Kieran (2007)

Learning and Teaching Algebra at the Middle School Through College Levels: Building Meaning for Symbols and Their Manipulation

• Author: Carolyn Kieran
• Book: Second Handbook of Research on Mathematics Teaching and Learning
• Year: 2007
• Source: http://www.infoagepub.com/products/Second-Handbook-Research-Mathematics-Teaching-Learning

Outline of Headings

• Part 1. School Algebra: Background Issues and Theoretical Considerations
  • The Current Content of School Algebra: Competing Views
  • Sources of Meaning
    • Algebraic Meaning: Where Does It Come From?
    • Meaning From the Algebraic Structure Itself, Involving the Letter-Symbolic Form
    • Meaning From Other Mathematical Representations, Including Multiple Representations
    • Meaning From the Problem Context
    • Meaning Derived From That Which Is Exterior to the Mathematics/Problem Context
  • Models for Conceptualizing Algebraic Activity
• Part 2. School Algebra: Findings from Research Studies
  • The Middle Grade and Lower Secondary Level Student
    • Background: International Assessments
    • Generational Activity: The Middle Grade and Lower Secondary Student
      • Generational Activity with a Primary Focus on the Letter-Symbolic Form
        • Variables, Expressions, and Equations
        • The Minus Sign and Negative Numbers
        • Beginnings of Structure Sense
      • Generational Activity with Multiple Representations
        • Tabular Representations and the Letter-Symbolic
        • Graphical Representations and the Letter-Symbolic
        • Connections Among Representations
      • Generational Activity Within the Context of Word Problems
        • Generating Multiple Representations in the Solving of Word Problems
        • Generating Equations in the Solving of Word Problems
    • Transformational Activity: The Middle Grade and Lower Secondary Level Student
      • Theoretical Elements of Transformational Activity: Equivalence and Theoretical Control
      • Technical Elements of Transformational Activity: Expressions, Equations, and Equation Solving
      • The Use of Concrete Manipulatives in Transformational Activity
    • Global/Meta-Level Activity: The Middle Grade and Lower Secondary Level Student
      • Global/Meta-Level Activity Involving Generalizing
      • Global/Meta-Level Activity Involving Proof and Proving
      • Global/Meta-Level Activity Involving Modeling
    • The Impact of Technology on Algebraic Activity With the Middle Grade and Lower Secondary Level Student
    • Concluding Remarks on the Algebra Research Involving the Middle Grade and Lower Secondary Level Student
  • The Upper Secondary and College Level Student
    • Generational Activity: The Upper Secondary and College Level Student
      • Generational Activity With a Primary Focus on the Letter-Symbolic Form
        • Form and structure
        • On parameters
      • Generational Activity with Multiple Representations
        • Functions and Their Meaning
        • The Interplay Between Symbolic and Graphical Representations and the Role of Visualization
    • Transformational Activity: The Upper Secondary and College Level Student
      • Transformational Activity Related to Notions of Equivalence
      • Transformational Activity Related to Expressions and Inequalities
      • Transformational Activity Related to Factoring Expressions
      • Transformational Activity Involving the Integration of Graphical and Symbolic Work
    • Global/Meta-Level Activity: The Upper Secondary and College Level Student
      • Global/Meta-Level Activity Involving Problem Solving
      • Global/Meta-Level Activity Involving Modeling
    • The Impact of Technology on Algebraic Activity With the Upper Secondary and College Level Student
      • Large-Scale Studies on the Effects of Technology Use
        • Calculators
        • Graphing Calculators
        • Computer Algebra Systems (CAS)
      • Technology and the Changing Roles of Students and Teachers
    • Concluding Remarks on the Algebra Research Involving the Upper Secondary and College Level Student
  • Algebra Teaching and the Algebra Teacher
    • Research Involving the Practicing Algebra Teacher
      • Algebra Teachers' Knowledge and Beliefs
      • The Practice of Algebra Teaching and Influences on That Practice
    • Research Involving the Algebra Teacher Within a Context of Professional Development or Inservice Training
      • Integrating New Curricula, Approaches, and Technological Environments Into the Algebra Classroom
      • Algebra Content Knowledge and Beliefs
    • Research Involving the Preservice Teacher of Algebra
    • Concluding Remarks on the Research Focusing on Algebra Teaching and the Algebra Teacher
• In Conclusion: What Does this Body of Research Tell Us?

Also

APA

Kieran, C. (2007). Learning and teaching algebra at the middle school through college levels. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 707–762). Charlotte, NC: Information Age.

BibTeX

@incollection{Kieran2007,
address = {Charlotte, NC},
author = {Kieran, Carolyn},
booktitle = {Second handbook of research on mathematics teaching and learning},
chapter = {16},
editor = {Lester, Frank K.},
pages = {707--762},
publisher = {Information Age},
title = {{Learning and teaching algebra at the middle school through college levels}},
year = {2007}
}