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U.S. — 25th in math

November 26, 2012
Adirondack Daily Enterprise

To the editor:

Since I haven't heard any reason as to how our students got to be 25th in the world in math, I'll offer one. It is because of PEMDAS (shorthand for "Parentheses, Exponents, Multiplication, Division, Addition and Subtraction," alias, "Please excuse my dear Aunt Sally), the order-of-operations procedure for simplifying math expressions taught in our schools that makes test slowpokes of students. This is because PEMDAS requires a student to only work on those terms associated with a particular PEMDAS step and to repeat everything else - thus the extra lines that can waste test time.

Now, since students often stay with the way that they were first taught, I think any student using PEMDAS on a timed test does so at a disadvantage. Imagine a student encountering an expression like this one from an '80s textbook: (+2) x (-3)squared - [(-5) + (-3)] x [(+4)-(-6)]. While it would take a PEMDAS student 11 lines to duplicate the author's work, any college math student could do it in four lines by simplifying each term of the expression as quickly as possible and combining the results for the answer. I named this alternate procedure "termutation" after the basic calculating unit of math - the term.

Article Photos

Example using termutation

Back in 1962, after covering PEMDAS in my first elementary algebra class, I introduced my students to termutation even though it wasn't in my lesson plan. I did so because I thought it was a better procedure than PEMDAS. Then, before the bell rang, the class not only got into a comparative discussion about the procedures but voted termutation the better one.

Termutation's steps are:

1. Recognize terms mentally or by underlining them (including minor terms inside quantity symbols).

2. Simplify each term of step 1 quickly.

3. Combine terms of step 2 for answer.

While I have no clue how to get PEMDAS out of textbooks, and thus out of our nation's classrooms, I'm hoping this article creates a miracle that gets it done. I don't like our students being 25th in the world in math, especially when I know that they can do more than one thing at a time.

Clarence Hanley

Retired, seven years high school and 29 years North Country Community College

Saranac Lake



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