Strategies for Teaching Whole Number Computation

David B. Spangler is the recipient of the 2014 Lee E. Yunker Mathematics Leadership Award, sponsored by the Illinois Council of Teachers of Mathematics. The award honors an Illinois teacher for providing outstanding resources to mathematics teachers. David has devoted his professional career of more than 40 years to mathematics education. He began as a middle-school mathematics teacher in an individualized setting. Later he taught at Triton Community College, where he gained direct experience interacting with struggling students in a developmental math laboratory. Currently he teachers mathematics methods courses through National-Louis University and ActiveMath Workshops, a professional development company he co-founded in 1994 (activemath.com). Some of the methods courses and workshops he facilitates address special needs students, intervention, computation, and error analysis at the elementary level. His workshops are designed to help teachers implement the Common Core State Standards for Mathematics. David has literally worked with thousands of students and teachers during his career. For many years David has worked as a mathematics textbook editor at the K-12 level. He has authored several books and has written numerous articles for mathematics journals, such as the popular "Cartoon Corner" for Mathematics Teaching in the Middle School. As an educator, David's goal has always been to teach mathematics for meaning rather than in a way that promotes rote memorization. Strategies for Teaching Whole Number Computation and Strategies for Teaching Fractions were written to help teachers achieve that goal. David's other professional goals include exploring ways to teach mathematics through engaging, real-world applications and to explore humorous aspects to mathematics, especially mathematical blunders that illustrate mathematics illiteracy. David is a frequent speaker at conferences of the National Council of Teachers of Mathematics and other professional organizations, addressing teaching mathematics for meaning, teaching mathematics through real-world applications, and teaching mathematics through humor. He also delivers after-dinner talks on the subject of mathematical humor. David lives with his wife, Bonnie, in Northbrook, Illinois. They have three grown children, Ben, Jamie, and Joey.

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 (1/4 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 "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 "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 "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 "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 "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 "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 * Teaching Children Mathematics Magazine, October 2012 *