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Strategies for Teaching Fractions

Using Error Analysis for Intervention and Assessment

David B. Spangler outlines powerful diagnostic and NCTM- and Common Core State Standards-aligned RTI strategies for analyzing student errors and provides specific interventions for each error pattern.

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Product Details
  • Grade Level: 3-8
  • ISBN: 9781412993982
  • Published By: Corwin
  • Year: 2011
  • Page Count: 248
  • Publication date: November 27, 2012
Price: $43.95
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Description

Any way you slice it, fractions are foundational

Many students struggle with fractions and must understand them before learning higher-level math. Veteran educator David B. Spangler provides research-based tools that are aligned with NCTM and Common Core State Standards. He describes powerful diagnostic methods for error analysis that pinpoint specific student misconceptions and supplies specific intervention strategies and activities for each error pattern. Also included are tools for analyzing student work and providing timely, specific, and meaningful interventions within an RTI framework.The targeted interventions for each error pattern promote teaching for conceptual understanding and are supported bydocumented academic research.Practical materials include:

  • Reproducibles for diagnostic tests
  • Practice pages for exercises keyed to the diagnostic tests and error patterns
  • Pages for practicing alternative algorithms and estimation
  • Teacher resources for hands-on activities, game sheets and pieces, and more
  • Worksheets, answer keys, and online resources

Each main unit, along with the sections on academic research and "Big Ideas," concludes with a set of teacher reflection questions for use in a professional development setting. Get ready, get set, and help your students tackle fractions with confidence!

Author(s)

David B. Spangler photo

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

Big Ideas in Fractions and Problem Solving

Unit 1: Fraction Concepts

Unit 2: Addition/Subtraction of Fractions and Mixed Numbers

Unit 3: Multiplication/Division of Fractions and Mixed Numbers

Resources: Worksheets, Activities, and Instructional Games (Blacklines)

Resources for Fraction Concepts

Resources for Addition/Subtraction of Fractions and Mixed Numbers

Resources for Multiplication/Division of Fractions and Mixed Numbers

Answers for Student Materials

References

Technology Resources Online

Reviews

Quote by Katharine Olson, Assistant Superintendent for Curriculum, Instruction, and Assessment, Northbrook School District 27, IL: "This book is an exceptional reference resource that demonstrates the critical importance of error analysis. Students have complex thinking patterns, and error analysis provides a systematic method for exposing the meaning behind students’ mathematical errors. Spangler does an exceptional job of explaining error types and providing instructional strategies to target students’ errors and misconceptions."
"This book is an exceptional reference resource that demonstrates the critical importance of error analysis. Students have complex thinking patterns, and error analysis provides a systematic method for exposing the meaning behind students’ mathematical errors. Spangler does an exceptional job of explaining error types and providing instructional strategies to target students’ errors and misconceptions."
Katharine Olson, Assistant Superintendent for Curriculum, Instruction, and Assessment
Northbrook School District 27, IL
Quote by Jean Krsak, Learning Support Faculty, California State University, Fullerton, CA: “This text would be most useful as part of professional in-service to improve math scores. The information is research based and follows RTI, scaffolding, and differentiation of instruction. It promotes the use of academic language and provides opportunities for the students to transfer their learning. The activities promote active engagement and involvement."
“This text would be most useful as part of professional in-service to improve math scores. The information is research based and follows RTI, scaffolding, and differentiation of instruction. It promotes the use of academic language and provides opportunities for the students to transfer their learning. The activities promote active engagement and involvement."
Jean Krsak, Learning Support Faculty
California State University, Fullerton, CA
Quote by Susan D'Angelo, Gifted Education Teacher, Pineview School for the Gifted, Nokomis, FL:

"If we are truly to help students understand and make sense of working with fractions, then we must find out where their weaknesses are. This book is filled with specific examples to help all teachers to work with students who are struggling with fraction concepts. After reading this book, teachers will feel confident in their abilities to teach fractions so students WILL understand."


 

"If we are truly to help students understand and make sense of working with fractions, then we must find out where their weaknesses are. This book is filled with specific examples to help all teachers to work with students who are struggling with fraction concepts. After reading this book, teachers will feel confident in their abilities to teach fractions so students WILL understand."


 

Susan D'Angelo, Gifted Education Teacher
Pineview School for the Gifted, Nokomis, FL
Quote by Brian Kriz, Middle School Mathematics Teacher, Wood Oaks Jr. High School, Northbrook, IL:

"This is the most complete resource I have ever used for the teaching of fractions. David Spangler does an excellent job of clearly explaining the research and utilizing it to produce activities, practice exercises, diagnostics tests, error pattern explanations and much more."

"This is the most complete resource I have ever used for the teaching of fractions. David Spangler does an excellent job of clearly explaining the research and utilizing it to produce activities, practice exercises, diagnostics tests, error pattern explanations and much more."

Brian Kriz, Middle School Mathematics Teacher
Wood Oaks Jr. High School, Northbrook, IL
Quote by Marcia Carlson, Sixth-Grade Teacher, Crestview Elementary School, Clive, IA: “This text provides a great depth of coverage, an in-depth discussion of the types of errors students may make, and great ideas for rectifying their misunderstanding. I think this could become the ONLY book I’d need on this subject.”
“This text provides a great depth of coverage, an in-depth discussion of the types of errors students may make, and great ideas for rectifying their misunderstanding. I think this could become the ONLY book I’d need on this subject.”
Marcia Carlson, Sixth-Grade Teacher
Crestview Elementary School, Clive, IA

Other Titles in: Mathematics | Student Assessment | Elementary Teaching Methods

Price: $43.95
Volume Discounts applied in Shopping Cart

Review Copies

This book is not available as a review copy.