Developing Essential Understanding Of Functions For Teaching Mathematics In Grades 9 12

Author : Thomas J. Cooney,Sybilla Beckmann,Gwendolyn M. Lloyd
Publisher : Unknown
Page : 109 pages
File Size : 48,5 Mb
Release : 2010
Category : Curriculum enrichment
ISBN : 0873536231

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Developing Essential Understanding of Functions for Teaching Mathematics in Grades 9-12 by Thomas J. Cooney,Sybilla Beckmann,Gwendolyn M. Lloyd Pdf

Are sequences functions? Why can’t the popular “vertical line test” be applied in some cases to determine if a relation is a function? How does the idea of rate of change connect with simpler ideas about proportionality as well as more advanced topics in calculus? How much do you know… and how much do you need to know? Helping your high school students develop a robust understanding of functions requires that you understand mathematics deeply. But what does that mean? This book focuses on essential knowledge for teachers about functions. It is organised around five big ideas, supported by multiple smaller, interconnected ideas-essential understandings. Taking you beyond a simple introduction to functions, this book will broaden and deepen your mathematical understanding of one of the most challenging topics for students and teachers. It will help you engage your students, anticipate their perplexities, avoid pitfalls and dispel misconceptions. You will also learn to develop appropriate tasks, techniques and tools for assessing students’ understanding of the topic. Focus on the ideas that you need to understand thoroughly to teach confidently.

Author : Robert N. Ronau,Dan Meyer,Terry Crites,Barbara J. Dougherty
Publisher : National
Page : 189 pages
File Size : 46,7 Mb
Release : 2014
Category : Functions
ISBN : 0873537149

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Putting Essential Understanding of Functions Into Practice in Grades 9-12 by Robert N. Ronau,Dan Meyer,Terry Crites,Barbara J. Dougherty Pdf

Do your students think that the vertical line test is indispensable and foolproof for determining whether a relationship is a function? Do they believe that every function can be modeled by an equation? Do they interpret the graph of a function as the function itself? What tasks can you offer - what questions can you ask - to determine what they know or don’t know - and move them forward in their thinking? This book focuses on the specialized pedagogical content knowledge that you need to teach functions effectively in grades 9–12. The authors demonstrate how to use this multifaceted knowledge to address the big ideas and essential understandings that students must develop for success with functions - not only in their current work, but also in higher-level mathematics and a myriad of real-world contexts. Explore rich, research-based strategies and tasks that show how students are reasoning about and making sense of functions. Use the opportunities that these and similar tasks provide to build on their understanding while identifying and correcting misunderstandings that may be keeping them from taking the next steps in learning. You have essential understanding. It’s time to put it into practice in your teaching. The Putting Essential Understanding into Practice Series moves NCTM’s Essential Understanding Series into the classroom. The new series details and explores best practices for teaching the essential ideas that students must grasp about fundamental topics in mathematics - topics that are challenging to learn and teach but are critical to the development of mathematical understanding. Classroom vignettes and samples of student work bring each topic to life, and questions for reader reflection open it up for hands-on exploration. Each volume underscores connections with the Common Core State Standards for Mathematics while highlighting the knowledge of learners, curriculum, instructional strategies, and assessment that pedagogical content knowledge entails. Resources and tasks are available at nctm.org/more4U. Maximize the potential of student-centered learning and teaching by putting essential understanding into practice.

Author : Joanne Elizabeth Lobato,Amy B. Ellis,Randall Inners Charles
Publisher : National Council of Teachers of English
Page : 0 pages
File Size : 40,8 Mb
Release : 2010
Category : Curriculum planning
ISBN : 0873536223

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Developing Essential Understanding of Ratios, Proportions, and Proportional Reasoning for Teaching Mathematics in Grades 6-8 by Joanne Elizabeth Lobato,Amy B. Ellis,Randall Inners Charles Pdf

"A series for teaching mathematics."--P. [1] of cover.

Author : Amy B. Ellis,Kristen Bieda,Eric J. Knuth
Publisher : National
Page : 128 pages
File Size : 54,5 Mb
Release : 2012
Category : Education
ISBN : UIUC:30112127286570

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Developing Essential Understanding of Proof and Proving for Teaching Mathematics in Grades 9-12 by Amy B. Ellis,Kristen Bieda,Eric J. Knuth Pdf

Focuses on essential knowledge for teachers about proof and the process of proving. It is organised around five big ideas, supported by multiple smaller, interconnected ideas-essential understandings. Taking you beyond a simple introduction to proof and the activities involved in proving, the book will broaden and deepen your mathematical understanding of one of the most challenging topics for students...and teachers.

Author : Nathalie Sinclair,David Pimm,Melanie Skelin
Publisher : National Council of Teachers of English
Page : 95 pages
File Size : 50,9 Mb
Release : 2012
Category : Education, Secondary
ISBN : 0873536924

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Developing Essential Understanding of Geometry for Teaching Mathematics in Grades 9-12 by Nathalie Sinclair,David Pimm,Melanie Skelin Pdf

Why does it matter whether we state definitions carefully when we all know what particular geometric figures look like? What does it mean to say that a reflection is a transformation—a function? How does the study of transformations and matrices in high school connect with later work with vector spaces in linear algebra? How much do you know… and how much do you need to know? Helping your students develop a robust understanding of geometry requires that you understand this mathematics deeply. But what does that mean? This book focuses on essential knowledge for teachers about geometry. It is organised around four big ideas, supported by multiple smaller, interconnected ideas—essential understandings. Taking you beyond a simple introduction to geometry, the book will broaden and deepen your mathematical understanding of one of the most challenging topics for students—and teachers. It will help you engage your students, anticipate their perplexities, avoid pitfalls, and dispel misconceptions. You will also learn to develop appropriate tasks, techniques, and tools for assessing students’ understanding of the topic. Focus on the ideas that you need to understand thoroughly to teach confidently. Move beyond the mathematics you expect your students to learn. Students who fail to get a solid grounding in pivotal concepts struggle in subsequent work in mathematics and related disciplines. By bringing a deeper understanding to your teaching, you can help students who don’t get it the first time by presenting the mathematics in multiple ways. The Essential Understanding Series addresses topics in school mathematics that are critical to the mathematical development of students but are often difficult to teach. Each book in the series gives an overview of the topic, highlights the differences between what teachers and students need to know, examines the big ideas and related essential understandings, reconsiders the ideas presented in light of connections with other mathematical ideas, and includes questions for readers’ reflection.

Author : Gwendolyn M. Lloyd,Beth A. Herbel-Eisenmann,Jon R. Star
Publisher : National Council of Teachers of English
Page : 116 pages
File Size : 40,7 Mb
Release : 2011
Category : Effective teaching
ISBN : 0873536703

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Developing Essential Understanding of Expressions, Equations, and Functions for Teaching Mathematics in Grades 6-8 by Gwendolyn M. Lloyd,Beth A. Herbel-Eisenmann,Jon R. Star Pdf

Why do some equations have one solution, others two or even more solutions and some no solutions? Why do we sometimes need to ""switch"" the direction of an inequality symbol in solving an inequality? What could you say if a student described a function as an equation? How much do you know...and how much do you need to know? Helping your students develop a robust understanding of expressions, equations and functions requires that you understand this mathematics deeply. But what does that mean? This book focuses on essential knowledge for teachers about expressions, equations and functions. It is organised around five big ideas, supported by multiple smaller, interconnected ideas - essential understandings. Taking you beyond a simple introduction to expressions, equations and functions, the book will broaden and deepen your mathematical understanding of one of the most challenging topics for students - and teachers. It will help you engage your students, anticipate their perplexities, avoid pitfalls and dispel misconceptions. You will also learn to develop appropriate tasks, techniques and tools for assessing students' understanding of the topic. Focus on the ideas that you need to understand thoroughly to teach confidently.

Author : Roxy Peck,Robert Gould,Stephen J. Miller
Publisher : National
Page : 122 pages
File Size : 47,9 Mb
Release : 2013
Category : Effective teaching
ISBN : 0873536762

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Developing Essential Understanding of Statistics for Teaching Mathematics in Grades 9-12 by Roxy Peck,Robert Gould,Stephen J. Miller Pdf

How does a statistical model differ from a mathematical model? What are the differences among the sample distribution, the sampling distribution, and the population distribution? In an experiment, what effect does the sampling method have on the results? What are the implications of the use of processes of random selection and random assignment? Can a small sample yield accurate estimates of population parameters? This book examines five big ideas and twenty-four related essential understandings for teaching statistics in grades 9–12. The authors distinguish mathematical and statistical models, explore distributions as descriptions of variability in data, focus on the fundamentals of testing hypotheses to draw conclusions from data, highlight the importance of the data collection method, and recognise the need to examine bias, precision, and sampling method in evaluating statistical estimators. Recognising that analysing data is an important part of understanding the world, the authors discuss the growth of students’ ideas about statistics and examine challenges to teaching, learning, and assessment. They intersperse their discussion with questions for teachers’ reflection.

Author : Joanne Lobato
Publisher : Unknown
Page : 80 pages
File Size : 46,5 Mb
Release : 2010
Category : Effective teaching
ISBN : 0873536533

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Teaching and Learning Mathematics by Joanne Lobato Pdf

How can teachers learn what they need to know? Every community of educators, regardless of field or specialisation, can benefit from being well informed about current research findings. A considerable amount of mathematics education research exists to inform teachers and administrators about teaching and learning mathematics. Research can show what is possible and what looks promising. It can demonstrate what is possible for students - what they can learn under specific kinds of conditions. Research can show that students can reach certain goals and that some kinds of instruction are especially effective in helping them get there. Learn how to use current research to improve the teaching and learning of mathematics. The Teaching and Learning Mathematics series presents ideas from research to improve mathematics education in schools. Each book presents findings from research to enhance the quality of classroom mathematics teaching and learning. Translating Research for Secondary School Teachers contains twelve stand-alone articles, each with a list of references, which put current research into the hands of school teachers. Each article addresses key practitioner-generated questions with brief, direct answers, devoid of technical language and theory. It also includes a “How to Use this Book” section that provides specific suggestions for using the book in professional development workshops and for making policy decisions.

Author : Gary Kader,Tim Jacobbe,Patricia S. Wilson
Publisher : National
Page : 112 pages
File Size : 55,7 Mb
Release : 2013
Category : Mathematical statistics
ISBN : 087353672X

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Developing Essential Understanding of Statistics for Teaching Mathematics in Grades 6-8 by Gary Kader,Tim Jacobbe,Patricia S. Wilson Pdf

How does working with data in statistics differ from working with numbers in mathematics? What is variability, and how can we describe and measure it? How can we display distributions of quantitative or categorical data? What is a data sample, and how can we choose one that will allow us to draw valid conclusions from data? How much do you know? and how much do you need to know? Helping your students develop a robust understanding of statistics requires that you understand fundamental statistical concepts deeply. But what does that mean? This book focuses on essential knowledge for mathematics teachers about statistics. It is organised around four big ideas, supported by multiple smaller, interconnected ideas. Taking you beyond a simple introduction to statistics, the book will broaden and deepen your understanding of one of the most challenging topics for students and teachers. It will help you engage your students, anticipate their perplexities, avoid pitfalls, and dispel misconceptions. You will also learn to develop appropriate tasks, techniques, and tools for assessing students’ understanding of the topic. Focus on the ideas that you need to understand thoroughly to teach confidently.

Author : Alfred S. Posamentier,Beverly S. Smith
Publisher : Pearson Higher Ed
Page : 750 pages
File Size : 50,6 Mb
Release : 2014-02-17
Category : Education
ISBN : 9780133808988

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Teaching Secondary Mathematics by Alfred S. Posamentier,Beverly S. Smith Pdf

Note: This is the loose-leaf version of Teaching Secondary Mathematics and does not include access to the Pearson eText. To order the Pearson eText packaged with the loose-leaf version, use ISBN 0133783677. Teaching Secondary Mathematics, 9/e combines methods of teaching mathematics, including all aspects and responsibilities of the job, with a collection of enrichment units appropriate for the entire secondary school curriculum spectrum to give teachers alternatives for making professional judgments about their teaching performance–and ensuring effective learning. The book is divided into two parts designed to ensure effective teaching and learning: Part I includes a focus on the job of teaching mathematics and Part II includes enrichment activities appropriate for the entire secondary school curriculum. Both the Common Core State Standards and The National Council of teachers of Mathematics Principles and Standards for School Mathematics are referred to throughout the book. The new Ninth Edition features an alignment with the Common Core State Standards (CCSS), with special focus on the mathematical practices, an updated technology chapter that shows how current tools and software can be used for teaching mathematics, and an updated chapter on assessment showing show to provide targeted feedback to advance the learning of every student.

Author : National Research Council,Division of Behavioral and Social Sciences and Education,Committee on How People Learn: A Targeted Report for Teachers
Publisher : National Academies Press
Page : 265 pages
File Size : 49,9 Mb
Release : 2005-01-28
Category : Education
ISBN : 9780309089500

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How Students Learn by National Research Council,Division of Behavioral and Social Sciences and Education,Committee on How People Learn: A Targeted Report for Teachers Pdf

How Students Learn: Science in the Classroom builds on the discoveries detailed in the best-selling How People Learn. Now these findings are presented in a way that teachers can use immediately, to revitalize their work in the classroom for even greater effectiveness. Organized for utility, the book explores how the principles of learning can be applied in science at three levels: elementary, middle, and high school. Leading educators explain in detail how they developed successful curricula and teaching approaches, presenting strategies that serve as models for curriculum development and classroom instruction. Their recounting of personal teaching experiences lends strength and warmth to this volume. This book discusses how to build straightforward science experiments into true understanding of scientific principles. It also features illustrated suggestions for classroom activities.

Author : Anne Watson,Keith Jones,Dave Pratt
Publisher : Oxford University Press
Page : 270 pages
File Size : 40,5 Mb
Release : 2013-02-21
Category : Education
ISBN : 9780199665518

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Key Ideas in Teaching Mathematics by Anne Watson,Keith Jones,Dave Pratt Pdf

International research is used to inform teachers and others about how students learn key ideas in higher school mathematics, what the common problems are, and the strengths and pitfalls of different teaching approaches. An associated website, hosted by the Nuffield Foundation, gives summaries of main ideas and access to sample classroom tasks.

Author : Marilyn Burns
Publisher : Math Solutions
Page : 512 pages
File Size : 43,8 Mb
Release : 2007
Category : Education
ISBN : STANFORD:36105123356870

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About Teaching Mathematics by Marilyn Burns Pdf

A compendium of more than 240 classroom-tested lessons, this essential resource helps teachers build student understanding and skills and understand how children best learn math. In this third edition, Marilyn Burns has completely revised the first section to reflect what she has learned over the years from her classroom experience with students and her professional development experience with teachers. This section has also been expanded to address these important topics: teaching math vocabulary, incorporating writing into math instruction, linking assessment and instruction, and using children¿s literature to teach key math concepts. In an entirely new section, Marilyn addresses a wide range of questions she has received over the years from elementary and middle school teachers regarding classroom management and instructional issues.

Author : Anonim
Publisher : Unknown
Page : 86 pages
File Size : 48,8 Mb
Release : 2001
Category : Algebra
ISBN : 0873535022

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Navigating Through Algebra in Grades 9-12 by Anonim Pdf

Author : Deborah Schifter,Virginia Bastable,Susan Jo Russell,Dale Seymour Publications
Publisher : Dale Seymour Publications
Page : 0 pages
File Size : 54,7 Mb
Release : 2007-03-15
Category : Mathematical models
ISBN : 1428405208

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Patterns, Functions, and Change Casebook by Deborah Schifter,Virginia Bastable,Susan Jo Russell,Dale Seymour Publications Pdf

Discover how the study of repeating patterns and number sequences can lead to ideas of functions, learn how to read tables and graphs to interpret phenomena of change, and use algebraic notation to write function rules.