Personal+Strategies+vs+Algorithms

= 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.

= 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 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.**

**THERE ARE SIGNIFICANT ADVANTAGES TO FLEXIBLE, NUMBER-ORIENTED “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.”**