About teaching mathematics : a K-8 resource

Burns, Marilyn 1941- (author.).

Summary: In this fourth edition of her signature resource, Marilyn presents her current thinking and insights and includes ideas from her most recent teaching experiences. Part 1, Starting Points, reflects the major overhaul of this book and addresses twenty-three issues important to thinking about teaching mathematics today. Part 2, Problem-Solving Investigations, opens with how to plan problem-solving lessons; followed by whole-class, small-group, and individual investigations organized into five areas of the curriculum: Measurement, Data, Geometry, Patterns and Algebraic Thinking, and Number and Operations. Part 3, Teaching Arithmetic, focuses on the cornerstone of elementary mathematics curriculum, offering ideas and assessments that build students understanding, confidence, and competence in arithmetic. In Part 4, Questions Teachers Ask, features Marilyn's responses to pedagogical questions she's received from teachers over the years.

Record details

ISBN: 1935099329
ISBN: 9781935099321
Physical Description: print
xxix, 506 pages ; illustrations (some color) ; 28 cm
Edition: Fourth edition.
Publisher: Sausalito, California : Math Solutions, [2015]

Content descriptions

Bibliography, etc. Note:

Includes bibliographical references (pages 497-498) and index.

Formatted Contents Note:

Machine generated contents note: pt. 1 Starting Points -- Overview -- General Pedagogical Issues -- Starting Point 1 Getting Started: Connecting Content, Practices, and Instruction -- Starting Point 2 Uncovering the Curriculum -- Starting Point 3 You Can't Teach What You Don't Understand -- Starting Point 4 Helping Students Become Effective Math Learners -- Number and Operations: The Mathematical Cornerstone -- Starting Point 5 Reasoning: A Perspective on Arithmetic -- Starting Point 6 Why Do Students Make Common Arithmetic Errors? -- Starting Point 7 Equal Sign: What It Really Means -- Starting Point 8 Word Problems: Developing Understanding of Arithmetic Operations -- From Arithmetic to Problem Solving -- Starting Point 9 From Word Problems to Problem Solving: A Broader View -- Starting Point 10 Tackling Problem-Solving Strategies and Issues -- Starting Point 11 Building Number Sense -- Starting Point 12 Developing Mental Math Skills -- Assessing Understanding and Skills -- Starting Point 13 Making Formative Assessment Integral to Instruction -- Starting Point 14 Importance of Classroom Discussions -- Starting Point 15 Incorporating Writing into Math Instruction -- Starting Point 16 Benefits of One-on-One Interviews -- Suggestions for Classroom Instruction -- Starting Point 17 Using Games in Math Class -- Starting Point 18 Role of Manipulative Materials -- Starting Point 19 Strategies for Intervention Instruction -- Starting Point 20 Four Structures for Organizing and Managing Classroom Instruction -- Connecting to English Language Arts Instruction -- Starting Point 21 Building a Teaching Bridge from Reading to Math -- Starting Point 22 Teaching Math Vocabulary -- Starting Point 23 Using Children's Literature to Teach Math -- pt. 2 Problem-Solving Investigations -- Overview -- Planning Whole-Class Lessons with Problem-Solving Investigations -- Three-Phase Structure for Planning Lessons -- Introducing -- Exploring -- Summarizing -- Sample Lesson Using the Three-Phase Structure -- Consecutive Sums Problem -- Planning Lessons Using the Three-Phase Structure Template -- Problem-Solving Investigations: Measurement -- Why Teach Measurement? -- Stages in Learning About Measurement -- Mathematical Practices -- Mathematical Content -- Sample Whole-Class Lessons -- Nonstandard Measuring Investigation (Body Ratios) -- Measuring with Standard Units (Introducing the Metric System) -- Additional Investigations for Whole-Class Lessons -- Round Things -- Perimeter Stays the Same -- Independent Investigations -- Longer, Shorter, or About the Same -- Are You a Square? -- Half-Size Me -- Index Card Portrait -- Statue of Liberty Measurements -- Practicing Measuring -- Writing a Measurement Story -- Foot Measuring #1: Foot Cutout -- Foot Measuring #2: Area and Perimeter -- Foot Measuring #3: Squaring Up -- Standing Broad Jumps -- Book Measuring -- Box Measuring -- Your Height in Money -- How Thick Is Paper? -- Wraparound -- How Long Is a Minute? -- Ratio with Cuisenaire Rods -- Yarn Shapes -- Perimeter with Cuisenaire Rods -- Double the Circumference -- Area Stays the Same -- Problem-Solving Investigations: Data -- Why Teach Data? -- Stages in Learning About Data -- Mathematical Practices -- Mathematical Content -- Sample Whole-Class Lessons -- Spinner Experiments -- Graphing in the Classroom -- Additional Investigations for Whole-Class Lessons -- Junk Sorting -- Tiles in the Bag (Version 1) -- Tiles in the Bag (Version 2) -- Sampling Bean Populations -- 1-2-3-4 Investigation -- Alphabetical Probability -- Independent Investigations -- Two-Person Spin -- Design Your Own Spinner -- Got a Match? -- Birthday Twins -- Left-Handed Experiment -- X-O Problem -- Two-Dice Sum Game -- How Many Throws? -- How Many Ways? -- How Many Rolls to Get a 1? -- What's the Record? -- Fair Game---Even and Odd Sums -- Tile Trading -- Shake and Peek -- Shake and Spill -- Two-Coin Toss -- Game of Pig -- Fair Game---Paper, Scissors, Rock -- Popcorn Problem -- Problem-Solving Investigations: Geometry -- Why Teach Geometry? -- Stages in Learning About Geometry -- Mathematical Practices -- Mathematical Content -- Sample Whole-Class Lessons -- Pentominoes -- Four-Triangle Problem -- Additional Investigations for Whole-Class Lessons -- Introductory Investigations with Pattern Blocks -- Tangram Puzzle -- Investigations with Four Toothpicks -- Introductory Investigations with Geoboards -- Sorting Shapes on the Geoboard -- Independent Investigations -- No-Lift Letters -- Area and Perimeter -- Square Partitioning -- Penticubes -- Banquet Table Problem -- Interior Regions -- Straight or Curved? -- Geometry Building -- Extending Metric Lengths to Volume and Capacity -- Pool Hall Math -- That's Just Half the Story -- More Geoboard Investigations -- Area on the Geoboard -- Geoboard Line Segments -- Areas of Four on the Geoboard -- Pick's Theorem -- Shape Construction on the Geoboard -- Geoboard Square Search -- Geoboard Triangle Search -- Square Up -- Mirror Cards -- Fold-and-Cut Investigation -- Rotating Shapes -- Hexagon Fill-in Puzzle -- Hexiamonds -- Angles with Pattern Blocks and Hinged Mirrors -- Making Topless Boxes -- Pentomino Game -- Pentomino One-Difference Loop -- Problem-Solving Investigations: Patterns and Algebraic Thinking -- Why Teach Patterns and Algebraic Thinking? -- Stages in Learning About Patterns and Algebraic Thinking -- Mathematical Practices -- Mathematical Content -- Sample Whole-Class Lessons -- Two of Everything -- Painting Towers -- Additional Investigations for Whole-Class Lessons or Independent Work -- Paper Folding -- Dot Connecting -- More Painting Towers -- Paper Tearing -- Diagonal Problem -- Points Dividing a Line -- Ice-Cream-Cone Problem -- Squares from Squares -- More Squares from Squares -- Rod Stamping -- More Rod Stamping -- Row of Triangles -- Row of Squares -- Row of Hexagons -- Row of Pentagons -- Interlocking Trains -- Toothpick Building -- Handshake Problem -- Problem-Solving Investigations: Number and Operations -- Why Teach Number and Operations? -- Stages in Learning About Number and Operations -- Mathematical Practices -- Mathematical Content -- Sample Whole-Class Lessons -- Number Sums -- Palindromes -- Additional Investigations for Whole-Class Lessons -- Investigations with Raisins -- Coin Riddles -- Border Problem -- Game of Poison -- Decision Making -- Riddles with Tiles -- Independent Investigations -- Making Change -- How Many Sums? -- Change from a $10.00 Bill -- Multiplication Possibilities -- Postage Stamp Investigation -- Arrow Arithmetic -- King Arthur's Problem -- Prison Problem -- Race for 20 -- Number Bracelets -- 0--99 Chart -- Pascal's Triangle -- Addition Table Investigations -- Where Does 100 Land? -- On Which Day of the Week Were You Born? -- Sally and the Peanuts -- Number Sorting -- Mathematical Tug-of-War -- Digit Place -- pt. 3 Teaching Arithmetic -- Overview -- Arithmetic: The Three-Legged Stool -- About the Three-Legged Stool -- Computation -- Problem Solving -- Number Sense -- Putting It All Together -- Teaching What to Do (Procedures) Versus Teaching What to Do and Why (Procedures and Understanding) -- Justifications for Teaching What to Do (Procedures) -- Justifications for Teaching What to Do and Why (Procedures and Understanding) -- Role of Algorithms -- Teaching Arithmetic: Scenarios from the Classroom -- Scenario 1 Fourth Graders Solve 19 x 21 -- Scenario 2 Fifth Graders Solve 47 x 23 -- Scenario 3 Study with Fourth, Fifth, and Sixth Graders -- Scenario 4 Third Graders Learn Division -- Scenario 5 Seventh and Eighth Graders Work with Percents -- Relating Arithmetic to Real Life -- Real-Life Arithmetic Problem: The Thanksgiving Turkey -- Real-Life Arithmetic Problem: Raising a Dog -- Other Examples of Real-Life Arithmetic Problems: Classroom or School Situations -- Beginning Number Concepts -- About Beginning Number Concepts -- Mathematical Practices -- Mathematical Content -- Whole-Class Instruction -- Creating Math Moments -- Number Game: Red + Black -- Number Game: Empty the Bowl -- Introducing Addition and Subtraction with Word Problems -- Problem-Solving Lesson: Making Necklaces -- Using Children's Literature -- Additional Instructional Suggestions -- Build a Stack -- Snap It -- Grow and Shrink -- Yarn Shapes -- Trace and Compare -- Grab-Bag Subtraction -- Assessing Understanding of Beginning Number Concepts -- Observing Students -- Individual Assessments -- Place Value -- About Place Value -- Mathematical Practices -- Mathematical Content -- Whole-Class Instruction -- Problem-Solving Lesson: How Many Fingers? -- Problem-Solving Lesson: How Many Pockets? -- Additional Counting Investigations -- Money Game: Race for $1.00 -- Logic Game: Digit Place -- Patterns on the 0--99 Chart -- Additional Instructional Suggestions -- Stars in 1 Minute -- Fill the Cube (Version 1) -- Number Puzzle -- Five-Tower Game -- Pinch a 10 -- Make a Shape -- Coloring 0--99 Patterns -- Assessing Understanding of Place Value -- Observing Students -- Individual Assessments -- Addition and Subtraction -- About Addition and Subtraction -- Mathematical Practices -- Mathematical Content -- Whole-Class Instruction -- Statistical Investigation: Name Graphs -- Problem-Solving Lesson: How Much Ribbon? -- Problem-Solving Lesson: How Big Is Your Hand? -- Number Game: Roll 15 --