Mathematizing Space
DOWNLOAD
Download Mathematizing Space PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Mathematizing Space book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Mathematizing Space
DOWNLOAD
Author : Vincenzo De Risi
language : en
Publisher: Birkhäuser
Release Date : 2015-01-31
Mathematizing Space written by Vincenzo De Risi and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-31 with Mathematics categories.
This book collects the papers of the conference held in Berlin, Germany, 27-29 August 2012, on 'Space, Geometry and the Imagination from Antiquity to the Modern Age'. The conference was a joint effort by the Max Planck Institute for the History of Science (Berlin) and the Centro die Ricerca Matematica Ennio De Giorgi (Pisa).
The Changing Faces Of Space
DOWNLOAD
Author : Maria Teresa Catena
language : en
Publisher: Springer
Release Date : 2018-01-11
The Changing Faces Of Space written by Maria Teresa Catena and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-11 with Philosophy categories.
This book focuses on various concepts of space and their historical evolution. In particular, it examines the variations that have modified the notions of place, orientation, distance, vacuum, limit, bound and boundary, form and figure, continuity and contingence, in order to show how spatial characteristics are decisive in a range of contexts: in the determination and comprehension of exteriority; in individuation and identification; in defining the meaning of nature and of the natural sciences; in aesthetical formations and representations; in determining the relationship between experience, behavior and environment; and in the construction of mental and social subjectivity. Accordingly, the book offers a comprehensive review of concepts of space as formulated by Kant, Husserl, Heidegger, Einstein, Heisenberg, Penrose and Thorne, subsequently comparing them to notions developed more recently, in the current age, which Foucault dubbed the age of space. The book is divided into four distinct yet deeply interconnected parts, which explore the space of life, the space of experience, the space of science and the space of the arts.
Mathematics As An Educational Task
DOWNLOAD
Author : Hans Freudenthal
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Mathematics As An Educational Task written by Hans Freudenthal and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Education categories.
Like preludes, prefaces are usually composed last. Putting them in the front of the book is a feeble reflection of what, in the style of mathe matics treatises and textbooks, I usually call thf didactical inversion: to be fit to print, the way to the result should be the inverse of the order in which it was found; in particular the key definitions, which were the finishing touch to the structure, are put at the front. For many years I have contrasted the didactical inversion with the thought-experiment. It is true that you should not communicate your mathematics to other people in the way it occurred to you, but rather as it could have occurred to you if you had known then what you know now, and as it would occur to the student if his learning process is being guided. This in fact is the gist of the lesson Socrates taught Meno's slave. The thought-experi ment tries to find out how a student could re-invent what he is expected to learn. I said about the preface that it is a feeble reflection of the didactical inversion. Indeed, it is not a constituent part of the book. It can even be torn out. Yet it is useful. Firstly, to the reviewer who then need not read the whole work, and secondly to the author himself, who like the composer gets an opportunity to review the Leitmotivs of the book.
Mathematizing Your School
DOWNLOAD
Author : Nicki Newton
language : en
Publisher: Routledge
Release Date : 2018-09-27
Mathematizing Your School written by Nicki Newton and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-27 with Education categories.
Learn the secrets to getting your entire school excited about math! This book from acclaimed author Dr. Nicki Newton and experienced instructional specialist Janet Nuzzie shows you how to integrate engaging math instruction at every level, from the small group project to the school-wide assembly. With contributions from math coaches, district leaders, and classroom teachers, this book will give you the practical tools you need to boost student proficiency, encourage collaboration between staff members, and make math an important part of school life. You’ll also learn how to: Create a safe and inviting environment for mathematics instruction; Devote adequate amounts of instructional time to help students develop their skill set as proficient mathematicians; Use real-world contexts and hands-on instruction to boost engagement; Give students the tools and opportunities to be confident, to question, to take risks, and to make mistakes; And much much more!
International Perspectives On The Teaching And Learning Of Geometry In Secondary Schools
DOWNLOAD
Author : Patricio Herbst
language : en
Publisher: Springer
Release Date : 2018-04-27
International Perspectives On The Teaching And Learning Of Geometry In Secondary Schools written by Patricio Herbst and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-27 with Education categories.
This book presents current perspectives on theoretical and empirical issues related to the teaching and learning of geometry at secondary schools. It contains chapters contributing to three main areas. A first set of chapters examines mathematical, epistemological, and curricular perspectives. A second set of chapters presents studies on geometry instruction and teacher knowledge, and a third set of chapters offers studies on geometry thinking and learning. Specific research topics addressed also include teaching practice, learning trajectories, learning difficulties, technological resources, instructional design, assessments, textbook analyses, and teacher education in geometry. Geometry remains an essential and critical topic in school mathematics. As they learn geometry, students develop essential mathematical thinking and visualization skills and learn a language that helps them relate to and interact with the physical world. Geometry has traditionally been included as a subject of study in secondary mathematics curricula, but it has also featured as a resource in out-of-school problem solving, and has been connected to various human activities such as sports, games, and artwork. Furthermore, geometry often plays a role in teacher preparation, undergraduate mathematics, and at the workplace. New technologies, including dynamic geometry software, computer-assisted design software, and geometric positioning systems, have provided more resources for teachers to design environments and tasks in which students can learn and use geometry. In this context, research on the teaching and learning of geometry will continue to be a key element on the research agendas of mathematics educators, as researchers continue to look for ways to enhance student learning and to understand student thinking and teachers’ decision making.
Becoming Fully Human
DOWNLOAD
Author : Rudolf Steiner
language : en
Publisher: SteinerBooks
Release Date : 2022-05-20
Becoming Fully Human written by Rudolf Steiner and has been published by SteinerBooks this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-20 with Body, Mind & Spirit categories.
6 lectures at The Hague, April 7-12, 1922; A written report by Rudolf Steiner on the course (CW 82) "There is no contradiction, if you look into the matter correctly, between destiny and freedom. However, in order to be able to present the concept of destiny to the world later on, it was first necessary that the concept of freedom be presented in the book The Philosophy of Freedom." -- Rudolf Steiner (lect. 6) Published here for the first time in English, these six public lectures are among Rudolf Steiner's most inspired --and inspiring --explorations of Anthroposophy as a true science of the spirit. Our age provides abundant explanations of the universe, its nature and evolution. But underlying most scientific modalities is a passive engagement with self and world, a taking-for-granted of the faculty of thinking, and, as a result, an indifferent arranging of phenomena through logical inference. But the question remains: What is thinking? A product of chemical processes in the brain, or a spiritual activity through which we become participants in a spiritual cosmos? This is Steiner's starting point in all his work. He aims to cast off the unnecessary limits imposed on knowledge by a science that fails to examine its most fundamental epistemological premises. The lectures here are a remarkable contribution to this lifelong project --a compelling, eloquent, insightful study and affirmation of our very humanness. Speaking to a youthful academic audience, Steiner does not confine himself to the arbitrary delineations of codified academic disciplines; on the contrary, he breaks down barriers, builds bridges, envisions a future academy in which the paths of knowledge are broadened through a genuine science of initiation to encompass our role as members and, ultimately, co-creators of the physical, soul, and spiritual universe. "Those who seek to prove something show, through the very fact that they seek to prove it, that for them what must be proved is not readily perceptible. We actually seek to prove something whenever we have no direct perception of it.... When in older, instinctive cognition people had a perception of what they called the divine being, they did not need proofs. Historically, the proofs for the existence of God began only when the perception was lost. Evidence is required wherever there is no perception." -- Rudolf Steiner (lect. 6) This volume is a translation from German of Damit der Mensch ganz Mensch werde. Die Bedeutung der Anthroposophieim Geistesleben der Gegenwart (GA 82), 2nd ed., Rudolf Steiner Verlag, Dornach, Switzerland, 1994. Cover image: The Golden Cell by Odilon Redon, 1892. Oil and colored chalks with gold, 30.1 cm x 24.7 cm. The British Museum, London.
Designing Learning Environments For Developing Understanding Of Geometry And Space
DOWNLOAD
Author : Richard Lehrer
language : en
Publisher: Routledge
Release Date : 2012-11-12
Designing Learning Environments For Developing Understanding Of Geometry And Space written by Richard Lehrer and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-11-12 with Education categories.
This volume reflects an appreciation of the interactive roles of subject matter, teacher, student, and technologies in designing classrooms that promote understanding of geometry and space. Although these elements of geometry education are mutually constituted, the book is organized to highlight, first, the editors' vision of a general geometry education; second, the development of student thinking in everyday and classroom contexts; and third, the role of technologies. Rather than looking to high school geometry as the locus--and all too often, the apex--of geometric reasoning, the contributors to this volume suggest that reasoning about space can and should be successfully integrated with other forms of mathematics, starting at the elementary level and continuing through high school. Reintegrating spatial reasoning into the mathematical mainstream--indeed, placing it at the core of K-12 mathematics environments that promote learning with understanding--will mean increased attention to problems in modeling, structure, and design and reinvigoration of traditional topics such as measure, dimension, and form. Further, the editors' position is that the teaching of geometry and spatial visualization in school should not be compressed into a characterization of Greek geometry, but should include attention to contributions to the mathematics of space that developed subsequent to those of the Greeks. This volume is essential reading for those involved in mathematics education at all levels, including university faculty, researchers, and graduate students.
Mathematize It Grades 3 5
DOWNLOAD
Author : Sara Delano Moore
language : en
Publisher: Corwin Press
Release Date : 2019-09-04
Mathematize It Grades 3 5 written by Sara Delano Moore and has been published by Corwin Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-04 with Education categories.
"The list of math books to truly synthesize what we know so far and what we need to know is a very short and exclusive list. Well, you can confidently add Mathematize It to this collection. Written by three of the most respected math educators today, the book zeros in on that often poorly traveled journey between the question and answer in problem solving. Mathematize It will be your go-to resource to install the mathematical play revolution in elementary classes everywhere!" Suni Singh Author of Pi of Life: the Hidden Happiness of Mathematics and Math Recess: Playful Learning in an Age of Disruption Help students reveal the math behind the words "I don’t get what I’m supposed to do!" This is a common refrain from students when asked to solve word problems. Solving problems is about more than computation. Students must understand the mathematics of a situation to know what computation will lead to an appropriate solution. Many students often pluck numbers from the problem and plug them into an equation using the first operation they can think of (or the last one they practiced). Students also tend to choose an operation by solely relying on key words that they believe will help them arrive at an answer, which without careful consideration of what the problem is actually asking of them. Mathematize It! Going Beyond Key Words to Make Sense of Word Problems, Grades 3-5 shares a reasoning approach that helps students dig into the problem to uncover the underlying mathematics, deeply consider the problem’s context, and employ strong operation sense to solve it. Through the process of mathematizing, the authors provide an explanation of a consistent method—and specific instructional strategies—to take the initial focus off specific numbers and computations and put it on the actions and relationships expressed in the problem. Sure to enhance teachers’ own operation sense, this user-friendly resource for Grades 3–5 • Offers a systematic mathematizing process for students to use when solving word problems • Gives practice opportunities and dozens of problems to leverage in the classroom • Provides specific examples of questions and explorations for all four operations (addition, subtraction, multiplication, and division) with whole numbers, fractions, and decimals • Demonstrates the use of concrete manipulatives to model problems with dozens of short videos • Includes end-of-chapter activities and reflection questions How can you help your students understand what is happening mathematically when solving word problems? Mathematize it!
Relativity Principles And Theories From Galileo To Einstein
DOWNLOAD
Author : Olivier Darrigol
language : en
Publisher: Oxford University Press
Release Date : 2021-12-22
Relativity Principles And Theories From Galileo To Einstein written by Olivier Darrigol and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-22 with Science categories.
Motion is always relative to some thing. Is this thing a concrete body like the earth, is it an abstract space, or is it an imagined frame? Do the laws of physics depend on the choice of reference? It there a choice for which the laws are simplest? Is this choice unique? Is there a physical cause for the choice made? These questions traverse the history of modern physics from Galileo to Einstein. The answers involved Galilean relativity, Newton's absolute space, the purely relational concepts of Descartes, Leibniz, and Mach, and many forgotten uses of relativity principles in mechanics, optics, and electrodynamics - until the relativity theories of Poincaré, Einstein, Minkowksi, and Laue radically redefined space and time to satisfy universal kinds of relativity. Accordingly, this book retraces the emergence of relativity principles in early modern mechanics, documents their constructive use in eighteenth- and nineteenth-century mechanics, optics, and electrodynamics, and gives a well-rooted account of the genesis of special and general relativity in the early twentieth century. As an exercise in long-term history, it demonstrates the connectivity of issues and approaches across several centuries, despite enormous changes in context and culture. As an account of the genesis of relativity theories, it brings unprecedented clarity and fullness by broadening the spectrum of resources on which the principal actors drew.
Truth Existence And Explanation
DOWNLOAD
Author : Mario Piazza
language : en
Publisher: Springer
Release Date : 2018-10-24
Truth Existence And Explanation written by Mario Piazza and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-24 with Mathematics categories.
This book contains more than 15 essays that explore issues in truth, existence, and explanation. It features cutting-edge research in the philosophy of mathematics and logic. Renowned philosophers, mathematicians, and younger scholars provide an insightful contribution to the lively debate in this interdisciplinary field of inquiry. The essays look at realism vs. anti-realism as well as inflationary vs. deflationary theories of truth. The contributors also consider mathematical fictionalism, structuralism, the nature and role of axioms, constructive existence, and generality. In addition, coverage also looks at the explanatory role of mathematics and the philosophical relevance of mathematical explanation. The book will appeal to a broad mathematical and philosophical audience. It contains work from FilMat, the Italian Network for the Philosophy of Mathematics. These papers collected here were also presented at their second international conference, held at the University of Chieti-Pescara, May 2016.