Early Algebra : : Research into Its Nature, Its Learning, Its Teaching.

• Superior document: ICME-13 Topical Surveys Series
• Author: Kieran, Carolyn.
• TeilnehmendeR: Pang, JeongSuk.; Schifter, Deborah.; Ng, Swee Fong.
• Place / Publishing House: Cham : : Springer International Publishing AG,, 2016.; Ã2016.
• Year of Publication: 2016
• Edition: 1st ed.
• Language: English
• Series: ICME-13 Topical Surveys Series
• Physical Description: 1 online resource (48 pages)

Table of Contents

• Intro
• Main Topics You Can Find in This ICME-13 Topical Survey
• Contents
• 1 Introduction
• 2 Survey of the State of the Art
• 2.1 Brief History of Early Algebra Movement and Its Research up to the Early 2000s
• 2.1.1 The Early Algebra Movement
• 2.1.2 The Development of Algebraic Thinking in the Early Grades: Some Examples
• 2.1.2.1 Generalizing Related to Patterning Activity
• 2.1.2.2 Generalizing Related to Properties of Operations and Numerical Structure
• 2.1.2.3 Representing Relationships Among Quantities
• 2.1.2.4 Introducing Alphanumeric Notation
• 2.1.3 Concluding Remarks: Early Algebra Research in Years Leading up to Early 2000s
• 2.2 Recent Research on Early Algebra Learning and Further Evolution of the Field
• 2.2.1 The Nature of Early Algebraic Thinking
• 2.2.2 Processes of Early Algebraic Thinking
• 2.2.3 Mathematical Content Areas of Early Algebraic Thinking
• 2.2.3.1 A Generalized Arithmetic Perspective on Content
• 2.2.3.2 A Functional Perspective on Content
• 2.2.4 Implications for Future Research
• 2.3 Bringing Early Algebra into Elementary Classrooms
• 2.3.1 The Nature of Early Algebraic Content in Classroom Contexts
• 2.3.2 Roles of Students and Teachers in Classrooms
• 2.3.3 What Can Happen in Classrooms in General?
• 2.3.4 Conclusion
• 2.4 A Neurocognitive Perspective on Early Algebra
• 2.4.1 Singapore Model Method to Solve Arithmetic and Algebra Problems
• 2.4.2 Different Methods Used to Solve Secondary Algebra Word Problems
• 2.4.3 Neuroimaging, the Model Method, and Algebra
• 2.4.4 Why Algebra May Be the More Resource Intensive of the Two Methods
• 2.4.4.1 The Transition to Letters as Unknowns Requires an Expansion of the Knowledge Related to the Use of Letters
• 2.4.4.2 Algebraic Expressions Are Legitimate Forms of Answers.
• 2.4.4.3 Algebraic Representations no Longer Adhere to the Same Set of Conventions Underpinning the Use of Numbers
• 2.4.4.4 Knowledge of Equality-Equivalence of Algebraic Expressions Is Crucial
• 2.4.5 Competent Adults and Children Process Arithmetic Information Differently
• 2.5 Concluding Remarks
• 3 Summary and Looking Ahead
• References
• Further Reading.