Unpacking Fractions

Classroom-Tested Strategies to Build Students’ Mathematical Understanding

Author: Monica Neagoy

Publisher: ASCD

ISBN: 1416621237

Category: Education

Page: 286

View: 2434

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For years, the teaching and learning of fractions has been associated with rote memorization. But this mechanical approach to instruction—which strips students of an ability to reason or make sense of math—has resulted in a failure of understanding. Author Monica Neagoy, drawing on decades of research studies, evidence from teacher practice, and 25 years of experience working around the world with teachers, students, and parents, addresses seven big ideas in the teaching and learning of fractions in grades 2–6. Each idea is supported by a vignette from a real classroom, common misconceptions, a thorough unpacking of productive mathematical thinking, and several multistep and thought-provoking problems for teachers to explore. She offers three fundamental reasons why it’s imperative for us to take a closer look at how we teach fractions: 1. Fractions play a key role in students’ feelings about mathematics. 2. Fractions are fundamental to school math and daily life. 3. Fractions are foundational to success in algebra. While a solid grounding in algebra is necessary for a STEM career, the worthy goal of “algebra for all” will not be possible until “fractions for all” is a reality. Unpacking Fractions provides teachers with concrete strategies for achieving that reality—in short, helping all students gain the knowledge they need to feel at ease with fractions.

Unpacking Fractions

Classroom-Tested Strategies to Build Students’ Mathematical Understanding

Author: Monica Neagoy

Publisher: ASCD

ISBN: 1416621253

Category: Education

Page: 286

View: 554

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For years, the teaching and learning of fractions has been associated with rote memorization. But this mechanical approach to instruction—which strips students of an ability to reason or make sense of math—has resulted in a failure of understanding. Author Monica Neagoy, drawing on decades of research studies, evidence from teacher practice, and 25 years of experience working around the world with teachers, students, and parents, addresses seven big ideas in the teaching and learning of fractions in grades 2–6. Each idea is supported by a vignette from a real classroom, common misconceptions, a thorough unpacking of productive mathematical thinking, and several multistep and thought-provoking problems for teachers to explore. She offers three fundamental reasons why it’s imperative for us to take a closer look at how we teach fractions: 1. Fractions play a key role in students’ feelings about mathematics. 2. Fractions are fundamental to school math and daily life. 3. Fractions are foundational to success in algebra. While a solid grounding in algebra is necessary for a STEM career, the worthy goal of “algebra for all” will not be possible until “fractions for all” is a reality. Unpacking Fractions provides teachers with concrete strategies for achieving that reality—in short, helping all students gain the knowledge they need to feel at ease with fractions.

The Coach Approach to School Leadership

Leading Teachers to Higher Levels of Effectiveness

Author: Jessica Johnson,Shira Leibowitz,Kathy Perret

Publisher: ASCD

ISBN: 1416623884

Category: Education

Page: 181

View: 9962

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Three coaching and leadership experts explore how using instructional coaching techniques enables principals to balance learning leadership with their evaluative and supervisory duties.

Planting the Seeds of Algebra, 3-5

Explorations for the Upper Elementary Grades

Author: Monica Neagoy

Publisher: Corwin Press

ISBN: 1412996619

Category: Education

Page: 248

View: 6697

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Give your students a foundation of algebra for math success – now and in the future! Students and teachers must become friendly with algebraic foundations, as they have increasingly become the gateway to careers in the STEM fields. Monica Neagoy empowers teachers to embrace algebra and connect it to higher math concepts, tuning you and your students to algebraic thinking, reasoning, and doing. You’ll discover: ?Four explorations to help you weave key algebraic ideas into everyday mathematics Step-by-step lessons from real classrooms that will guide you in teaching concepts and in establishing their relevance and applicability New methods that break down difficult algebraic concepts and build a critical foundation for higher math

Making Thinking Visible

How to Promote Engagement, Understanding, and Independence for All Learners

Author: Ron Ritchhart,Mark Church,Karin Morrison

Publisher: John Wiley & Sons

ISBN: 9781118015032

Category: Education

Page: 320

View: 9800

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A proven program for enhancing students' thinking and comprehension abilities Visible Thinking is a research-based approach to teaching thinking, begun at Harvard's Project Zero, that develops students' thinking dispositions, while at the same time deepening their understanding of the topics they study. Rather than a set of fixed lessons, Visible Thinking is a varied collection of practices, including thinking routines?small sets of questions or a short sequence of steps?as well as the documentation of student thinking. Using this process thinking becomes visible as the students' different viewpoints are expressed, documented, discussed and reflected upon. Helps direct student thinking and structure classroom discussion Can be applied with students at all grade levels and in all content areas Includes easy-to-implement classroom strategies The book also comes with a DVD of video clips featuring Visible Thinking in practice in different classrooms.

Essential Questions

Opening Doors to Student Understanding

Author: Jay McTighe,Grant Wiggins

Publisher: ASCD

ISBN: 1416615709

Category: Education

Page: 119

View: 731

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What are "essential questions," and how do they differ from other kinds of questions? What's so great about them? Why should you design and use essential questions in your classroom? Essential questions (EQs) help target standards as you organize curriculum content into coherent units that yield focused and thoughtful learning. In the classroom, EQs are used to stimulate students' discussions and promote a deeper understanding of the content. Whether you are an Understanding by Design (UbD) devotee or are searching for ways to address standards--local or Common Core State Standards--in an engaging way, Jay McTighe and Grant Wiggins provide practical guidance on how to design, initiate, and embed inquiry-based teaching and learning in your classroom. Offering dozens of examples, the authors explore the usefulness of EQs in all K-12 content areas, including skill-based areas such as math, PE, language instruction, and arts education. As an important element of their backward design approach to designing curriculum, instruction, and assessment, the authors *Give a comprehensive explanation of why EQs are so important; *Explore seven defining characteristics of EQs; *Distinguish between topical and overarching questions and their uses; *Outline the rationale for using EQs as the focal point in creating units of study; and *Show how to create effective EQs, working from sources including standards, desired understandings, and student misconceptions. Using essential questions can be challenging--for both teachers and students--and this book provides guidance through practical and proven processes, as well as suggested "response strategies" to encourage student engagement. Finally, you will learn how to create a culture of inquiry so that all members of the educational community--students, teachers, and administrators--benefit from the increased rigor and deepened understanding that emerge when essential questions become a guiding force for learners of all ages.

The School Leader’s Guide to Building and Sustaining Math Success

Author: Marian Small,Doug Duff

Publisher: ASCD

ISBN: 1416626387

Category: Education

Page: 174

View: 7209

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The pressure is on. Principals, expected to improve math performance at their schools, often don’t know where to begin—as they may be uncomfortable with math themselves or believe that their schools are already doing all that they can. How can K–12 school leaders recognize and ensure that their school or district is supporting good math instruction? Marian Small and Doug Duff provide the answer to that and other questions in The School Leader’s Guide to Building and Sustaining Math Success. Drawing on their vast experience working with administrators, Small and Duff provide practical advice and helpful tools for improving math instruction. They guide you through the initial steps of establishing a strong math culture, developing common tasks, and getting buy-in, and then offer specific suggestions for monitoring, supporting, and sustaining improvement. You’ll learn what sort of data to collect, what to look for in the classroom, what to listen for in conversations with teachers and students, and how to deal with reluctant staff or parents. With its real-world examples and insights, this book is essential reading for any principal who wants to bring about positive change and real growth in the teaching and learning of math in their school.

Mastering Basic Math Skills

Games for kindergarten through second grade

Author: Bonnie Adama Britt

Publisher: National

ISBN: 9780873537575

Category: Early childhood education

Page: 220

View: 4933

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Math + Games = Learning + Fun Can children develop better math skills and deeper understanding of mathematical concepts and have fun? Absolutely! This collection of games for children in kindergarten through second grade proves it. Games are organized in each chapter from simpler to more advanced, and many have variations that change the rules of play or make it more challenging once the basic game is mastered. Children need lots of practice to learn new concepts and math facts, and games can keep them engaged. Designed for use in the classroom and at home, this book includes access to downloadable More4U materials such as ten-frame cards, game boards, and recording sheets. And all the games are correlated with the Common Core State Standards for Mathematics. Research shows that games have many benefits. Math games: increase curiosity and motivation; allow for cooperative learning opportunities; reinforce mathematical learning and skills; build strategy and reasoning know-how; teach life skills, and reduce math anxiety. There are games for many topics: number recognition and counting subtraction comparing numbers to 10 multiple operations addition multiplication place value money multidigit addition fractions

Modeling Mathematical Ideas

Developing Strategic Competence in Elementary and Middle School

Author: Jennifer M. Suh,Padmanabhan Seshaiyer

Publisher: Rowman & Littlefield

ISBN: 1475817606

Category: Education

Page: 220

View: 1353

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Modeling Mathematical Ideas combining current research and practical strategies to build teachers and students strategic competence in problem solving.This must-have book supports teachers in understanding learning progressions that addresses conceptual guiding posts as well as students’ common misconceptions in investigating and discussing important mathematical ideas related to number sense, computational fluency, algebraic thinking and proportional reasoning. In each chapter, the authors opens with a rich real-world mathematical problem and presents classroom strategies (such as visible thinking strategies & technology integration) and other related problems to develop students’ strategic competence in modeling mathematical ideas.

Adding It Up

Helping Children Learn Mathematics

Author: National Research Council,Division of Behavioral and Social Sciences and Education,Center for Education,Mathematics Learning Study Committee

Publisher: National Academies Press

ISBN: 9780309132848

Category: Education

Page: 480

View: 1737

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Adding It Up explores how students in pre-K through 8th grade learn mathematics and recommends how teaching, curricula, and teacher education should change to improve mathematics learning during these critical years. The committee identifies five interdependent components of mathematical proficiency and describes how students develop this proficiency. With examples and illustrations, the book presents a portrait of mathematics learning: Research findings on what children know about numbers by the time they arrive in pre-K and the implications for mathematics instruction. Details on the processes by which students acquire mathematical proficiency with whole numbers, rational numbers, and integers, as well as beginning algebra, geometry, measurement, and probability and statistics. The committee discusses what is known from research about teaching for mathematics proficiency, focusing on the interactions between teachers and students around educational materials and how teachers develop proficiency in teaching mathematics.

Visible Learning for Mathematics, Grades K-12

What Works Best to Optimize Student Learning

Author: John Hattie,Douglas Fisher,Nancy Frey,Linda M. Gojak,Sara Delano Moore,William Mellman

Publisher: Corwin Press

ISBN: 1506362974

Category: Education

Page: 304

View: 2747

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Rich tasks, collaborative work, number talks, problem-based learning, direct instruction…with so many possible approaches, how do we know which ones work the best? In Visible Learning for Mathematics, six acclaimed educators assert it’s not about which one—it’s about when—and show you how to design high-impact instruction so all students demonstrate more than a year’s worth of mathematics learning for a year spent in school. That’s a high bar, but with the amazing K-12 framework here, you choose the right approach at the right time, depending upon where learners are within three phases of learning: surface, deep, and transfer. This results in “visible” learning because the effect is tangible. The framework is forged out of current research in mathematics combined with John Hattie’s synthesis of more than 15 years of education research involving 300 million students. Chapter by chapter, and equipped with video clips, planning tools, rubrics, and templates, you get the inside track on which instructional strategies to use at each phase of the learning cycle: Surface learning phase: When—through carefully constructed experiences—students explore new concepts and make connections to procedural skills and vocabulary that give shape to developing conceptual understandings. Deep learning phase: When—through the solving of rich high-cognitive tasks and rigorous discussion—students make connections among conceptual ideas, form mathematical generalizations, and apply and practice procedural skills with fluency. Transfer phase: When students can independently think through more complex mathematics, and can plan, investigate, and elaborate as they apply what they know to new mathematical situations. To equip students for higher-level mathematics learning, we have to be clear about where students are, where they need to go, and what it looks like when they get there. Visible Learning for Math brings about powerful, precision teaching for K-12 through intentionally designed guided, collaborative, and independent learning.

Development of Mathematical Cognition

Neural Substrates and Genetic Influences

Author: Daniel B. Berch,David C. Geary,Kathleen Mann Koepke

Publisher: Academic Press

ISBN: 0128019093

Category: Psychology

Page: 414

View: 6089

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Development of Mathematical Cognition: Neural Substrates and Genetic Influences reviews advances in extant imaging modalities and the application of brain stimulation techniques for improving mathematical learning. It goes on to explore the role genetics and environmental influences have in the development of math abilities and disabilities. Focusing on the neural substrates and genetic factors associated with both the typical and atypical development of mathematical thinking and learning, this second volume in the Mathematical Cognition and Learning series integrates the latest in innovative measures and methodological advances from the top researchers in the field. Provides details about new progress made in the study of neural correlates of numerical and arithmetic cognition Addresses recent work in quantitative and molecular genetics Works to improve instruction in numerical, arithmetical, and algebraic thinking and learning Informs policy to help increase the level of mathematical proficiency among the general public

Mathematics Inside the Black Box

Assessment for Learning in the Mathematics Classroom

Author: Dylan Wiliam,King's College (Londres). Department of education and professional studies

Publisher: Granada Learning

ISBN: 9780708716878

Category: Educational tests and measurements

Page: 24

View: 9480

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Graffiti Coloring Book for Adults

Author: Georgia A. Georgia A. Dabney,Hipster Coloring Book

Publisher: Createspace Independent Publishing Platform

ISBN: 9781542335935

Category:

Page: 74

View: 9488

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AMAZON BEST SELLER - BEST GIFT IDEAS This incredible adult coloring book by best-selling artist is the perfect way to relieve stress and aid relaxation while enjoying beautiful and highly detailed images. Each coloring page will transport you into a world of your own while your responsibilities will seem to fade away... Use Any of Your Favorite Tools Including colored pencils, pens, and fine-tipped markers. One Image Per Page Each image is printed on black-backed pages to prevent bleed-through. Display Your Artwork You can display your artwork with a standard 8.5" x 11" frame. Two Copies of Every Image Enjoy coloring your favorite images a second time, color with a friend, or have an extra copy in case you make a mistake. Includes FREE Digital Version As a special bonus, you can download a PDF and print your favorite images to as many times as you want. Now on Sale Regular Price: $9.99 - SAVE $6.99, 60% OFF - Limited time only. Makes the Perfect Gift Surprise that special someone in your life and make them smile. Buy two copies and enjoy coloring together. Buy Now, Start Coloring, and Relax... Scroll to the top of the page and click the buy button.

Strategies for Teaching Fractions

Using Error Analysis for Intervention and Assessment

Author: David B. Spangler

Publisher: Corwin Press

ISBN: 1412993989

Category: Education

Page: 227

View: 2406

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David B. Spangler outlines powerful diagnostic and NCTM- and Common Core State Standards-aligned RTI strategies for analyzing student errors and provides specific interventions for each error pattern.

Interactive Modeling

A Powerful Technique for Teaching Children

Author: Margaret Berry Wilson

Publisher: Center for Responsive Schools, Inc.

ISBN: 1892989530

Category: Education

Page: 204

View: 9355

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Use Interactive Modeling to teach academic and social skills, routines, transitions, use of materials - any behavior, skill, or routine that needs to be done in a specific way. When teachers use this technique, children quickly learn exactly what to do, and they remember better. You'll spend less time reteaching, and your students will spend more time learning. book includes sample lessons, scripts, a planning guide, and a summary of research on the principles behind Interactive Modeling. -- website

Mastering Formative Assessment Moves

7 High-Leverage Practices to Advance Student Learning

Author: Brent Duckor,Carrie Holmberg

Publisher: ASCD

ISBN: 1416624783

Category: Education

Page: 333

View: 1905

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How do you know if students are with you at the beginning, middle, and end of a lesson? Can formative assessment offer a key to better teaching and learning during instruction? What if you could blend different formative assessment moves in your classroom, with intention and care for all students, to help make better instructional decisions on the fly and enjoy more teachable moments? Educators Brent Duckor and Carrie Holmberg invite you on the journey to becoming a formative assessor. They encourage you to focus on these seven research-based, high-leverage formative assessment moves: ▪ Priming--building on background knowledge and creating a formative assessment–rich, equitable classroom culture ▪ Posing--asking questions in relation to learning targets across the curriculum that elicit Habits of Mind ▪ Pausing--waiting after powerful questions and rich tasks to encourage more student responses by supporting them to think aloud and use speaking and listening skills related to academic language ▪ Probing--deepening discussions, asking for elaborations, and making connections using sentence frames and starters ▪ Bouncing--sampling student responses systematically to broaden participation, manage flow of conversation, and gather more “soft data” for instructional use ▪ Tagging--describing and recording student responses without judgment and making public how students with different styles and needs approach learning in real-time ▪ Binning--interpreting student responses with a wide range of tools, categorizing misconceptions and “p-prims,” and using classroom generated data to make more valid and reliable instructional decisions on next steps in the lesson and unit Each chapter explores a classroom-tested move, including foundational research, explaining how and when to best use it, and describing what it looks like in practice. Highlights include case studies, try-now tasks and tips, and advice from beginning and seasoned teachers who use these formative assessment moves in their classrooms.

Planting the Seeds of Algebra, PreK–2

Explorations for the Early Grades

Author: Monica Neagoy

Publisher: Corwin Press

ISBN: 1412996600

Category: Education

Page: 208

View: 9344

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The author provides in-depth math “explorations,” strategies, grade-banded lessons, and step-by-step guidance for building a strong foundation in algebra for very young children.

Routines for Reasoning

Fostering the Mathematical Practices in All Students

Author: Grace Kelemanik,Amy Lucenta,Susan Janssen Creighton

Publisher: Heinemann Educational Books

ISBN: 9780325078151

Category: Education

Page: N.A

View: 1951

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