By Karen S. Karp, Sarah B. Bush, and Barbara J. Dougherty, Posted July 14, 2014 –
the August 2014 issue of Teaching Children Mathematics, authors Karen S. Karp, Sarah B. Bush,
and Barbara J. Dougherty initiated an important conversation in the elementary
mathematics education community. We are dedicating this discussion space as a
place where that conversation can continue.
their article, “13 Rules That Expire,” the authors point out thirteen math rules commonly taught in
the elementary grades that no longer hold true in later grades; in fact, these
rules “expire.” For example—
Rule 1: When you
multiply a number by ten, just add a zero to the end of the number.
rule is often taught when students are learning to multiply a whole number
times ten. However, the rule is not true when multiplying decimals (e.g., 0.25
× 10 = 2.5, not 0.250). Although the statement may reflect a regular pattern
that students identify with whole numbers, it is not generalizable to other
types of numbers. Expiration date: Grade 5 (5.NBT.2).
the article for the other
the comment section that follows this blog post, submit additional instances of
“rules that expire” or expired language that the article does not address. If
you would like to share an example, please use the format of the article (as
you submit an example of expired language that was not in the article, include
“What is stated” and “What should be stated” as shown in the table below (for
additional examples, see table 1 in
the published article.
"Cancel" for dividing out common factors in any situation. Cancel should only be used when additive inverses are added and the result is zero. Yes, cancel has be used for over a century, yet it is very confusing for students when reducing/simplifying fraction operations. I was taught this in graduate (Teaching of Algebra) school 45 years ago by Dr. Rolands at TAMU; I have practiced it ever since and it work. He got doctorate during University of Illinois math projects in the 1960s.
FOIL. This mnemonic device teachers use to try to help students understand the distributive property fails once the student tries to multiply trinomials.