Mathematical Thinking And Communication

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Mathematical Thinking and Communication

Author : Mark Driscoll
Publisher : Heinemann Educational Books
ISBN 13 : 9780325074771
Total Pages : 0 pages
Book Rating : 4.0/5 (747 download)

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Book Synopsis Mathematical Thinking and Communication by : Mark Driscoll

Download or read book Mathematical Thinking and Communication written by Mark Driscoll and published by Heinemann Educational Books. This book was released on 2016 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Language is deeply involved in learning mathematics as students both communicate and think about mathematical ideas. Because of this, teachers of English learners have particular challenges to overcome. Mathematical Thinking and Communication addresses perhaps the most significant challenge: providing access to mathematics for these students. For all students-and English learners in particular-access means finding effective, authentic ways to make language clear and thinking visible so they can reason more, speak more, and write more in mathematics. Based on extensive research and collaboration with teachers, coaches, and schools, Mark Driscoll, Johannah Nikula, and Jill Neumayer DePiper outline four principles for designing instruction that creates this kind of access: challenging tasks, multimodal representations, development of mathematical communication, and repeated structured practice. Starting from the perspective that English learners are capable of mathematical thinking (even as they are learning to express their ideas verbally), the authors highlight techniques for using gestures, drawings, models, manipulatives, and technology as tools for reasoning and communication. By embedding these visual representations into instruction-and encouraging their regular use-teachers support engagement in problem solving, facilitate mathematical dialogue, and notice evidence of students' thinking that propels them to create more engaging and equitable instruction. Enhanced by an extensive online collection of companion professional development resources, this book highlights classroom-ready strategies and routines for fostering mathematics success in all students and helping them recognize their potential.

Humans-with-Media and the Reorganization of Mathematical Thinking

Author : Marcelo C. Borba
Publisher : Springer Science & Business Media
ISBN 13 : 0387242643
Total Pages : 239 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Humans-with-Media and the Reorganization of Mathematical Thinking by : Marcelo C. Borba

Download or read book Humans-with-Media and the Reorganization of Mathematical Thinking written by Marcelo C. Borba and published by Springer Science & Business Media. This book was released on 2005-07-25 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a new conceptual framework for reflecting on the role of information and communication technology in mathematics education. Discussion focuses on how computers, writing and oral discourse transform education at an epistemological as well as a political level. Building on examples, research and theory, the authors propose that knowledge is not constructed solely by humans, but by collectives of humans and technologies of intelligence.

Reasoning, Communication and Connections in Mathematics

Author : Berinderjeet Kaur
Publisher : World Scientific
ISBN 13 : 9814405434
Total Pages : 335 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Reasoning, Communication and Connections in Mathematics by : Berinderjeet Kaur

Download or read book Reasoning, Communication and Connections in Mathematics written by Berinderjeet Kaur and published by World Scientific. This book was released on 2012 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: This fourth volume in the series of yearbooks by the Association of Mathematics Educators in Singapore entitled Reasoning, Communication and Connections in Mathematics is unique in that it focuses on a single theme in mathematics education. The objective is to encourage teachers and researchers to advance reasoning, communication and connections in mathematics classrooms. Several renowned international researchers in the field have published their work in this volume. The fifteen chapters of the book illustrate evidence-based practices that school teachers and researchers can experiment with in their own classrooms to bring about meaningful learning outcomes. Three major themes: mathematical tasks, classroom discourse, and connectivity within and beyond mathematics, shape the ideas underpinning reasoning, communication and connections in these chapters. The book makes a significant contribution towards mathematical processes essential for learners of mathematics. It is a good resource for mathematics educators and research students.

Thinking as Communicating

Author : Anna Sfard
Publisher : Cambridge University Press
ISBN 13 : 1139467999
Total Pages : 295 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Thinking as Communicating by : Anna Sfard

Download or read book Thinking as Communicating written by Anna Sfard and published by Cambridge University Press. This book was released on 2008-01-21 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an attempt to change our thinking about thinking. Anna Sfard undertakes this task convinced that many long-standing, seemingly irresolvable quandaries regarding human development originate in ambiguities of the existing discourses on thinking. Standing on the shoulders of Vygotsky and Wittgenstein, the author defines thinking as a form of communication. The disappearance of the time-honoured thinking-communicating dichotomy is epitomised by Sfard's term, commognition, which combines communication with cognition. The commognitive tenet implies that verbal communication with its distinctive property of recursive self-reference may be the primary source of humans' unique ability to accumulate the complexity of their action from one generation to another. The explanatory power of the commognitive framework and the manner in which it contributes to our understanding of human development is illustrated through commognitive analysis of mathematical discourse accompanied by vignettes from mathematics classrooms.

Introduction to Mathematical Thinking

Author : Keith J. Devlin
Publisher :
ISBN 13 : 9780615653631
Total Pages : 0 pages
Book Rating : 4.6/5 (536 download)

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Book Synopsis Introduction to Mathematical Thinking by : Keith J. Devlin

Download or read book Introduction to Mathematical Thinking written by Keith J. Devlin and published by . This book was released on 2012 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Mathematical thinking is not the same as 'doing math'--unless you are a professional mathematician. For most people, 'doing math' means the application of procedures and symbolic manipulations. Mathematical thinking, in contrast, is what the name reflects, a way of thinking about things in the world that humans have developed over three thousand years. It does not have to be about mathematics at all, which means that many people can benefit from learning this powerful way of thinking, not just mathematicians and scientists."--Back cover.

Teaching Students to Communicate Mathematically

Author : Laney Sammons
Publisher : ASCD
ISBN 13 : 1416625607
Total Pages : 222 pages
Book Rating : 4.4/5 (166 download)

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Book Synopsis Teaching Students to Communicate Mathematically by : Laney Sammons

Download or read book Teaching Students to Communicate Mathematically written by Laney Sammons and published by ASCD. This book was released on 2018-04-04 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: Students learning math are expected to do more than just solve problems; they must also be able to demonstrate their thinking and share their ideas, both orally and in writing. As many classroom teachers have discovered, these can be challenging tasks for students. The good news is, mathematical communication can be taught and mastered. In Teaching Students to Communicate Mathematically, Laney Sammons provides practical assistance for K–8 classroom teachers. Drawing on her vast knowledge and experience as a classroom teacher, she covers the basics of effective mathematical communication and offers specific strategies for teaching students how to speak and write about math. Sammons also presents useful suggestions for helping students incorporate correct vocabulary and appropriate representations when presenting their mathematical ideas. This must-have resource will help you help your students improve their understanding of and their skill and confidence in mathematical communication.

Teaching Students to Communicate Mathematically

Author : Laney Sammons
Publisher : ASCD
ISBN 13 : 1416625593
Total Pages : 222 pages
Book Rating : 4.4/5 (166 download)

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Book Synopsis Teaching Students to Communicate Mathematically by : Laney Sammons

Download or read book Teaching Students to Communicate Mathematically written by Laney Sammons and published by ASCD. This book was released on 2018 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers the basics of effective mathematical communication and offers specific strategies for teaching students how to speak and write about math.

The Mathematical Theory of Communication

Author : Claude Elwood Shannon
Publisher :
ISBN 13 :
Total Pages : 136 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis The Mathematical Theory of Communication by : Claude Elwood Shannon

Download or read book The Mathematical Theory of Communication written by Claude Elwood Shannon and published by . This book was released on 1962 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Mathematical Theory of Communication

Author : Claude E Shannon
Publisher : University of Illinois Press
ISBN 13 : 025209803X
Total Pages : 144 pages
Book Rating : 4.2/5 (52 download)

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Book Synopsis The Mathematical Theory of Communication by : Claude E Shannon

Download or read book The Mathematical Theory of Communication written by Claude E Shannon and published by University of Illinois Press. This book was released on 1998-09-01 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scientific knowledge grows at a phenomenal pace--but few books have had as lasting an impact or played as important a role in our modern world as The Mathematical Theory of Communication, published originally as a paper on communication theory more than fifty years ago. Republished in book form shortly thereafter, it has since gone through four hardcover and sixteen paperback printings. It is a revolutionary work, astounding in its foresight and contemporaneity. The University of Illinois Press is pleased and honored to issue this commemorative reprinting of a classic.

Introduction to Communication

Author : Susan O'Connell
Publisher : Math Process Standards Series
ISBN 13 : 9780325017327
Total Pages : 0 pages
Book Rating : 4.0/5 (173 download)

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Book Synopsis Introduction to Communication by : Susan O'Connell

Download or read book Introduction to Communication written by Susan O'Connell and published by Math Process Standards Series. This book was released on 2008 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: NCTM's Process Standards support teaching that helps students develop independent, effective mathematical thinking. The books in the Heinemann Math Process Standards Series give every middle grades math teacher the opportunity to explore each standard in depth. The series offers friendly, reassuring advice and ready-to-use examples to any teacher ready to embrace the Process Standards. In Introduction to Communication, Susan O'Connell and Suzanne Croskey show you ways to help students explore, express, and better understand mathematical content through talking and writing. They offer an array of entry points for understanding, planning, and teaching, including strategies that help students put their ideas into words, clarify them, elaborate on them, and ultimately produce clear and organized math writing. The book and accompanying CD-ROM are filled with activities that are modifiable for immediate use with students of all levels customizable to match your specific lessons. In addition, a correlation guide helps you match the math content you teach with the mathematical processes it utilizes. If your students struggle to describe their mathematical thinking, or if you're simply looking for new ways to work the communication standard into your curriculum, read, dog-ear, and teach with Introduction to Communication. And if you'd like to learn about any of NCTM's process standards, or if you're looking for new, classroom-tested ways to address them in your math teaching, look no further than Heinemann's Math Process Standards Series. You'll find them explained in the most understandable and practical way: from one teacher to another.

Mathematical Thinking and Problem Solving

Author : Alan H. Schoenfeld
Publisher : Routledge
ISBN 13 : 113544093X
Total Pages : 303 pages
Book Rating : 4.1/5 (354 download)

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Book Synopsis Mathematical Thinking and Problem Solving by : Alan H. Schoenfeld

Download or read book Mathematical Thinking and Problem Solving written by Alan H. Schoenfeld and published by Routledge. This book was released on 2016-05-06 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the early 1980s there was virtually no serious communication among the various groups that contribute to mathematics education -- mathematicians, mathematics educators, classroom teachers, and cognitive scientists. Members of these groups came from different traditions, had different perspectives, and rarely gathered in the same place to discuss issues of common interest. Part of the problem was that there was no common ground for the discussions -- given the disparate traditions and perspectives. As one way of addressing this problem, the Sloan Foundation funded two conferences in the mid-1980s, bringing together members of the different communities in a ground clearing effort, designed to establish a base for communication. In those conferences, interdisciplinary teams reviewed major topic areas and put together distillations of what was known about them.* A more recent conference -- upon which this volume is based -- offered a forum in which various people involved in education reform would present their work, and members of the broad communities gathered would comment on it. The focus was primarily on college mathematics, informed by developments in K-12 mathematics. The main issues of the conference were mathematical thinking and problem solving.

How Not to Be Wrong

Author : Jordan Ellenberg
Publisher : Penguin
ISBN 13 : 0143127535
Total Pages : 482 pages
Book Rating : 4.1/5 (431 download)

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Book Synopsis How Not to Be Wrong by : Jordan Ellenberg

Download or read book How Not to Be Wrong written by Jordan Ellenberg and published by Penguin. This book was released on 2015-05-26 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: “Witty, compelling, and just plain fun to read . . ." —Evelyn Lamb, Scientific American The Freakonomics of math—a math-world superstar unveils the hidden beauty and logic of the world and puts its power in our hands The math we learn in school can seem like a dull set of rules, laid down by the ancients and not to be questioned. In How Not to Be Wrong, Jordan Ellenberg shows us how terribly limiting this view is: Math isn’t confined to abstract incidents that never occur in real life, but rather touches everything we do—the whole world is shot through with it. Math allows us to see the hidden structures underneath the messy and chaotic surface of our world. It’s a science of not being wrong, hammered out by centuries of hard work and argument. Armed with the tools of mathematics, we can see through to the true meaning of information we take for granted: How early should you get to the airport? What does “public opinion” really represent? Why do tall parents have shorter children? Who really won Florida in 2000? And how likely are you, really, to develop cancer? How Not to Be Wrong presents the surprising revelations behind all of these questions and many more, using the mathematician’s method of analyzing life and exposing the hard-won insights of the academic community to the layman—minus the jargon. Ellenberg chases mathematical threads through a vast range of time and space, from the everyday to the cosmic, encountering, among other things, baseball, Reaganomics, daring lottery schemes, Voltaire, the replicability crisis in psychology, Italian Renaissance painting, artificial languages, the development of non-Euclidean geometry, the coming obesity apocalypse, Antonin Scalia’s views on crime and punishment, the psychology of slime molds, what Facebook can and can’t figure out about you, and the existence of God. Ellenberg pulls from history as well as from the latest theoretical developments to provide those not trained in math with the knowledge they need. Math, as Ellenberg says, is “an atomic-powered prosthesis that you attach to your common sense, vastly multiplying its reach and strength.” With the tools of mathematics in hand, you can understand the world in a deeper, more meaningful way. How Not to Be Wrong will show you how.

Introduction to Communication, Grades Prek-2

Author : Susan O'Connell
Publisher : Math Process Standards Series
ISBN 13 : 9780325074757
Total Pages : 176 pages
Book Rating : 4.0/5 (747 download)

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Book Synopsis Introduction to Communication, Grades Prek-2 by : Susan O'Connell

Download or read book Introduction to Communication, Grades Prek-2 written by Susan O'Connell and published by Math Process Standards Series. This book was released on 2015-05-06 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: NCTM's Process Standards support teaching that helps children develop independent, effective mathematical thinking. The books in the Heinemann Math Process Standards Series give every teacher the opportunity to explore each standard in depth. With language and examples that don't require prior math training to understand, the series offers friendly, reassuring advice and ready-to-use examples to any teacher looking to improve and enhance their math instruction. In Introduction to Communication, Susan O'Connell and Kelly O'Connor show you ways to help students explore, express, and better understand mathematical content through talking and writing. They offer an array of entry points for understanding, planning, and teaching, including strategies that help students put their ideas into words, clarify them, elaborate on them, and ultimately produce clear and organized math writing. The book and accompanying online resources are filled with activities that are modifiable for immediate use with students of all levels customizable to match your specific lessons. In addition, a correlation guide helps you match the math content you teach with the mathematical processes it utilizes. If your students struggle to describe their mathematical thinking, or if you're simply looking for new ways to work the communication standard into your curriculum, Introduction to Communication will be much-used, dog-eared resource. And if you'd like to learn about any of NCTM's process standards, or if you're looking for new, classroom-tested ways to address them in your math teaching, look no further than the entire Math Process Standards Series. You'll find them explained in the most understandable and practical way: from one teacher to another.

Mathematical Reasoning

Author : Theodore A. Sundstrom
Publisher : Prentice Hall
ISBN 13 : 9780131877184
Total Pages : 0 pages
Book Rating : 4.8/5 (771 download)

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Book Synopsis Mathematical Reasoning by : Theodore A. Sundstrom

Download or read book Mathematical Reasoning written by Theodore A. Sundstrom and published by Prentice Hall. This book was released on 2007 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focusing on the formal development of mathematics, this book shows readers how to read, understand, write, and construct mathematical proofs.Uses elementary number theory and congruence arithmetic throughout. Focuses on writing in mathematics. Reviews prior mathematical work with “Preview Activities” at the start of each section. Includes “Activities” throughout that relate to the material contained in each section. Focuses on Congruence Notation and Elementary Number Theorythroughout.For professionals in the sciences or engineering who need to brush up on their advanced mathematics skills. Mathematical Reasoning: Writing and Proof, 2/E Theodore Sundstrom

TIMSS 2011 International Results in Mathematics

Author : Ina V. S. Mullis
Publisher :
ISBN 13 : 9789079549177
Total Pages : 516 pages
Book Rating : 4.5/5 (491 download)

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Book Synopsis TIMSS 2011 International Results in Mathematics by : Ina V. S. Mullis

Download or read book TIMSS 2011 International Results in Mathematics written by Ina V. S. Mullis and published by . This book was released on 2012-12 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Language and Communication in Mathematics Education

Author : Judit N. Moschkovich
Publisher : Springer
ISBN 13 : 3319750550
Total Pages : 279 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Language and Communication in Mathematics Education by : Judit N. Moschkovich

Download or read book Language and Communication in Mathematics Education written by Judit N. Moschkovich and published by Springer. This book was released on 2018-03-27 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book considers some of the outstanding questions regarding language and communication in the teaching and learning of mathematics – an established theme in mathematics education research, which is growing in prominence. Recent research has demonstrated the wide range of theoretical and methodological resources that can contribute to this area of study, including those drawing on cross-disciplinary perspectives influenced by, among others, sociology, psychology, linguistics, and semiotics. Examining language in its broadest sense to include all modes of communication, including visual and gestural as well as spoken and written modes, it features work presented and discussed in the Language and Communication topic study group (TSG 31) at the 13th International Congress on Mathematical Education (ICME-13). A joint session with participants of the Mathematics Education in a Multilingual and Multicultural Environment topic study group (TSG 32) enhanced discussions, which are incorporated in elaborations included in this book. Discussing cross-cutting topics it appeals to readers from a wide range of disciplines, such as mathematics education and research methods in education, multilingualism, applied linguistics and beyond.

Humans-with-Media and the Reorganization of Mathematical Thinking

Author : Marcelo C. Borba
Publisher : Springer Science & Business Media
ISBN 13 : 9780387242637
Total Pages : 264 pages
Book Rating : 4.2/5 (426 download)

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Book Synopsis Humans-with-Media and the Reorganization of Mathematical Thinking by : Marcelo C. Borba

Download or read book Humans-with-Media and the Reorganization of Mathematical Thinking written by Marcelo C. Borba and published by Springer Science & Business Media. This book was released on 2005-03-22 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a new conceptual framework for reflecting on the role of information and communication technology in mathematics education. Discussion focuses on how computers, writing and oral discourse transform education at an epistemological as well as a political level. Building on examples, research and theory, the authors propose that knowledge is not constructed solely by humans, but by collectives of humans and technologies of intelligence.