the language of mathematics utilizing math in practice

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The Language Of Mathematics

Author : Robert L. Baber
ISBN : 9781118061763
Genre : Mathematics
File Size : 76. 7 MB
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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 The Standards Number Operations Grade 2

Author : Becky Daniel
ISBN : 9781624421013
Genre : Juvenile Nonfiction
File Size : 54. 72 MB
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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

Academic Language In Diverse Classrooms Mathematics Grades 3 5

Author : Margo Gottlieb
ISBN : 9781452278056
Genre : Education
File Size : 82. 81 MB
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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

Academic Language In Diverse Classrooms Mathematics Grades 6 8

Author : Margo Gottlieb
ISBN : 9781452234830
Genre : Education
File Size : 38. 2 MB
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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
ISBN : 9781317743637
Genre : Education
File Size : 64. 83 MB
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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.

Using Children S Literature To Teach Problem Solving In Math

Author : Jeanne White
ISBN : 9781317909231
Genre : Education
File Size : 20. 61 MB
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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

Winning At Math

Author : Paul D. Nolting
ISBN : 094028734X
Genre : Mathematics
File Size : 80. 18 MB
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Omdoc An Open Markup Format For Mathematical Documents Version 1 2

Author : Michael Kohlhase
ISBN : 9783540378976
Genre : Computers
File Size : 76. 52 MB
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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.

Common Core Sense

Author : Christine Moynihan
ISBN : 9781625310521
Genre : Mathematics
File Size : 81. 40 MB
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The Standards for Mathematical Practice provide an excellent foundation for encouraging students to think, reason, and persevere like mathematicians. Many elementary school teachers, however, face a challenge unpacking these practices and figuring out how to implement them in their classrooms. Christine Moynihan wrote "Common Core Sense: Tapping the Power of the Mathematical Practices" with the goal of making the practices more explicit, learnable, and accessible. Moynihan shows what each practice might look, sound, and feel like in the classroom using the four-part GOLD framework: G Go for the goals. What are the major purposes of the practice? O Open your eyes & Observe. What should you see students doing as they utilize the practice? What should you see yourself doing? L Listen. What should you hear students saying as they utilize the practice? What should you hear yourself saying? D Decide what you need to do in order to make the most of the practice. This timely text devotes one chapter to each practice. The consistent framework of the book, similar in structure to Moynihan s "Math Sense," provides an easy way to learn, assess, and deepen your own understanding of each practice to mine the GOLD. "

Teaching As A Reflective Practice

Author : Ian Westbury
ISBN : 9781136601705
Genre : Education
File Size : 90. 24 MB
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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.

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