1. 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

2. 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.
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3. 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
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4. 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
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5. 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
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6. Element Four Transitional Activities
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7. Transition Activities
Connect symbols to manipulatives
The actions of symbols mimic the actions already mastered with manipulatives
Now we use symbols…but with meaning
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8. 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
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9. Element Six Checking the Solution for Reasonableness
Using “upper and lower limits” rounding technique
Helps students develop number sense.
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10. Element Seven Checking the Solution for Accuracy
Using “Casting Out Nines”
Helps with learning basic facts and in the development of number sense.
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11. Element Eight Reporting Quantitative Solutions
Finding the numerical solution. It’s the number value
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12. Element Nine Reporting Referential Meaning
It’s what the quantitative solution refers to.
Every real problem has a meaning attached.
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13. 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