The Language of Mathematics

Author: Robert L. Baber
Publisher: John Wiley & Sons
ISBN: 9781118061763
Release Date: 2011-09-09
Genre: Mathematics

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.

Academic Language in Diverse Classrooms Mathematics Grades 3 5

Author: Margo Gottlieb
Publisher: Corwin Press
ISBN: 9781452278056
Release Date: 2013-03-12
Genre: Education

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

Using Children s Literature to Teach Problem Solving in Math

Author: Jeanne White
Publisher: Routledge
ISBN: 9781317909231
Release Date: 2013-11-12
Genre: Education

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

Beyond Answers

Author: Mike Flynn
Publisher: Stenhouse Publishers
ISBN: 9781571109026
Release Date: 2016-08-28
Genre: Education

The Standards for Mathematical Practice are written in clear, concise language. Even so, to interpret them and visualize what they mean for your teaching practice isn't always easy. In this practical, easy-to-read book, Mike Flynn provides teachers with a clear and deep sense of these standards and shares ideas on how best to implement them in K-2 classrooms. Each chapter is dedicated to a different practice. Using examples from his own teaching and vignettes from many other K-2 teachers, Mike does the following: Invites you to break the cycle of teaching math procedurally Demonstrates what it means for children to understand--not just do--math Explores what it looks like when young children embrace the important behaviors espoused by the practices The book's extensive collection of stories from K-2 classroom provides readers with glimpses of classroom dialogue, teacher reflections, and examples of student work. Focus questions at the beginning of each vignette help you analyze the examples and encourage further reflection. Beyond Answers is a wonderful resource that can be used by individual teachers, study groups, professional development staff, and in math methods courses.

Academic Language in Diverse Classrooms Mathematics Grades 6 8

Author: Margo Gottlieb
Publisher: Corwin Press
ISBN: 9781452234830
Release Date: 2013-05-07
Genre: Education

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

Using Developmentally Appropriate Practices to Teach the Common Core

Author: Lisa S. Goldstein
Publisher: Routledge
ISBN: 9781317743637
Release Date: 2015-07-16
Genre: Education

Using Developmentally Appropriate Practices to Teach the Common Core: Grades PreK–3 provides current and prospective primary grade teachers with an understanding of the CCSS-ELA and CCSS-M that highlights their compatibility with developmentally appropriate practices (DAP), the instructional approach generally preferred by teachers of young children. The book begins by framing the CCSS as a distinct improvement over lengthy lists of academic content standards and as a carefully conceptualized and DAP-friendly set of curriculum guidelines. Next, the CCSS-ELA and CCSS-M for Grades K–3 are unpacked, analyzed, synthesized, and cross-referenced to key features of DAP. Finally, several "hot topic" issues—differentiating instruction to meet the needs of all learners, ensuring equitable access to the curriculum for English Language Learners, addressing assessment and accountability expectations, and educating parents and families about the CCSS and DAP—are prioritized and examined in depth. Using Developmentally Appropriate Practices to Teach the Common Core: Grades PreK–3 is a highly useful guide for both pre-service and in-service early childhood education teachers.

Introduction to Problem Solving Grades Prek 2

Author: Susan O'Connell
Publisher: Math Process Standards Series
ISBN: 0325092591
Release Date: 2016-12-30
Genre: Education

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 primary 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 ready to embrace the Process Standards. In Introduction to Problem Solving, Susan O'Connell highlights practical techniques for making problem solving doable for your students. O'Connell eases you into problem solving, giving you an array of entry points for understanding, planning, and teaching, including strategies that help students develop the mathematical thinking necessary to discover effective approaches for solving a wide range of math problems. 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 problem solving is a problem you'd like to solve, or if you're simply looking for new ways to work the problem-solving standards into your curriculum, read, dog-ear, and teach with Introduction to Problem Solving. 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.

Winning at Math

Author: Paul D. Nolting
Publisher: Academic Success Press Inc.
ISBN: 094028734X
Release Date: 2002
Genre: Mathematics


English Language Learners and Math

Author: Holly HansenThomas
Publisher: IAP
ISBN: 9781607522553
Release Date: 2009-08-01
Genre: Education

Taking a community of practice perspective that highlights the learner as part of a community, rather than a lone individual responsible for her/his learning, this ethnographicallyinfluenced study investigates how Latina/o English Language Learners (ELLs) in middle school mathematics classes negotiated their learning of mathematics and mathematical discourse. The classes in which the Latina/o students were enrolled used a reformoriented approach to math learning; the math in these classes was—to varying degrees—taught using a handson, discovery approach to learning where group learning was valued, and discussions in and about math were critical. This book presents the stories of how six immigrant and Americanborn ELLs worked with their three teachers of varied ethnicity, education, experience with second language learners, and training in reformoriented mathematics curricula to gain a degree of competence in the mathematical discourse they used in class. Identity, participation, situated learning, discourse use by learners of English as a Second Language (ESL), framing in language, and student success in mathematics are all critical notions that are highlighted within this schoolbased research.

OMDoc An Open Markup Format for Mathematical Documents version 1 2

Author: Michael Kohlhase
Publisher: Springer Science & Business Media
ISBN: 9783540378976
Release Date: 2006-08-17
Genre: Computers

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.

Teaching As A Reflective Practice

Author: Ian Westbury
Publisher: Routledge
ISBN: 9781136601705
Release Date: 2012-08-06
Genre: Education

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.

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

Author: Donald Bindner
Publisher: CRC Press
ISBN: 9781439846070
Release Date: 2010-11-29
Genre: Mathematics

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.

Mathematics Across the Curriculum

Author: Sue Fox
Publisher: A&C Black
ISBN: 9781441123565
Release Date: 2010-07-08
Genre: Education

Looks at the theory and practice of providing inspiring, challenging and engaging cross curricular mathematics lesson. >

Introduction to Communication

Author: Susan O'Connell
Publisher: Heinemann Educational Books
ISBN: 0325011060
Release Date: 2007
Genre: Education

NCTM's Process Standards were designed to support teaching that helps children develop independent, effective mathematical thinking. The books in the Heinemann Math Process Standards Series give every elementary teacher the opportunity to explore each one of the standards in depth. And with language and examples that don't require prior math training to understand, the series offers friendly, reassuring advice to any teacher preparing to embrace the Process Standards. In Introduction to Communication, Susan O'Connell shows you ways to help students explore, express, and better understand mathematical content through talking and writing. She offers 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 conjecture about them. Full of activities that are modifiable for immediate use with students of all levels and written by a veteran teacher for teachers of every level of experience, Introduction to Communication highlights the importance of encouraging children to develop insights through writing and speaking, while also recommending ways to implement language-based teaching without rewriting your curriculum. Best of all, like all the titles in the Math Process Standards Series, Introduction to Communication comes with two powerful tools to help you get started and plan well: a CD-ROM with activities customizable to match your lessons and a correlation guide that helps you match mathematical content with the 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.