Mathematical Thinking And Communication
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Mathematical Thinking And Communication
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Author : Mark Driscoll
language : en
Publisher: Heinemann Educational Books
Release Date : 2016
Mathematical Thinking And Communication written by Mark Driscoll and has been published by Heinemann Educational Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with Education categories.
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.
Thinking As Communicating
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Author : Anna Sfard
language : en
Publisher: Cambridge University Press
Release Date : 2008-01-21
Thinking As Communicating written by Anna Sfard 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 2008-01-21 with Psychology categories.
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.
Reasoning Communication And Connections In Mathematics
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Author : Berinderjeet Kaur
language : en
Publisher: World Scientific
Release Date : 2012
Reasoning Communication And Connections In Mathematics written by Berinderjeet Kaur and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Business & Economics categories.
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.
Humans With Media And The Reorganization Of Mathematical Thinking
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Author : Marcelo C. Borba
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-03-22
Humans With Media And The Reorganization Of Mathematical Thinking written by Marcelo C. Borba 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 2005-03-22 with Education categories.
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.
Introduction To Communication
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Author : Susan O'Connell
language : en
Publisher: Math Process Standards Series
Release Date : 2008
Introduction To Communication written by Susan O'Connell and has been published by Math Process Standards Series this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Education categories.
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.
Language And Communication In Mathematics Education
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Author : Judit N. Moschkovich
language : en
Publisher: Springer
Release Date : 2018-03-27
Language And Communication In Mathematics Education written by Judit N. Moschkovich and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-27 with Education categories.
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.
Teaching Students To Communicate Mathematically
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Author : Laney Sammons
language : en
Publisher: ASCD
Release Date : 2018
Teaching Students To Communicate Mathematically written by Laney Sammons and has been published by ASCD this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with Education categories.
This book covers the basics of effective mathematical communication and offers specific strategies for teaching students how to speak and write about math.
Introduction To Communication Grades Prek 2
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Author : Susan O'Connell
language : en
Publisher: Math Process Standards Series
Release Date : 2015-05-06
Introduction To Communication Grades Prek 2 written by Susan O'Connell and has been published by Math Process Standards Series this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-06 with Education categories.
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.
Emerging Perspectives On Gesture And Embodiment In Mathematics
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Author : Laurie D. Edwards
language : en
Publisher: IAP
Release Date : 2014-07-01
Emerging Perspectives On Gesture And Embodiment In Mathematics written by Laurie D. Edwards and has been published by IAP this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-01 with Education categories.
The purpose of the book is to establish a common language for, and understanding of, embodiment as it applies to mathematical thinking, and to link mathematics education research to recent work in gesture studies, cognitive linguistics and the theory of embodied cognition. Just as in past decades, mathematics education experienced a "turn to the social" in which socio-cultural factors were explored, in recent years there has been a nascent "turn to the body." An increasing number of researchers and theorists in mathematics education have become interested in the fact that, although mathematics may be socially constructed, this construction is not arbitrary or unconstrained, but rather is rooted in, and shaped by, the body. All those who engage with mathematics, whether at an elementary or advanced level, share the same basic biological and cognitive capabilities, as well as certain common physical experiences that come with being humans living in a material world. In addition, the doing and communicating of mathematics is never a purely intellectual activity: it involves a wide range of bodily actions, from committing inscriptions to paper or whiteboard, to speaking, listening, gesturing and gazing. This volume will present recent research on gesture and mathematics, within a framework that addresses several levels of mathematical development. The chapters will begin with contributions that examine early mathematical and proto-mathematical knowledge, for example, the conservation of volume and counting. The role of gesture in teaching and learning arithmetic procedures will be addressed. Core concepts and tools from secondary level mathematics will be investigated, including algebra, functions and graphing. And finally, research into the embodied understanding of advanced topics in geometry and calculus will be presented. The overall goal for the volume is to acknowledge the multimodal nature of mathematical knowing, and to contribute to the creation of a model of the interactions and mutual influences of bodily motion, spatial thinking, gesture, speech and external inscriptions on mathematical thinking, communication and learning. The intended audience is researchers and theorists in mathematics education as well as graduate students in the field.
Problem Solving Reasoning And Communicating K 8
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Author : Arthur J. Baroody
language : en
Publisher: Prentice Hall
Release Date : 1993
Problem Solving Reasoning And Communicating K 8 written by Arthur J. Baroody and has been published by Prentice Hall this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Education categories.
Examines in depth how teachers can help foster children's mathematical thinking. Provides practical suggestions, builds on the most recent research, uses case studies, encourages interactive learning, presents challenging problems, discusses the importanct of process-oriented math instruction, demonstrates "writing-to-learn" mathematics