Procedural vs Conceptual Information

Do We Really Want To Keep the Traditional Algorithms for Whole Numbers?

John A. Van de Walle

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0137149611.jpgWhy Not to Teach the Traditional Algorithm
The traditional algorithms are digit-oriented rather than number-oriented.

The traditional algorithms are right-handed instead of left-handed.

The traditional algorithms must be taught in a teacher-directed 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, number-oriented, flexible strategies are more than adequate.


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.”