# Carraher & Schliemann (2007)

Early Algebra and Algebraic Reasoning

• Why Algebraic Reasoning?
• Rationale and Structure of Chapter
• The Recent Focus on Algebraic Reasoning in the Early Grades
• A Decisive Moment
• Event 1: NCTM's Endorsement
• Event 2: The RAND Mathematics Study Panel Report
• Five Key Issues
• Issue 1: The Relations Between Arithmetic and Algebra
• Issue 2: Process versus Object
• Issue 3: The Referential Role of Algebra
• Issue 4: Symbolic Representation (narrowly defined)
• Issue 5: Symbolic Representation (broadly defined)
• A Traveler's Guide to Early Algebra
• School Algebra and EA
• EA Versus Pre-Algebra
• Pre-Algebra Approaches
• EA Approaches
• On the Possibilities of EA
• Parsing (Early) Algebra
• Algebra Is Latent in the Existing Early Mathematics Curriculum
• Arithmetic and Numerical Reasoning as an Entry Point Into EA
• The Field Axioms and Other Properties of Numbers
• Studies That Introduce Algebra Through Generalizations About Numbers
• Quasi-Variables
• Summary: Numerical Reasoning and EA
• Arithmetic and Quantitative Reasoning as an Entry Point Into EA
• Quantities, Measures, and Magnitudes
• Quantitative Thinking and Number Lines
• Can Students Apply Other Properties of Arithmetic to Magnitudes?
• Referent-Transforming Properties
• EA Studies that Focus on Magnitudes and Measures
• Why Quantitative Thinking Is Unavoidable in EA
• The Davydov Approach to EA
• The Measure Up Project
• Summary: Quantitative Reasoning and EA
• Arithmetic and Functions as an Entry Point Into EA
• Can Young Students Reason with Functions?
• Functions As Rules for Generating Collections of Figures
• Functions Expressed Through Multiple Representations: The Early Algebra, Early Arithmetic Project
• Summary: What Can Young Student Learn About Functions?
• Concluding Thoughts
• What Kinds of Representations Express Algebraic Ideas?
• Patterns and Functions
• Issues Common to Patterns and Tables
• Is a Scalar Approach Valid?
• What Goals Are Achievable in the Short Term, Mid Term, and Long Term (for Students and Teachers)?

## Corrolary

APA
Carraher, D. W., & Schliemann, A. D. (2007). Early algebra and algebraic reasoning. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 669–705). Charlotte, NC: Information Age.
BibTeX
@incollection{Carraher2007,