Putting Essential Understanding Of Functions Into Practice In Grades 9 12

Author : Robert N. Ronau,Dan Meyer,Terry Crites,Barbara J. Dougherty
Publisher : National
Page : 189 pages
File Size : 50,8 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 : Thomas J. Cooney,Sybilla Beckmann,Gwendolyn M. Lloyd
Publisher : Unknown
Page : 109 pages
File Size : 46,5 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 : Terry Crites,Barbara J. Dougherty,Hannah Slovin,Karen S. Karp
Publisher : National Council of Teachers of English
Page : 0 pages
File Size : 51,7 Mb
Release : 2018
Category : Geometry
ISBN : 0873537343

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Putting Essential Understanding of Geometry Into Practice in Grades 6-8 by Terry Crites,Barbara J. Dougherty,Hannah Slovin,Karen S. Karp Pdf

Learn about the specialized pedagogical content knowledge you need to teach geometry effectively in grades 6-8. The authors demonstrate how to use this multifaceted knowledge to address the big ideas and essential understandings that students must develop for success with geometry-not only in their current work, but also in higher-level mathematics and a myriad of real-world contexts.

Author : Frederick L. Dillon,Ayanna D. Perry,Andrea Cheng,Jennifer Outzs
Publisher : Corwin Press
Page : 185 pages
File Size : 43,6 Mb
Release : 2022-03-02
Category : Education
ISBN : 9781071870839

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Answers to Your Biggest Questions About Teaching Secondary Math by Frederick L. Dillon,Ayanna D. Perry,Andrea Cheng,Jennifer Outzs Pdf

Let’s face it, teaching secondary math can be hard. So much about how we teach math today may look and feel different from how we learned it. Teaching math in a student-centered way changes the role of the teacher from one who traditionally "delivers knowledge" to one who fosters thinking. Most importantly, we must ensure our practice gives each and every student the opportunity to learn, grow, and achieve at high levels, while providing opportunities to develop their agency and authority in the classroom which results in a positive math identity. Whether you are a brand new teacher or a veteran, if you find teaching math to be quite the challenge, this is the guide you want by your side. Designed for just-in-time learning and support, this practical resource gives you brief, actionable answers to your most pressing questions about teaching secondary math. Written by four experienced math educators representing diverse experiences, these authors offer the practical advice they wish they received years ago, from lessons they′ve learned over decades of practice, research, coaching, and through collaborating with teams, teachers and colleagues—especially new teachers—every day. Questions and answers are organized into five areas of effort that will help you most thrive in your secondary math classroom: How do I build a positive math community? How do I structure, organize, and manage my math class? How do I engage my students in math? How do I help my students talk about math? How do I know what my students know and move them forward? Woven throughout, you′ll find helpful sidebar notes on fostering identity and agency; access and equity; teaching in different settings; and invaluable resources for deeper learning. The final question—Where do I go from here?— offers guidance for growing your practice over time. Strive to become the best math educator you can be; your students are counting on it! What will be your first step on the journey?

Author : Frederick L. Dillon,W. Gary Martin,Basil M. Conway IV,Marilyn E. Strutchens
Publisher : Corwin Press
Page : 504 pages
File Size : 44,8 Mb
Release : 2017-09-12
Category : Education
ISBN : 9781506395630

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The Common Core Mathematics Companion: The Standards Decoded, High School by Frederick L. Dillon,W. Gary Martin,Basil M. Conway IV,Marilyn E. Strutchens Pdf

When it comes to math, standards-aligned is achievement-aligned… Since The Common Core Mathematics Companions for grades K–2, 3–5 and 6–8 burst on the scene, they have been lauded as the best resources for making critical math ideas easy to teach. With this brand-new volume, high school mathematics success is at your fingertips. The authors lay out the pieces of an in-depth explanation, showing the mathematical progression of each conceptual category, how standards connect within and across domains, and what teachers and students should be doing every day to foster deep learning.

Author : Frederick L. Dillon,W. Gary Martin,Basil M. Conway IV,Marilyn E. Strutchens
Publisher : Corwin Press
Page : 536 pages
File Size : 43,9 Mb
Release : 2018-02-06
Category : Education
ISBN : 9781544317434

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Your Mathematics Standards Companion, High School by Frederick L. Dillon,W. Gary Martin,Basil M. Conway IV,Marilyn E. Strutchens Pdf

Transforming the standards into learning outcomes just got a lot easier This expansion of the popular Common Core Mathematics Companions provides a Cross-Referencing Index for states implementing their own specific mathematics standards. This index allows you to see in an instant which of your standards are the same as CCSS-M, which differ and how—and which page number to turn to for standards-based teaching ideas. Beyond that? It’s the same great go-to guide for guide for teaching, planning, assessing, collaborating, and designing powerful high school mathematics curriculum, in any state or district.

Author : Zandra De Araujo,Fay Zenigami
Publisher : National
Page : 128 pages
File Size : 42,6 Mb
Release : 2018-08
Category : Equations
ISBN : 0873537351

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Putting Essential Understanding of Expressions and Equations Into Practice in Grades 6-8 by Zandra De Araujo,Fay Zenigami Pdf

Author : Robert N. Ronau,Dan Meyer,Terry Crites
Publisher : Unknown
Page : 205 pages
File Size : 45,8 Mb
Release : 2015-07
Category : Mathematics
ISBN : 087353736X

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

Author : Jennifer T.H. Wathall
Publisher : Corwin Press
Page : 297 pages
File Size : 45,7 Mb
Release : 2016-01-14
Category : Education
ISBN : 9781506332635

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Concept-Based Mathematics by Jennifer T.H. Wathall Pdf

Give math students the connections between what they learn and how they do math—and suddenly math makes sense If your secondary-school students are fearful of or frustrated by math, it’s time for a new approach. When you teach concepts rather than rote processes, you help students discover their own natural mathematical abilities. This book is a road map to retooling how you teach math in a deep, clear, and meaningful way to help students achieve higher-order thinking skills. Jennifer Wathall shows you how to plan units, engage students, assess understanding, incorporate technology, and there’s even a companion website with additional resources.

Author : Daniel J. Brahier
Publisher : Routledge
Page : 548 pages
File Size : 41,5 Mb
Release : 2020-04-01
Category : Education
ISBN : 9780429627989

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Teaching Secondary and Middle School Mathematics by Daniel J. Brahier Pdf

Teaching Secondary and Middle School Mathematics combines the latest developments in research, technology, and standards with a vibrant writing style to help teachers prepare for the excitement and challenges of teaching secondary and middle school mathematics. The book explores the mathematics teaching profession by examining the processes of planning, teaching, and assessing student progress through practical examples and recommendations. Beginning with an examination of what it means to teach and learn mathematics, the reader is led through the essential components of teaching, concluding with an examination of how teachers continue with professional development throughout their careers. Hundreds of citations are used to support the ideas presented in the text, and specific websites and other resources are presented for future study by the reader. Classroom scenarios are presented to engage the reader in thinking through specific challenges that are common in mathematics classrooms. The sixth edition has been updated and expanded with particular emphasis on the latest technology, resources, and standards. The reader is introduced to the ways that students think and how to best meet their needs through planning that involves attention to differentiation, as well as how to manage a classroom for success. Features include: The entire text has been reorganized so that assessment takes a more central role in planning and teaching. Unit 3 (of 5) now addresses the use of summative and formative assessments to inform classroom teaching practices. ● A new feature, "Links and Resources," has been added to each of the 13 chapters. While the book includes a substantial listing of citations and resources after the chapters, five strongly recommended and practical resources are spotlighted at the end of each chapter as an easy reference to some of the most important materials on the topic. ● Approximately 150 new citations have either replaced or been added to the text to reflect the latest in research, materials, and resources that support the teaching of mathematics. ● A Quick Reference Guide has been added to the front of the book to assist the reader in identifying the most useful chapter features by topic. ● A significant revision to Chapter 13 now includes discussions of common teaching assessments used for field experiences and licensure, as well as a discussion of practical suggestions for success in methods and student teaching experiences. ● Chapter 9 on the practical use of classroom technology has been revised to reflect the latest tools available to classroom teachers, including apps that can be run on handheld, personal devices. An updated Instructor’s Manual features a test bank, sample classroom activities, Powerpoint slides, chapter summaries, and learning outcomes for each chapter, and can be accessed by instructors online at www.routledge.com/9780367146511

Author : Barbara J. Dougherty,Sarah B. Bush,Karen S. Karp
Publisher : Corwin Press
Page : 201 pages
File Size : 46,5 Mb
Release : 2020-09-19
Category : Education
ISBN : 9781544399638

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The Math Pact, High School by Barbara J. Dougherty,Sarah B. Bush,Karen S. Karp Pdf

A schoolwide solution for mathematics success! When "rules" seem to change from year to year, mathematics can seem like a disconnected mystery for students. Clear up the confusion with a Mathematics Whole-School Agreement! Expanded from the highly popular "Rules that Expire" series of NCTM articles, this essential guide leads educators through the collaborative step-by-step process of establishing a coherent and consistent learner-centered and equitable approach to mathematics instruction. You’ll learn to avoid "rules that expire"—tricks that may seem to help students in one grade but hurt in the long run. Features include · Abundant grade-specific examples · Effective working plans for sustainability · Barrier-busting tips, to-dos, and try-it-outs · PLC prompts and discussion points

Author : Association of Mathematics Teacher Educators (AMTE)
Publisher : IAP
Page : 199 pages
File Size : 40,9 Mb
Release : 2020-02-01
Category : Mathematics
ISBN : 9781641139984

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Standards for Preparing Teachers of Mathematics by Association of Mathematics Teacher Educators (AMTE) Pdf

Also available in a black + white version AMTE, in the Standards for Preparing Teachers of Mathematics (SPTM), puts forward a national vision of initial preparation for all Pre-K–12 teachers who teach mathematics. SPTM contains critical messages for all who teach mathematics, including elementary school teachers teaching all disciplines, middle and high school mathematics teachers who may teach mathematics exclusively, special education teachers, teachers of emergent multilingual students, and other teaching professionals and administrators who have responsibility for students’ mathematical learning. SPTM has broad implications for teacher preparation programs, in which stakeholders include faculty and administrators in both education and mathematics at the university level; teachers, principals, and district leaders in the schools with which preparation programs partner; and the communities in which preparation programs and their school partners are situated. SPTM is intended as a national guide that articulates a vision for mathematics teacher preparation and supports the continuous improvement of teacher preparation programs. Such continuous improvement includes changes to preparation program courses and structures, partnerships involving schools and universities and their leaders, the ongoing accreditation of such programs regionally and nationally, and the shaping of state and national mathematics teacher preparation policy. SPTM is also designed to inform assessment practices for mathematics teacher preparation programs, to influence policies related to preparation of teachers of mathematics, and to promote national dialogue around preparing teachers of mathematics. The vision articulated in SPTM is aspirational in that it describes a set of high expectations for developing a well-prepared beginning teacher of mathematics who can support meaningful student learning. The vision is research-based and establishes a set of goals for the continued development and refinement of a mathematics teacher preparation program and a research agenda for the study of the effects of such a program. SPTM contains detailed depictions of what a well-prepared beginning teacher knows and is able to do related to content, pedagogy, and disposition, and what a strong preparation program entails with respect to learning experiences, assessments, and partnerships. Stakeholders in mathematics teacher preparation will find messages related to their roles. Standards for Preparing Teachers of Mathematics includes standards and indicators for teacher candidates and for the design of teacher preparation programs. SPTM outlines assessment practices related to overall quality, program effectiveness, and candidate performance. SPTM describes specific focal practices by grade band and provides guidance to stakeholders regarding processes for productive change.

Author : Travis Olson,Melfried Olson,Hannah Slovin
Publisher : National Council of Teachers of English
Page : 0 pages
File Size : 46,6 Mb
Release : 2015
Category : Ratio and proportion
ISBN : 0873537173

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Putting Essential Understanding of Ratios and Proportions Into Practice in Grades 6-8 by Travis Olson,Melfried Olson,Hannah Slovin Pdf

Focuses on the specialized pedagogical content knowledge that you need to teach ratios and proportions effectively in grades 6-8. The authors demonstrate how to use this multifaceted knowledge to address the big ideas and essential understandings that students must develop for success with ratios and proportions.

Author : Ruth Harbin Miles,Beth McCord Kobett,Lois A. Williams
Publisher : Corwin Press
Page : 248 pages
File Size : 50,5 Mb
Release : 2018-07-13
Category : Education
ISBN : 9781506387871

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The Mathematics Lesson-Planning Handbook, Grades 3-5 by Ruth Harbin Miles,Beth McCord Kobett,Lois A. Williams Pdf

YOU are the architect in the mathematics classroom. This daily reference offers practical guidance for when and how to pull together mathematics routines, resources, and effective teaching techniques into a coherent and manageable set of lesson plans. This resource will Lead teachers through a process of lesson planning based on various learning objectives Set the stage for lesson planning using relatable vignettes Offer sample lesson plans for Grades 3–5 Create opportunities to reflect on each component of a mathematics lesson Suggest next steps for building a unit from the lessons Provide teachers the space and tools to create their own lesson plans going forward

Author : National Council of Teachers of Mathematics
Publisher : National Council of Teachers of Mathematics, Incorporated
Page : 139 pages
File Size : 45,7 Mb
Release : 2014-02
Category : Curriculum planning
ISBN : 0873537742

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Principles to Actions by National Council of Teachers of Mathematics Pdf

This text offers guidance to teachers, mathematics coaches, administrators, parents, and policymakers. This book: provides a research-based description of eight essential mathematics teaching practices ; describes the conditions, structures, and policies that must support the teaching practices ; builds on NCTM's Principles and Standards for School Mathematics and supports implementation of the Common Core State Standards for Mathematics to attain much higher levels of mathematics achievement for all students ; identifies obstacles, unproductive and productive beliefs, and key actions that must be understood, acknowledged, and addressed by all stakeholders ; encourages teachers of mathematics to engage students in mathematical thinking, reasoning, and sense making to significantly strengthen teaching and learning.