It was at the first meeting of the Challenger Middle School Mathematics Department that I first heard of GEMDAS. What an obviously good idea!

Remember PEMDAS

PEMDAS is a mnemonic device used to remember the order of operations. The order of operations is a set of rules that specify in which order to perform the mathematical operations in an expression. Such a convention is necessary so that everyone in the world gets the same results when working a math problem (assuming they don’t make a mistake!).

You're history Aunt Sally (but fess up before you go) (Nono via Picasa)

PEMDAS is also remembered as “Please Excuse My Dear Aunt Sally” (what for, no one is quite sure). It means that when evaluating an expression that includes more than one operator, anything in parentheses is evaluated first, followed by exponents, then multiplication and/or division (whichever comes first, left to right), and finally addition and/or subtraction (whichever comes first, left to right). That is the order of operations.

GEMDAS is Better

At the aforementioned department meeting, Ms. Hertzog, a math teacher at Challenger, said something about GEMDAS being superior to PEMDAS because with PEMDAS some learners get it stuck in their heads that parentheses are the only grouping symbols that need to be taken into account, or else they get confused when some other grouping symbol is used instead of parentheses. She made no claim to inventing GEMDAS, but apparently heard about it at a workshop somewhere.

In GEMDAS, the G stands for Grouping symbol, and all the other letters keep the same meanings that they have in PEMDAS.  So with GEMDAS, learners are better able to keep in mind that ALL expressions in, on, or under grouping symbols need to be evaluated first. Grouping symbols include parentheses (), brackets [], braces {}, the vinculum ^____ (which is the technical name for what most people call a fraction bar, which is also a repetition symbol used in decimal notation) , and the radical √ (also known as the square root symbol).

Google hits for PEMDAS outnumber hits for GEMDAS by a bit more than 10 to 1 (40,400 to 3,030, as of the date of this posting) so clearly PEMDAS is still a more popular mnemonic that GEMDAS.

I for one am switching over to using and teaching GEMDAS, and I have the impression that all the math teachers at my school are going to do the same so we are using a common vocabulary.  It is traditional to teach and use PEMDAS, but tradition is no reason to keep an old idea around when a better alternative exists. It’s time to get rid of PEMDAS. Long live GEMDAS!

"Hey, teacher! Leave us kids alone!" (Mel Lindstrom)

A short bit of personal history. When I first got into teaching about seven years ago, it was because the charter school where my kids went needed a math teacher and I figured I could do at least as good a job as the people who had been doing it up until that time. This was at Frontier Charter Academy (FCA), which is still doing alright despite being located in an often backwards-thinking and sometimes outright hostile community. At least that is the way it was when I was there and I’ve heard as recently as late last year that the environment hasn’t changed much.

Life at a Small Charter School

Anyway, they hired me (mostly I think because I knew that any number raised to the zeroth power equals 1!) and that started my teaching career. At the time, the school director was Claudia Horn, and her husband and teacher John was also a major influence on how the school was run.

The Horn’s had a philosophy of “no punishment and no reward.” In other words, they believed students needed to be intrinsically motivated to learn and there would be neither a reward for doing well, nor a punishment for causing problems (within reason, one would suppose).

I thought that was crazy. The school was not doing all that well in its CSAP results and I thought this lax attitude was one of the reasons for it. As fate would have it, the Horn’s left shortly thereafter and new management took over. We tightened down the screws, made some curriculum changes, and within a couple of years, our middle school was outperforming the local public school. Good enough right?

Debating the Merits of Alfie Kohn’s Ideas

I remember having some interesting philosophical debates with John Horn about education and classroom management. He referred me to some of the writings of Alfie Kohn, who’s ideas he strongly believed in. I wasn‘t a believer, and argued forcefully that a firm hand was required to keep kids in line and to prevent them from taking over and derailing the classroom environment.

I implemented a detention policy and assigned plenty of homework. John was disappointed in this new direction the school was taking, but hey–results are results! We never did agree on things but the discussions were civil and thoughtful.

I Didn’t Like Alfie Kohn

Actually that is not true because I didn’t even know Alfie Kohn. It is fair to say though that I thought his ideas on de-emphasizing grading, running a more democratic classroom, and cutting back on homework, were terribly misguided.

A few years later, my first year at Challenger Middle School in fact (FCA had to cut their middle school due to a lack of enrollment and funding), I was in a seminar with a guy from Boys Town, who was training us on what we call the “Challenger Learning Model” (which is the boys town model of classroom management just given a more appealing name).

The instructor at one point asked if anyone had heard of Alfie Kohn. I was the only one who raised my hand. “What do you think of his ideas?” he asked. “Not much,” was my glib reply. That seemed to hit the spot because he responded with a rather pleased, “neither do we.” My how things change.

The Greatest Power, is the Power to Change One’s Mind

Hey, that's more like it! (Chris Lott/Flickr)

Funny. Now I am a compete convert to the philosophy and classroom management theories of Alfie Kohn! This has truly been a 180 degree turn in thinking. How could such a thing have happened? It has been the result of more than a year of exposure to many new ideas in educational theory.

When the notion of “21st Century Learning” was first brought to the attention of the staff at Challenger, I was still firmly in authoritarian mode. I scoffed at the notion that these perceived “soft” skills were what was needed to pull America out of the dismal place it had earned in the pantheon of global education. American kids  were lacking (on average) at math and science and what we needed was more, greater, and deeper immersion in math and science by golly! That is still true, but the way to do it is clearly through the use of collaboration,  appropriate use of technology, a more democratic classroom environment, and development of a space where one feels free to make mistakes and to learn in the process of doing so.

I really cannot pinpoint how, when, and where I cam to realize that the old-school way of teaching wasn’t working. I think it probably was because I had taken that method as far as I could and had stalled out and wasn’t making much more progress with my students. You really can make progress with the old-school approach, but only up to a point, and then you hit a plateau and have to take it to the next level.

My thinking has also been inspired by Dan Pink, with respect to research on motivation. When it comes to creative thinking and challenging work, both carrots and sticks are a recipe for mediocrity. Look into it, you’ll see what I mean.

The next level is mastery learning and a leaner-centered environment, where kids are in charge of their own learning, and make progress with the guidance of a subject matter expert (that’s me). So now I am quite convinced that John Horn was right and that kids need to be intrinsically motivated to learn and there should be neither a reward for doing well, nor a punishment for causing problems (with some egregious exceptions).

Hey John Horn! If you’re out there, drop me a line. We need to talk!