Online Curricular Resource Binder (CRB)
For Math ADEPT Conceptual Algebra

Course Outline and Highlights

Course Outline of Topics and Concepts:

What is Algebra? What is Conceptual Algebra? Diagnosing students' errors and conceptual trouble-spots NCTM Standards & Conceptual Algebra in K12. "Algebrization": how Does one get from ?I see the pattern? to a formula? Understanding Functions Towards a Deeper Understanding of lines and "linearity" Hands On Equations, Algebra Tiles, and other manipulatives. Java applets, graphing calculators, and other technologies. Instructional and Pedagogical context. Putting it all together.

Course Highlights:

• Paradigm: "Spiral" -- an inter-weaving of:

  • A safe but challenging environment
  • Middle school curriculum at a teacher's (higher, conceptual) level
  • Relevant "Mental Pushups" increase mathematical reasoning skill
  • Pedagogy/Methods from a Math-content point of view

• Key Elements

  • Problem-Solving / Modeling / Frequent Groupwork
  • Mathematical Reasoning: How and Why?
  • Algebra Concept Map/revised ; Analyzing errors
  • Weekly written assignments
  • Use of correct notation and "Mathematical Grammar"
  • Enrichment readings: NCTM journals, Glenn Commission
  • Manipulatives & Technology:
    Integrated with Content-based discussion and analysis

• Assignments and Pedagogical Focus

  • Lesson-Plans assignment, based on Rubric
  • Full-class discussions & Oral Presentations
  • Final Course Portfolio
  • Model National Curricula (CMP, MiC)
  • Pre/Post assessment
  • Class Email list &web-based discussion board

• Content Focus

  • Patterns, "Algebraization", and Functions
  • "Picture Proofs" -- connections with geometry
    and underlying meaning of algebraic. properties
  • Graphical interpretation
  • Converting among graphical numerical, written, symbolic
  • Lines, Linearity, Slope, Proportions
  • Non-linearity, quadratics, optimization
  • Exponential functions.
  • Qualitative analysis of graphs and functions

---

Back to Online CRB for Conceptual Algebra

---