perspectives on Conceptual Change brings together an extensive team of expert contributors from around the world, and offers a unique examination of how distinct lines of inquiry can complement each other and have converged over time. Amin and Levrini adopt a new approach to assembling the diverse research on conceptual change: the combination of short position pieces with extended synthesis chapters within each section, as well as an overall synthesis chapter at the end of the volume, provide a coherent and comprehensive perspective on conceptual change research. Arranged over five parts, the book covers a number of topics including: the nature of concepts and conceptual change representation, language, and discourse in conceptual change modeling, explanation, and argumentation in conceptual change metacognition and epistemology in conceptual change identity and conceptual change. Throughout this wide-ranging volume, the editors present researchers and practitioners with a more internally consistent picture of conceptual change by exploring convergence and complementarity across perspectives. By mapping features of an emerging paradigm, they challenge newcomers and established scholars alike to embrace a more programmatic orientation towards conceptual change.
Download or read book Contemporary Debates in Philosophy of Mind written by Brian P. McLaughlin and published by John Wiley & Sons. This book was released on 2023-03-20 with total page 645 pages. Available in PDF, EPUB and Kindle. Book excerpt: A timely collection of debates concerning the major themes and topics in philosophy of mind, fully updated with new topics covering the latest developments in the field Contemporary Debates in Philosophy of Mind provides a lively and engaging introduction to the conceptual background, ongoing debates, and contentious issues in the field today. Original essays by more than 30 of the discipline’s most influential thinkers offer opposing perspectives on a series of contested questions regarding mental content, physicalism, the place of consciousness in the physical world, and the nature of perception and mental capacities. Written to appeal to non-specialists and professional philosophers alike, the second edition of Contemporary Debates in Philosophy of Mind features five entirely new debates on the relation between perception and cognition, whether pain is a natural kind, whether perception is best understood through representational content or direct contact with the world, whether we need imagination that goes beyond imagery and supposition, and whether perceptual contents are general, particular, or a hybrid. Presents 15 sets of specially commissioned essays with opposing viewpoints on central topics in philosophy of mind Offers head-to-head debates on central topics such as consciousness, intentionality, normativity, mental causation, materialism, and perception Provides a dynamic view of contemporary thinking about fundamental and controversial issues Includes a thorough introduction providing a comprehensive background to the issues explored in each debate Part of Wiley-Blackwell’s acclaimed Contemporary Debates in Philosophy series, Contemporary Debates in Philosophy of Mind, Second Edition is essential reading for undergraduate and graduate students, academics, professional philosophers, and sophisticated general readers with an interest in the subject.
Download or read book Number Theory Analysis and Geometry written by Dorian Goldfeld and published by Springer Science & Business Media. This book was released on 2011-12-21 with total page 715 pages. Available in PDF, EPUB and Kindle. Book excerpt: Serge Lang was an iconic figure in mathematics, both for his own important work and for the indelible impact he left on the field of mathematics, on his students, and on his colleagues. Over the course of his career, Lang traversed a tremendous amount of mathematical ground. As he moved from subject to subject, he found analogies that led to important questions in such areas as number theory, arithmetic geometry, and the theory of negatively curved spaces. Lang's conjectures will keep many mathematicians occupied far into the future. In the spirit of Lang’s vast contribution to mathematics, this memorial volume contains articles by prominent mathematicians in a variety of areas of the field, namely Number Theory, Analysis, and Geometry, representing Lang’s own breadth of interest and impact. A special introduction by John Tate includes a brief and fascinating account of the Serge Lang’s life. This volume's group of 6 editors are also highly prominent mathematicians and were close to Serge Lang, both academically and personally. The volume is suitable to research mathematicians in the areas of Number Theory, Analysis, and Geometry.
Download or read book Methodological Approaches to STEM Education Research Volume 3 written by Peta J. White and published by Cambridge Scholars Publishing. This book was released on 2022-09-30 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: We live in challenging and uncertain times, with profound implications for the purpose and nature of education. The crises of the Anthropocene, with the related climate-related challenges, biodiversity loss, a global pandemic, and changes to the world of work driven by science and technology innovation and the ascendency of data and knowledge, pressure us to rethink how we prepare people for such futures. This, in turn, has changed the landscape of educational research, perhaps particularly in the areas of mathematics, health and environmental education research that are so central to responding to these global pressures and potential solutions. We need to think critically about education research design and practice as part of a considered and robust discussion of education research theory and practice that will inform and help shape education systems into the future. This volume responds to these challenges, casting fresh light on contemporary methodologies fit for reconsidering education into the future. Chapters explore post-qualitative inquiry, with overviews and practices, arts-based and interdisciplinary methodologies, self-study and auto-ethnography for the Anthropocene, co-design with teachers, researching for system change, the ethics of ‘netnography’, and principles and practices of literature review.
