6/4/2016Anne Bussell1 CAMMP: Comprehensively Applied Manipulative Mathematics Program: A Differentiated Instruction Approach The Nine Elements of CAMMP

6/4/20162 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.

6/4/20163 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

6/4/20164 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

6/4/20165 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

6/4/20166 Element Four Transitional Activities Expanded Notation Partial Sums (or Products, Differences, Quotients) Use of an Array

6/4/20167 Transition Activities Connect symbols to manipulatives T he actions of symbols mimic the actions already mastered with manipulatives Now we use symbols…but with meaning

6/4/20168 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

6/4/20169 Element Six Checking the Solution for Reasonableness Using “upper and lower limits” rounding technique Helps students develop number sense.

6/4/ Element Seven Checking the Solution for Accuracy Using “Casting Out Nines” Helps with learning basic facts and in the development of number sense.

6/4/ Element Eight Reporting Quantitative Solutions Finding the numerical solution. It’s the number value

6/4/ Element Nine Reporting Referential Meaning It’s what the quantitative solution refers to. Every real problem has a meaning attached.

6/4/ 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!!!