Strategies for Teaching Whole Number Computation

Using Error Analysis for Intervention and Assessment
David B. Spangler - ActiveMath
Strategies for Teaching Whole Number Computation
June 2010 | 224 pages | Corwin
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eBook
ISBN: 9781452296340
Available from January 0001
Paperback
ISBN: 9781412981064
Available from January 0001

Description

"This book is a must-have for anyone working to remediate students struggling with math. It gets into the types of misconceptions students have and gives multiple ways to correct them."
—Donna Adkins, First-Grade Teacher
Perritt Primary School, Arkadelphia, AR

"The nuts-and-bolts approach to assessment and error analysis make this book a real tool for everyday use."
—Judith A. Filkins, K–8 Math Curriculum Coordinator
Lebanon School District, NH

A proven approach to mathematics teaching that adds up to student success!

When students make computational errors in mathematics, often the prescribed solution is more drilling. However, by combining error analysis with timely and specific intervention based on conceptual understanding, teachers can get to the cause of students' errors, uncover underlying misconceptions, and help students understand and correct their mistakes. The targeted interventions for each error pattern promote teaching for conceptual understanding and are supported by documented academic research.

David B. Spangler, a school math consultant with more than 35 years of experience, provides a model that focuses on student error patterns in addition, subtraction, multiplication, and division. This book offers targeted instructional strategies based on the five NCTM process standards and includes four units, each containing:

  • A diagnostic test in a multiple-choice format
  • An item analysis table that correlates incorrect test responses with student error patterns
  • A detailed section of supporting intervention activities to address specific types of errors
  • Practice exercises for students, with answer keys
  • Reflection questions for teachers to use in a professional development setting, workshop, or methods course

With supporting research, a section on "big ideas" in computation and problem solving, and student reproducibles for games and activities, Strategies for Teaching Whole Number Computation promotes a proactive and scaffolded approach to teaching mathematics in a meaningful way.

Contents

Preface

Preface

Acknowledgments

Acknowledgments

About the Author

  • A Look at the Academic Research: Intervention in the Mathematics Classroom
  • Introduction to the Academic Research
  • Equity and Quality in the Math Classroom
  • Student Dispositions
  • Activating Prior Knowledge
  • Representations
  • Estimation and Mental Math
  • Alternative Algorithms
  • Differentiating Instruction
  • Instructional Games
  • Response to Intervention
  • Questions for Teacher Reflection
  • Big Ideas in Computation and Problem Solving
  • The Base-Ten Place-Value System and Multidigit Computation
  • Actions and Operations
  • Questions for Teacher Reflection
  • Unit 1. Addition of Whole Numbers
  • Diagnostic Test
  • Item Analysis for Diagnostic Test
  • Error Patterns & Intervention Activities
  • Practice Exercises
  • Questions for Teacher Reflection
  • Unit 2. Subtraction of Whole Numbers
  • Diagnostic Test
  • Item Analysis for Diagnostic Test
  • Error Patterns & Intervention Activities
  • Practice Exercises
  • Questions for Teacher Reflection
  • Unit 3. Multiplication of Whole Numbers
  • Diagnostic Test
  • Item Analysis for Diagnostic Test
  • Error Patterns & Intervention Activities
  • Practice Exercises
  • Questions for Teacher Reflection
  • Unit 4. Division of Whole Numbers
  • Diagnostic Test
  • Item Analysis for Diagnostic Test
  • Error Patterns & Intervention Activities
  • Practice Exercises
  • Questions for Teacher Reflection

Resources for Estimation, Instructional Games, and Follow-Up Activities (Blacklines)

  • Resources for Addition
  • Follow-Up Activity: Next Number, Please
  • Roller Coaster Rounding
  • Using Front-End Estimation to Check for Reasonableness: Addition
  • Instructional Game: Keeping Score in Bowling
  • Resources for Subtraction
  • Using Front-End Estimation to Check for Reasonableness: Subtraction
  • Instructional Game: Balance the +/- Number Sentence!
  • Follow-Up Activity: Editor Error Search (+/-)
  • Instructional Game: Target Math (+/-)
  • Resources for Multiplication
  • Touching on the Facts With Your Fingers
  • Using Front-End Estimation to Check for Reasonableness: Multiplication
  • Instructional Game: How Close Can You Get?
  • Follow-Up Activity: Editor Error Seach (x)
  • Resources for Division
  • Using Front-End Estimation to Check for Reasonableness: Division
  • Using Compatible Numbers to Check for Reasonableness (+, -, x, ÷)
  • Instructional Game: Balance the x/÷ Number Sentence!
  • Follow-Up Activity: Abbott and Costello's Number Nonsense
  • Instructional Game: Target Math (x/÷)
  • Multiuse Resources (Blacklines)
  • Play Money
  • Place-Value Mat for Addition/Subtraction
  • Place-Value Grids for Addition/Subtraction
  • Place-Value Grids for Division
  • Tables for Addition/Subtraction
  • Tables for Multiplication/Division
  • Grid Paper (¼ inch)
  • Answers for Student Materials
  • Answers for Unit 1: Addition of Whole Numbers
  • Answers for Unit 2: Subtraction of Whole Numbers
  • Answers for Unit 3: Multiplication of Whole Numbers
  • Answers for Unit 4: Division of Whole Numbers

References

References

Description

"This book is a must-have for anyone working to remediate students struggling with math. It gets into the types of misconceptions students have and gives multiple ways to correct them."
—Donna Adkins, First-Grade Teacher
Perritt Primary School, Arkadelphia, AR

"The nuts-and-bolts approach to assessment and error analysis make this book a real tool for everyday use."
—Judith A. Filkins, K–8 Math Curriculum Coordinator
Lebanon School District, NH

A proven approach to mathematics teaching that adds up to student success!

When students make computational errors in mathematics, often the prescribed solution is more drilling. However, by combining error analysis with timely and specific intervention based on conceptual understanding, teachers can get to the cause of students' errors, uncover underlying misconceptions, and help students understand and correct their mistakes. The targeted interventions for each error pattern promote teaching for conceptual understanding and are supported by documented academic research.

David B. Spangler, a school math consultant with more than 35 years of experience, provides a model that focuses on student error patterns in addition, subtraction, multiplication, and division. This book offers targeted instructional strategies based on the five NCTM process standards and includes four units, each containing:

  • A diagnostic test in a multiple-choice format
  • An item analysis table that correlates incorrect test responses with student error patterns
  • A detailed section of supporting intervention activities to address specific types of errors
  • Practice exercises for students, with answer keys
  • Reflection questions for teachers to use in a professional development setting, workshop, or methods course

With supporting research, a section on "big ideas" in computation and problem solving, and student reproducibles for games and activities, Strategies for Teaching Whole Number Computation promotes a proactive and scaffolded approach to teaching mathematics in a meaningful way.

Contents

Preface

Preface

Acknowledgments

Acknowledgments

About the Author

  • A Look at the Academic Research: Intervention in the Mathematics Classroom
  • Introduction to the Academic Research
  • Equity and Quality in the Math Classroom
  • Student Dispositions
  • Activating Prior Knowledge
  • Representations
  • Estimation and Mental Math
  • Alternative Algorithms
  • Differentiating Instruction
  • Instructional Games
  • Response to Intervention
  • Questions for Teacher Reflection
  • Big Ideas in Computation and Problem Solving
  • The Base-Ten Place-Value System and Multidigit Computation
  • Actions and Operations
  • Questions for Teacher Reflection
  • Unit 1. Addition of Whole Numbers
  • Diagnostic Test
  • Item Analysis for Diagnostic Test
  • Error Patterns & Intervention Activities
  • Practice Exercises
  • Questions for Teacher Reflection
  • Unit 2. Subtraction of Whole Numbers
  • Diagnostic Test
  • Item Analysis for Diagnostic Test
  • Error Patterns & Intervention Activities
  • Practice Exercises
  • Questions for Teacher Reflection
  • Unit 3. Multiplication of Whole Numbers
  • Diagnostic Test
  • Item Analysis for Diagnostic Test
  • Error Patterns & Intervention Activities
  • Practice Exercises
  • Questions for Teacher Reflection
  • Unit 4. Division of Whole Numbers
  • Diagnostic Test
  • Item Analysis for Diagnostic Test
  • Error Patterns & Intervention Activities
  • Practice Exercises
  • Questions for Teacher Reflection

Resources for Estimation, Instructional Games, and Follow-Up Activities (Blacklines)

  • Resources for Addition
  • Follow-Up Activity: Next Number, Please
  • Roller Coaster Rounding
  • Using Front-End Estimation to Check for Reasonableness: Addition
  • Instructional Game: Keeping Score in Bowling
  • Resources for Subtraction
  • Using Front-End Estimation to Check for Reasonableness: Subtraction
  • Instructional Game: Balance the +/- Number Sentence!
  • Follow-Up Activity: Editor Error Search (+/-)
  • Instructional Game: Target Math (+/-)
  • Resources for Multiplication
  • Touching on the Facts With Your Fingers
  • Using Front-End Estimation to Check for Reasonableness: Multiplication
  • Instructional Game: How Close Can You Get?
  • Follow-Up Activity: Editor Error Seach (x)
  • Resources for Division
  • Using Front-End Estimation to Check for Reasonableness: Division
  • Using Compatible Numbers to Check for Reasonableness (+, -, x, ÷)
  • Instructional Game: Balance the x/÷ Number Sentence!
  • Follow-Up Activity: Abbott and Costello's Number Nonsense
  • Instructional Game: Target Math (x/÷)
  • Multiuse Resources (Blacklines)
  • Play Money
  • Place-Value Mat for Addition/Subtraction
  • Place-Value Grids for Addition/Subtraction
  • Place-Value Grids for Division
  • Tables for Addition/Subtraction
  • Tables for Multiplication/Division
  • Grid Paper (¼ inch)
  • Answers for Student Materials
  • Answers for Unit 1: Addition of Whole Numbers
  • Answers for Unit 2: Subtraction of Whole Numbers
  • Answers for Unit 3: Multiplication of Whole Numbers
  • Answers for Unit 4: Division of Whole Numbers

References

References

SAGE Publishing Logo

Strategies for Teaching Whole Number Computation

Using Error Analysis for Intervention and Assessment


June 2010 | 224 pages | Corwin

Format Published Date ISBN Price
Paperback 27/02/2023 9781412981064 $43.95
Lifetime 27/02/2023 9781452296340 $40.00

"This book is a must-have for anyone working to remediate students struggling with math. It gets into the types of misconceptions students have and gives multiple ways to correct them."
—Donna Adkins, First-Grade Teacher
Perritt Primary School, Arkadelphia, AR

"The nuts-and-bolts approach to assessment and error analysis make this book a real tool for everyday use."
—Judith A. Filkins, K–8 Math Curriculum Coordinator
Lebanon School District, NH

A proven approach to mathematics teaching that adds up to student success!

When students make computational errors in mathematics, often the prescribed solution is more drilling. However, by combining error analysis with timely and specific intervention based on conceptual understanding, teachers can get to the cause of students' errors, uncover underlying misconceptions, and help students understand and correct their mistakes. The targeted interventions for each error pattern promote teaching for conceptual understanding and are supported by documented academic research.

David B. Spangler, a school math consultant with more than 35 years of experience, provides a model that focuses on student error patterns in addition, subtraction, multiplication, and division. This book offers targeted instructional strategies based on the five NCTM process standards and includes four units, each containing:

  • A diagnostic test in a multiple-choice format
  • An item analysis table that correlates incorrect test responses with student error patterns
  • A detailed section of supporting intervention activities to address specific types of errors
  • Practice exercises for students, with answer keys
  • Reflection questions for teachers to use in a professional development setting, workshop, or methods course

With supporting research, a section on "big ideas" in computation and problem solving, and student reproducibles for games and activities, Strategies for Teaching Whole Number Computation promotes a proactive and scaffolded approach to teaching mathematics in a meaningful way.


Table Of Contents:

  • Preface
  • Acknowledgments
  • About the Author
  • A Look at the Academic Research: Intervention in the Mathematics Classroom
  • Introduction to the Academic Research
  • Equity and Quality in the Math Classroom
  • Student Dispositions
  • Activating Prior Knowledge
  • Representations
  • Estimation and Mental Math
  • Alternative Algorithms
  • Differentiating Instruction
  • Instructional Games
  • Response to Intervention
  • Questions for Teacher Reflection
  • Big Ideas in Computation and Problem Solving
  • The Base-Ten Place-Value System and Multidigit Computation
  • Actions and Operations
  • Questions for Teacher Reflection
  • Unit 1. Addition of Whole Numbers
  • Diagnostic Test
  • Item Analysis for Diagnostic Test
  • Error Patterns & Intervention Activities
  • Practice Exercises
  • Questions for Teacher Reflection
  • Unit 2. Subtraction of Whole Numbers
  • Diagnostic Test
  • Item Analysis for Diagnostic Test
  • Error Patterns & Intervention Activities
  • Practice Exercises
  • Questions for Teacher Reflection
  • Unit 3. Multiplication of Whole Numbers
  • Diagnostic Test
  • Item Analysis for Diagnostic Test
  • Error Patterns & Intervention Activities
  • Practice Exercises
  • Questions for Teacher Reflection
  • Unit 4. Division of Whole Numbers
  • Diagnostic Test
  • Item Analysis for Diagnostic Test
  • Error Patterns & Intervention Activities
  • Practice Exercises
  • Questions for Teacher Reflection
  • Resources for Estimation, Instructional Games, and Follow-Up Activities (Blacklines)
  • Resources for Addition
  • Follow-Up Activity: Next Number, Please
  • Roller Coaster Rounding
  • Using Front-End Estimation to Check for Reasonableness: Addition
  • Instructional Game: Keeping Score in Bowling
  • Resources for Subtraction
  • Using Front-End Estimation to Check for Reasonableness: Subtraction
  • Instructional Game: Balance the +/- Number Sentence!
  • Follow-Up Activity: Editor Error Search (+/-)
  • Instructional Game: Target Math (+/-)
  • Resources for Multiplication
  • Touching on the Facts With Your Fingers
  • Using Front-End Estimation to Check for Reasonableness: Multiplication
  • Instructional Game: How Close Can You Get?
  • Follow-Up Activity: Editor Error Seach (x)
  • Resources for Division
  • Using Front-End Estimation to Check for Reasonableness: Division
  • Using Compatible Numbers to Check for Reasonableness (+, -, x, ÷)
  • Instructional Game: Balance the x/÷ Number Sentence!
  • Follow-Up Activity: Abbott and Costello's Number Nonsense
  • Instructional Game: Target Math (x/÷)
  • Multiuse Resources (Blacklines)
  • Play Money
  • Place-Value Mat for Addition/Subtraction
  • Place-Value Grids for Addition/Subtraction
  • Place-Value Grids for Division
  • Tables for Addition/Subtraction
  • Tables for Multiplication/Division
  • Grid Paper (¼ inch)
  • Answers for Student Materials
  • Answers for Unit 1: Addition of Whole Numbers
  • Answers for Unit 2: Subtraction of Whole Numbers
  • Answers for Unit 3: Multiplication of Whole Numbers
  • Answers for Unit 4: Division of Whole Numbers
  • References

Recent Product Reviews:

"This well-designed handbook is for educators whose students struggle with arithmetic operations. It offers valuable assistance to tutors, special educators, and classroom teachers."
Sally Moomaw, University of Cincinnati, Ohio
"A wonderful addition to any professional library. All too often when a student makes a computational error, the prescribed remediation is further drilling. Based on recognized cognitive research, this book provides a model that helps the teacher analyze student work for error patterns and then provide timely, targeted, and meaningful intervention. This book provides well-organized, comprehensive strategies to meet the learning needs of all students."
Hope Martin, Author/Consultant, ActiveMath Workshop
"Highly recommended for all K-8 teachers to help all students learn math and be successful! Spangler captures the essence of teaching mathematics to all children through the Response to Intervention focus. This is a very practical and useful math resource for all teachers, including general education teachers as well as special educators."
Edna F. Bazik, Mathematics Education Program Coordinator, National-Louis University
“I can see this book becoming a very important and seminal piece in mathematics instruction and teaching practice. It allows the instructor to take a proactive and scaffolded approach for teaching students experiencing difficulties in mathematics, and it builds upon the mathematical knowledge of the teacher."
Cathy Patterson, Assistant Principal, Evergreen Elementary School, Diamond Bar, CA
“This book is a must-have for anyone working to remediate students struggling with math. It gets into the types of mistakes/misconceptions students have and gives multiple ways to correct them. It is also a great resource for teachers who need a stronger math background."
Donna Adkins, First-Grade Teacher, Perritt Primary School, Arkadelphia, AR

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