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| discovering geometry an investigative approach 2008: The Language of Mathematics Education Shannon W. Dingman, Laura B. Kent, Kim K. McComas, Cynthia C. Orona, 2019-08-26 The Language of Mathematics Education: An Expanded Glossary of Key Terms and Concepts in Mathematics Teaching and Learning offers mathematics teachers, mathematics education professionals and students a valuable resource in which common terms are defined and expounded upon in short essay format. The shared vocabulary and terminology relating to mathematics teaching and learning, and used by mathematics educators is an essential component of work conducted in the field. The authors provide an overview of more than 100 terms commonly used in mathematics teaching and learning. Each term is defined and is followed by a short overview of the concept under discussion that includes several bibliographic references the reader can use for further investigation. In addition to terms specific to the domain of mathematics education, select key terms common across all fields of education (e.g., curriculum, epistemology, metacognition) are included. The goal for this book is to serve as a resource for those entering the field as they navigate the language and terminology of mathematics education and as an asset for more established professionals who wish to gain additional insights into these ideas. |
| discovering geometry an investigative approach 2008: Teaching Mathematics in Grades 6 - 12 Randall E. Groth, 2012-08-10 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. |
| discovering geometry an investigative approach 2008: Resources for Preparing Middle School Mathematics Teachers Cheryl Beaver, Laurie J. Burton, Maria Gueorguieva Gargova Fung, Klay Kruczek, 2013 Cheryl Beaver, Laurie Burton, Maria Fung, Klay Kruczek, editors--Cover. |
| discovering geometry an investigative approach 2008: Adventures in Dynamic Geometry Gerry Stahl, 2015-10-06 Math games and workbooks with topics for online small groups of teachers or students to collaboratively learn dynamic geometry. The approach is based on Translating Euclid. The many GeoGebra files used in VMT courses are pictured in the workbook. Several versions of the workbooks are available, including the version used in WinterFest 2013 and analyzed in Translating Euclid and Constructing Dynamic Triangles Together. Also includes the content of a game version that is available as a GeoGebraBook. |
| discovering geometry an investigative approach 2008: Critical Literacy as Resistance Laraine Wallowitz, 2008 Critical Literacy as Resistance is a collaborate effort among secondary and university educators from across the United States that addresses questions such as: What does a critical literacy classroom look like? What various texts are used? What strategies do teachers use to encourage students and teacher candidates to recognize how texts construct power and privilege? How do educators inspire activism in and out of the classroom? This book documents the experiences of scholars and teachers who have successfully bridged theory and practice by applying critical literacy into their respective content areas. The authors spell out the difference between critical thinking and critical literacy, then show how to write and implement curriculum that incorporates diverse texts and multiple literacies in all content areas (including world language), and includes the voices of students as they confront issues of race, class, gender, and power. The principles and practices laid out here will help teachers use literacy to liberate and empower students both in and outside the classroom by respecting and studying the literacies students bring to school, while simultaneously teaching (and challenging) the literacies of those in power. This is a book for pre- and in-service teachers in all content areas, staff developers, secondary literacy specialists, university professors, and anyone interested in social justice. |
| discovering geometry an investigative approach 2008: Teaching Secondary and Middle School Mathematics Daniel J. Brahier, 2020-04-01 Teaching Secondary and Middle School Mathematics combines the latest developments in research, technology, and standards with a vibrant writing style to help teachers prepare for the excitement and challenges of teaching secondary and middle school mathematics. The book explores the mathematics teaching profession by examining the processes of planning, teaching, and assessing student progress through practical examples and recommendations. Beginning with an examination of what it means to teach and learn mathematics, the reader is led through the essential components of teaching, concluding with an examination of how teachers continue with professional development throughout their careers. Hundreds of citations are used to support the ideas presented in the text, and specific websites and other resources are presented for future study by the reader. Classroom scenarios are presented to engage the reader in thinking through specific challenges that are common in mathematics classrooms. The sixth edition has been updated and expanded with particular emphasis on the latest technology, resources, and standards. The reader is introduced to the ways that students think and how to best meet their needs through planning that involves attention to differentiation, as well as how to manage a classroom for success. Features include: The entire text has been reorganized so that assessment takes a more central role in planning and teaching. Unit 3 (of 5) now addresses the use of summative and formative assessments to inform classroom teaching practices. ● A new feature, Links and Resources, has been added to each of the 13 chapters. While the book includes a substantial listing of citations and resources after the chapters, five strongly recommended and practical resources are spotlighted at the end of each chapter as an easy reference to some of the most important materials on the topic. ● Approximately 150 new citations have either replaced or been added to the text to reflect the latest in research, materials, and resources that support the teaching of mathematics. ● A Quick Reference Guide has been added to the front of the book to assist the reader in identifying the most useful chapter features by topic. ● A significant revision to Chapter 13 now includes discussions of common teaching assessments used for field experiences and licensure, as well as a discussion of practical suggestions for success in methods and student teaching experiences. ● Chapter 9 on the practical use of classroom technology has been revised to reflect the latest tools available to classroom teachers, including apps that can be run on handheld, personal devices. An updated Instructor’s Manual features a test bank, sample classroom activities, Powerpoint slides, chapter summaries, and learning outcomes for each chapter, and can be accessed by instructors online at www.routledge.com/9780367146511 |
| discovering geometry an investigative approach 2008: Discovering Geometry Michael Serra, Key Curriculum Press Staff, 2003-03-01 |
| discovering geometry an investigative approach 2008: Understanding Geometry for a Changing World Timothy Craine, 2009 CD-ROM contains lessons, activity sheets, application files, video clips, and Web links. |
| discovering geometry an investigative approach 2008: Preparing Classroom Teachers to Succeed with Second Language Learners Thomas Levine, Elizabeth Howard, David Moss, 2014-07-11 This volume identifies resources, models, and specific practices for improving teacher preparation for work with second language learners. It shows how faculty positioned themselves to learn from resources, experts, preservice teachers, their own practice, and each other. The teacher education professionals leverage their experience to offer theoretical and practical insights regarding how other faculty could develop their own knowledge, improve their courses, and understand their influence on the preservice teachers they serve. The book addresses challenges others are likely to experience while improving teacher preparation, including preservice teacher resistance, the challenge of adding to already-packed courses, the difficulty of recruiting and retaining busy faculty members, and the question of how to best frame the larger issues. The authors also address options for integrating the work of improving teacher preparation for linguistic diversity into a variety of different teacher education program designs. Finally, the book demonstrates a data-driven approach that makes this work consistent with many institutions’ mandate to produce research and to collect evidence supporting accreditation. |
| discovering geometry an investigative approach 2008: Computational Geometry Franco P. Preparata, Michael I. Shamos, 2012-12-06 From the reviews: This book offers a coherent treatment, at the graduate textbook level, of the field that has come to be known in the last decade or so as computational geometry. ... ... The book is well organized and lucidly written; a timely contribution by two founders of the field. It clearly demonstrates that computational geometry in the plane is now a fairly well-understood branch of computer science and mathematics. It also points the way to the solution of the more challenging problems in dimensions higher than two. #Mathematical Reviews#1 ... This remarkable book is a comprehensive and systematic study on research results obtained especially in the last ten years. The very clear presentation concentrates on basic ideas, fundamental combinatorial structures, and crucial algorithmic techniques. The plenty of results is clever organized following these guidelines and within the framework of some detailed case studies. A large number of figures and examples also aid the understanding of the material. Therefore, it can be highly recommended as an early graduate text but it should prove also to be essential to researchers and professionals in applied fields of computer-aided design, computer graphics, and robotics. #Biometrical Journal#2 |
| discovering geometry an investigative approach 2008: Curriculum Planning and Instructional Design for Gifted Learners Joyce VanTassel-Baska, Ariel Baska, 2021-09-23 This updated third edition of Curriculum Planning and Instructional Design for Gifted Learners: |
| discovering geometry an investigative approach 2008: The Theory and Practice of Online Learning Terry Anderson, 2008 Neither an academic tome nor a prescriptive 'how to' guide, The Theory and Practice of Online Learning is an illuminating collection of essays by practitioners and scholars active in the complex field of distance education. Distance education has evolved significantly in its 150 years of existence. For most of this time, it was an individual pursuit defined by infrequent postal communication. But recently, three more developmental generations have emerged, supported by television and radio, teleconferencing, and computer conferencing. The early 21st century has produced a fifth generation, based on autonomous agents and intelligent, database-assisted learning, that has been referred to as Web 2.0. The second edition of The Theory and Practice of Online Learning features updates in each chapter, plus four new chapters on current distance education issues such as connectivism and social software innovations.--BOOK JACKET. |
| discovering geometry an investigative approach 2008: The Classification of Quadrilaterals Zalman Usiskin, 2008-01-01 This monograph reports on an analysis of a small part of the mathematics curriculum, the definitions given to quadrilaterals. This kind of research, which we call micro-curricular analysis, is often undertaken by those who create curriculum, but it is not usually done systematically and it is rarely published. Many terms in mathematics education can be found to have different definitions in mathematics books. Among these are “natural number,” “parallel lines” and “congruent triangles,” “trapezoid” and “isosceles trapezoid,” the formal definitions of the trigonometric functions and absolute value, and implicit definitions of the arithmetic operations addition, subtraction, multiplication, and division. Yet many teachers and students do not realize there is a choice of definitions for mathematical terms. And even those who realize there is a choice may not know who decides which definition of any mathematical term is better, and under what criteria. Finally, rarely are the mathematical implications of various choices discussed. As a result, many students misuse and otherwise do not understand the role of definition in mathematics. We have chosen in this monograph to examine a bit of mathematics for its definitions: the quadrilaterals. We do so because there is some disagreement in the definitions and, consequently, in the ways in which quadrilaterals are classified and relate to each other. The issues underlying these differences have engaged students, teachers, mathematics educators, and mathematicians. There have been several articles and a number of essays on the definitions and classification of quadrilaterals. But primarily we chose this specific area of definition in mathematics because it demonstrates how broad mathematical issues revolving around definitions become reflected in curricular materials. While we were undertaking this research, we found that the area of quadrilaterals supplied grist for broader and richer discussions than we had first anticipated. The intended audience includes curriculum developers, researchers, teachers, teacher trainers, and anyone interested in language and its use. |
| discovering geometry an investigative approach 2008: Transforming the Workforce for Children Birth Through Age 8 National Research Council, Institute of Medicine, Board on Children, Youth, and Families, Committee on the Science of Children Birth to Age 8: Deepening and Broadening the Foundation for Success, 2015-07-23 Children are already learning at birth, and they develop and learn at a rapid pace in their early years. This provides a critical foundation for lifelong progress, and the adults who provide for the care and the education of young children bear a great responsibility for their health, development, and learning. Despite the fact that they share the same objective - to nurture young children and secure their future success - the various practitioners who contribute to the care and the education of children from birth through age 8 are not acknowledged as a workforce unified by the common knowledge and competencies needed to do their jobs well. Transforming the Workforce for Children Birth Through Age 8 explores the science of child development, particularly looking at implications for the professionals who work with children. This report examines the current capacities and practices of the workforce, the settings in which they work, the policies and infrastructure that set qualifications and provide professional learning, and the government agencies and other funders who support and oversee these systems. This book then makes recommendations to improve the quality of professional practice and the practice environment for care and education professionals. These detailed recommendations create a blueprint for action that builds on a unifying foundation of child development and early learning, shared knowledge and competencies for care and education professionals, and principles for effective professional learning. Young children thrive and learn best when they have secure, positive relationships with adults who are knowledgeable about how to support their development and learning and are responsive to their individual progress. Transforming the Workforce for Children Birth Through Age 8 offers guidance on system changes to improve the quality of professional practice, specific actions to improve professional learning systems and workforce development, and research to continue to build the knowledge base in ways that will directly advance and inform future actions. The recommendations of this book provide an opportunity to improve the quality of the care and the education that children receive, and ultimately improve outcomes for children. |
| discovering geometry an investigative approach 2008: Symmetry, Shape and Space L.Christine Kinsey, Teresa E. Moore, 2006-05-09 This book will appeal to at least three groups of readers: prospective high school teachers, liberal arts students, and parents whose children are studying high school or college math. It is modern in its selection of topics, and in the learning models used by the authors. The book covers some exciting but non-traditional topics from the subject area of geometry. It is also intended for undergraduates and tries to engage their interest in mathematics. Many innovative pedagogical modes are used throughout. |
| discovering geometry an investigative approach 2008: Geometry: Euclid and Beyond Robin Hartshorne, 2005-09-28 This book offers a unique opportunity to understand the essence of one of the great thinkers of western civilization. A guided reading of Euclid's Elements leads to a critical discussion and rigorous modern treatment of Euclid's geometry and its more recent descendants, with complete proofs. Topics include the introduction of coordinates, the theory of area, history of the parallel postulate, the various non-Euclidean geometries, and the regular and semi-regular polyhedra. |
| discovering geometry an investigative approach 2008: Computational Complexity Sanjeev Arora, Boaz Barak, 2009-04-20 New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students. |
| discovering geometry an investigative approach 2008: Algebraic Geometry And Its Applications: Dedicated To Gilles Lachaud On His 60th Birthday - Proceedings Of The First Saga Conference Robert Rolland, James Hirschfeld, Jean Chaumine, 2008-04-17 This volume covers many topics, including number theory, Boolean functions, combinatorial geometry, and algorithms over finite fields. It contains many new, theoretical and applicable results, as well as surveys that were presented by the top specialists in these areas. New results include an answer to one of Serre's questions, posted in a letter to Top; cryptographic applications of the discrete logarithm problem related to elliptic curves and hyperelliptic curves; construction of function field towers; construction of new classes of Boolean cryptographic functions; and algorithmic applications of algebraic geometry. |
| discovering geometry an investigative approach 2008: Statistical Power Analysis for the Behavioral Sciences Jacob Cohen, 2013-05-13 Statistical Power Analysis is a nontechnical guide to power analysis in research planning that provides users of applied statistics with the tools they need for more effective analysis. The Second Edition includes: * a chapter covering power analysis in set correlation and multivariate methods; * a chapter considering effect size, psychometric reliability, and the efficacy of qualifying dependent variables and; * expanded power and sample size tables for multiple regression/correlation. |
| discovering geometry an investigative approach 2008: Thinking in Systems Donella H. Meadows, 2009 Thinking in Systems is a concise and crucial book offering insight for problem-solving on scales ranging from the personal to the global. This essential primer brings systems thinking out of the realm of computers and equations and into the tangible world, showing readers how to develop the systems-thinking skills that thought leaders across the globe consider critical for 21st-century life.While readers will learn the conceptual tools and methods of systems thinking, the heart of the book is grander than methodology. Donella Meadows was known as much for nurturing positive outcomes as she was for delving into the science behind global dilemmas. She reminds readers to pay attention to what is important, not just what is quantifiable, to stay humble and to continue to learn.In a world growing ever more complicated, crowded, and interdependent, Thinking in Systems helps readers avoid confusion and helplessness, the first step toward finding proactive and effective solutions. A vital read for students, professionals and all those concerned with economics, business, sustainability and the environment |
| discovering geometry an investigative approach 2008: The Second Handbook of Research on the Psychology of Mathematics Education Ángel Gutiérrez, Gilah C. Leder, Paolo Boero, 2016-07-23 Since its establishment in 1976, PME (The International Group for the Psychology of Mathematics Education) is serving as a much sought after venue for scientific debate among those at the cutting edge of the field, as well as an engine for the development of research in mathematics education. A wide range of research activities conducted over the last ten years by PME members and their colleagues are documented and critically reviewed in this handbook, released to celebrate the Group’s 40 year anniversary milestone. The book is divided into four main sections: Cognitive aspects of learning and teaching content areas; Cognitive aspects of learning and teaching transverse areas; Social aspects of learning and teaching mathematics; and Professional aspects of teaching mathematics. The selection for each chapter of a team of at least two authors, mostly located in different parts of the world, ensured effective coverage of each field. High quality was further enhanced by the scrupulous review of early chapter drafts by two leaders in the relevant field. The resulting volume with its compilation of the most relevant aspects of research in the field, and its emphasis on trends and future developments, will be a rich and welcome resource for both mature and emerging researchers in mathematics education. |
| discovering geometry an investigative approach 2008: Nurse as Educator Susan B. Bastable, 2007-12-12 Nurse as Educator: Principles of Teaching and Learning for Nursing Practice prepares nurse educators, clinical nurse specialists, and nurse practitioners for their ever-increasing roles in patient teaching, health education, health promotion, and nursing education. Designed to teach nurses about the development, motivational, and sociocultural differences that affect teaching and learning, this text combines theoretical and pragmatic content in a balanced, complete style. The Third Edition of this best-selling text has been updated and revised to include the latest research. Nurse as Educator is used extensively in nursing educations courses and programs, as well as in both institutional and community-based settings. |
| discovering geometry an investigative approach 2008: Discovering Geometry Michael Serra, 2008 |
| discovering geometry an investigative approach 2008: The Geography of Thought Richard Nisbett, 2010-10-26 A “landmark book” (Robert J. Sternberg, president of the American Psychological Association) by one of the world's preeminent psychologists that proves human behavior is not “hard-wired” but a function of culture. Everyone knows that while different cultures think about the world differently, they use the same equipment for doing their thinking. But what if everyone is wrong? The Geography of Thought documents Richard Nisbett's groundbreaking international research in cultural psychology and shows that people actually think about—and even see—the world differently because of differing ecologies, social structures, philosophies, and educational systems that date back to ancient Greece and China. As a result, East Asian thought is “holistic”—drawn to the perceptual field as a whole and to relations among objects and events within that field. By contrast, Westerners focus on salient objects or people, use attributes to assign them to categories, and apply rules of formal logic to understand their behavior. From feng shui to metaphysics, from comparative linguistics to economic history, a gulf separates the children of Aristotle from the descendants of Confucius. At a moment in history when the need for cross-cultural understanding and collaboration have never been more important, The Geography of Thought offers both a map to that gulf and a blueprint for a bridge that will span it. |
| discovering geometry an investigative approach 2008: Decolonizing Methodologies Linda Tuhiwai Smith, 2016-03-15 'A landmark in the process of decolonizing imperial Western knowledge.' Walter Mignolo, Duke University To the colonized, the term 'research' is conflated with European colonialism; the ways in which academic research has been implicated in the throes of imperialism remains a painful memory. This essential volume explores intersections of imperialism and research - specifically, the ways in which imperialism is embedded in disciplines of knowledge and tradition as 'regimes of truth.' Concepts such as 'discovery' and 'claiming' are discussed and an argument presented that the decolonization of research methods will help to reclaim control over indigenous ways of knowing and being. Now in its eagerly awaited second edition, this bestselling book has been substantially revised, with new case-studies and examples and important additions on new indigenous literature, the role of research in indigenous struggles for social justice, which brings this essential volume urgently up-to-date. |
| discovering geometry an investigative approach 2008: Digital Media, Youth, and Credibility Miriam J. Metzger, Andrew J. Flanagin, 2008 The difficulties in determining the quality of information on the Internet--in particular, the implications of wide access and questionable credibility for youth and learning. Today we have access to an almost inconceivably vast amount of information, from sources that are increasingly portable, accessible, and interactive. The Internet and the explosion of digital media content have made more information available from more sources to more people than at any other time in human history. This brings an infinite number of opportunities for learning, social connection, and entertainment. But at the same time, the origin of information, its quality, and its veracity are often difficult to assess. This volume addresses the issue of credibility--the objective and subjective components that make information believable--in the contemporary media environment. The contributors look particularly at youth audiences and experiences, considering the implications of wide access and the questionable credibility of information for youth and learning. They discuss such topics as the credibility of health information online, how to teach credibility assessment, and public policy solutions. Much research has been done on credibility and new media, but little of it focuses on users younger than college students. Digital Media, Youth, and Credibility fills this gap in the literature. Contributors Matthew S. Eastin, Gunther Eysenbach, Brian Hilligoss, Frances Jacobson Harris, R. David Lankes, Soo Young Rieh, S. Shyam Sundar, Fred W. Weingarten |
| discovering geometry an investigative approach 2008: Discovering Geometry Michael Serra, 2008 |
| discovering geometry an investigative approach 2008: The Shape of Inner Space Shing-Tung Yau, Steven J. Nadis, 2010-09-07 The leading mind behind the mathematics of string theory discusses how geometry explains the universe we see. Illustrations. |
| discovering geometry an investigative approach 2008: Matematika Geometri Konsep & Pemecahan Masalah Dian Fitri Argarini,S.Pd.,M.Pd; Nok Izatul Yazidah,S.Pd.,M.Pd.; Anik Kurniawati,S.Pd.,M.Pd, 2022-11-30 Buku ini merupakan buku penunjang bagi siswa-siswa yang ingin mendalami konsep dasar geometri yang diperoleh di jenjang SMP maupun SMA sederajat. Berbasis konstruktivisme adalah dasar yang digunakan penulis dalam menyusun buku ini. Diharapkan nantinya isi buku dapat melaih siswa berpikir konstruktif mampu menghubungkan mengaitkan pengetahuan lama dan baru yang dimiliki. |
| discovering geometry an investigative approach 2008: Visible Learning for Literacy, Grades K-12 Douglas Fisher, Nancy Frey, John Hattie, 2016-03-29 Ensure students demonstrate more than a year’s worth of learning during a school year Renowned literacy experts Douglas Fisher and Nancy Frey work with John Hattie to apply his 15 years of research, identifying instructional routines that have the biggest impact on student learning, to literacy practices. These practices are “visible” because their purpose is clear, they are implemented at the right moment in a student’s learning, and their effect is tangible. Through dozens of classroom scenarios, learn how to use the right approach at the right time for surface, deep, and transfer learning and which routines are most effective at each phase of learning. |
| discovering geometry an investigative approach 2008: Introductory Statistics 2e Barbara Illowsky, Susan Dean, 2023-12-13 Introductory Statistics 2e provides an engaging, practical, and thorough overview of the core concepts and skills taught in most one-semester statistics courses. The text focuses on diverse applications from a variety of fields and societal contexts, including business, healthcare, sciences, sociology, political science, computing, and several others. The material supports students with conceptual narratives, detailed step-by-step examples, and a wealth of illustrations, as well as collaborative exercises, technology integration problems, and statistics labs. The text assumes some knowledge of intermediate algebra, and includes thousands of problems and exercises that offer instructors and students ample opportunity to explore and reinforce useful statistical skills. This is an adaptation of Introductory Statistics 2e by OpenStax. You can access the textbook as pdf for free at openstax.org. Minor editorial changes were made to ensure a better ebook reading experience. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution 4.0 International License. |
| discovering geometry an investigative approach 2008: Developing Research in Mathematics Education Tommy Dreyfus, Michèle Artigue, Despina Potari, Susanne Prediger, Kenneth Ruthven, 2018-04-27 Developing Research in Mathematics Education is the first book in the series New Perspectives on Research in Mathematics Education, to be produced in association with the prestigious European Society for Research in Mathematics Education. This inaugural volume sets out broad advances in research in mathematics education which have accumulated over the last 20 years through the sustained exchange of ideas and collaboration between researchers in the field. An impressive range of contributors provide specifically European and complementary global perspectives on major areas of research in the field on topics that include: the content domains of arithmetic, geometry, algebra, statistics, and probability; the mathematical processes of proving and modeling; teaching and learning at specific age levels from early years to university; teacher education, teaching and classroom practices; special aspects of teaching and learning mathematics such as creativity, affect, diversity, technology and history; theoretical perspectives and comparative approaches in mathematics education research. This book is a fascinating compendium of state-of-the-art knowledge for all mathematics education researchers, graduate students, teacher educators and curriculum developers worldwide. |
| discovering geometry an investigative approach 2008: Advances In Algebraic Geometry Codes Edgar Martinez-moro, Carlos Munuera, Diego Ruano, 2008-10-08 Advances in Algebraic Geometry Codes presents the most successful applications of algebraic geometry to the field of error-correcting codes, which are used in the industry when one sends information through a noisy channel. The noise in a channel is the corruption of a part of the information due to either interferences in the telecommunications or degradation of the information-storing support (for instance, compact disc). An error-correcting code thus adds extra information to the message to be transmitted with the aim of recovering the sent information. With contributions from renowned researchers, this pioneering book will be of value to mathematicians, computer scientists, and engineers in information theory. |
| discovering geometry an investigative approach 2008: Formative Assessment Improving Learning in Secondary Classrooms OECD, 2005-01-25 This study features a collection of eight case studies of exemplary cases from secondary schools as well as international literature reviews and policy analysis related to formative assessment. |
| discovering geometry an investigative approach 2008: Teaching Physical Education Muska Mosston, Sara Ashworth, 1994 The definitive source for the groundbreaking ideas of the Spectrum of Teaching Styles introduced by Mosston and Ashworth and developed during 35 years in the field. This book offers teachers a foundation for understanding the decision-making structures that exist in all teaching/learning environments and for recognizing the variables that increase effectiveness while teaching physical education. In this thoroughly revised and streamlined edition, all chapters have been updated to include hundreds of real-world examples, concise charts, practical forms, and concrete suggestions for deliberate teaching so that teachers can understand their classrooms' flow of events, analyze decision structures, implement adjustments that are appropriate for particular classroom situations, and deliberately combine styles to achieve effective variations. As in prior editions, individual chapters describe the anatomy of the decision structure as it relates to teachers and learners, the objectives (O-T-L-O) of each style, and the application of each style to various activities and educational goals. For physical education teachers. |
| discovering geometry an investigative approach 2008: Teaching and Learning High School Mathematics Charlene E. Beckmann, Denisse R. Thompson, Rheta N. Rubenstein, 2009-11-02 Too many high school students, faced with mathematics in courses at the level of algebra and beyond, find themselves struggling with abstract concepts and unwilling to pursue further study of mathematics. When students curtail their course taking in mathematics, they may be impacting their college and career options. Thus, high school mathematics teachers have the responsibility to help students recognize the value and importance of mathematics while also designing instruction that makes mathematics accessible to all students. Ball and Bass (2000), as well as other mathematics educators, have recognized that mathematics teachers not only need to know mathematics content and mathematics pedagogy (i.e., teaching strategies) but they also need to know how these ideas are integrated. This mathematical knowledge for teaching is the knowledge that teachers of mathematics need and it differs from the knowledge that research or applied mathematicians must know. This text is designed to provide teachers with insights into this mathematical knowledge for teaching. Teaching and Learning High School Mathematics is likely different from many other texts that you have used. It integrates both content and pedagogy to help you develop and build your own understanding of teaching. The text is designed to help you develop “deep conceptual understanding of fundamental mathematics” (Ma 1999) so that you are able to approach mathematics from multiple perspectives with many tools. Such flexibility in teaching is essential if teachers are to help all students become mathematically proficient. Throughout this book, you are encouraged to work in cooperative teams. This strategy is designed to help you develop a mathematics learning community and build a professional network that will be a valuable resource during your professional career. Hopefully, you will experience the benefits of engaging in rich mathematical discussions with peers and consider how to encourage such learning environments in your own classrooms. Lesson planning is another element pervasive throughout this text. To help teachers plan for effective student-centered lessons, the Question Response Support (QRS) Guide is introduced in Lesson 1.1 and used throughout the remainder of the lessons. The QRS Guide is a tool on which teachers may record tasks or questions (Q) for students, expected and observed student responses (R), and teacher support (S) in the form of additional “just enough” questions to support students in their progress on the task. In each unit, teachers expand their repertoire of teaching and learning elements and strategies and incorporate these elements as they plan additional lesson segments. In Unit 4 lesson planning is formally introduced as teachers put together elements from previous units into complete, cohesive lesson plans. |
| discovering geometry an investigative approach 2008: Mathematical Epidemiology Fred Brauer, Pauline van den Driessche, J. Wu, 2008-04-30 Based on lecture notes of two summer schools with a mixed audience from mathematical sciences, epidemiology and public health, this volume offers a comprehensive introduction to basic ideas and techniques in modeling infectious diseases, for the comparison of strategies to plan for an anticipated epidemic or pandemic, and to deal with a disease outbreak in real time. It covers detailed case studies for diseases including pandemic influenza, West Nile virus, and childhood diseases. Models for other diseases including Severe Acute Respiratory Syndrome, fox rabies, and sexually transmitted infections are included as applications. Its chapters are coherent and complementary independent units. In order to accustom students to look at the current literature and to experience different perspectives, no attempt has been made to achieve united writing style or unified notation. Notes on some mathematical background (calculus, matrix algebra, differential equations, and probability) have been prepared and may be downloaded at the web site of the Centre for Disease Modeling (www.cdm.yorku.ca). |
| discovering geometry an investigative approach 2008: Geometric Control Theory Velimir Jurdjevic, 1997 Geometric control theory is concerned with the evolution of systems subject to physical laws but having some degree of freedom through which motion is to be controlled. This book describes the mathematical theory inspired by the irreversible nature of time evolving events. The first part of the book deals with the issue of being able to steer the system from any point of departure to any desired destination. The second part deals with optimal control, the question of finding the best possible course. An overlap with mathematical physics is demonstrated by the Maximum principle, a fundamental principle of optimality arising from geometric control, which is applied to time-evolving systems governed by physics as well as to man-made systems governed by controls. Applications are drawn from geometry, mechanics, and control of dynamical systems. The geometric language in which the results are expressed allows clear visual interpretations and makes the book accessible to physicists and engineers as well as to mathematicians. |
| discovering geometry an investigative approach 2008: Geometry John Tabak, 2014-05-14 Greek ideas about geometry, straight-edge and compass constructions, and the nature of mathematical proof dominated mathematical thought for about 2,000 years. |
Meaning of discovering in English - Cambridge Dictionary
DISCOVERING meaning: 1. present participle of discover 2. to find information, a place, or an object, especially for the…. Learn more.
DISCOVERING Synonyms: 147 Similar and Opposite Words ...
Synonyms for DISCOVERING: realizing, learning, seeing, hearing, finding, ascertaining, finding out, getting on (to); Antonyms of DISCOVERING: missing, ignoring, overlooking, disregarding, …
107 Synonyms & Antonyms for DISCOVERING - Thesaurus.com
Find 107 different ways to say DISCOVERING, along with antonyms, related words, and example sentences at Thesaurus.com.
discover verb - Definition, pictures, pronunciation and usage ...
Definition of discover verb in Oxford Advanced American Dictionary. Meaning, pronunciation, picture, example sentences, grammar, usage notes, synonyms and more.
Discovering - definition of discovering by The Free Dictionary
1. to be the first to find or find out about: Fleming discovered penicillin. 2. to learn about or encounter for the first time; realize: she discovered the pleasures of wine. 3. to find after study …
Discover Definition & Meaning | Britannica Dictionary
Scientists claim to have discovered [= found] a new way of controlling high blood pressure. It took her several weeks to discover the solution. The autopsy discovered [= revealed, uncovered] …
Discover - Definition, Meaning & Synonyms | Vocabulary.com
When you discover something, it can be by surprise or the result of a search. You might discover the fact that your dad used to travel with the circus as a trapeze artist or discover a band none …
DISCOVER Synonyms: 146 Similar and Opposite Words | Merriam ...
Some common synonyms of discover are ascertain, determine, learn, and unearth. While all these words mean "to find out what one did not previously know," discover may apply to something …
What does discovering mean? - Definitions.net
With reference to sciences and academic disciplines, discovery is the observation of new phenomena, new actions, or new events and providing new reasoning to explain the …
discover | meaning of discover in Longman Dictionary of ...
discover meaning, definition, what is discover: to find someone or something, either by ...: Learn more.
Meaning of discovering in English - Cambridge Dictionary
DISCOVERING meaning: 1. present participle of discover 2. to find information, a place, or an object, especially for the…. Learn more.
DISCOVERING Synonyms: 147 Similar and Opposite Words ...
Synonyms for DISCOVERING: realizing, learning, seeing, hearing, finding, ascertaining, finding out, getting on (to); Antonyms of DISCOVERING: missing, ignoring, overlooking, disregarding, …
107 Synonyms & Antonyms for DISCOVERING - Thesaurus.com
Find 107 different ways to say DISCOVERING, along with antonyms, related words, and example sentences at Thesaurus.com.
discover verb - Definition, pictures, pronunciation and usage ...
Definition of discover verb in Oxford Advanced American Dictionary. Meaning, pronunciation, picture, example sentences, grammar, usage notes, synonyms and more.
Discovering - definition of discovering by The Free Dictionary
1. to be the first to find or find out about: Fleming discovered penicillin. 2. to learn about or encounter for the first time; realize: she discovered the pleasures of wine. 3. to find after study …
Discover Definition & Meaning | Britannica Dictionary
Scientists claim to have discovered [= found] a new way of controlling high blood pressure. It took her several weeks to discover the solution. The autopsy discovered [= revealed, uncovered] …
Discover - Definition, Meaning & Synonyms | Vocabulary.com
When you discover something, it can be by surprise or the result of a search. You might discover the fact that your dad used to travel with the circus as a trapeze artist or discover a band none …
DISCOVER Synonyms: 146 Similar and Opposite Words
Some common synonyms of discover are ascertain, determine, learn, and unearth. While all these words mean "to find out what one did not previously know," discover may apply to something …
What does discovering mean? - Definitions.net
With reference to sciences and academic disciplines, discovery is the observation of new phenomena, new actions, or new events and providing new reasoning to explain the …
discover | meaning of discover in Longman Dictionary of ...
discover meaning, definition, what is discover: to find someone or something, either by ...: Learn more.
