1, 2, 3 - Let's PEMDAS
PEMDAS is an acronym that stands for
- Parentheses
- Exponentiation
- Multiplication
- Division
- Addition
- Subtraction
The acronym is supposed to help students memorize the order of operations. I consider introducing and using it an educational outrage. Let me explain.
First of all, the arithmetic operations are neither taught simultaneously nor learned all at the same time. The fact that that memory device is introduced when students are supposed to have mastered the basic operation (+, -, ×, ÷) and using the parentheses is an indication that the operations have not been mastered. The PEMDAS acronym is then offered as a quick fix to a fundamental failure of education to teach order of operations - otherwise it should not be necessary.
By the time a student is offered the crutch of PEMDAS, a better solution could (and should) be to go back and refresh in a better way than has been done before the notion and order of operations - sequentially, so that the basic properties of operations have the time to sink in.
Second of all, PEMDAS does not tell the whole story and is liable to convey a wrong message. What is 8 - 2 + 3? According to PEMDAS, it may well be 8 - 5 = 3 because "A" that stands for addition precedes in the acronym "S" that stands for subtraction. Of course a good teacher would not fail to mention that - order-wise - the two operations have the same precedence and are being executed left-to-right so that the right answer to the big question is 8 - 2 + 3 = 6 + 3 = 9. However, for students in need of that memory device the imposition of the left-to-right order may have to be supported by some other acronym. Of course, to compound it all, when it comes to exponentiation, the order of execution is right-to-left and, unless there is a good understanding of how it comes about, the difficulty the change creates is next to insurmountable.
The PEMDAS acronym may at best help sweep under the rug and away from the public eye the failure of earlier education. At worst, it perpetuates that failure, building on top of it a wobbly memory device without addressing the real education issues. Wait till the functions are introduced. What high school teacher has not seen a derivation like
log 4 / log 2 = 4/2 = 2?
Which is of course right! Or is it wrong?
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July 17th, 2011 at 9:18 pmMy kid had to learn it in regular school and then also in a Sunday one where I hoped math would be more interesting. Obviously, if the system felt necessary to introduce this notion, somewhere along the line there was a systemic failure, which PEMDAS does not even come close to patching.
July 17th, 2011 at 9:24 pmIt is another sad statement about the underestimation of students' ability to understand math. I loathe PEMDAS. The best explanation I have seen for those who feel they must resort to teaching it because the "teacher's guide" tells them to do so, is to explain that when they see the mathematical expression 53-4x3+1 is to read it as 53 minus 4 groups of 3 plus 1, thereby emphasizing the reason we must multiply before the other operations. The worst I have see teachers do is instruct students to insert parentheses to "make it clearer" what to do first. And what guides them as to where to insert these useful parentheses. The change must begin with the education of elementary teachers.
August 11th, 2011 at 12:47 amI agree with you - the change should start in elementary school. Having better educated teachers from the outset will certainly help. But I am afraid that is not enough.
All the math most people will ever need could be taught and learned in under two years. Elementary school must help students develop motivation which they later will ride to learn as much math as they feel they like or may need.
The threat of failure in math hangs over students like a Damocles' sword. This is just plain wrong.
August 14th, 2011 at 7:12 pm