Welcome CMP / CMC Partnership: Algebra Initiative CaSMP Network Meeting October 13, 2009 UCLA Mathematics ProjectCalifornia Mathematics Council

California Mathematics Project Susie Hakansson Executive Director CMP UCLA

CMC Sheri Willebrand President 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-up 2) 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: = 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: = 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. Opposite Negative 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 Thinking Research Instruction Adult 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 8 Adoption Process/Frameworks State: National: Common Core State Standards Initiative Race to the Top

Issues Websites CDE: COMET access from CMP homepage CMC Website State: National: Common Core State Standards

THANK YOU CMP: CMC: UCLA Mathematics ProjectCalifornia Mathematics Council

CONTACT US! Susie: Sheri: UCLA Mathematics ProjectCalifornia Mathematics Council