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Welcome
CMP / CMC Partnership:
Algebra Initiative CaSMP Network Meeting
October 13, 2009
UCLA Mathematics Project California Mathematics Council
California Mathematics Project
Susie HakanssonExecutive Director CMP
UCLA
CMC
Sheri WillebrandPresident Elect, CMC State
CMP / CMC Partnership: Algebra Initiative
Overview: K - 8 Professional Development (PD) focusing on student success in Algebra by grade 8.
Goals: 1) Extensive PD with follow-up2) Sustained, systematic support
for the classroom
CMP / CMC Partnership: Algebra Initiative
Organized around:
Big Ideas Across the Grades
Ways of Mathematical Thinking
CMP / CMC Partnership: Algebra Initiative
Big Ideas Across the Grades Structures of Number Systems and Operations
Equivalence
Proportional Reasoning
Patterns, Relations, and Functions
Variables and Symbols
CMP / CMC Partnership: Algebra Initiative
Ways of Mathematical Thinking Make connections within mathematics and applying mathematics to other disciplines
Use multiple representations and tools (including manipulatives, visuals, and technology)
Use relational thinking vs. computation-oriented thinking
Use reasoning and sense making (including justification, generalization, specialization)
Use problem solving
CMP / CMC Partnership: Algebra Initiative
Think back to elementary school…
What were some math concepts or ideas that were taught (and you learned)
that had to be “untaught” (and unlearned)in later grades?
Lies my teacher told me.
CMP / CMC Partnership: Algebra Initiative
“You cannot take a larger number from a smaller number.”
Let’s think about subtraction…
Structures of Number Systems and Operations
Subtraction:
CMP / CMC Partnership: Algebra Initiative
Subtraction:
8 - 6 =
What does the “ - ” represent in this equation?
CMP / CMC Partnership: Algebra Initiative
“You cannot take a larger number from a smaller number.”
Why is this misleading? Why is this taught?
Subtraction:
CMP / CMC Partnership: Algebra Initiative
Elementary: Moving beyond subtraction as “take away”.
Why?
Subtraction: 8 - 6 = 2
CMP / CMC Partnership: Algebra Initiative
Change: “Take Away”
Equalize: “Add To”
Comparison: “Difference”
Notice how dependent on language
Subtraction is complex
CMP / CMC Partnership: Algebra Initiative
Research: PROBLEM TYPES Carpenter, Moser, Bebout, (1988)
Cognitive Guided Instruction (CGI) Karen Fuson, (1992, 1997) Broody & Standifer, (1993)
Details are in your handout.
Subtraction is complex
CMP / CMC Partnership: Algebra Initiative
Middle Grades:Subtraction vs. OppositeNegative vs. Opposite
What is the confusion for students?
Structures of Number Systems and
Operations: - 6
CMP / CMC Partnership: Algebra Initiative
Big Ideas Math Processes
Refer to your handout
Matrix Structure: Equivalence
CMP / CMC Partnership: Algebra Initiative
Big Ideas Across the Grades Structures of Number Systems and Operations
Equivalence
Proportional Reasoning
Patterns, Relations, and Functions
Variables and Symbols
CMP / CMC Partnership: Algebra Initiative
Ways of Mathematical Thinking Make connections within mathematics and applying mathematics to other disciplines
Use multiple representations and tools (including manipulatives, visuals, and technology)
Use relational thinking vs. computation-oriented thinking
Use reasoning and sense making (including justification, generalization, specialization)
Use problem solving
CMP / CMC Partnership: Algebra Initiative
Tie to Algebraic ThinkingResearchInstructionAdult Learner Assessment
Support behind the Matrix
In Matrix format using Math Processes
CMP / CMC Partnership: Algebra Initiative
Big Ideas Math Processes
Refer to your handout
Matrix: Subtraction
Issues in Mathematics
Algebra in Grade 8Adoption Process/Frameworks
State:
National: Common Core State Standards InitiativeRace to the Top
Issues Websites
CDE: http://www.cde.ca.gov/ COMET access from CMP homepageCMC Website
State:
National: Common Core State Standards http://www.corestandards.org/
THANK YOU
CMP: www.cmpso.org
CMC: www.cmc-math.org
UCLA Mathematics Project California Mathematics Council
CONTACT US!
Susie: [email protected]
Sheri: [email protected]
UCLA Mathematics Project California Mathematics Council
