On p.26 of the report:

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"Conceptual understanding of mathematical operations, fluent execution of procedures and fast access to number combinations together support effective and efficient problem solving...

Studies of children in the United States, comparisons of these children with children from other nations with higher mathematics achievement and even cross-generational changes within the U.S. indicate that

**many contemporary U.S. children do not reach the point of fast and efficient solving of single-digit addition, subtraction, mulitiplication, and division with whole numbers, much less fluent execution of more complex algorithms as early as other children in many countries.**

*Surprisingly, many never gain such proficiency.*The reasons for differences in computational fluency of children in the U.S. ... are multifaceted. They include quantity and quality of practice, emphases within curricula, and parental involvement in mathematics learning...

**Few curricula in the United States provide sufficient practice to ensure fast and efficient solving of basic fact combinations and execution of the standard algorithms.**"

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Clearly Standard Algorithms and a good curriculum matter. Both are of huge importance.

It would be nice if the Seattle Public Schools believed this obvious fact. Seattle has yet to effectively deal with k-8 mathematics.

## 2 comments:

You might try using the following type of problem to demonstrate the importance of fluency with basic facts and their connection to higher levels of mathematics.

Divide 279 by 7, using the standard algorithm, on the left side of the paper.

On the right side of the paper, divide the polynomial 2x^2+7x+9 by x-3.

When comparing the two results, explain that the problem on the right is equivalent to the problem on the left for x = 10 (by substituting)

Is this parallel easily accessible when using a different strategy for the simpler division problem?

Sadly how many students do I know that couldn't solve 279/9 without a calculator.

This link provides two good examples using long division and synthetic division of polynomials.

http://www.algebralab.org/lessons/lesson.aspx?file=Algebra_poly_division.xml

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