Fluency Fallacy # 6
Standard Algorithms are Standard Everywhere
It may surprise you that the standard algorithms we use in the U.S. are not internationally standard. While concepts are universal, notations and procedures vary. For example, there are differences between the U.S. and Latin American traditional subtraction algorithm as shown below. Could your students make sense of this different method?
Click here to check out comparisons in notations and algorithms between the U.S. and Latin America. You will note that even when the algorithms are alike, the notation may vary greatly.
We must work to respect the strategies students bring from their cultures. This may help to strengthen partnerships between the school and community. Including “cultural” algorithms will affirm that there are many ways to do a math problem. It may provide an opportunity to deepen an understanding of concepts such as place value while strengthening an understanding of procedures themselves. Honoring strategies from other countries may also expose students to more fluent thinking.
The Truth about Fallacy #6
Different cultures use different standard algorithms and notations and that is OK!
Fluency Fallacy #7
Some Students are Better Off with Knowing Just One Way
Limiting instruction to one method is not in anyone’s best interest. Students who do not memorize and recall well are not aided by learning just one set of procedures. Without connections to concepts and reasoning, the recall of steps is uncertain at best. The key is to not overwhelm students with processes that are not useful. Focus on the most useful strategies and help students decide when to choose them.
Consider the grade 4 concept of comparing fractions. Finding a common denominator is generalizable to all problems.
However, in reviewing these problems, is it necessary for this method to be used with these problems? Students need to be given the opportunity to reason through different methods for a variety of problems.
The Truth about Fallacy # 7
Every student is better off knowing a set of useful strategies and learning when each is most useful and when they are not.
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