The Language of Mathematics

Utilizing Math in Practice


Author: Robert L. Baber

Publisher: John Wiley & Sons

ISBN: 1118061764

Category: Mathematics

Page: 440

View: 439

A new and unique way of understanding the translation of concepts and natural language into mathematical expressions Transforming a body of text into corresponding mathematical expressions and models is traditionally viewed and taught as a mathematical problem; it is also a task that most find difficult. The Language of Mathematics: Utilizing Math in Practice reveals a new way to view this process—not as a mathematical problem, but as a translation, or language, problem. By presenting the language of mathematics explicitly and systematically, this book helps readers to learn mathematics¿and improve their ability to apply mathematics more efficiently and effectively to practical problems in their own work. Using parts of speech to identify variables and functions in a mathematical model is a new approach, as is the insight that examining aspects of grammar is highly useful when formulating a corresponding mathematical model. This book identifies the basic elements of the language of mathematics, such as values, variables, and functions, while presenting the grammatical rules for combining them into expressions and other structures. The author describes and defines different notational forms for expressions, and also identifies the relationships between parts of speech and other grammatical elements in English and components of expressions in the language of mathematics. Extensive examples are used throughout that cover a wide range of real-world problems and feature diagrams and tables to facilitate understanding. The Language of Mathematics is a thought-provoking book of interest for readers who would like to learn more about the linguistic nature and aspects of mathematical notation. The book also serves as a valuable supplement for engineers, technicians, managers, and consultants who would like to improve their ability to apply mathematics effectively, systematically, and efficiently to practical problems.

Using Children’s Literature to Teach Problem Solving in Math

Addressing the Common Core in K–2


Author: Jeanne White

Publisher: Routledge

ISBN: 1317909232

Category: Education

Page: 110

View: 1353

Learn how to use children’s literature to engage students in mathematical problem solving. Teaching with children’s literature helps build a positive math environment, encourages students to think abstractly, shows students the real-world purposes of math, builds content-area literacy, and appeals to students with different learning styles and preferences. This practical book provides specific children’s book ideas and standards-based lessons that you can use to bring math alive in your own classroom. Special Features: Step-by-step ideas for using children’s literature to teach lessons based on the Common Core Standards for Mathematical Content in kindergarten, first, and second grade Scripting, modeling, and discussion prompts for each lesson Information on alignment to the Standards for Mathematical Practice and how to put them into student-friendly language Reference to a wide variety of specific children’s literature that can provide a context for young children learning to engage in the standards Differentiated activities for students who are early, developing, and advanced problem solvers

Teaching As A Reflective Practice

The German Didaktik Tradition


Author: Ian Westbury,Stefan Hopmann,Kurt Riquarts

Publisher: Routledge

ISBN: 1136601708

Category: Education

Page: 360

View: 1001

This volume presents a mix of translations of classical and modern papers from the German Didaktik tradition, newly prepared essays by German scholars and practitioners writing from within the tradition, and interpretive essays by U.S. scholars. It brings this tradition, which virtually dominated German curricular thought and teacher education until the 1960s when American curriculum theory entered Germany--and which is now experiencing a renaissance--to the English-speaking world, where it has been essentially unknown. The intent is to capture in one volume the core (at least) of the tradition of Didaktik and to communicate its potential relevance to English-language curricularists and teacher educators. It introduces a theoretical tradition which, although very different in almost every respect from those we know, offers a set of approaches that suggest ways of thinking about problems of reflection on curricular and teaching praxis (the core focus of the tradition) which the editors believe are accessible to North American readers--with appropriate "translation." These ways of thinking and related praxis are very relevant to notions such as reflective teaching and the discourse on teachers as professionals. By raising the possibility that the "new" tradition of Didaktik can be highly suggestive for thinking through issues related to a number of central ideas within contemporary discourse--and for exploring the implications of these ideas for both teacher education and for a curriculum theory appropriate to these new contexts for theorizing, this book opens up a gold mine of theoretical and practical possibilities.

Using the Standards - Number & Operations, Grade 2


Author: Becky Daniel

Publisher: Carson-Dellosa Publishing

ISBN: 1624421016

Category: Juvenile Nonfiction

Page: 128

View: 3170

Focusing entirely on Number and Operations, this book delves into three major content areas of the NCTM standards—Number Systems, Operations, and Computation. Students explore the relationships between numbers, the meaning of various operations and how they relate, and the techniques that make computation a breeze. Various formats of questions allow students to address one or more of the NCTM process strands on each page. The standards correlation chart and icons at the top of each page identify effective activities utilizing Problem Solving, Reasoning and Proof, Communication, Connections, and Representation. Skill checks and cumulative tests are included as well as vocabulary cards to help reinforce mathematical terms and symbols. Answer key provided

Caring for School-Age Children


Author: Phyllis M. Click,Jennifer Parker

Publisher: Cengage Learning

ISBN: 1133421644

Category: Education

Page: 416

View: 9240

CARING FOR SCHOOL-AGE CHILDREN, 6th Edition, presents the most pertinent information needed by those involved in after-school programs. Current research has established the importance of quality after-school programs due to their tremendous impact on children's academic achievement, overall happiness, and self-esteem. To address this reality, the new edition presents the latest research and information on school-age child care, and offers numerous practical applications and activities that can be put to use immediately in a child care setting. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

A Student's Guide to the Study, Practice, and Tools of Modern Mathematics


Author: Donald Bindner,Martin Erickson

Publisher: CRC Press

ISBN: 1439846073

Category: Mathematics

Page: 280

View: 361

A Student’s Guide to the Study, Practice, and Tools of Modern Mathematics provides an accessible introduction to the world of mathematics. It offers tips on how to study and write mathematics as well as how to use various mathematical tools, from LaTeX and Beamer to Mathematica® and MapleTM to MATLAB® and R. Along with a color insert, the text includes exercises and challenges to stimulate creativity and improve problem solving abilities. The first section of the book covers issues pertaining to studying mathematics. The authors explain how to write mathematical proofs and papers, how to perform mathematical research, and how to give mathematical presentations. The second section focuses on the use of mathematical tools for mathematical typesetting, generating data, finding patterns, and much more. The text describes how to compose a LaTeX file, give a presentation using Beamer, create mathematical diagrams, use computer algebra systems, and display ideas on a web page. The authors cover both popular commercial software programs and free and open source software, such as Linux and R. Showing how to use technology to understand mathematics, this guide supports students on their way to becoming professional mathematicians. For beginning mathematics students, it helps them study for tests and write papers. As time progresses, the book aids them in performing advanced activities, such as computer programming, typesetting, and research.

RTI and Math

The Classroom Connection: Estimates Considered, Logic Required, Data Imperative


Author: Karen A. Kemp,Mary Ann Eaton,Sharon Poole

Publisher: National Professional Resources Inc./Dude Publishing

ISBN: 1934032832

Category: Education

Page: 305

View: 517

This comprehensive resource provides research-based techniques based on the early grade standards and and principles of mathematics as identified by the National Council of Teachers of Mathematics. Though provoking questions about student learning guide the teacher to the appropriate intervention. There are step by step procedures for implementation of each technique, along with measures to monitor students' progress. Reproducible forms allow for easy management and data collection, making this a valuable resource for every classroom. This book specifically addresses the fundamentals of math including the number system, computation, problem solving and the all important language and vocabulary of math. The important topic of motivation is also included.

The Language of Physics

The Calculus and the Development of Theoretical Physics in Europe, 1750-1914


Author: Elizabeth Garber

Publisher: Springer Science & Business Media

ISBN: 9780817640392

Category: Language Arts & Disciplines

Page: 399

View: 6859

Modern physics and mathematics are so closely associated that mathematics has long been regarded as the tool and language for physics. This book chronicles the development of this mathematical integration by physicists. Beginning with the mathematical giants of the 18th century, Garber convincingly demonstrates that the essential tools employed by 20th century theoretical physicists were in place by the year 1870.

Academic Language in Diverse Classrooms: Mathematics, Grades 3–5

Promoting Content and Language Learning


Author: Margo Gottlieb,Gisela Ernst-Slavit

Publisher: Corwin Press

ISBN: 1452278059

Category: Education

Page: 200

View: 4903

Make every student fluent in the language of learning. The Common Core and ELD standards provide pathways to academic success through academic language. Using an integrated Curricular Framework, districts, schools and professional learning communities can: Design and implement thematic units for learning Draw from content and language standards to set targets for all students Examine standards-centered materials for academic language Collaborate in planning instruction and assessment within and across lessons Consider linguistic and cultural resources of the students Create differentiated content and language objectives Delve deeply into instructional strategies involving academic language Reflect on teaching and learning

Good Practice in Implementing the Pre-School Curriculum


Author: Sally Neaum,Jill Tallack

Publisher: Nelson Thornes

ISBN: 9780748755530

Category: Education

Page: 216

View: 3928

Good Practice in Implementing the Pre-school Curriculum, Second Edition is the leading early years curriculum text. Updated throughout to reflect QCA's new framework for early learning, it is the essntial guide for students and nursery managers.

Improving Reading Comprehension of Middle and High School Students


Author: Kristi L. Santi,Deborah K. Reed

Publisher: Springer

ISBN: 3319147358

Category: Education

Page: 197

View: 2520

This volume focuses on our understanding of the reading comprehension of adolescents in a high stakes academic environment. Leading researchers share their most current research on each issue, covering theory and empirical research from a range of specializations, including various content areas, English language learners, students with disabilities, and reading assessment. Topics discussed include: cognitive models of reading comprehension and how they relate to typical or atypical development of reading comprehension, reading in history classes, comprehension of densely worded and symbolic mathematical texts, understanding causality in science texts, the more rigorous comprehension standards in English language arts classes, balancing the practical and measurement constraints of the assessment of reading comprehension, understanding the needs and challenges of English language learners and students in special education with respect to the various content areas discussed in this book. This book is of interest to researchers in literacy and educational psychology as well as curriculum developers.

Winning at Math

Your Guide to Learning Mathematics Through Successful Study Skills


Author: Paul D. Nolting

Publisher: Academic Success Press Inc.

ISBN: 9780940287341

Category: Mathematics

Page: 301

View: 6096

Basics of Speed Mathematics


Author: Chandramouli Mahadevan


ISBN: 0557678978


Page: 246

View: 3833

This book brings the techniques from Vedic Mathematics and Trachtenberg System together. We have not attempted to do a comparative study of these techniques and make a judgment on which one is better. Instead we have simply, presented the techniques in a sequence that makes most sense. There are inherent strengths in these two approaches. While looking at all the speed improvement techniques, we have ensured that we focus on techniques for defect prevention and error minimization as well. Speed coupled with improved accuracy must be our paramount focus during any problem solving process. This book attempts to elucidate several key techniques, examples and practice problem sets.

Think It, Show it Mathematics

Strategies for Explaining Thinking


Author: Gregory Denman

Publisher: Shell Education

ISBN: 9781425810511

Category: Education

Page: 192

View: 4294

This timely book for grades 3-8 provides step-by-step strategies for developing students' clear, concise writing and discussion skills about math problems. Strategy instruction is supported by the included student activities, rubrics, and exemplar writing samples. The Digital Resource CD contains student activity pages and graphic organizers.

Integrating Literacy and Math

Strategies for K-6 Teachers


Author: Carole Skalinder,Patti Satz

Publisher: Guilford Press

ISBN: 1593857187

Category: Education

Page: 184

View: 2732

Many K–6 teachers--and students--still think of mathematics as a totally separate subject from literacy. Yet incorporating math content into the language arts block helps students gain skills for reading many kinds of texts. And bringing reading, writing, and talking into the math classroom supports the development of conceptual knowledge and problem solving, in addition to computational skills. This invaluable book thoroughly explains integrated instruction and gives teachers the tools to make it a reality. Grounded in current best practices for both language arts and math, the book includes planning advice, learning activities, assessment strategies, reproducibles, and resources, plus a wealth of examples from actual classrooms.

Speaking Mathematically

Communication in Mathematics Classrooms


Author: David Pimm

Publisher: Taylor & Francis

ISBN: 9780415037082

Category: Communication in education

Page: 217

View: 2465

This stimulating study focuses on mathematics as a language with its own rules and conventions and explores the implications of this for classroom practice.

OMDoc -- An Open Markup Format for Mathematical Documents [version 1.2]

Foreword by Alan Bundy


Author: Michael Kohlhase

Publisher: Springer Science & Business Media

ISBN: 3540378979

Category: Computers

Page: 428

View: 8402

Computers arechanging the way wethink. Of course,nearly all desk-workers have access to computers and use them to email their colleagues, search the Web for information and prepare documents. But I’m not referring to that. I mean that people have begun to think about what they do in compu- tional terms and to exploit the power of computers to do things that would previously have been unimaginable. This observation is especially true of mathematicians. Arithmetic c- putation is one of the roots of mathematics. Since Euclid’s algorithm for ?nding greatest common divisors, many seminal mathematical contributions have consisted of new procedures. But powerful computer graphics have now enabled mathematicians to envisage the behaviour of these procedures and, thereby, gain new insights, make new conjectures and explore new avenues of research. Think of the explosive interest in fractals, for instance. This has been driven primarily by our new-found ability rapidly to visualise fractal shapes, such as the Mandelbrot set. Taking advantage of these new oppor- nities has required the learning of new skills, such as using computer algebra and graphics packages.

Researching Mathematics Education in South Africa

Perspectives, Practices and Possibilities


Author: Renuka Vithal,Jill Adler,Christine Keitel

Publisher: HSRC Press

ISBN: 9780796920478

Category: Education

Page: 360

View: 7392

Reflecting on the theoretical and ideological work that has contributed to the growth of mathematics education research in South Africa, this study provides a historical analysis of forces that have changed and shaped mathematics curricula over the years. The themes researched and explored include radical pedagogy, progressive classroom practices, ethnomathematics, and South African mathematics education research within both its local and international contexts.

Creativity Across the Primary Curriculum

Framing and Developing Practice


Author: Anna Craft

Publisher: Routledge

ISBN: 1134635710

Category: Education

Page: 208

View: 3622

This book takes an inspirational look at how to foster children's creativity as well as following the guidelines in the National Curriculum. The book: explores the nature of the creative mind investigates the role of play and the concept of creativity examines appropriate continuing professional development for teachers looks at the personal and professional identities of teachers considers ways of analysing and describing creative practice. This text looks at the bigger picture in education, asking what sort of systems need to be designed to develop children's learning in the 21st century. It will be a resource to teachers, head teachers and advisory staff committed to asking questions, encouraging play and not allowing problems or circumstances to block action.