1st Edition

Creating a Language-Rich Math Class
Strategies and Activities for Building Conceptual Understanding

ISBN 9781138916296
Published October 6, 2015 by Routledge
135 Pages 106 B/W Illustrations

USD $29.95

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Book Description

What meanings do your students have for key mathematics concepts? What meanings do you wish them to have? Creating a Language-Rich Math Class offers practical approaches for developing conceptual understandings by connecting concrete, pictorial, verbal, and symbolic representations. The focus is on making mathematics memorable instead of on memorizing.

You’ll learn strategies for introducing students to math language that gives meaning to the terms and symbols they use everyday; for building flexibility and precision in students’ use of math language; and for structuring activities to make them more language-rich.

Book Features:

    • Detailed directions for sample games and activities for immediate classroom use;
    • Investigations to Try and Questions for Reflection to assist in implementing these ideas into your practice;
    • Graphic organizer for helping students first understand, solve, and defend their solutions to word problems;
    • Blackline masters of game cards and puzzles (also available at http://www.routledge.com/books/details/9781138916296/)

Table of Contents


About the Author


Introduction: Language? It’s Mathematics!

Chapter 1: What Are They Really Thinking? Determining the Meaning Kids Have for Terms

Chapter 2: Investigating Symbolic Decoding vs. Conceptual Language

Chapter 3: Understanding the Meaning of the Operations


    • Partitive Division (Partitioning)
    • Quotitive Division (Quotitioning)


    • Equal Grouping Model
    • Array Model
    • Area Model
    • Scaling


    • Removal
    • Comparison
    • Difference as Distance


    • Joining
    • Part-Part-Total

Chapter 4: Tips for Creating a Language-Rich Math Class

Consider Sitting Down

Are you sure? How did you get your answer?

Don’t Be the Answer Key

Ask a question to help them change their mind

Think, Pair, Share—Tell me what your partner said

Have students use four representations (Concrete, Pictorial, Verbal, Symbolic) whenever possible

Conceptual Language versus Symbolic Decoding

Building and Using Language

Chapter 5: Purposefully Choose and Use Materials


Ten Frame Domino Match

Increasing the Cognitive Demand of the Experience

Combinations for Ten

Using materials to build conceptual understandings

Chapter 6: Changing the Order for Introducing Mathematical Language: Experience then Name

Experience First—A Look at Symmetry

Area Investigations

Chapter 7: Structuring Activities to Make Language-Rich

Tangram Communication Activity

Memory or Concentration Type Activities

Chapter 8: Building Precision and Flexibility in Using Mathematical Language

Chapter 9: Making Sense of Word Problems: Developing Independent Problem Solvers

Beware of Key Words

Building Independent Problem Solvers

Problem Solving Graphic Organizer

The Word Problem Solving Process

Sample Problem 1—Introducing the Process

Debriefing Problems—Sample Problem 2

Sample Problem 3—Don’t let your past interfere with the students’ problem solving

Conclusion: Giving students the Gift of Time

Blackline Masters

Ten Frame Dominos

Sample Concentration Game Cards

Tangram Piece Master

Sample Tangram Puzzles

Sample "I Have…Who Has?" Cards

Word Problem Graphic Organizer

Sample Word Problems


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Sandra L. Atkins is committed to finding those ‘AHA moments’ when mathematical connections are made by teachers and students. She currently works with school districts across the United States through her company, Creating AHAs.


"Having worked with Dr. Atkins in an elementary math classroom, I observed how her approach built conceptual understandings and mathematical connections for students. These practices build the foundation for true mathematical proficiency." --Dana McCauley, Ed.D., Teaching Principal, Crellin Elementary School, MD

"If you want to get to the root cause of students’ misconceptions, misunderstandings and disconnects associated with their mathematical thinking, this book is your go-to-guide. This powerful resource doesn’t offer rules, gimmicks, or tricks to help in sustaining students understanding, but rather provides clear and precise strategies and investigations that will help with creating and navigating a language-rich classroom. The use of this well-organized and detailed book will certainly result in learning for all stakeholders in the classroom, students as well as teachers." --Melinda Hamilton, Instructional Coach of Professional Development Services and Former Secondary Math Teacher of Orange County Public Schools, FL

"This book shows the importance of listening--really listening--to what students tell us are their understandings of mathematics. The strategies Dr. Atkins shares for gaining this important information are described in such detail that it’s easy to envision using them. I’ll recommend this easy read to teachers often in the coming years." --Lori Williams, Ph.D., K-12 Math Specialist, Manitowoc Public School District, WI

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