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Personal Strategies vs Algorithms
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Procedural vs Conceptual Information
Do We Really Want To Keep the Traditional Algorithms for Whole Numbers?
John A. Van de Walle
no_algorithms.pdf
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197 KB
View these wonderful videos. Better yet  share them with students and parents.
Ma and Pa Kettle
Ma and Pa Kettle Math
Tom Lehrer  New Math
The Harmful Effects of Carrying and Borrowing
 Constance Kami
Double Column Addition
Part 1
Mental Math Strategies.pdf
Why Not to Teach the Traditional Algorithm
The traditional algorithms are digitoriented rather than numberoriented.
The traditional algorithms are righthanded instead of lefthanded.
The traditional algorithms must be taught in a teacherdirected manner.
Students make more errors with traditional algorithms than with their invented strategies.
The traditional algorithms are unnecessarily tedious due to lack of flexibility.
The traditional algorithms do not lend themselves to mental methods or to estimation.
We no longer can afford the time required for teaching, reteaching, and remediation of
outmoded skills.
In the workplace, technology does virtually all of the required computation.
Outside of the workplace, numberoriented, flexible strategies are more than adequate.
THERE ARE SIGNIFICANT ADVANTAGES TO FLEXIBLE, NUMBERORIENTED “INVENTED STRATEGIES.”
Students make fewer errors .
Less reteaching is required.
Students develop number sense.
Invented strategies are the basis for mental computation and estimation.
Flexible methods are often faster than the traditional algorithms.
Algorithm invention is itself a significantly important process of “doing mathematics.”
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Procedural vs Conceptual Information
Do We Really Want To Keep the Traditional Algorithms for Whole Numbers?
John A. Van de Walle
View these wonderful videos. Better yet  share them with students and parents.
Tom Lehrer  New Math
The Harmful Effects of Carrying and Borrowing  Constance Kami
Double Column Addition Part 1
Mental Math Strategies.pdf
Why Not to Teach the Traditional Algorithm
The traditional algorithms are digitoriented rather than numberoriented.
The traditional algorithms are righthanded instead of lefthanded.
The traditional algorithms must be taught in a teacherdirected manner.
Students make more errors with traditional algorithms than with their invented strategies.
The traditional algorithms are unnecessarily tedious due to lack of flexibility.
The traditional algorithms do not lend themselves to mental methods or to estimation.
We no longer can afford the time required for teaching, reteaching, and remediation of
outmoded skills.
In the workplace, technology does virtually all of the required computation.
Outside of the workplace, numberoriented, flexible strategies are more than adequate.
THERE ARE SIGNIFICANT ADVANTAGES TO FLEXIBLE, NUMBERORIENTED “INVENTED STRATEGIES.”
Students make fewer errors .
Less reteaching is required.
Students develop number sense.
Invented strategies are the basis for mental computation and estimation.
Flexible methods are often faster than the traditional algorithms.
Algorithm invention is itself a significantly important process of “doing mathematics.”