Monday, September 3, 2012

PEMDAS must die!

Here is my third blog post for the new math teacher blogger/twitterer initiation. My prompt is:

2. Your students come into class rife with misconceptions. EEEP! What is a misconception that you see a lot? If you haven't done so yet, brainstorm a way to deal with that misconception so that students will leave your class with that misconception fixed. (Or if you have a misconception that you deal effectively with, how do you do that?)

True to fashion, I will now sort of answer the prompt:

My buddy Andrew Stadel just made a great song about PEMDAS.

It is tough to write a math song that is not ridiculously cheesy. In fact, most math songs drive me insane. They're usually so terrible that I can't bare to force my students to listen to them. Of course, that doesn't stop me from making my own songs and thinking they're not cheesy. (The video below was made with the help of my eighth grade students last year.)

But I'm getting a little off topic here. I love Andrew's song. It's very catchy and I think I have most of it memorized. But I still hate PEMDAS. Every year I get a few eighth graders who insist that you always multiply before you divide. And you always add before you subtract. There is no doubt in my mind that the acronym, PEMDAS, is the culprit.

Once in a while students will even go so far as to tell me that I'm wrong and their teacher from last year is right. I then hand them a piece of paper with "18/6*3" written on it, tell them to go find their teacher from last year, and have them simplify the expression. The last time I did this, the paper suspiciously got lost in transit.

It takes a ton of warm-ups and review to finally break them of this dirty habit.

So I more PEMDAS. No more "Please Excuse My Dear Aunt Sally". It only does more harm than good. We tell them to remember left to right, but they don't. They only remember PEMDAS.

Nathan Kraft


  1. I'm with you on the memory crutches. I created a dynamic unit circle for my grade 11s last year and we spent days going through the meaning of trigonometry. Try as I might, I still resorted to SOH CAH TOA.
    Ironically, Canadian students have the exact opposite problem. We use BEDMAS up here, and some insist that you "must" then divide before multiplying. I think these problems can be fixed (or at least diluted) by showing students the why behind the acronym. Why must we use PEMDAS? What would happen if we didn't?
    Great Post.

  2. You're too cool, Mr. Kraft. I almost lost my job over PEMDAS, let me tell you. So that's another conversation at another time :)

  3. Have you heard of the Rhianna Umbrella song for the order of operations? I used that instead of PEMDAS this year.

  4. I thought it was Please Excuse My Damn Algebra Students. Oops! Gotta go print out a new classroom poster...

    Just in case you decide the battle against PEMDAS is more trouble than it's worth, here's a thought. Perhaps you could mix it up by having, for example, six pieces of paper on the wall with the six letters on them. Every day, or whenever, you could switch around the M and D, and/or the A and S. Make the P yellow (get it? middle school humor!), the E green, the M and D both red, and the A and S both blue (or whatever color scheme you like, of course). "Why are there only four colors instead of six, Mr. Kraft?" "Why, indeed. Anyone?" And if someone notices that only the like-color letters ever change places, perhaps that would make an important connection for them as well. And maybe you could put left-to-right arrows (color-coded with the letters) underneath the MD and the AS, so that no matter which order the S and A (for example) are in, you are reminded to always work them left to right.

    Two cents' worth, no more.

  5. I have been saying this for YEARS! DEATH TO PEMDAS! It's too misleading and in my eyes nonsense. Sorry PEMDAS lovers. *:)

  6. I've used a triangle with sixth and eighth graders to pretty good effect:

    / \
    /brackets \
    /exponents \
    /________________________ \
    /multiplication and division \
    /____________________________ \
    / addition and subtraction \

    I'm sure that will look like complete garbage when I press submit :) Anyway, it's like the food pyramid, but with delicious math instead of gross vegetables. I tell them to work their way from top to bottom of the triangle. It seems to help them that multiplication and division, and addition and subtraction, are literally on the same level, so they have the same precedence.

  7. I feel your pain man! It baffles me when I talk to elementary teachers and even some middle school teachers that don't know about the left-to-right rule with multiplication/division and addition/subtraction. I really tried to emphasize the "OR" with the lyrics: multiply OR divide. There's a choice there: choose the operation on the left. I seriously take the time to stop playing my guitar in class and emphasize that there's a whole verse devoted to the left-to-right rule... like reading a book y'all. Furthermore, I really like the extension idea of challenging students to rewrite the second verse so they remember the left-to-right rule.
    Maybe we should take it one step further and challenge our students with this: rewrite Order of Operations without the acronym PEMDAS or BEDMAS.
    *As much as I'd like to do away with PEMDAS, it's not going away. Therefore, I tried to embrace it. I also remind my students it could have been written PEDMSA (ped-ma-saw).
    Glad you dig the song!
    We can still be friends! :D

  8. I am 100% with you on this. BTW a couple of days ago somebody put on Facebook a problem
    6-1*0+2/2 and mentioned that his girlfriend and he cannot agree on the answer. There were more than 120,000 responses, the majority of the 1 and 5. What can I say?

  9. I just don't get it because I learned to solve order of operations using PEMDAS as I'm sure most of us educators did. What is with the generational shift in mindset? Why is it so difficult to remember that MD and AS go together? Ah, well. Great video, by the way!