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Strategies for Teaching Whole Number Computation

Using Error Analysis for Intervention and Assessment

By: David B. Spangler

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

This comprehensive resource helps elementary teachers uncover the misconceptions behind students' errors and help students understand and correct their own mistakes. The text's interventions for each error pattern promote teaching for conceptual understanding and are supported by documented academic research. Included are units for addition, subtraction, multiplication, and division, 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
Open-ended reflection questions for teachers

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Product Details

Grade Level: 2-5
ISBN: 9781412981064
Published By: Corwin
Year: 2010
Page Count: 224
Publication date: April 10, 2014

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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.

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

Author(s)

David B. Spangler

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.

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