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:
eResources
About the Author
Acknowledgments
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
Division
- Partitive Division (Partitioning)
- Quotitive Division (Quotitioning)
Multiplication
- Equal Grouping Model
- Array Model
- Area Model
- Scaling
Subtraction
- Removal
- Comparison
- Difference as Distance
Addition
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
Subitizing
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
About the Author :
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.
Review :
"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
