{"product_id":"helping-children-learn-mathematics-isbn-9781118654101","title":"Helping Children Learn Mathematics","description":"The 11th Edition of \u003cb\u003e\u003ci\u003eHelping Children Learn\u003c\/i\u003e \u003ci\u003eMathematics\u003c\/i\u003e\u003c\/b\u003e is designed to help those who are or will be teachers of mathematics in elementary schools help children develop understanding and proficiency with mathematics so they can solve problems. This text is built around three main themes: helping children make sense of mathematics, incorporating practical experiences, and using research to guide teaching. It also integrates connections and implications from the Common Core Standards: Mathematics (CCSS-M). \u003cp\u003ePreface iv\u003c\/p\u003e \u003cp\u003eAcknowledgments vi\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 1 school mathematics in a changing world 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eSnapshot of a Lesson 1\u003c\/p\u003e \u003cp\u003eChapter Learning Outcomes 1\u003c\/p\u003e \u003cp\u003eIntroduction 1\u003c\/p\u003e \u003cp\u003eWhat is Mathematics? 2\u003c\/p\u003e \u003cp\u003eWhat Determines the Mathematics Being Taught? 2\u003c\/p\u003e \u003cp\u003eWhere Can You Turn? 6\u003c\/p\u003e \u003cp\u003eWhat is Your Role Now? 9\u003c\/p\u003e \u003cp\u003eThings to Do: From What You’ve Read 9\u003c\/p\u003e \u003cp\u003eThings to Do: Going Beyond This Book 9\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 2 Helping All Children Learn Mathematics with Understanding 11\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eSnapshot of a Lesson 11\u003c\/p\u003e \u003cp\u003eChapter Learning Outcomes 11\u003c\/p\u003e \u003cp\u003eIntroduction 12\u003c\/p\u003e \u003cp\u003eWhat do We Know About Learning Mathematics? 12\u003c\/p\u003e \u003cp\u003eHow Can We Support the Diverse Learners in Our Classroom? 12\u003c\/p\u003e \u003cp\u003eHelping Children Acquire Both Procedural and Conceptual Knowledge 17\u003c\/p\u003e \u003cp\u003eHow do Children Learn Mathematics? 18\u003c\/p\u003e \u003cp\u003eHow Can We Help Children Make Sense of Mathematics? 22\u003c\/p\u003e \u003cp\u003eCultural Connections 28\u003c\/p\u003e \u003cp\u003eA Glance at Where We’ve Been 28\u003c\/p\u003e \u003cp\u003eThings to Do: From What You’ve Read 29\u003c\/p\u003e \u003cp\u003eThings to Do: Going Beyond This Book 29\u003c\/p\u003e \u003cp\u003eBook Nook for Children 30\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 3 Planning and Teaching 31\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eSnapshot of a Lesson 31\u003c\/p\u003e \u003cp\u003eChapter Learning Outcomes 31\u003c\/p\u003e \u003cp\u003eIntroduction 31\u003c\/p\u003e \u003cp\u003ePreparing to Teach: Questions to Ask 32\u003c\/p\u003e \u003cp\u003ePlanning for Effective Teaching 43\u003c\/p\u003e \u003cp\u003eMeeting the Needs of all Students 52\u003c\/p\u003e \u003cp\u003eCultural Connections 55\u003c\/p\u003e \u003cp\u003eA Glance at Where We’ve Been 56\u003c\/p\u003e \u003cp\u003eThings to Do: From What You’ve Read 56\u003c\/p\u003e \u003cp\u003eThings to Do: Going Beyond This Book 57\u003c\/p\u003e \u003cp\u003eBook Nook for Children 57\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 4 Using Assessment to Enhance Learning and Teaching 58\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eSnapshot of a Lesson 58\u003c\/p\u003e \u003cp\u003eChapter Learning Outcomes 58\u003c\/p\u003e \u003cp\u003eIntroduction 59\u003c\/p\u003e \u003cp\u003eSummative and Formative Assessments 59\u003c\/p\u003e \u003cp\u003eFour Phases of Formative Assessment 59\u003c\/p\u003e \u003cp\u003ePurposes for Formative Assessment 61\u003c\/p\u003e \u003cp\u003eWays to Assess Students’ Abilities and Dispositions 62\u003c\/p\u003e \u003cp\u003eKeeping Records and Communicating About Assessments 74\u003c\/p\u003e \u003cp\u003eCultural Connections 77\u003c\/p\u003e \u003cp\u003eA Glance at Where We’ve Been 78\u003c\/p\u003e \u003cp\u003eThings to Do: From What You’ve Read 79\u003c\/p\u003e \u003cp\u003eThings to Do: Going Beyond This Book 79\u003c\/p\u003e \u003cp\u003eBook Nook for Children 80\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 5 Practices and Processes of Doing Mathematics 81\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eSnapshot of a Lesson 81\u003c\/p\u003e \u003cp\u003eChapter Learning Outcomes 81\u003c\/p\u003e \u003cp\u003eIntroduction 81\u003c\/p\u003e \u003cp\u003eMathematical Practices from the Common Core State Standards for Mathematics—CCSSM 83\u003c\/p\u003e \u003cp\u003eMathematical Processes from NCTM’s Principles and Standards for School Mathematics 87\u003c\/p\u003e \u003cp\u003eCultural Connections 96\u003c\/p\u003e \u003cp\u003eA Glance at Where We’ve Been 97\u003c\/p\u003e \u003cp\u003eThings to Do: From What You’ve Read 98\u003c\/p\u003e \u003cp\u003eThings to Do: Going Beyond This Book 98\u003c\/p\u003e \u003cp\u003eBook Nook for Children 99\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 6 Helping Children with Problem Solving 100\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eSnapshot of a Lesson 100\u003c\/p\u003e \u003cp\u003eChapter Learning Outcomes 100\u003c\/p\u003e \u003cp\u003eIntroduction 101\u003c\/p\u003e \u003cp\u003eWhat is a Problem and What is Problem Solving? 101\u003c\/p\u003e \u003cp\u003eTeaching Mathematics Through Problem Solving 103\u003c\/p\u003e \u003cp\u003eStrategies for Problem Solving 112\u003c\/p\u003e \u003cp\u003eThe Importance of Looking Back 119\u003c\/p\u003e \u003cp\u003eHelping All Students with Problem Solving 120\u003c\/p\u003e \u003cp\u003eCultural Connections 121\u003c\/p\u003e \u003cp\u003eA Glance at Where We’ve Been 123\u003c\/p\u003e \u003cp\u003eThings to Do: From What You’ve Read 123\u003c\/p\u003e \u003cp\u003eThings to Do: Going Beyond This Book 123\u003c\/p\u003e \u003cp\u003eBook Nook for Children 124\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 7 Developing Counting and Number Sense 125\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eSnapshot of a Lesson 125\u003c\/p\u003e \u003cp\u003eChapter Learning Outcomes 125\u003c\/p\u003e \u003cp\u003eIntroduction 125\u003c\/p\u003e \u003cp\u003eNumber Sense 125\u003c\/p\u003e \u003cp\u003ePrenumber Concepts 127\u003c\/p\u003e \u003cp\u003eEarly Number Development 131\u003c\/p\u003e \u003cp\u003eCounting Principles 134\u003c\/p\u003e \u003cp\u003eCardinal, Ordinal, and Nominal Numbers 141\u003c\/p\u003e \u003cp\u003eWriting Numerals 141\u003c\/p\u003e \u003cp\u003eCultural Connections 143\u003c\/p\u003e \u003cp\u003eA Glance at Where We’ve Been 144\u003c\/p\u003e \u003cp\u003eThings to Do: From What You’ve Read 145\u003c\/p\u003e \u003cp\u003eThings to Do: Going Beyond This Book 145\u003c\/p\u003e \u003cp\u003eBook Nook for Children 146\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 8 Place Value and Decimals 147 \u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eSnapshot of a Lesson 147\u003c\/p\u003e \u003cp\u003eChapter Learning Outcomes 147\u003c\/p\u003e \u003cp\u003eIntroduction 147\u003c\/p\u003e \u003cp\u003eOur Numeration System 148\u003c\/p\u003e \u003cp\u003eNature of Place Value 149\u003c\/p\u003e \u003cp\u003eBeginning Place Value 152\u003c\/p\u003e \u003cp\u003eExtending Place Value 155\u003c\/p\u003e \u003cp\u003eDecimals 162\u003c\/p\u003e \u003cp\u003eConnecting Decimals to Place Value 163\u003c\/p\u003e \u003cp\u003eRounding 165\u003c\/p\u003e \u003cp\u003eCultural Connections 167\u003c\/p\u003e \u003cp\u003eA Glance at Where We’ve Been 168\u003c\/p\u003e \u003cp\u003eThings to Do: From What You’ve Read 168\u003c\/p\u003e \u003cp\u003eThings to Do: Going Beyond This Book 168\u003c\/p\u003e \u003cp\u003eBook Nook for Children 169\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 9 Operations: Meanings and Basic Facts 170\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eSnapshot of a Lesson 170\u003c\/p\u003e \u003cp\u003eChapter Learning Outcomes 170\u003c\/p\u003e \u003cp\u003eIntroduction 171\u003c\/p\u003e \u003cp\u003eHelping Children Develop Number Sense and Computational Fluency 172\u003c\/p\u003e \u003cp\u003eDeveloping Meanings for the Operations 173\u003c\/p\u003e \u003cp\u003eMathematical Properties 177\u003c\/p\u003e \u003cp\u003eOverview of Basic Fact Instruction 178\u003c\/p\u003e \u003cp\u003eThinking Strategies for Basic Facts 183\u003c\/p\u003e \u003cp\u003eCultural Connections 193\u003c\/p\u003e \u003cp\u003eA Glance at Where We’ve Been 194\u003c\/p\u003e \u003cp\u003eThings to Do: From What You’ve Read 195\u003c\/p\u003e \u003cp\u003eThings to Do: Going Beyond This Book 195\u003c\/p\u003e \u003cp\u003eBook Nook for Children 196\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 10 Computation Methods: Calculators, Mental Computation, and Estimation 197\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eSnapshot of a Lesson 197\u003c\/p\u003e \u003cp\u003eChapter Learning Outcomes 197\u003c\/p\u003e \u003cp\u003eIntroduction 197\u003c\/p\u003e \u003cp\u003eBalancing Your Instruction 198\u003c\/p\u003e \u003cp\u003eCalculators 199\u003c\/p\u003e \u003cp\u003eMental Computation 202\u003c\/p\u003e \u003cp\u003eEstimation 207\u003c\/p\u003e \u003cp\u003eCultural Connections 213\u003c\/p\u003e \u003cp\u003eA Glance at Where We’ve Been 214\u003c\/p\u003e \u003cp\u003eThings to Do: From What You’ve Read 215\u003c\/p\u003e \u003cp\u003eThings to Do: Going Beyond This Book 215\u003c\/p\u003e \u003cp\u003eBook Nook for Children 216\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 11 Standard and Alternative Computational Algorithms 217\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eSnapshot of a Lesson 217\u003c\/p\u003e \u003cp\u003eChapter Learning Outcomes 217\u003c\/p\u003e \u003cp\u003eIntroduction 218\u003c\/p\u003e \u003cp\u003eTeaching Algorithms with Understanding 220\u003c\/p\u003e \u003cp\u003eAddition 221\u003c\/p\u003e \u003cp\u003eSubtraction 225\u003c\/p\u003e \u003cp\u003eMultiplication 228\u003c\/p\u003e \u003cp\u003eDivision 232\u003c\/p\u003e \u003cp\u003eBeyond Learning Computational Algorithms 237\u003c\/p\u003e \u003cp\u003eCultural Connections 238\u003c\/p\u003e \u003cp\u003eA Glance at Where We’ve Been 239\u003c\/p\u003e \u003cp\u003eThings to Do: From What You’ve Read 240\u003c\/p\u003e \u003cp\u003eThings to Do: Going Beyond This Book 240\u003c\/p\u003e \u003cp\u003eBook Nook for Children 241\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 12 Fractions 242\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eSnapshot of a Lesson 242\u003c\/p\u003e \u003cp\u003eChapter Learning Outcomes 242\u003c\/p\u003e \u003cp\u003eIntroduction 242\u003c\/p\u003e \u003cp\u003eBackground Knowledge 243\u003c\/p\u003e \u003cp\u003eMaking Sense of Fractions 245\u003c\/p\u003e \u003cp\u003eExtending Understandings of Fractions 249\u003c\/p\u003e \u003cp\u003eComparing Fractions and Equivalent Fractions 252\u003c\/p\u003e \u003cp\u003eAdding and Subtracting Fractions 256\u003c\/p\u003e \u003cp\u003eMultiplying and Dividing Fractions 258\u003c\/p\u003e \u003cp\u003eCultural Connections 261\u003c\/p\u003e \u003cp\u003eA Glance at Where We’ve Been 261\u003c\/p\u003e \u003cp\u003eThings to Do: From What You’ve Read 262\u003c\/p\u003e \u003cp\u003eThings to Do: Going Beyond This Book 262\u003c\/p\u003e \u003cp\u003eBook Nook for Children 262\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 13 Ratio, Proportion, and Percent: Meanings and Applications 263\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eSnapshot of a Lesson 263\u003c\/p\u003e \u003cp\u003eChapter Learning Outcomes 263\u003c\/p\u003e \u003cp\u003eIntroduction 263\u003c\/p\u003e \u003cp\u003eRatios 264\u003c\/p\u003e \u003cp\u003eProportions 267\u003c\/p\u003e \u003cp\u003ePercents 271\u003c\/p\u003e \u003cp\u003eCultural Connections 277\u003c\/p\u003e \u003cp\u003eA Glance at Where We’ve Been 277\u003c\/p\u003e \u003cp\u003eThings to Do: From What You’ve Read 278\u003c\/p\u003e \u003cp\u003eThings to Do: Going Beyond This Book 278\u003c\/p\u003e \u003cp\u003eBook Nook for Children 279\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 14 Algebraic Thinking 280\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eSnapshot of a Lesson 280\u003c\/p\u003e \u003cp\u003eChapter Learning Outcomes 280\u003c\/p\u003e \u003cp\u003eIntroduction 280\u003c\/p\u003e \u003cp\u003eProblems, Patterns, and Relations 281\u003c\/p\u003e \u003cp\u003eLanguage and Symbols of Algebra 287\u003c\/p\u003e \u003cp\u003eRepresenting, Generalizing, and Justifying 289\u003c\/p\u003e \u003cp\u003eAnother Look at Representing, Generalizing, and Justifying 297\u003c\/p\u003e \u003cp\u003eCultural Connections 298\u003c\/p\u003e \u003cp\u003eA Glance at Where We’ve Been 299\u003c\/p\u003e \u003cp\u003eThings to Do: From What You’ve Read 299\u003c\/p\u003e \u003cp\u003eThings to Do: Going Beyond This Book 299\u003c\/p\u003e \u003cp\u003eBook Nook for Children 300\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 15 Geometry 301\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eSnapshot of a Lesson 301\u003c\/p\u003e \u003cp\u003eChapter Learning Outcomes 301\u003c\/p\u003e \u003cp\u003eIntroduction 301\u003c\/p\u003e \u003cp\u003eThree-Dimensional Shapes 303\u003c\/p\u003e \u003cp\u003eTwo-Dimensional Shapes 309\u003c\/p\u003e \u003cp\u003eSpace 317\u003c\/p\u003e \u003cp\u003eTransformations 319\u003c\/p\u003e \u003cp\u003eVisualization and Spatial Reasoning 320\u003c\/p\u003e \u003cp\u003eCultural Connections 323\u003c\/p\u003e \u003cp\u003eA Glance at Where We’ve Been 323\u003c\/p\u003e \u003cp\u003eThings to Do: From What You’ve Read 323\u003c\/p\u003e \u003cp\u003eThings to Do: Going Beyond This Book 324\u003c\/p\u003e \u003cp\u003eBook Nook for Children 324\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 16 Measurement 325\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eSnapshot of a Lesson 325\u003c\/p\u003e \u003cp\u003eChapter Learning Outcomes 325\u003c\/p\u003e \u003cp\u003eIntroduction 325\u003c\/p\u003e \u003cp\u003eThe Measurement Process 326\u003c\/p\u003e \u003cp\u003eOther Aspects of Measuring 340\u003c\/p\u003e \u003cp\u003eConnecting Attributes 344\u003c\/p\u003e \u003cp\u003eCultural Connections 346\u003c\/p\u003e \u003cp\u003eA Glance at Where We’ve Been 347\u003c\/p\u003e \u003cp\u003eThings to Do: From What You’ve Read 347\u003c\/p\u003e \u003cp\u003eThings to Do: Going Beyond This Book 347\u003c\/p\u003e \u003cp\u003eBook Nook for Children 348\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 17 Data Analysis, Statistics, and Probability 349\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eSnapshot of a Lesson 349\u003c\/p\u003e \u003cp\u003eChapter Learning Outcomes 349\u003c\/p\u003e \u003cp\u003eIntroduction 349\u003c\/p\u003e \u003cp\u003eFormulating Questions 351\u003c\/p\u003e \u003cp\u003eCollecting Data 353\u003c\/p\u003e \u003cp\u003eAnalyzing Data: Graphical Organization 354\u003c\/p\u003e \u003cp\u003eMisleading Graphs 361\u003c\/p\u003e \u003cp\u003eAnalyzing Data: Descriptive Statistics 363\u003c\/p\u003e \u003cp\u003eInterpreting Results 368\u003c\/p\u003e \u003cp\u003eProbability 369\u003c\/p\u003e \u003cp\u003eProbability of an Event 370\u003c\/p\u003e \u003cp\u003eRandomness 373\u003c\/p\u003e \u003cp\u003eCultural Connections 374\u003c\/p\u003e \u003cp\u003eA Glance at Where We’ve Been 375\u003c\/p\u003e \u003cp\u003eThings to Do: From What You’ve Read 375\u003c\/p\u003e \u003cp\u003eThings to Do: Going Beyond This Book 376\u003c\/p\u003e \u003cp\u003eBook Nook for Children 377\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 18 Number Theory 378\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eSnapshot of a Lesson 378\u003c\/p\u003e \u003cp\u003eChapter Learning Outcomes 378\u003c\/p\u003e \u003cp\u003eIntroduction 378\u003c\/p\u003e \u003cp\u003eNumber Theory in Elementary School Mathematics 381\u003c\/p\u003e \u003cp\u003eDivisibility 387\u003c\/p\u003e \u003cp\u003eOther Number Theory Topics 389\u003c\/p\u003e \u003cp\u003eCultural Connections 393\u003c\/p\u003e \u003cp\u003eA Glance at Where We’ve Been 393\u003c\/p\u003e \u003cp\u003eThings to Do: From What You’ve Read 394\u003c\/p\u003e \u003cp\u003eThings to Do: Going Beyond This Book 394\u003c\/p\u003e \u003cp\u003eBook Nook for Children 394\u003c\/p\u003e \u003cp\u003eReferences 395\u003c\/p\u003e \u003cp\u003eAppendix 407\u003c\/p\u003e \u003cp\u003eIndex 409\u003c\/p\u003e \u003cb\u003eRobert E. Reys\u003c\/b\u003e began his career as a mathematics teacher at Horton Watkins High School in Ladue, Missouri. He has taught mathematics education courses at the University of Missouri since 1966. He has also been a visiting professor in Georgia, Canada, and Japan and was a Fulbright Fellow in Mexico and Sweden. Reys's work has earned him a widely recognized international reputation.","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47989356593381,"sku":"NP9781118654101","price":152.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781118654101.jpg?v=1761783796","url":"https:\/\/k12savings.com\/es\/products\/helping-children-learn-mathematics-isbn-9781118654101","provider":"K12savings","version":"1.0","type":"link"}