Teaching and Learning Algebraic Thinking with 5- to 12-Year-Olds

Part I. Theoretical Perspectives for Developing Early Algebraic Thinking

1. The Emergence of Symbolic Algebraic Thinking in Primary School
Luis Radford

2. Implementing a Framework for Early Algebra
Maria Blanton, Bárbaras M. Brizuela, Ana Stephens, Eric Knuth, Isil Isler, Angela Murphy Gardiner, Rena Stroud, Nicole L. Fonger, Despina Stylianou

3. New Words and Concepts for Early Algebra Teaching: Sharing with Teachers Epistemological Issues in Early Algebra to Develop Students’ Early Algebraic Thinking
Nicolina A. Malara, Giancarlo Navarra

4. Seeking, Using, and Expressing Structure in Numbers and Numerical Operations: A Fundamental Path to Developing Early Algebraic Thinking
Carolyn Kieran

5. Cultivating Early Algebraic Thinking
David W. Carraher, Analúcia D. Schliemann

Part II. Learning to Think Algebraically in Primary and Lower Middle School

6. Characteristics of Korean Students’ Early Algebraic Thinking: A Generalized Arithmetic Perspective
JeongSuk Pang, JeongWon Kim

7. Function Tasks, Input, Output, and the Predictive Rule: How Some Singapore Primary Children Construct the Rule
Swee Fong Ng

8. Algebraic Understanding of Equalities in Primary Classes
Ralph Schwarzkopf, Marcus Nührenbörger, Carolin Mayer

9. Observations of Structure Within Shape Patterns
Aisling Twohill

10. Generalizing Fractional Structures: A Critical Precursor to Algebraic Thinking
Catherine Pearn, Max Stephens

11. First Encounter with Variables by First and Third Grade Spanish Students
Marta Molina, Rebecca Ambrose, Aurora Rio

Part III. Teaching for the Development of Early Algebraic Thinking

12. Making Implicit Algebraic Thinking Explicit: Exploiting National Characteristics of German Approaches
Anna S. Steinweg, Kathrin Akinwunmi, Denise Lenz

13. Early Algebra as Analysis of Structure: A Focus on Operations
Deborah Schifter

14. How Early Is Too Early for Thinking Algebraically?
John Mason

15. Cycles of Generalizing Activities in the Classroom
Susanne Strachota, Eric Knuth, Maria Blanton

16. Scaffolding Teacher Practice to Develop Early Algebraic Reasoning
Jodie Hunter, Glenda Anthony, David Burghes

17. Preservice Teachers’ Knowledge to Teach Functional Thinking
Sharon Mc Auliffe, Cornelis Vermeulen

Keywords: Education, Mathematics Education, Learning & Instruction, Teaching and Teacher Education