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Strategies for Teaching Whole Number Computation
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Strategies for Teaching Whole Number Computation
Using Error Analysis for Intervention and Assessment



June 2010 | 224 pages | Corwin

"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.


 
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

“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

"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

“The nuts-and-bolts approach to assessment and error analysis make this a real tool for everyday use in real classrooms."

Judith A. Filkins, K-8 Math Curriculum Coordinator
Lebanon School District, NH

“The comprehensive examples and explanations are exemplary. The book contains a goldmine of information, strategies, and interventions. Most teachers do not have error analysis on their radar—they should, as it is critical for informing instruction and facilitating student learning.”

Katharine Olson, Assistant Superintendent for Curriculum, Instruction, and Assessment
Northbrook Elementary School District 27, IL

"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

"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
Teaching Children Mathematics Magazine, October 2012
Key features
  • The focus on interventions for struggling students makes it ideal for use in an RTI framework
  • Includes many examples of typical error patterns that students make along with interventions that correspond to the errors
  • Covers mathematical problems in the areas of addition, subtraction, multiplication, and division that can be used with elementary students who have varied levels of math knowledge and skills
  • Each unit includes a diagnostic test
  • Author's company, ActiveMath, provides professional development services and workshops to teachers 

For instructors

Select a Purchasing Option

ISBN: 9781412981064
$39.95