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Author : David K. Pugalee
Publisher : Christopher-Gordon Pub
ISBN 13 : 9781929024865
Total Pages : 195 pages
Book Rating : 4.0/5 (248 download)
Download or read book Writing to Develop Mathematical Understanding written by David K. Pugalee and published by Christopher-Gordon Pub. This book was released on 2005-01-01 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Theodore A. Sundstrom
Publisher : Prentice Hall
ISBN 13 : 9780131877184
Total Pages : 0 pages
Book Rating : 4.8/5 (771 download)
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
Author : Linda Schulman Dacey
Publisher : Stenhouse Publishers
ISBN 13 : 1625311613
Total Pages : 175 pages
Book Rating : 4.6/5 (253 download)
Download or read book Why Write in Math Class? written by Linda Schulman Dacey and published by Stenhouse Publishers. This book was released on 2018 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: To help students communicate their mathematical thinking, many teachers have created classrooms where math talk has become a successful and joyful instructional practice. Building on that success, the ideas in Why Write in Math Class? help students construct, explore, represent, refine, connect, and reflect on mathematical ideas. Writing also provides teachers with a window into each student's thinking and informs instructional decisions. Focusing on five types of writing in math (exploratory, explanatory, argumentative, creative, and reflective), Why Write in Math Class? offers a variety of ways to integrate writing into the math class. The ideas in this book will help you make connections to what you already know about the teaching of writing within literacy instruction and build on what you've learned about the development of classroom communities that support math talk. The authors offer practical advice about how to support writing in math, as well as many specific examples of writing prompts and tasks that require high-cognitive demand. Extensive stories and samples of student work from K-5 classrooms give a vision of how writing in math class can successfully unfold.
Author : Randall Maddox
Publisher : Academic Press
ISBN 13 : 0124649769
Total Pages : 324 pages
Book Rating : 4.1/5 (246 download)
Download or read book Mathematical Thinking and Writing written by Randall Maddox and published by Academic Press. This book was released on 2002 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: The ability to construct proofs is one of the most challenging aspects of the world of mathematics. It is, essentially, the defining moment for those testing the waters in a mathematical career. Instead of being submerged to the point of drowning, readers of Mathematical Thinking and Writing are given guidance and support while learning the language of proof construction and critical analysis. Randall Maddox guides the reader with a warm, conversational style, through the task of gaining a thorough understanding of the proof process, and encourages inexperienced mathematicians to step up and learn how to think like a mathematician. A student's skills in critical analysis will develop and become more polished than previously conceived. Most significantly, Dr. Maddox has the unique approach of using analogy within his book to clarify abstract ideas and clearly demonstrate methods of mathematical precision.
Author : Keith J. Devlin
Publisher :
ISBN 13 : 9780615653631
Total Pages : 0 pages
Book Rating : 4.6/5 (536 download)
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.
Author : Colonnese, Madelyn W.
Publisher : IGI Global
ISBN 13 : 166846540X
Total Pages : 410 pages
Book Rating : 4.6/5 (684 download)
Download or read book Illuminating and Advancing the Path for Mathematical Writing Research written by Colonnese, Madelyn W. and published by IGI Global. This book was released on 2023-11-20 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical writing is essential for students’ math learning, but it’s often underutilized due to unclear guidelines. Mathematical writing is a mode of communication that provides teachers access to their students’ thinking and, importantly, offers students an opportunity to deepen their mathematical understanding, engage in mathematical reasoning, and learn a fundamental way to communicate mathematically. Notably, one needs to be able to judiciously combine mathematical symbols, representations, and text. However, more research is needed to exemplify the qualities of mathematical writing, develop implementation methods, and support teachers. Illuminating and Advancing the Path for Mathematical Writing Research, is a necessary comprehensive resource designed to enhance mathematical writing and promote equitable learning. This research book provides a comprehensive understanding of the current state of mathematical writing and illuminates various perspectives on moving the teaching and learning of k-12 mathematical writing forward. Mathematical writing is an important yet underutilized component of mathematical discourse, and this book offers further insight into understanding what it means to write mathematically for mathematics educators and researchers. It informs with research-based implementation strategies and creates purposeful professional learning opportunities. Ultimately, k-12 students will benefit from a more informed field because they will have access to a vital mode of mathematical reasoning and communication.
Author : Donald E. Knuth
Publisher : Cambridge University Press
ISBN 13 : 9780883850633
Total Pages : 132 pages
Book Rating : 4.8/5 (56 download)
Download or read book Mathematical Writing written by Donald E. Knuth and published by Cambridge University Press. This book was released on 1989 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book will help those wishing to teach a course in technical writing, or who wish to write themselves.
Author : Robert Gerver
Publisher : IAP
ISBN 13 : 1641131993
Total Pages : 147 pages
Book Rating : 4.6/5 (411 download)
Download or read book Write On! Math written by Robert Gerver and published by IAP. This book was released on 2018-02-01 with total page 147 pages. Available in PDF, EPUB and Kindle. Book excerpt: Student success in mathematics is dependent on focusing in class, practice, and the ability to verbally express mathematical thoughts. Write On! Math is a program that engages secondary school mathematics students in on-going writing projects that will strengthen their focus, their mathematics, and their oral and written communication skills. The program teaches technical writing strategies while demonstrating seven different levels of note taking and dozens of strategies to improve the sentence structure of students’ mathematical explanations. Today’s curricula and extensive testing policies require students to supply written explanations as part of their answers. Write On! Math will systematically teach students how to take better notes in math class. There is no better way to ensure you know something well than to have to teach it to somebody else, and the Write On! Math program requires students to do exactly that—that is why it improves their mathematics as well as teaches them valuable communication and writing techniques not taught in Humanities classes. For teachers using the program, Write On! Math will improve they way you, as a teacher, present material to your students in class and on your handouts! For students using the program, the strategies will apply to college classes and to other disciplines in addition to mathematics.
Author : Mark Driscoll
Publisher : Heinemann Educational Books
ISBN 13 : 9780325074771
Total Pages : 0 pages
Book Rating : 4.0/5 (747 download)
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.
Author : Peter Liljedahl
Publisher : Corwin Press
ISBN 13 : 1544374844
Total Pages : 454 pages
Book Rating : 4.5/5 (443 download)
Download or read book Building Thinking Classrooms in Mathematics, Grades K-12 written by Peter Liljedahl and published by Corwin Press. This book was released on 2020-09-28 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: A thinking student is an engaged student Teachers often find it difficult to implement lessons that help students go beyond rote memorization and repetitive calculations. In fact, institutional norms and habits that permeate all classrooms can actually be enabling "non-thinking" student behavior. Sparked by observing teachers struggle to implement rich mathematics tasks to engage students in deep thinking, Peter Liljedahl has translated his 15 years of research into this practical guide on how to move toward a thinking classroom. Building Thinking Classrooms in Mathematics, Grades K–12 helps teachers implement 14 optimal practices for thinking that create an ideal setting for deep mathematics learning to occur. This guide Provides the what, why, and how of each practice and answers teachers’ most frequently asked questions Includes firsthand accounts of how these practices foster thinking through teacher and student interviews and student work samples Offers a plethora of macro moves, micro moves, and rich tasks to get started Organizes the 14 practices into four toolkits that can be implemented in order and built on throughout the year When combined, these unique research-based practices create the optimal conditions for learner-centered, student-owned deep mathematical thinking and learning, and have the power to transform mathematics classrooms like never before.
Author : Kathryn B. Chval
Publisher : Corwin Press
ISBN 13 : 1071810839
Total Pages : 317 pages
Book Rating : 4.0/5 (718 download)
Download or read book Teaching Math to Multilingual Students, Grades K-8 written by Kathryn B. Chval and published by Corwin Press. This book was released on 2021-01-07 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using strengths-based approaches to support development in mathematics It’s time to re-imagine what’s possible and celebrate the brilliance multilingual learners bring to today’s classrooms. Innovative teaching strategies can position these learners as leaders in mathematics. Yet, as the number of multilingual learners in North American schools grows, many teachers have not had opportunities to gain the competencies required to teach these learners effectively, especially in disciplines such as mathematics. Multilingual learners—historically called English Language Learners—are expected to interpret the meaning of problems, analyze, make conjectures, evaluate their progress, and discuss and understand their own approaches and the approaches of their peers in mathematics classrooms. Thus, language plays a vital role in mathematics learning, and demonstrating these competencies in a second (or third) language is a challenging endeavor. Based on best practices and the authors’ years of research, this guide offers practical approaches that equip grades K-8 teachers to draw on the strengths of multilingual learners, partner with their families, and position these learners for success. Readers will find: • A focus on multilingual students as leaders • A strength-based approach that draws on students’ life experiences and cultural backgrounds • An emphasis on maintaining high expectations for learners’ capacity for mastering rigorous content • Strategies for representing concepts in different formats • Stop and Think questions throughout and reflection questions at the end of each chapter • Try It! Implementation activities, student work examples, and classroom transcripts With case studies and activities that provide a solid foundation for teachers’ growth and exploration, this groundbreaking book will help teachers and teacher educators engage in meaningful, humanized mathematics instruction.
Author : Linda Dacey
Publisher : Taylor & Francis
ISBN 13 : 1003842666
Total Pages : 242 pages
Book Rating : 4.0/5 (38 download)
Download or read book Why Write in Math Class? written by Linda Dacey and published by Taylor & Francis. This book was released on 2023-10-10 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: To help students communicate their mathematical thinking, many teachers have created classrooms where math talk has become a successful and joyful instructional practice. Building on that success, the ideas in Why Write in Math Class? help students construct, explore, represent, refine, connect, and reflect on mathematical ideas. Writing also provides teachers with a window into each student's thinking and informs instructional decisions.Focusing on five types of writing in math (exploratory, explanatory, argumentative, creative, and reflective), Why Write in Math Class? offers a variety of ways to integrate writing into the math class. The ideas in this book will help you make connections to what you already know about the teaching of writing within literacy instruction and build on what you've learned about the development of classroom communities that support math talk.The authors offer practical advice about how to support writing in math, as well as many specific examples of writing prompts and tasks that require high-cognitive demand. Extensive stories and samples of student work from K-5 classrooms give a vision of how writing in math class can successfully unfold.
Author : Candia Morgan
Publisher : Routledge
ISBN 13 : 1135709548
Total Pages : 243 pages
Book Rating : 4.1/5 (357 download)
Download or read book Writing Mathematically written by Candia Morgan and published by Routledge. This book was released on 2002-01-04 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: School mathematics curricula internationally tend to emphasise problem-solving and have led to the development of opportunities for children to do maths in a more open, creative way. This has led to increased interest in 'performance-based' assessment, which involves children in substantial production of written language to serve as 'evidence' of their mathematical activity and achievement. However, this raises two important questions. Firstly, does this writing accurately present children's mathematical activity and ability? Secondly, do maths teachers have sufficient linguistic awareness to support their students in developing skills and knowledge necessary for writing effectively in their subject area? The author of this book takes a critical perspective on these questions and, through an investigation of teachers' readings and evaluations of coursework texts, identifies the crucial issues affecting the accurate assessment of school mathematics.
Author : Ashley Harlan
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (137 download)
Download or read book Writing in Mathematics to Increase Student Understanding written by Ashley Harlan and published by . This book was released on 2018 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this action research study was to understand the impact of introducing writing into the math sequence of a third-grade class. The teacher-researcher sought to understand students’ perceptions of as well as her personal perceptions of introducing writing into math and how this impacted student achievement. Data was collected through writing samples, assessment scores, observations and reflections, surveys, and interviews. The data was analyzed using the constant comparative method as well as quantitative methods of analysis. Three major themes emerged from the qualitative analysis of the data: process of introducing writing into math, student attitudes and ideas, and developing mathematical understanding. The analysis of students’ assessment scores showed that four students’ achievement increased. This study will enable educators to gain a better understanding of what it looks to introduce writing into the math sequence of a classroom as well as how it impacts students’ perceptions and achievement.
Author : Grace Kelemanik
Publisher :
ISBN 13 : 9780325120072
Total Pages : 184 pages
Book Rating : 4.1/5 (2 download)
Download or read book Teaching for Thinking written by Grace Kelemanik and published by . This book was released on 2022-01-24 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: Teaching our children to think and reason mathematically is a challenge, not because students can't learn to think mathematically, but because we must change our own often deeply-rooted teaching habits. This is where instructional routines come in. Their predictable design and repeatable nature support both teachers and students to develop new habits. In Teaching for Thinking, Grace Kelemanik and Amy Lucenta pick up where their first book, Routines for Reasoning, left off. They draw on their years of experience in the classroom and as instructional coaches to examine how educators can make use of routines to make three fundamental shifts in teaching practice: Focus on thinking: Shift attention away from students' answers and toward their thinking and reasoning Step out of the middle: Shift the balance from teacher-student interactions toward student-student interactions Support productive struggle: Help students do the hard thinking work that leads to real learning With three complete new routines, support for designing your own routine, and ideas for using routines in your professional learning as well as in your classroom teaching, Teaching for Thinking will help you build new teaching habits that will support all your students to become and see themselves as capable mathematicians.
Author : National Research Council
Publisher : National Academies Press
ISBN 13 : 0309131987
Total Pages : 53 pages
Book Rating : 4.3/5 (91 download)
Download or read book Helping Children Learn Mathematics written by National Research Council and published by National Academies Press. This book was released on 2002-07-31 with total page 53 pages. Available in PDF, EPUB and Kindle. Book excerpt: Results from national and international assessments indicate that school children in the United States are not learning mathematics well enough. Many students cannot correctly apply computational algorithms to solve problems. Their understanding and use of decimals and fractions are especially weak. Indeed, helping all children succeed in mathematics is an imperative national goal. However, for our youth to succeed, we need to change how we're teaching this discipline. Helping Children Learn Mathematics provides comprehensive and reliable information that will guide efforts to improve school mathematics from pre-kindergarten through eighth grade. The authors explain the five strands of mathematical proficiency and discuss the major changes that need to be made in mathematics instruction, instructional materials, assessments, teacher education, and the broader educational system and answers some of the frequently asked questions when it comes to mathematics instruction. The book concludes by providing recommended actions for parents and caregivers, teachers, administrators, and policy makers, stressing the importance that everyone work together to ensure a mathematically literate society.
Author : Jonathan D. Katz
Publisher : Rowman & Littlefield
ISBN 13 : 147581058X
Total Pages : 145 pages
Book Rating : 4.4/5 (758 download)
Download or read book Developing Mathematical Thinking written by Jonathan D. Katz and published by Rowman & Littlefield. This book was released on 2014-07-07 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this country we have done a poor job of helping students come to see the wonder, beauty and power of mathematics. Standards can be brought into the picture, but unless we think about what it means to truly engage students in mathematics we will continue to be unsuccessful. The goal of this book is to begin to change the way students experience mathematics in the middle and high school classrooms. In this book you will find a theoretical basis for this approach to teaching mathematics, multiple guides and questions for teachers to think about in relation to their everyday teaching, and over 30 examples of problems, lessons, tasks, and projects that been used effectively with urban students.
