The Nine Elements of CAMMP CAMMP: Comprehensively Applied Manipulative Mathematics Program: A Differentiated Instruction Approach The Nine Elements of CAMMP 11/23/2018 Anne Bussell

Effective Teachers know each student’s cognitive development so as to differentiate instruction. Effective Teachers know that since not all students are the same; instruction must be differentiated. Effective teachers know how to diagnose errors and prescribe instructional tactics that overcome errors or misunderstandings. 11/23/2018

Element One Action Language Addition – “joined with” Subtraction – “take away” “Compared to” “Joined with” the no action of subset Multiplication – “sets of” Division – “grouped into” Action language determines how number sentence will look 11/23/2018

Element Two Concrete Manipulatives Manipulatives have one to one relationship You can hold manipulative in your hand Example - Cuisenaire Rods Counters Fingers up to 10 11/23/2018

Element Three Representational Manipulatives Hold in your hand AND one to many relationship Example – Base 10 Blocks Hold in your mind AND one to one, or one to many relationship Example – Worksheets Computer software 11/23/2018

Element Four Transitional Activities 11/23/2018

Transition Activities Connect symbols to manipulatives The actions of symbols mimic the actions already mastered with manipulatives Now we use symbols…but with meaning 11/23/2018

Element Five Standard Algorithms + Alternative Alternatives Help children see connections to simple, beautiful, and elegant algorithms Alternatives are only for those with a demonstrated history of poor performance 11/23/2018

Element Six Checking the Solution for Reasonableness Using “upper and lower limits” rounding technique Helps students develop number sense. 11/23/2018

Element Seven Checking the Solution for Accuracy Using “Casting Out Nines” Helps with learning basic facts and in the development of number sense. 11/23/2018

Element Eight Reporting Quantitative Solutions Finding the numerical solution. It’s the number value 11/23/2018

Element Nine Reporting Referential Meaning It’s what the quantitative solution refers to. Every real problem has a meaning attached. 11/23/2018

Summary Use differentiated instruction to optimize students’ learning potential. Use manipulatives each time new mathematical concept is introduced. “You never learn anything completely new in the abstract, you only make adjustments to what you have learned in the past!” Teachers make the difference, a curriculum can’t make the difference…but teachers can!!! 11/23/2018