What Is A Mathematical Concept

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What Is A Mathematical Concept

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Author : Elizabeth de Freitas
language : en
Publisher: Cambridge University Press
Release Date : 2017-06-22

What Is A Mathematical Concept written by Elizabeth de Freitas 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 2017-06-22 with Education categories.

Leading thinkers in mathematics, philosophy and education offer new insights into the fundamental question: what is a mathematical concept?

Effects Of Integrated Learning Explicating A Mathematical Concept In Inquiry Based Science Camps

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Author : Louise Bindel
language : en
Publisher: Logos Verlag Berlin GmbH
Release Date : 2018

Effects Of Integrated Learning Explicating A Mathematical Concept In Inquiry Based Science Camps written by Louise Bindel and has been published by Logos Verlag Berlin GmbH this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with Education categories.

Although various arguments for integrated learning of mathematics and science exist, empirical evidence that integrated learning is as beneficial as anticipated is limited. Therefore this quasi-experimental study investigates the effect of integrated learning of mathematics and science on eight student variables by comparing it to a control group. Results show that integrated learning is no miracle cure but has positive and negative effects on specific student outcomes. Whereas integrated learning effects students' view of the relation between mathematics and science positively, it effects students' scientific self-concept negatively. Thus, integrated learning should not substitute but rather complement disciplinary learning. Obwohl zahlreiche Argumente für das integrierte Lernen von Mathematik und Naturwissenschaften existieren, ist die vorteilhafte Wirkung integrierten Lernens begrenzt empirisch belegt. Im Rahmen dieser quasi-experimentellen Studie wird der Effekt integrierten Lernens auf acht Schülervariablen durch Vergleiche mit einer Kontrollgruppe untersucht. Die Ergebnisse zeigen, dass integriertes Lernen kein Allheilmittel ist sondern positive und negative Effekte auf bestimmte Schülervariablen hat. Während integriertes Lernen die Sicht der Schülerinnen und Schüler auf die Beziehung zwischen Mathematik und Naturwissenschaften positiv beeinflusst, hat es einen negativen Effekt auf das naturwissenschaftliche Selbstkonzept. Daher sollte integriertes Lernen nicht stellvertretend sondern ergänzend zu disziplinärem Lernen implementiert werden.

Basic Math Concepts

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Author : Joanne K. Price
language : en
Publisher: CRC Press
Release Date : 1991-07-01

Basic Math Concepts written by Joanne K. Price and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-07-01 with Technology & Engineering categories.

FROM THE PREFACE In the years since the first edition, I have continued to consider ways in which the texts could be improved. In this regard, I researched several topics including how people learn (learning styles, etc.), how the brain functions in storing and retrieving information, and the fundamentals of memory systems. Many of the changes incorporated in this second edition are a result of this research. The changes were field-tested during a three-year period in which I taught a water and wastewater mathematics course for Palomar Community College, San Marcos, California. All the fundamental math concepts and skills needed for daily water/wastewater treatment plant operations. This first volume, "Basic Math Concepts for Water and Wastewater Plant Operators," provides a thorough review of the necessary mathematical concepts and skills encountered in the daily operations of a water and wastewater treatment plant. Each chapter begins with a skills check to allow the student to determine whether or not a review of the topic is needed. Practice problems illustrate the concepts presented in each section.

Modeling Mathematical Ideas

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Author : Jennifer M. Suh
language : en
Publisher: Bloomsbury Publishing PLC
Release Date : 2016-12-27

Modeling Mathematical Ideas written by Jennifer M. Suh and has been published by Bloomsbury Publishing PLC this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-27 with Education categories.

Modeling Mathematical Ideas combining current research and practical strategies to build teachers and students strategic competence in problem solving.This must-have book supports teachers in understanding learning progressions that addresses conceptual guiding posts as well as students’ common misconceptions in investigating and discussing important mathematical ideas related to number sense, computational fluency, algebraic thinking and proportional reasoning. In each chapter, the authors opens with a rich real-world mathematical problem and presents classroom strategies (such as visible thinking strategies & technology integration) and other related problems to develop students’ strategic competence in modeling mathematical ideas.

Precursor Math Concepts

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Author : Mary Hynes-Berry
language : en
Publisher: Teachers College Press
Release Date : 2021

Precursor Math Concepts written by Mary Hynes-Berry 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 2021 with Education categories.

This groundbreaking book looks at the development of mathematical thinking in infants and toddlers, with an emphasis on the earliest stage, from zero to three, when mathematical thinking and problem solving first emerge as natural instincts. The text explores the four precursor math concepts—Attribute, Comparison, Change, and Pattern—with an emphasis on how development occurs when it is nurtured by loving knowledgeable others. The authors call this the CAIR principle: Closely Attend & Intentionally Respond. Sharing their stories of working with a wide range of zero to three caregivers and educators, the authors stress the difference between arithmetic skills and their definition of mathematics as “a logical way of thinking that allows for increasing precision.” Each user-friendly chapter includes suggestions for highly effective practices that are embedded into everyday interactions and routines. Early care providers can use this resource to develop young children’s interest in mathematics, ensuring that they are ready for the big ideas they will encounter in preschool. Book Features: Combines the most current research on infant and toddler cognitive development in relation to mathematical thinking.Offers concrete ways to help caregivers and professionals draw out the math that is all around us.Blends three domains of human development—social-emotional, physical, and cognitive.Examines the What, Who, and How of each precursor concept, with authentic anecdotes and “What the Research Says” sections.

Logos And Alogon

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Author : Arkady Plotnitsky
language : en
Publisher: Springer Nature
Release Date : 2023-01-16

Logos And Alogon written by Arkady Plotnitsky and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-16 with Mathematics categories.

This book is a philosophical study of mathematics, pursued by considering and relating two aspects of mathematical thinking and practice, especially in modern mathematics, which, having emerged around 1800, consolidated around 1900 and extends to our own time, while also tracing both aspects to earlier periods, beginning with the ancient Greek mathematics. The first aspect is conceptual, which characterizes mathematics as the invention of and working with concepts, rather than only by its logical nature. The second, Pythagorean, aspect is grounded, first, in the interplay of geometry and algebra in modern mathematics, and secondly, in the epistemologically most radical form of modern mathematics, designated in this study as radical Pythagorean mathematics. This form of mathematics is defined by the role of that which beyond the limits of thought in mathematical thinking, or in ancient Greek terms, used in the book’s title, an alogon in the logos of mathematics. The outcome of this investigation is a new philosophical and historical understanding of the nature of modern mathematics and mathematics in general. The book is addressed to mathematicians, mathematical physicists, and philosophers and historians of mathematics, and graduate students in these fields.

Handbook Of The History And Philosophy Of Mathematical Practice

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Author : Bharath Sriraman
language : en
Publisher: Springer Nature
Release Date : 2024-04-26

Handbook Of The History And Philosophy Of Mathematical Practice written by Bharath Sriraman and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-26 with Mathematics categories.

The purpose of this unique handbook is to examine the transformation of the philosophy of mathematics from its origins in the history of mathematical practice to the present. It aims to synthesize what is known and what has unfolded so far, as well as to explore directions in which the study of the philosophy of mathematics, as evident in increasingly diverse mathematical practices, is headed. Each section offers insights into the origins, debates, methodologies, and newer perspectives that characterize the discipline today. Contributions are written by scholars from mathematics, history, and philosophy – as well as other disciplines that have contributed to the richness of perspectives abundant in the study of philosophy today – who describe various mathematical practices throughout different time periods and contrast them with the development of philosophy. Editorial Advisory Board Andrew Aberdein, Florida Institute ofTechnology, USA Jody Azzouni, Tufts University, USA Otávio Bueno, University of Miami, USA William Byers, Concordia University, Canada Carlo Cellucci, Sapienza University of Rome, Italy Chandler Davis, University of Toronto, Canada (1926-2022) Paul Ernest, University of Exeter, UK Michele Friend, George Washington University, USA Reuben Hersh, University of New Mexico, USA (1927-2020) Kyeong-Hwa Lee, Seoul National University, South Korea Yuri Manin, Max Planck Institute for Mathematics, Germany (1937-2023) Athanase Papadopoulos, University of Strasbourg, France Ulf Persson, Chalmers University of Technology, Sweden John Stillwell, University of San Francisco, USA David Tall, University of Warwick, UK (1941-2024) This book with its exciting depth and breadth, illuminates us about the history, practice, and the very language of our subject; about the role of abstraction, ofproof and manners of proof; about the interplay of fundamental intuitions; about algebraic thought in contrast to geometric thought. The richness of mathematics and the philosophy encompassing it is splendidly exhibited over the wide range of time these volumes cover---from deep platonic and neoplatonic influences to the most current experimental approaches. Enriched, as well, with vivid biographies and brilliant personal essays written by (and about) people who play an important role in our tradition, this extraordinary collection of essays is fittingly dedicated to the memory of Chandler Davis, Reuben Hersh, and Yuri Manin. ---Barry Mazur, Gerhard Gade University Professor, Harvard University This encyclopedic Handbook will be a treat for all those interested in the history and philosophy of mathematics. Whether one is interested in individuals (from Pythagoras through Newton and Leibniz to Grothendieck), fields (geometry, algebra, number theory, logic, probability, analysis), viewpoints (from Platonism to Intuitionism), or methods (proof, experiment, computer assistance), the reader will find a multitude of chapters that inform and fascinate. ---John Stillwell, Emeritus Professor of Mathematics, University of San Francisco; Recipient of the 2005 Chauvenet Prize Dedicating a volume to the memory of three mathematicians – Chandler Davis, Reuben Hersh, and Yuri Manin –, who went out of their way to show to a broader audience that mathematics is more than what they might think, is an excellent initiative. Gathering authors coming from many different backgrounds but who are very strict about the essays they write was successfully achieved by the editor-in-chief. The result: a great source of potential inspiration! ---Jean-Pierre Bourguignon; Nicolaas Kuiper Honorary Professor at the Institut des Hautes Études Scientifiques

Multivariate Calculus And Geometry Concepts

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Author : Chirag Verma
language : en
Publisher: Educohack Press
Release Date : 2025-02-20

Multivariate Calculus And Geometry Concepts written by Chirag Verma and has been published by Educohack Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-20 with Science categories.

"Multivariate Calculus and Geometry Concepts" is a comprehensive textbook designed to provide students, researchers, and practitioners with a thorough understanding of fundamental concepts, techniques, and applications in multivariate calculus and geometry. Authored by experts, we offer a balanced blend of theoretical foundations, practical examples, and computational methods, making it suitable for both classroom instruction and self-study. We cover a wide range of topics, including partial derivatives, gradients, line and surface integrals, parametric equations, polar coordinates, conic sections, and differential forms. Each topic is presented clearly and concisely, with detailed explanations and illustrative examples to aid understanding. Our emphasis is on developing a conceptual understanding of key concepts and techniques, rather than rote memorization of formulas. We include numerous figures, diagrams, and geometric interpretations to help readers visualize abstract mathematical concepts and their real-world applications. Practical applications of multivariate calculus and geometry are highlighted throughout the book, with examples drawn from physics, engineering, computer graphics, and other fields. We demonstrate how these concepts are used to solve real-world problems and inspire readers to apply their knowledge in diverse areas. We discuss computational methods and numerical techniques used in multivariate calculus and geometry, such as numerical integration, optimization algorithms, and finite element methods. Programming exercises and computer simulations provide hands-on experience with implementing and applying these methods. Our supplementary resources include online tutorials, solution manuals, and interactive simulations, offering additional guidance, practice problems, and opportunities for further exploration and self-assessment. "Multivariate Calculus and Geometry Concepts" is suitable for undergraduate and graduate students in mathematics, engineering, physics, computer science, and related disciplines. It also serves as a valuable reference for researchers, educators, and professionals seeking a comprehensive overview of multivariate calculus and geometry and its applications in modern science and technology.

Mathematics Teaching And Learning

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Author : Rina Kim
language : en
Publisher: Springer
Release Date : 2015-03-24

Mathematics Teaching And Learning written by Rina Kim and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-24 with Education categories.

The purpose of this research is to identify the categories of South Korean elementary teachers’ knowledge for teaching mathematics. Emerging from the data collected and the subsequent analysis are five categories of South Korean elementary teachers’ knowledge for teaching mathematics: Mathematics Curriculum Knowledge, Mathematics Learner Knowledge, Fundamental Mathematics Conceptual Knowledge, Mathematics Pedagogical Content Knowledge, and Mathematics Pedagogical Procedural Knowledge. The first three categories of knowledge play a significant role in mathematics instruction as an integrated form within Mathematics Pedagogical Content Knowledge. This study also demonstrated that Mathematics Pedagogical Procedural Knowledge might play a pivotal role in constructing Mathematics Pedagogical Content Knowledge. These findings are connected to results from relevant studies in terms of the significant role of teachers’ knowledge in mathematics instruction.

Burn Math Class

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Author : Jason Wilkes
language : en
Publisher: Basic Books
Release Date : 2016-03-22

Burn Math Class written by Jason Wilkes and has been published by Basic Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-22 with Mathematics categories.

A manifesto for a mathematical revolution Forget everything you've been taught about math. In Burn Math Class, Jason Wilkes takes the traditional approach to how we learn math -- with its unwelcoming textbooks, unexplained rules, and authoritarian assertions-and sets it on fire. Focusing on how mathematics is created rather than on mathematical facts, Wilkes teaches the subject in a way that requires no memorization and no prior knowledge beyond addition and multiplication. From these simple foundations, Burn Math Class shows how mathematics can be (re)invented from scratch without preexisting textbooks and courses. We can discover math on our own through experimentation and failure, without appealing to any outside authority. When math is created free from arcane notations and pretentious jargon that hide the simplicity of mathematical concepts, it can be understood organically -- and it becomes fun! Following this unconventional approach, Burn Math Class leads the reader from the basics of elementary arithmetic to various "advanced" topics, such as time-dilation in special relativity, Taylor series, and calculus in infinite-dimensional spaces. Along the way, Wilkes argues that orthodox mathematics education has been teaching the subject backward: calculus belongs before many of its so-called prerequisites, and those prerequisites cannot be fully understood without calculus. Like the smartest, craziest teacher you've ever had, Wilkes guides you on an adventure in mathematical creation that will radically change the way you think about math. Revealing the beauty and simplicity of this timeless subject, Burn Math Class turns everything that seems difficult about mathematics upside down and sideways until you understand just how easy math can be.