Thursday, August 23, 2012


I finally recorded my PEMDAS song!
Listen/Download here.

*[Update] Here's a video for those visual learners: Vimeo or YouTube.
I know, I know, I know... math teachers need another PEMDAS song just as much as we need another Michael Bolton ballad. Oh well! I wrote this song a few years ago and brought it into my students at the beginning of the year. I think I had reached the point as a teacher where I didn't like any other PEMDAS song I came across (sure, call me a snob). I was getting more comfortable as a teacher, making a fool of myself in front of my students. And if there was one math concept to write a song about, Order of Operations was it!  I had a couple of lines that made sense lyrically. I picked up my acoustic guitar, threw down a few chords, and put some lyrics to PEMDAS. I wanted to keep it short, to the point, have a call and response feel, and something my students could remember for the rest of the year. Mastering Order of Operations at the beginning of the year pays dividends throughout the year.

Sorry, I'm not here to discuss where Order of Operations came from, why does it exist, or what underground math cult magically persuaded the entire universe to evaluate mathematical expressions in the way we do. My twitter cohorts @MrPicc112, @jreulback, @druinok, @ChrisHunter36, @fnoschese, and @ray_emily had a fantastic discussion the other week. It would be nice to know why, where, and how Order of Operations came to be. However, I've reached the point of acceptance. Honestly! I've learned to accept acceptance. So, on with the show.

I get together with my nephew (16 years younger and still in HS) and we jam out to our favorite bands in my garage every once in a while. This last time we jammed, I asked him to throw a beat down for my PEMDAS song since I actually wanted to record it. Being the phenomenal young drummer that he is, he was happy to do so! He did a fantastic job in about 10 minutes. Every other noise you hear is me... guitar, bass, and vocals. So at least the drumming is good. You don't dig it, blame everything on me. I dig it! Many of my former students dig the song and sometimes sing it back to me in class. Very cool. Many times throughout the year, all I have to say is, "Parentheses" and without skipping a beat, the students respond, "Start with these."

If you decide to torture your students with the PEMDAS song, here are a few tips:
1. Do a 'call & response.' You start each line of the verse and they finish it:
Teacher: Parentheses
Students: Start with these
2. Tell your students it will only take a minute to learn and a lifetime to forget!
3. Hire me and I'll come perform at your school. Ha!
4. Don't forget to actually teach them how to simplify/evaluate expressions.

If you're looking for an extension to torturing your students with learning the song, have them rewrite the lyrics of the second verse. Have them write lyrics for the Left to Right rule that applies to Multiplication/Division and Addition/Subtraction. I did this one year and really received some cool lyrics. I also received some terrible ones because those kids could have given a rip about the assignment. Guess what though! They remembered the Left to Right rule. Who's laughing now?

This was a labor of love. I hope you get some mileage out of it, no matter what grade you teach. Lastly, not all your students are the biggest fans of cheesy songs like this. I never was! Hence, my reluctance to record and share. I'm seriously thinking about making a video to accompany the song for those visual learners. Stay tuned!


P.S.  Apologies to my Canadian and British readers! PEMDAS is kind of limited to the States. Let me know and maybe I'll upload an instrumental version and you guys can change the lyrics to suit your needs.

Sunday, August 19, 2012

In the Name of Efficiency

See anything weird about this?

I started college as a Mechanical Engineer major since some college advisor (who knew nothing about me) thought ME (Mechanical Engineering) would be the most fitting major based on some test I completed coupled with my interest in math and science. As I was taking my prerequisite courses in math and science I switched gears to Electrical Engineering because my love for music swayed me into thinking I could design amplifiers and effects pedals (stompboxes) for musicians. I took a couple of EE classes and really didn't enjoy it. I wasn't passionate about it and saw many others in the same boat who kept making comments such as, "I have to finish this [major] now" or "I can't not major in electrical engineering" or "It's what my [insert parent gender] does." As for me, I really enjoyed my introductory Philosophy classes because they allowed me to explore some pretty radical thinkers and we had all these wonderful debates about logic, God, metaphysics, existentialism, human rights, medical rights, law, etc. I became a Philosophy major and the rest is history... I think. My point is, if anyone (me included) knew me well enough, they should have highly suggested I major in Civil Engineering.
Here's why CE:
I'm one of those people who drives by construction (road, building, bridges, pipes, etc.) and is always trying to figure out what is being built, modified, or enhanced in the name of efficiency. I'm also that person that drives by an area and will vocalize how inefficient the lane configurations are, or offramp, or stoplight sequence, etc. That's usually followed by a suggestion on how to improve it. My poor wife gets an earful at times. I'm also that guy that looks at products and either loves and respects an efficiently designed product or will completely be baffled that a company releases a product so poorly engineered and wreaking of inefficiency. Then, I spend the next 30 minutes thinking of ways to make it a better product or design while restraining myself from emailing the company. I know the latter example isn't necessarily classified as CE. However, I could see myself out there designing things to help improve civilian efficiency. Thank goodness I'm not. Instead, I'm in the classroom with normal adolescent  middle schoolers who are always are in a good mood and never have social problems or woes. Right? One can dream. I love my job. I love teaching those wonderful teenagers. There's never a dull moment with middle schoolers. As their teacher, my objective is to strengthen their young impressionable minds and help them be better critical thinkers.
Enough about me, the point of this post [In the Name of Efficiency] is I have an idea for my class this year. Dare I say 'theme'! And if it goes well, could easily become a staple for the remainder of my teaching career. That's how much I value this idea! We look for products that fit one of two categories:
  1. The product is very efficiently designed. We explore everything about it that makes it a superbly designed product. What math is involved? How is math involved?
  2. The product is inefficiently designed in one or more ways. Identify the area(s) of inefficiency and propose a well-thought out modification/enhancement. Again, how would math be involved? 
Here's a simple one for the first category: efficient.
A modern ketchup bottle.
The ketchup bottle that rests on its lid uses gravity to its advantage and you rarely have to shake the dang thing. Plus, your burger, dog, or fries will actually still be warm when you're done getting ketchup out of the bottle. Why did it take someone so long to think if this, right?
Here's an example that fits the second category: inefficient.
A depleted salt container.
Take that salt container at the top of this post. Granted, it took a couple of years to deplete the salt in the container, and maybe there's a new design out there, but I got to the end and there's still salt in it. No matter what angle I hold the container, or shake the cylindrical container, it won't pour out every little grain of salt. My question would be: How could we better design the spout? Should its location change? What would happen if the spout were closer to the rim? What would be the easiest, yet most effective change?
Companies do this all the time (or at least should). They reassess the efficiency of their products. Why can't a classroom full of students do the same? We/they complain about things all the time. I want my students to bring in stuff: pictures, products, construction site pictures, machines, etc. We discuss it for a week. We make a bulletin board of ideas. We split the board in half for efficient vs. inefficient. I want each student to be responsible for at least one contribution throughout the year. They do a brief write-up. Pick from a collection of modifications/enhancements submitted by their peers. Sketch or draw a new design. I'm ranting here because I want to flesh this out... I want this to work!
I want my students to bring things in that drive them bonkers. Fine, if you don't like it, think of something better. How would you design it? What would you want it to do? On the other hand, I want my kids to bring in things that they absolutely adore. Things they couldn't live without. Things that they take for granted on how awesome they are. This might require them to give it more thought. Usually something that is efficient, well-designed, well-made, and awesome can be overseen because of how great it is. The second it stops working, is gone, or replaced with an inferior product we pine. Talk about an opportunity for students to appreciate many of the wonderful, amazing, and unbelievable inventions of our time. I think this would foster a sense of gratitude for some of the cool things we experience every single day. It's not just about complaining and finding things that could be better. 
This is one thing I'll be doing differently this year. Am I off base here? This wouldn't be the foundation of my teaching, but it sure feels naturally appropriate to a math class. Aren't we teaching our kids to be better problem solvers? better critical thinkers? better contributors to society? I always tell them to better problem solvers and not better problem complainers. Don't we have things that drive us nuts? Within reason. I'm not talking about losing your internet in the middle of an airplane ride. Your life will go on without the internet for a few hours. Yes, it will! Don't even start with me. If you got a problem with losing the internet on a plane, read a book, pay attention to your kid for a few minutes, or talk to the person next to you. Everybody has a story to tell. Ask them what their story is. If you're not convinced, talk to my man Louis CK. Tell 'em CK: