Instructor


Jeffrey O. Bauer

107 Carhart Science

Phone: 402-375-7334

Email: jebauer1@wsc.edu


Course Description: (Developing Thinking in Algebra) The course is designed to help mathematics teachers in their teaching of secondary algebra. Emphasis will also be placed on learning theories associated with algebra instruction, aligning the algebra curriculum with national, state and local standards, and assessment.


Textbook: Developing Thinking in Algebra. Mason, John, Graham, Alan, & Johnston-Wilder, Sue (2005). Thousand Oaks, CA: The Open University in association with Paul Chapman Publishing. (ISBN: 1-4129-1171-0)


Course Syllabus

Course Outline


  1. Algebra Curriculum
    1. History of Algebra
    2. Definition of Algebra
    3. U.S. Algebra Curriculum
  2. Jerome Bruner
    1. Stages of Learning
    2. Manipulatives
    3. Difficulties
  3. Fostering Algebraic Thinking
    1. Habits of Mind
    2. Transition from Algorithmic Thinking to Algebra
    3. Number Sense and Number Theory
    4. Generalization about Structure
    5. Functional Relations
    6. Symbol Sense
    7. Multiple Representation
  4. Generalizing and Abstracting
    1. Generality in Numbers
    2. Generality in Diagrams
    3. Generality Outside of School
    4. More Generality
    5. Pedagogy
  5. Mathematical Powers and Themes
    1. Generalizing
    2. Structure
    3. Reading Diagramsl
    4. Imagining and Expressing
    5. Pedagogy
  6. Using Symbols
    1. Symbols in Algebra
    2. Expressing Relationships
    3. Multiple Expressions
    4. Arithmetic and Algebaic Thinking
    5. Pedagogy
  7. Depicting Relationships
    1. Straight Line Graph
    2. Quadratic Relationships
    3. Linear Relationships and the Graphic Calculator
    4. Quadratic Relationships and the Graphic Calculator
    5. Pedagogy
  8. Symbol Manipulation
    1. Types of Expressions
    2. Generalized Arithmetic
    3. Manipulating and Rearranging
    4. Identifying Errors
    5. Pedagogy
  9. Changing Representations
    1. To Symbols
    2. To Graphs
    3. To Tables
    4. To and between Diagrams
    5. Pedagogy
  10. Solving Problems
    1. Arithmetic to Algebra
    2. Using Letters
    3. Story Problems
    4. Exploiting Story Problems
    5. Pedagogy
  11. Reasoning
    1. About Types of Numbers
    2. About Generalizing
    3. With and from Diagrams
    4. With Generalities
    5. Pedagogy